diff --git a/changelog b/changelog index ca9ce8d..77fa5f2 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,14 @@ +20100526 tpd src/axiom-website/patches.html 20100526.01.tpd.patch +20100526 tpd src/input/Makefile add paff.input test case for PAFF +20100526 tpd src/input/paff.input test case for PAFF package +20100526 tpd src/share/algebra/libdb.text updated for PAFF +20100526 tpd src/share/algebra/users.daase/users.daase/index.kaf +20100526 tpd src/share/algebra/dependents.daase/dependents.daase/index.kaf +20100526 tpd src/share/algebra/operation.daase updated for PAFF +20100526 tpd src/share/algebra/interp.daase updated for PAFF +20100526 tpd src/share/algebra/compress.daase updated for PAFF +20100526 tpd src/share/algebra/category.daase updated for PAFF +20100526 tpd src/share/algebra/browse.daase updated for PAFF 20100525 tpd src/axiom-website/patches.html 20100525.02.tpd.patch 20100525 tpd books/bookvol5 fix )describe to accept abbreviations 20100525 tpd src/axiom-website/patches.html 20100525.01.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 09fdbfc..3fb6d53 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2801,6 +2801,9 @@ books/bookvol10.4 add GeneralPackageForAlgebraicFunctionField
books/bookvol10.4 add PackageForAlgebraicFunctionFieldOverFiniteField
books/bookvol10.4 add PackageForAlgebraicFunctionField
20100525.02.tpd.patch -books/bookvol5 fix )describe to accept abbreviations +books/bookvol5 fix )describe to accept abbreviations
+20100526.01.tpd.patch +src/input/paff.input test cases for PAFF package
+*.daase updated for PAFF
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index d2710c5..6eca629 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -359,8 +359,8 @@ REGRES= ackermann.regress \ nqip.regress nsfip.regress numbers.regress octonion.regress \ oct.regress ode.regress odpol.regress op1.regress \ opalg.regress operator.regress op.regress ovar.regress \ - overload.regress \ - padic.regress parabola.regress pascal1.regress pascal.regress \ + overload.regress padic.regress paff.regress \ + parabola.regress pascal1.regress pascal.regress \ patch51.regress page.regress \ patmatch.regress pat.regress perman.regress perm.regress \ pfaffian.regress pfr1.regress pfr.regress pmint.regress \ @@ -662,7 +662,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/octonion.input ${OUT}/odpol.input \ ${OUT}/opalg.input ${OUT}/operator.input ${OUT}/op.input \ ${OUT}/op1.input ${OUT}/ovar.input ${OUT}/overload.input \ - ${OUT}/padic.input ${OUT}/palette.input \ + ${OUT}/padic.input ${OUT}/paff.input ${OUT}/palette.input \ ${OUT}/parpcurv.input ${OUT}/parscurv.input ${OUT}/parsurf.input \ ${OUT}/pascal1.input \ ${OUT}/pascal.input \ @@ -997,7 +997,8 @@ DOCFILES= \ ${DOC}/opalg.input.dvi ${DOC}/operator.input.dvi \ ${DOC}/op.input.dvi ${DOC}/ovar.input.dvi \ ${DOC}/overload.input.dvi \ - ${DOC}/padic.input.dvi ${DOC}/palette.input.dvi \ + ${DOC}/padic.input.dvi ${DOC}/paff.input.dvi \ + ${DOC}/palette.input.dvi \ ${DOC}/parabola.input.dvi ${DOC}/parpcurv.input.dvi \ ${DOC}/parscurv.input.dvi ${DOC}/parsurf.input.dvi \ ${DOC}/pascal1.input.dvi ${DOC}/pascal.input.dvi \ diff --git a/src/input/paff.input.pamphlet b/src/input/paff.input.pamphlet new file mode 100644 index 0000000..e6d41e1 --- /dev/null +++ b/src/input/paff.input.pamphlet @@ -0,0 +1,336 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input paff.input} +\author{Gaetan Hache} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)spool paff.output +)set message test on +)set message auto off +)clear all + +--S 1 of 26 +K:= PACRAT +--R +--R +--R (1) PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 1 + +--S 2 of 26 +symb:=[x,y,z] +--R +--R +--R (2) [x,y,z] +--R Type: List OrderedVariableList [x,y,z] +--E 2 + +--S 3 of 26 +PolyRing:=DMP(symb,K) +--R +--R +--R (3) +--R DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNum +--R ber) +--R Type: Domain +--E 3 + +--S 4 of 26 +E:=DIRPROD(#symb,NNI) +--R +--R +--R (4) DirectProduct(3,NonNegativeInteger) +--R Type: Domain +--E 4 + +--S 5 of 26 +ProjPt := ProjectivePlane(K) +--R +--R +--R (5) ProjectivePlane PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 5 + +--S 6 of 26 +AFP:= AffinePlane(K) +--R +--R +--R (6) AffinePlane PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 6 + +\end{chunk} + +There are two possible BlowUp methods. The alternative method is +invoked by: +\begin{verbatim} +BLMET := BLHN -- BlowUpWithHamburgerNoether +\end{verbatim} + +\begin{chunk}{*} + +--S 7 of 26 +BLMET := BLQT +--R +--R +--R (7) BlowUpWithQuadTrans +--R Type: Domain +--E 7 + +--S 8 of 26 +PCS := NeitherSparseOrDensePowerSeries(K) +--R +--R +--R (8) NeitherSparseOrDensePowerSeries PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 8 + +--S 9 of 26 +Plc:= PLACES K +--R +--R +--R (9) Places PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 9 + +--S 10 of 26 +DIVISOR:= DIV Plc +--R +--R +--R (10) Divisor Places PseudoAlgebraicClosureOfRationalNumber +--R Type: Domain +--E 10 + +--S 11 of 26 +InfClsPoint := InfClsPt(K,symb,BLMET) +--R +--R +--R (11) +--R InfClsPt(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],BlowUpWithQuadTrans) +--R Type: Domain +--E 11 + +--S 12 of 26 +DesTree := DesingTree InfClsPoint +--R +--R +--R (12) +--R DesingTree InfClsPt(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],BlowUpWith +--R QuadTrans) +--R Type: Domain +--E 12 + +--S 13 of 26 +BB:=BlowUpPackage(K,symb,PolyRing,E,BLMET) +--R +--R +--R (13) +--R BlowUpPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],DistributedMulti +--R variatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),DirectProdu +--R ct(3,NonNegativeInteger),BlowUpWithQuadTrans) +--R Type: Domain +--E 13 + +--S 14 of 26 +P:= GeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt, PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET) +--R +--R +--R (14) +--R GeneralPackageForAlgebraicFunctionField(PseudoAlgebraicClosureOfRationalNumbe +--R r,[x,y,z],DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfR +--R ationalNumber),DirectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlge +--R braicClosureOfRationalNumber,NeitherSparseOrDensePowerSeries PseudoAlgebraicC +--R losureOfRationalNumber,Places PseudoAlgebraicClosureOfRationalNumber,Divisor +--R Places PseudoAlgebraicClosureOfRationalNumber,InfClsPt(PseudoAlgebraicClosure +--R OfRationalNumber,[x,y,z],BlowUpWithQuadTrans),DesingTree InfClsPt(PseudoAlgeb +--R raicClosureOfRationalNumber,[x,y,z],BlowUpWithQuadTrans),BlowUpWithQuadTrans) +--R Type: Domain +--E 14 + +--S 15 of 26 +ParamPackFC := _ + LocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc) +--R +--R +--R (15) +--R LocalParametrizationOfSimplePointPackage(PseudoAlgebraicClosureOfRationalNumb +--R er,[x,y,z],DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOf +--R RationalNumber),DirectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlg +--R ebraicClosureOfRationalNumber,NeitherSparseOrDensePowerSeries PseudoAlgebraic +--R ClosureOfRationalNumber,Places PseudoAlgebraicClosureOfRationalNumber) +--R Type: Domain +--E 15 + +--S 16 of 26 +ParamPack := ParametrizationPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc) +--R +--R +--R (16) +--R ParametrizationPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],Distrib +--R utedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),Di +--R rectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlgebraicClosureOfRat +--R ionalNumber,NeitherSparseOrDensePowerSeries PseudoAlgebraicClosureOfRationalN +--R umber,Places PseudoAlgebraicClosureOfRationalNumber) +--R Type: Domain +--E 16 + +--S 17 of 26 +RatSingPack := ProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt) +--R +--R +--R (17) +--R ProjectiveAlgebraicSetPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z], +--R DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNum +--R ber),DirectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlgebraicClosu +--R reOfRationalNumber) +--R Type: Domain +--E 17 + +--S 18 of 26 +IntDivPack := IntersectionDivisorPackage(K,symb,PolyRing,E,ProjPt,PCS,_ + Plc,DIVISOR,InfClsPoint,DesTree,BLMET) +--R +--R +--R (18) +--R IntersectionDivisorPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],Dis +--R tributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber +--R ),DirectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlgebraicClosureO +--R fRationalNumber,NeitherSparseOrDensePowerSeries PseudoAlgebraicClosureOfRatio +--R nalNumber,Places PseudoAlgebraicClosureOfRationalNumber,Divisor Places Pseudo +--R AlgebraicClosureOfRationalNumber,InfClsPt(PseudoAlgebraicClosureOfRationalNum +--R ber,[x,y,z],BlowUpWithQuadTrans),DesingTree InfClsPt(PseudoAlgebraicClosureOf +--R RationalNumber,[x,y,z],BlowUpWithQuadTrans),BlowUpWithQuadTrans) +--R Type: Domain +--E 18 + +--S 19 of 26 +IntFrmPack := InterpolateFormsPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR) +--R +--R +--R (19) +--R InterpolateFormsPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],Distri +--R butedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),D +--R irectProduct(3,NonNegativeInteger),ProjectivePlane PseudoAlgebraicClosureOfRa +--R tionalNumber,NeitherSparseOrDensePowerSeries PseudoAlgebraicClosureOfRational +--R Number,Places PseudoAlgebraicClosureOfRationalNumber,Divisor Places PseudoAlg +--R ebraicClosureOfRationalNumber) +--R Type: Domain +--E 19 + +--S 20 of 26 +DesTrPack:= DesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,_ + InfClsPoint,DesTree,BLMET) +--R +--R +--R (20) +--R DesingTreePackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],DistributedM +--R ultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),DirectP +--R roduct(3,NonNegativeInteger),ProjectivePlane PseudoAlgebraicClosureOfRational +--R Number,NeitherSparseOrDensePowerSeries PseudoAlgebraicClosureOfRationalNumber +--R ,Places PseudoAlgebraicClosureOfRationalNumber,Divisor Places PseudoAlgebraic +--R ClosureOfRationalNumber,InfClsPt(PseudoAlgebraicClosureOfRationalNumber,[x,y, +--R z],BlowUpWithQuadTrans),DesingTree InfClsPt(PseudoAlgebraicClosureOfRationalN +--R umber,[x,y,z],BlowUpWithQuadTrans),BlowUpWithQuadTrans) +--R Type: Domain +--E 20 + +--S 21 of 26 +PackPoly := PackageForPoly(K,PolyRing,E,#symb) +--R +--R +--R (21) +--R PackageForPoly(PseudoAlgebraicClosureOfRationalNumber,DistributedMultivariate +--R Polynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),DirectProduct(3,No +--R nNegativeInteger),3) +--R Type: Domain +--E 21 + +--S 22 of 26 +BB:= BlowUpPackage(K,symb,PolyRing,E, BLMET) +--R +--R +--R (22) +--R BlowUpPackage(PseudoAlgebraicClosureOfRationalNumber,[x,y,z],DistributedMulti +--R variatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber),DirectProdu +--R ct(3,NonNegativeInteger),BlowUpWithQuadTrans) +--R Type: Domain +--E 22 + +--S 23 of 26 +LinSer := LinearSystemFromPowerSeriesPackage(K,PCS) +--R +--R +--R (23) +--R LinearSystemFromPowerSeriesPackage(PseudoAlgebraicClosureOfRationalNumber,Nei +--R therSparseOrDensePowerSeries PseudoAlgebraicClosureOfRationalNumber) +--R Type: Domain +--E 23 + +--S 24 of 26 +f:PolyRing:= x**28*z**8 + 4*x**26*z**10 + 6*x**24*z**12 + 4*x**22*z**14 + _ + 4*x**21*y**9*z**6 + x**20*z**16 + 12*x**19*y**9*z**8 + _ + 12*x**17*y**9*z**10 + 4*x**15*y**9*z**12 + 6*x**14*y**18*z**4 + _ + 12*x**12*y**18*z**6 + 6*x**10*y**18*z**8 + 4*x**7*y**27*z*z + _ + 4*x**5*y**27*z**4 + y**36 + (-2*y**20*z**16) +--R +--R +--R (24) +--R 28 8 26 10 24 12 22 14 21 9 6 20 16 19 9 8 +--R x z + 4x z + 6x z + 4x z + 4x y z + x z + 12x y z +--R + +--R 17 9 10 15 9 12 14 18 4 12 18 6 10 18 8 7 27 2 +--R 12x y z + 4x y z + 6x y z + 12x y z + 6x y z + 4x y z +--R + +--R 5 27 4 36 20 16 +--R 4x y z + y - 2y z +--RType: DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber) +--E 24 + +--S 25 of 26 +fh:=homogenize(f,3)$P +--R +--R +--R (25) +--R 28 8 26 10 24 12 22 14 21 9 6 20 16 19 9 8 +--R x z + 4x z + 6x z + 4x z + 4x y z + x z + 12x y z +--R + +--R 17 9 10 15 9 12 14 18 4 12 18 6 10 18 8 7 27 2 +--R 12x y z + 4x y z + 6x y z + 12x y z + 6x y z + 4x y z +--R + +--R 5 27 4 36 20 16 +--R 4x y z + y - 2y z +--RType: DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber) +--E 25 + +--S 26 of 26 +setCurve(fh)$P +--R +--R +--R (26) +--R 28 8 26 10 24 12 22 14 21 9 6 20 16 19 9 8 +--R x z + 4x z + 6x z + 4x z + 4x y z + x z + 12x y z +--R + +--R 17 9 10 15 9 12 14 18 4 12 18 6 10 18 8 7 27 2 +--R 12x y z + 4x y z + 6x y z + 12x y z + 6x y z + 4x y z +--R + +--R 5 27 4 36 20 16 +--R 4x y z + y - 2y z +--RType: DistributedMultivariatePolynomial([x,y,z],PseudoAlgebraicClosureOfRationalNumber) +--E 26 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase old mode 100755 new mode 100644 index a9fb9d5..722574a --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,4636 +1,4984 @@ -(2135125 . 3269429133) +(2456427 . 3483827107) (-18 A S) -NIL +((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) -NIL -((-4168 . T) (-4167 . T) (-2951 . T)) +((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL (-20 S) -((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) +((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{-(-x) = x}\\spad{\\br} \\tab{5}\\spad{x+(-x) = 0}")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) NIL NIL (-21) -((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) +((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{-(-x) = x}\\spad{\\br} \\tab{5}\\spad{x+(-x) = 0}")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) NIL NIL (-22 S) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|Zero|) (($) "0 is the additive identity element."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftIdentity(\"+\":(\\%,{}\\%)->\\%,{}0)}\\tab{5}\\spad{ 0+x=x }\\spad{\\br} \\tab{5}\\spad{rightIdentity(\"+\":(\\%,{}\\%)->\\%,{}0)}\\tab{4}\\spad{ x+0=x }")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|Zero|) (($) "0 is the additive identity element."))) NIL NIL (-23) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|Zero|) (($) "0 is the additive identity element."))) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftIdentity(\"+\":(\\%,{}\\%)->\\%,{}0)}\\tab{5}\\spad{ 0+x=x }\\spad{\\br} \\tab{5}\\spad{rightIdentity(\"+\":(\\%,{}\\%)->\\%,{}0)}\\tab{4}\\spad{ x+0=x }")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|Zero|) (($) "0 is the additive identity element."))) NIL NIL (-24 S) -((|constructor| (NIL "the class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) +((|constructor| (NIL "The class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{associative(\"+\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ (x+y)+z = x+(y+z) }\\spad{\\br} \\tab{6}\\spad{commutative(\"+\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ x+y = y+x }")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) NIL NIL (-25) -((|constructor| (NIL "the class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) +((|constructor| (NIL "The class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{associative(\"+\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ (x+y)+z = x+(y+z) }\\spad{\\br} \\tab{6}\\spad{commutative(\"+\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ x+y = y+x }")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) NIL NIL (-26 S) -((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) +((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{zerosOf(\\spad{p},{} \\spad{y}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise} \\indented{1}{as implicit algebraic quantities} \\indented{1}{which display as \\spad{'yi}.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zerosOf(a,{}\\spad{x})") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\indented{1}{zerosOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise} \\indented{1}{as implicit algebraic quantities.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zerosOf(a)") (((|List| $) (|Polynomial| $)) "\\indented{1}{zerosOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible.} \\indented{1}{Otherwise they are implicit algebraic quantities.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^2+2*x-13 \\spad{X} zerosOf(a)")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{zeroOf(\\spad{p},{} \\spad{y}) returns \\spad{y} such that \\spad{p(y) = 0};} \\indented{1}{if possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity which} \\indented{1}{displays as \\spad{'y}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zeroOf(a,{}\\spad{x})") (($ (|SparseUnivariatePolynomial| $)) "\\indented{1}{zeroOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0};} \\indented{1}{if possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zeroOf(a)") (($ (|Polynomial| $)) "\\indented{1}{zeroOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{If possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^2+2*x-13 \\spad{X} zeroOf(a)")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{rootsOf(\\spad{p},{} \\spad{y}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0};} \\indented{1}{The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a,{}\\spad{x})") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\indented{1}{rootsOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a)") (((|List| $) (|Polynomial| $)) "\\indented{1}{rootsOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the} \\indented{1}{interpreter to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a)")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{rootOf(\\spad{p},{} \\spad{y}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{The object returned displays as \\spad{'y}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a,{}\\spad{x})") (($ (|SparseUnivariatePolynomial| $)) "\\indented{1}{rootOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a)") (($ (|Polynomial| $)) "\\indented{1}{rootOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a)"))) NIL NIL (-27) -((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{zerosOf(\\spad{p},{} \\spad{y}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise} \\indented{1}{as implicit algebraic quantities} \\indented{1}{which display as \\spad{'yi}.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zerosOf(a,{}\\spad{x})") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\indented{1}{zerosOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise} \\indented{1}{as implicit algebraic quantities.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zerosOf(a)") (((|List| $) (|Polynomial| $)) "\\indented{1}{zerosOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{The \\spad{yi}\\spad{'s} are expressed in radicals if possible.} \\indented{1}{Otherwise they are implicit algebraic quantities.} \\indented{1}{The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^2+2*x-13 \\spad{X} zerosOf(a)")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{zeroOf(\\spad{p},{} \\spad{y}) returns \\spad{y} such that \\spad{p(y) = 0};} \\indented{1}{if possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity which} \\indented{1}{displays as \\spad{'y}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zeroOf(a,{}\\spad{x})") (($ (|SparseUnivariatePolynomial| $)) "\\indented{1}{zeroOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0};} \\indented{1}{if possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} zeroOf(a)") (($ (|Polynomial| $)) "\\indented{1}{zeroOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{If possible,{} \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^2+2*x-13 \\spad{X} zeroOf(a)")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{rootsOf(\\spad{p},{} \\spad{y}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0};} \\indented{1}{The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a,{}\\spad{x})") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\indented{1}{rootsOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a)") (((|List| $) (|Polynomial| $)) "\\indented{1}{rootsOf(\\spad{p}) returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}.} \\indented{1}{Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the} \\indented{1}{interpreter to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootsOf(a)")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\indented{1}{rootOf(\\spad{p},{} \\spad{y}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{The object returned displays as \\spad{'y}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a,{}\\spad{x})") (($ (|SparseUnivariatePolynomial| $)) "\\indented{1}{rootOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\blankline \\spad{X} a:SparseUnivariatePolynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a)") (($ (|Polynomial| $)) "\\indented{1}{rootOf(\\spad{p}) returns \\spad{y} such that \\spad{p(y) = 0}.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y}.} \\blankline \\spad{X} a:Polynomial(Integer)\\spad{:=}-3*x^3+2*x+13 \\spad{X} rootOf(a)"))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL (-28 S R) -((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) +((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) NIL NIL (-29 R) -((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4164 . T) (-4162 . T) (-4161 . T) ((-4169 "*") . T) (-4160 . T) (-4165 . T) (-4159 . T) (-2951 . T)) +((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note that the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) +((-4502 . T) (-4500 . T) (-4499 . T) ((-4507 "*") . T) (-4498 . T) (-4503 . T) (-4497 . T) (-2537 . T)) NIL (-30) -((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) +((|constructor| (NIL "Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.")) (|refine| (($ $ (|DoubleFloat|)) "\\indented{1}{refine(\\spad{p},{}\\spad{x}) is not documented} \\blankline \\spad{X} sketch:=makeSketch(x+y,{}\\spad{x},{}\\spad{y},{}\\spad{-1/2}..1/2,{}\\spad{-1/2}..1/2)\\$ACPLOT \\spad{X} refined:=refine(sketch,{}0.1)")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\indented{1}{makeSketch(\\spad{p},{}\\spad{x},{}\\spad{y},{}a..\\spad{b},{}\\spad{c}..\\spad{d}) creates an ACPLOT of the} \\indented{1}{curve \\spad{p = 0} in the region a \\spad{<=} \\spad{x} \\spad{<=} \\spad{b},{} \\spad{c} \\spad{<=} \\spad{y} \\spad{<=} \\spad{d}.} \\indented{1}{More specifically,{} 'makeSketch' plots a non-singular algebraic curve} \\indented{1}{\\spad{p = 0} in an rectangular region xMin \\spad{<=} \\spad{x} \\spad{<=} xMax,{}} \\indented{1}{yMin \\spad{<=} \\spad{y} \\spad{<=} yMax. The user inputs} \\indented{1}{\\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}.} \\indented{1}{Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with} \\indented{1}{integer coefficients (\\spad{p} belongs to the domain} \\indented{1}{\\spad{Polynomial Integer}). The case} \\indented{1}{where \\spad{p} is a polynomial in only one of the variables is} \\indented{1}{allowed.\\space{2}The variables \\spad{x} and \\spad{y} are input to specify the} \\indented{1}{the coordinate axes.\\space{2}The horizontal axis is the \\spad{x}-axis and} \\indented{1}{the vertical axis is the \\spad{y}-axis.\\space{2}The rational numbers} \\indented{1}{xMin,{}...,{}yMax specify the boundaries of the region in} \\indented{1}{which the curve is to be plotted.} \\blankline \\spad{X} makeSketch(x+y,{}\\spad{x},{}\\spad{y},{}\\spad{-1/2}..1/2,{}\\spad{-1/2}..1/2)\\$ACPLOT"))) +NIL +NIL +(-31 K |symb| |PolyRing| E |ProjPt|) +((|constructor| (NIL "The following is part of the PAFF package")) (|affineRationalPoints| (((|List| |#5|) |#3| (|PositiveInteger|)) "\\axiom{rationalPoints(\\spad{f},{}\\spad{d})} returns all points on the curve \\axiom{\\spad{f}} in the extension of the ground field of degree \\axiom{\\spad{d}}. For \\axiom{\\spad{d} > 1} this only works if \\axiom{\\spad{K}} is a \\axiomType{LocallyAlgebraicallyClosedField}"))) +NIL +NIL +(-32 K |symb| |PolyRing| E |ProjPt|) +((|constructor| (NIL "The following is part of the PAFF package"))) +NIL +NIL +(-33 K) +((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) +NIL NIL +(-34 K) +((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) NIL -(-31 R -2958) +NIL +(-35 -2050 K) +((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) +NIL +NIL +(-36 R -1333) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501))))) -(-32 S) -((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) +((|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560))))) +(-37 K) +((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package")) (|pointValue| (((|List| |#1|) $) "\\spad{pointValue returns} the coordinates of the point or of the point of origin that represent an infinitly close point")) (|setelt| ((|#1| $ (|Integer|) |#1|) "\\spad{setelt sets} the value of a specified coordinates")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates")) (|list| (((|List| |#1|) $) "\\spad{list returns} the list of the coordinates")) (|rational?| (((|Boolean|) $) "\\spad{rational?(p)} test if the point is rational according to the characteristic of the ground field.") (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{rational?(p,{}n)} test if the point is rational according to \\spad{n}.")) (|removeConjugate| (((|List| $) (|List| $)) "\\spad{removeConjugate(lp)} returns removeConjugate(\\spad{lp},{}\\spad{n}) where \\spad{n} is the characteristic of the ground field.") (((|List| $) (|List| $) (|NonNegativeInteger|)) "\\spad{removeConjugate(lp,{}n)} returns a list of points such that no points in the list is the conjugate (according to \\spad{n}) of another point.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns conjugate(\\spad{p},{}\\spad{n}) where \\spad{n} is the characteristic of the ground field.") (($ $ (|NonNegativeInteger|)) "\\spad{conjugate(p,{}n)} returns p**n,{} that is all the coordinates of \\spad{p} to the power of \\spad{n}")) (|orbit| (((|List| $) $ (|NonNegativeInteger|)) "\\spad{orbit(p,{}n)} returns the orbit of the point \\spad{p} according to \\spad{n},{} that is orbit(\\spad{p},{}\\spad{n}) = \\spad{\\{} \\spad{p},{} p**n,{} \\spad{p**}(\\spad{n**2}),{} \\spad{p**}(\\spad{n**3}),{} ..... \\spad{\\}}") (((|List| $) $) "\\spad{orbit(p)} returns the orbit of the point \\spad{p} according to the characteristic of \\spad{K},{} that is,{} for \\spad{q=} char \\spad{K},{} orbit(\\spad{p}) = \\spad{\\{} \\spad{p},{} p**q,{} \\spad{p**}(\\spad{q**2}),{} \\spad{p**}(\\spad{q**3}),{} ..... \\spad{\\}}")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce a} list of \\spad{K} to a affine point.")) (|affinePoint| (($ (|List| |#1|)) "\\spad{affinePoint creates} a affine point from a list"))) +NIL NIL -((|HasAttribute| |#1| (QUOTE -4167))) -(-33) -((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2951 . T)) +(-38 S) +((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation \\spad{r}(\\spad{x})\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note that The \\$\\spad{D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note that for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -(-34) +((|HasAttribute| |#1| (QUOTE -4505))) +(-39) +((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation \\spad{r}(\\spad{x})\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note that The \\$\\spad{D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note that for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) +((-2537 . T)) +NIL +(-40) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) NIL NIL -(-35 |Key| |Entry|) -((|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-41 |Key| |Entry|) +((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-36 S R) -((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) +(-42 S R) +((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{(b+c)::\\% = (b::\\%) + (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(b*c)::\\% = (b::\\%) * (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(1::R)::\\% = 1::\\%}\\spad{\\br} \\tab{5}\\spad{b*x = (b::\\%)*x}\\spad{\\br} \\tab{5}\\spad{r*(a*b) = (r*a)*b = a*(r*b)}")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) NIL NIL -(-37 R) -((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) -((-4161 . T) (-4162 . T) (-4164 . T)) +(-43 R) +((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{(b+c)::\\% = (b::\\%) + (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(b*c)::\\% = (b::\\%) * (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(1::R)::\\% = 1::\\%}\\spad{\\br} \\tab{5}\\spad{b*x = (b::\\%)*x}\\spad{\\br} \\tab{5}\\spad{r*(a*b) = (r*a)*b = a*(r*b)}")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) +((-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-38 UP) -((|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) +(-44 UP) +((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-39 -2958 UP UPUP -3121) -((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4160 |has| (-375 |#2|) (-331)) (-4165 |has| (-375 |#2|) (-331)) (-4159 |has| (-375 |#2|) (-331)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-375 |#2|) (QUOTE (-132))) (|HasCategory| (-375 |#2|) (QUOTE (-134))) (|HasCategory| (-375 |#2|) (QUOTE (-318))) (|HasCategory| (-375 |#2|) (QUOTE (-331))) (-1405 (|HasCategory| (-375 |#2|) (QUOTE (-331))) (|HasCategory| (-375 |#2|) (QUOTE (-318)))) (|HasCategory| (-375 |#2|) (QUOTE (-336))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-336))) (-1405 (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-1405 (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-318))))) (-12 (|HasCategory| (-375 |#2|) (QUOTE (-206))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-1405 (-12 (|HasCategory| (-375 |#2|) (QUOTE (-206))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (|HasCategory| (-375 |#2|) (QUOTE (-318))))) -(-40 R -2958) +(-45 -1333 UP UPUP -3254) +((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} is not documented"))) +((-4498 |has| (-403 |#2|) (-359)) (-4503 |has| (-403 |#2|) (-359)) (-4497 |has| (-403 |#2|) (-359)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-403 |#2|) (QUOTE (-146))) (|HasCategory| (-403 |#2|) (QUOTE (-148))) (|HasCategory| (-403 |#2|) (QUOTE (-344))) (|HasCategory| (-403 |#2|) (QUOTE (-359))) (-2318 (|HasCategory| (-403 |#2|) (QUOTE (-359))) (|HasCategory| (-403 |#2|) (QUOTE (-344)))) (|HasCategory| (-403 |#2|) (QUOTE (-364))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-364))) (-2318 (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-2318 (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-344))))) (-12 (|HasCategory| (-403 |#2|) (QUOTE (-221))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-2318 (-12 (|HasCategory| (-403 |#2|) (QUOTE (-221))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (|HasCategory| (-403 |#2|) (QUOTE (-344))))) +(-46 R -1333) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -389) (|devaluate| |#1|))))) -(-41 OV E P) -((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -426) (|devaluate| |#1|))))) +(-47 OV E P) +((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL NIL -(-42 R A) -((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,{}A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,{}a) = 0} and \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}x,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}b,{}x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,{}a,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,{}a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis."))) +(-48 R A) +((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,{}A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note that right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note that left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,{}a) = 0} and \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}x,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}b,{}x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,{}a,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,{}a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis. Note that if \\spad{A} has a unit,{} then doubleRank,{} weakBiRank,{} and biRank coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis."))) NIL -((|HasCategory| |#1| (QUOTE (-276)))) -(-43 R |n| |ls| |gamma|) +((|HasCategory| |#1| (QUOTE (-296)))) +(-49 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4164 |has| |#1| (-508)) (-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) -(-44 |Key| |Entry|) -NIL -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001)))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-777))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001)))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-777)))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))))) -(-45 S R E) +((-4502 |has| |#1| (-550)) (-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) +(-50 |Key| |Entry|) +((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082)))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-834))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082)))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-834)))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))))) +(-51 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-331)))) -(-46 R E) +((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-359)))) +(-52 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-47) +(-53) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| $ (QUOTE (-959))) (|HasCategory| $ (LIST (QUOTE -950) (QUOTE (-501))))) -(-48) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1029) (QUOTE (-560))))) +(-54) ((|constructor| (NIL "This domain implements anonymous functions"))) NIL NIL -(-49 R |lVar|) +(-55 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4164 . T)) +((-4502 . T)) NIL -(-50) +(-56 S) +((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) +NIL +NIL +(-57) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL -(-51 S) -((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) +(-58) +((|constructor| (NIL "This package contains useful functions that expose Axiom system internals")) (|summary| (((|Void|)) "\\indented{1}{summary() prints a short list of useful console commands} \\blankline \\spad{X} summary()")) (|credits| (((|Void|)) "\\indented{1}{credits() prints a list of people who contributed to Axiom} \\blankline \\spad{X} credits()")) (|getDomains| (((|Set| (|Symbol|)) (|Symbol|)) "\\indented{1}{The getDomains(\\spad{s}) takes a category and returns the list of domains} \\indented{1}{that have that category} \\blankline \\spad{X} getDomains 'IndexedAggregate"))) NIL NIL -(-52 R M P) +(-59 R M P) ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-53 |Base| R -2958) +(-60 |Base| R -1333) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL -(-54 S R |Row| |Col|) -((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $ |#2|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#4|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#3|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#2|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#4| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#3| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#2| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#2| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#2|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) +(-61 S R |Row| |Col|) +((|constructor| (NIL "Two dimensional array categories and domains")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\indented{1}{map!(\\spad{f},{}a)\\space{2}assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map!(-,{}arr)")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $ |#2|) "\\indented{1}{map(\\spad{f},{}a,{}\\spad{b},{}\\spad{r}) returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))}} \\indented{1}{when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist;} \\indented{1}{else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist;} \\indented{1}{else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist;} \\indented{1}{otherwise \\spad{c(i,{}j) = f(r,{}r)}.} \\blankline \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} \\spad{arr1} : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} \\spad{arr2} : \\spad{ARRAY2} INT \\spad{:=} new(3,{}3,{}10) \\spad{X} map(adder,{}\\spad{arr1},{}\\spad{arr2},{}17)") (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\indented{1}{map(\\spad{f},{}a,{}\\spad{b}) returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\blankline \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map(adder,{}arr,{}arr)") (($ (|Mapping| |#2| |#2|) $) "\\indented{1}{map(\\spad{f},{}a) returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map(-,{}arr) \\spad{X} map((\\spad{x} +-> \\spad{x} + \\spad{x}),{}arr)")) (|setColumn!| (($ $ (|Integer|) |#4|) "\\indented{1}{setColumn!(\\spad{m},{}\\spad{j},{}\\spad{v}) sets to \\spad{j}th column of \\spad{m} to \\spad{v}} \\blankline \\spad{X} T1:=TwoDimensionalArray Integer \\spad{X} arr:T1:= new(5,{}4,{}0) \\spad{X} T2:=OneDimensionalArray Integer \\spad{X} acol:=construct([1,{}2,{}3,{}4,{}5]::List(INT))\\$\\spad{T2} \\spad{X} setColumn!(arr,{}1,{}acol)\\$\\spad{T1}")) (|setRow!| (($ $ (|Integer|) |#3|) "\\indented{1}{setRow!(\\spad{m},{}\\spad{i},{}\\spad{v}) sets to \\spad{i}th row of \\spad{m} to \\spad{v}} \\blankline \\spad{X} T1:=TwoDimensionalArray Integer \\spad{X} arr:T1:= new(5,{}4,{}0) \\spad{X} T2:=OneDimensionalArray Integer \\spad{X} arow:=construct([1,{}2,{}3,{}4]::List(INT))\\$\\spad{T2} \\spad{X} setRow!(arr,{}1,{}arow)\\$\\spad{T1}")) (|qsetelt!| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\indented{1}{qsetelt!(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) sets the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of \\spad{m} to \\spad{r}} \\indented{1}{NO error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} qsetelt!(arr,{}1,{}1,{}17)")) (|setelt| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\indented{1}{setelt(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) sets the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of \\spad{m} to \\spad{r}} \\indented{1}{error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} setelt(arr,{}1,{}1,{}17)")) (|parts| (((|List| |#2|) $) "\\indented{1}{parts(\\spad{m}) returns a list of the elements of \\spad{m} in row major order} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} parts(arr)")) (|column| ((|#4| $ (|Integer|)) "\\indented{1}{column(\\spad{m},{}\\spad{j}) returns the \\spad{j}th column of \\spad{m}} \\indented{1}{error check to determine if index is in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} column(arr,{}1)")) (|row| ((|#3| $ (|Integer|)) "\\indented{1}{row(\\spad{m},{}\\spad{i}) returns the \\spad{i}th row of \\spad{m}} \\indented{1}{error check to determine if index is in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} row(arr,{}1)")) (|qelt| ((|#2| $ (|Integer|) (|Integer|)) "\\indented{1}{qelt(\\spad{m},{}\\spad{i},{}\\spad{j}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m}} \\indented{1}{NO error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} qelt(arr,{}1,{}1)")) (|elt| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\indented{1}{elt(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{}} \\indented{1}{and returns \\spad{r} otherwise} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} elt(arr,{}1,{}1,{}6) \\spad{X} elt(arr,{}1,{}10,{}6)") ((|#2| $ (|Integer|) (|Integer|)) "\\indented{1}{elt(\\spad{m},{}\\spad{i},{}\\spad{j}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m}} \\indented{1}{error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} elt(arr,{}1,{}1)")) (|ncols| (((|NonNegativeInteger|) $) "\\indented{1}{ncols(\\spad{m}) returns the number of columns in the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} ncols(arr)")) (|nrows| (((|NonNegativeInteger|) $) "\\indented{1}{nrows(\\spad{m}) returns the number of rows in the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} nrows(arr)")) (|maxColIndex| (((|Integer|) $) "\\indented{1}{maxColIndex(\\spad{m}) returns the index of the 'last' column of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} maxColIndex(arr)")) (|minColIndex| (((|Integer|) $) "\\indented{1}{minColIndex(\\spad{m}) returns the index of the 'first' column of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} minColIndex(arr)")) (|maxRowIndex| (((|Integer|) $) "\\indented{1}{maxRowIndex(\\spad{m}) returns the index of the 'last' row of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} maxRowIndex(arr)")) (|minRowIndex| (((|Integer|) $) "\\indented{1}{minRowIndex(\\spad{m}) returns the index of the 'first' row of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} minRowIndex(arr)")) (|fill!| (($ $ |#2|) "\\indented{1}{fill!(\\spad{m},{}\\spad{r}) fills \\spad{m} with \\spad{r}\\spad{'s}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} fill!(arr,{}10)")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\indented{1}{new(\\spad{m},{}\\spad{n},{}\\spad{r}) is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0)")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) NIL NIL -(-55 R |Row| |Col|) -((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-62 R |Row| |Col|) +((|constructor| (NIL "Two dimensional array categories and domains")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map!(\\spad{f},{}a)\\space{2}assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map!(-,{}arr)")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\indented{1}{map(\\spad{f},{}a,{}\\spad{b},{}\\spad{r}) returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))}} \\indented{1}{when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist;} \\indented{1}{else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist;} \\indented{1}{else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist;} \\indented{1}{otherwise \\spad{c(i,{}j) = f(r,{}r)}.} \\blankline \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} \\spad{arr1} : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} \\spad{arr2} : \\spad{ARRAY2} INT \\spad{:=} new(3,{}3,{}10) \\spad{X} map(adder,{}\\spad{arr1},{}\\spad{arr2},{}17)") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\indented{1}{map(\\spad{f},{}a,{}\\spad{b}) returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\blankline \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map(adder,{}arr,{}arr)") (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map(\\spad{f},{}a) returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))}} \\indented{1}{for all \\spad{i,{} j}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} map(-,{}arr) \\spad{X} map((\\spad{x} +-> \\spad{x} + \\spad{x}),{}arr)")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\indented{1}{setColumn!(\\spad{m},{}\\spad{j},{}\\spad{v}) sets to \\spad{j}th column of \\spad{m} to \\spad{v}} \\blankline \\spad{X} T1:=TwoDimensionalArray Integer \\spad{X} arr:T1:= new(5,{}4,{}0) \\spad{X} T2:=OneDimensionalArray Integer \\spad{X} acol:=construct([1,{}2,{}3,{}4,{}5]::List(INT))\\$\\spad{T2} \\spad{X} setColumn!(arr,{}1,{}acol)\\$\\spad{T1}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\indented{1}{setRow!(\\spad{m},{}\\spad{i},{}\\spad{v}) sets to \\spad{i}th row of \\spad{m} to \\spad{v}} \\blankline \\spad{X} T1:=TwoDimensionalArray Integer \\spad{X} arr:T1:= new(5,{}4,{}0) \\spad{X} T2:=OneDimensionalArray Integer \\spad{X} arow:=construct([1,{}2,{}3,{}4]::List(INT))\\$\\spad{T2} \\spad{X} setRow!(arr,{}1,{}arow)\\$\\spad{T1}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\indented{1}{qsetelt!(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) sets the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of \\spad{m} to \\spad{r}} \\indented{1}{NO error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} qsetelt!(arr,{}1,{}1,{}17)")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\indented{1}{setelt(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) sets the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of \\spad{m} to \\spad{r}} \\indented{1}{error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} setelt(arr,{}1,{}1,{}17)")) (|parts| (((|List| |#1|) $) "\\indented{1}{parts(\\spad{m}) returns a list of the elements of \\spad{m} in row major order} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} parts(arr)")) (|column| ((|#3| $ (|Integer|)) "\\indented{1}{column(\\spad{m},{}\\spad{j}) returns the \\spad{j}th column of \\spad{m}} \\indented{1}{error check to determine if index is in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} column(arr,{}1)")) (|row| ((|#2| $ (|Integer|)) "\\indented{1}{row(\\spad{m},{}\\spad{i}) returns the \\spad{i}th row of \\spad{m}} \\indented{1}{error check to determine if index is in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} row(arr,{}1)")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\indented{1}{qelt(\\spad{m},{}\\spad{i},{}\\spad{j}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m}} \\indented{1}{NO error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} qelt(arr,{}1,{}1)")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\indented{1}{elt(\\spad{m},{}\\spad{i},{}\\spad{j},{}\\spad{r}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{}} \\indented{1}{and returns \\spad{r} otherwise} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} elt(arr,{}1,{}1,{}6) \\spad{X} elt(arr,{}1,{}10,{}6)") ((|#1| $ (|Integer|) (|Integer|)) "\\indented{1}{elt(\\spad{m},{}\\spad{i},{}\\spad{j}) returns the element in the \\spad{i}th row and \\spad{j}th} \\indented{1}{column of the array \\spad{m}} \\indented{1}{error check to determine if indices are in proper ranges} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} elt(arr,{}1,{}1)")) (|ncols| (((|NonNegativeInteger|) $) "\\indented{1}{ncols(\\spad{m}) returns the number of columns in the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} ncols(arr)")) (|nrows| (((|NonNegativeInteger|) $) "\\indented{1}{nrows(\\spad{m}) returns the number of rows in the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} nrows(arr)")) (|maxColIndex| (((|Integer|) $) "\\indented{1}{maxColIndex(\\spad{m}) returns the index of the 'last' column of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} maxColIndex(arr)")) (|minColIndex| (((|Integer|) $) "\\indented{1}{minColIndex(\\spad{m}) returns the index of the 'first' column of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} minColIndex(arr)")) (|maxRowIndex| (((|Integer|) $) "\\indented{1}{maxRowIndex(\\spad{m}) returns the index of the 'last' row of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} maxRowIndex(arr)")) (|minRowIndex| (((|Integer|) $) "\\indented{1}{minRowIndex(\\spad{m}) returns the index of the 'first' row of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}10) \\spad{X} minRowIndex(arr)")) (|fill!| (($ $ |#1|) "\\indented{1}{fill!(\\spad{m},{}\\spad{r}) fills \\spad{m} with \\spad{r}\\spad{'s}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0) \\spad{X} fill!(arr,{}10)")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\indented{1}{new(\\spad{m},{}\\spad{n},{}\\spad{r}) is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,{}4,{}0)")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-56 S) -((|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-57 A B) -((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) +(-63 A B) +((|constructor| (NIL "This package provides tools for operating on one-dimensional arrays with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\indented{1}{map(\\spad{f},{}a) applies function \\spad{f} to each member of one-dimensional array} \\indented{1}{\\spad{a} resulting in a new one-dimensional array over a} \\indented{1}{possibly different underlying domain.} \\blankline \\spad{X} \\spad{T1:=OneDimensionalArrayFunctions2}(Integer,{}Integer) \\spad{X} map(\\spad{x+}-\\spad{>x+2},{}[\\spad{i} for \\spad{i} in 1..10])\\$\\spad{T1}")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\indented{1}{reduce(\\spad{f},{}a,{}\\spad{r}) applies function \\spad{f} to each} \\indented{1}{successive element of the} \\indented{1}{one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}.} \\indented{1}{For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)}} \\indented{1}{does \\spad{3+(2+(1+0))}. Note that third argument \\spad{r}} \\indented{1}{may be regarded as the identity element for the function \\spad{f}.} \\blankline \\spad{X} \\spad{T1:=OneDimensionalArrayFunctions2}(Integer,{}Integer) \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} reduce(adder,{}[\\spad{i} for \\spad{i} in 1..10],{}0)\\$\\spad{T1}")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\indented{1}{scan(\\spad{f},{}a,{}\\spad{r}) successively applies} \\indented{1}{\\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays} \\indented{1}{\\spad{x} of one-dimensional array \\spad{a}.} \\indented{1}{More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then} \\indented{1}{\\spad{scan(f,{}a,{}r)} returns} \\indented{1}{\\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.} \\blankline \\spad{X} \\spad{T1:=OneDimensionalArrayFunctions2}(Integer,{}Integer) \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} scan(adder,{}[\\spad{i} for \\spad{i} in 1..10],{}0)\\$\\spad{T1}"))) NIL NIL -(-58 R) -((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-59 -3986) -((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-64 S) +((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\indented{1}{oneDimensionalArray(\\spad{n},{}\\spad{s}) creates an array from \\spad{n} copies of element \\spad{s}} \\blankline \\spad{X} oneDimensionalArray(10,{}0.0)") (($ (|List| |#1|)) "\\indented{1}{oneDimensionalArray(\\spad{l}) creates an array from a list of elements \\spad{l}} \\blankline \\spad{X} oneDimensionalArray [\\spad{i**2} for \\spad{i} in 1..10]"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-65 R) +((|constructor| (NIL "A TwoDimensionalArray is a two dimensional array with 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-66 -1337) +((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine d02kef. This ASP computes the values of a set of functions,{} for example: \\blankline \\tab{5}SUBROUTINE COEFFN(\\spad{P},{}\\spad{Q},{}DQDL,{}\\spad{X},{}ELAM,{}JINT)\\spad{\\br} \\tab{5}DOUBLE PRECISION ELAM,{}\\spad{P},{}\\spad{Q},{}\\spad{X},{}DQDL\\spad{\\br} \\tab{5}INTEGER JINT\\spad{\\br} \\tab{5}\\spad{P=1}.0D0\\spad{\\br} \\tab{5}\\spad{Q=}((\\spad{-1}.0D0*X**3)+ELAM*X*X-2.0D0)/(\\spad{X*X})\\spad{\\br} \\tab{5}\\spad{DQDL=1}.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -3986) -((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-67 -1337) +((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine d02kef etc.,{} for example: \\blankline \\tab{5}SUBROUTINE MONIT (MAXIT,{}IFLAG,{}ELAM,{}FINFO)\\spad{\\br} \\tab{5}DOUBLE PRECISION ELAM,{}FINFO(15)\\spad{\\br} \\tab{5}INTEGER MAXIT,{}IFLAG\\spad{\\br} \\tab{5}IF(MAXIT.EQ.\\spad{-1})THEN\\spad{\\br} \\tab{7}PRINT*,{}\"Output from Monit\"\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}PRINT*,{}MAXIT,{}IFLAG,{}ELAM,{}(FINFO(\\spad{I}),{}\\spad{I=1},{}4)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -3986) -((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) +(-68 -1337) +((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{LSFUN2}(\\spad{M},{}\\spad{N},{}\\spad{XC},{}FVECC,{}FJACC,{}\\spad{LJC})\\spad{\\br} \\tab{5}DOUBLE PRECISION FVECC(\\spad{M}),{}FJACC(\\spad{LJC},{}\\spad{N}),{}\\spad{XC}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{M},{}\\spad{N},{}\\spad{LJC}\\spad{\\br} \\tab{5}INTEGER \\spad{I},{}\\spad{J}\\spad{\\br} \\tab{5}DO 25003 \\spad{I=1},{}\\spad{LJC}\\spad{\\br} \\tab{7}DO 25004 \\spad{J=1},{}\\spad{N}\\spad{\\br} \\tab{9}FJACC(\\spad{I},{}\\spad{J})\\spad{=0}.0D0\\spad{\\br} 25004 CONTINUE\\spad{\\br} 25003 CONTINUE\\spad{\\br} \\tab{5}FVECC(1)=((\\spad{XC}(1)\\spad{-0}.14D0)\\spad{*XC}(3)+(15.0D0*XC(1)\\spad{-2}.1D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{+15}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(2)=((\\spad{XC}(1)\\spad{-0}.18D0)\\spad{*XC}(3)+(7.0D0*XC(1)\\spad{-1}.26D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{+7}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(3)=((\\spad{XC}(1)\\spad{-0}.22D0)\\spad{*XC}(3)+(4.333333333333333D0*XC(1)\\spad{-0}.953333\\spad{\\br} \\tab{4}\\spad{&3333333333D0})\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+4}.333333333333333D0*XC(2))\\spad{\\br} \\tab{5}FVECC(4)=((\\spad{XC}(1)\\spad{-0}.25D0)\\spad{*XC}(3)+(3.0D0*XC(1)\\spad{-0}.75D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{+3}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(5)=((\\spad{XC}(1)\\spad{-0}.29D0)\\spad{*XC}(3)+(2.2D0*XC(1)\\spad{-0}.6379999999999999D0)*\\spad{\\br} \\tab{4}\\spad{&XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+2}.2D0*XC(2))\\spad{\\br} \\tab{5}FVECC(6)=((\\spad{XC}(1)\\spad{-0}.32D0)\\spad{*XC}(3)+(1.666666666666667D0*XC(1)\\spad{-0}.533333\\spad{\\br} \\tab{4}\\spad{&3333333333D0})\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+1}.666666666666667D0*XC(2))\\spad{\\br} \\tab{5}FVECC(7)=((\\spad{XC}(1)\\spad{-0}.35D0)\\spad{*XC}(3)+(1.285714285714286D0*XC(1)\\spad{-0}.45D0)*\\spad{\\br} \\tab{4}\\spad{&XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+1}.285714285714286D0*XC(2))\\spad{\\br} \\tab{5}FVECC(8)=((\\spad{XC}(1)\\spad{-0}.39D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-0}.39D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)+\\spad{\\br} \\tab{4}\\spad{&XC}(2))\\spad{\\br} \\tab{5}FVECC(9)=((\\spad{XC}(1)\\spad{-0}.37D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-0}.37D0)\\spad{*XC}(2)\\spad{+1}.285714285714\\spad{\\br} \\tab{4}\\spad{&286D0})/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(10)=((\\spad{XC}(1)\\spad{-0}.58D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-0}.58D0)\\spad{*XC}(2)\\spad{+1}.66666666666\\spad{\\br} \\tab{4}\\spad{&6667D0})/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(11)=((\\spad{XC}(1)\\spad{-0}.73D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-0}.73D0)\\spad{*XC}(2)\\spad{+2}.2D0)/(\\spad{XC}(3)\\spad{\\br} \\tab{4}&+XC(2))\\spad{\\br} \\tab{5}FVECC(12)=((\\spad{XC}(1)\\spad{-0}.96D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-0}.96D0)\\spad{*XC}(2)\\spad{+3}.0D0)/(\\spad{XC}(3)\\spad{\\br} \\tab{4}&+XC(2))\\spad{\\br} \\tab{5}FVECC(13)=((\\spad{XC}(1)\\spad{-1}.34D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-1}.34D0)\\spad{*XC}(2)\\spad{+4}.33333333333\\spad{\\br} \\tab{4}\\spad{&3333D0})/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(14)=((\\spad{XC}(1)\\spad{-2}.1D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-2}.1D0)\\spad{*XC}(2)\\spad{+7}.0D0)/(\\spad{XC}(3)\\spad{+X}\\spad{\\br} \\tab{4}\\spad{&C}(2))\\spad{\\br} \\tab{5}FVECC(15)=((\\spad{XC}(1)\\spad{-4}.39D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-4}.39D0)\\spad{*XC}(2)\\spad{+15}.0D0)/(\\spad{XC}(3\\spad{\\br} \\tab{4}&)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FJACC(1,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(1,{}2)=-15.0D0/(\\spad{XC}(3)\\spad{**2+30}.0D0*XC(2)\\spad{*XC}(3)\\spad{+225}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(1,{}3)=-1.0D0/(\\spad{XC}(3)\\spad{**2+30}.0D0*XC(2)\\spad{*XC}(3)\\spad{+225}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(2,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(2,{}2)=-7.0D0/(\\spad{XC}(3)\\spad{**2+14}.0D0*XC(2)\\spad{*XC}(3)\\spad{+49}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(2,{}3)=-1.0D0/(\\spad{XC}(3)\\spad{**2+14}.0D0*XC(2)\\spad{*XC}(3)\\spad{+49}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(3,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(3,{}2)=((\\spad{-0}.1110223024625157D-15*XC(3))\\spad{-4}.333333333333333D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{**2+8}.666666666666666D0*XC(2)\\spad{*XC}(3)\\spad{+18}.77777777777778D0*XC(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(3,{}3)=(0.1110223024625157D-15*XC(2)\\spad{-1}.0D0)/(\\spad{XC}(3)\\spad{**2+8}.666666\\spad{\\br} \\tab{4}&666666666D0*XC(2)\\spad{*XC}(3)\\spad{+18}.77777777777778D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(4,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(4,{}2)=-3.0D0/(\\spad{XC}(3)\\spad{**2+6}.0D0*XC(2)\\spad{*XC}(3)\\spad{+9}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(4,{}3)=-1.0D0/(\\spad{XC}(3)\\spad{**2+6}.0D0*XC(2)\\spad{*XC}(3)\\spad{+9}.0D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(5,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(5,{}2)=((\\spad{-0}.1110223024625157D-15*XC(3))\\spad{-2}.2D0)/(\\spad{XC}(3)\\spad{**2+4}.399\\spad{\\br} \\tab{4}&999999999999D0*XC(2)\\spad{*XC}(3)\\spad{+4}.839999999999998D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(5,{}3)=(0.1110223024625157D-15*XC(2)\\spad{-1}.0D0)/(\\spad{XC}(3)\\spad{**2+4}.399999\\spad{\\br} \\tab{4}&999999999D0*XC(2)\\spad{*XC}(3)\\spad{+4}.839999999999998D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(6,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(6,{}2)=((\\spad{-0}.2220446049250313D-15*XC(3))\\spad{-1}.666666666666667D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{**2+3}.333333333333333D0*XC(2)\\spad{*XC}(3)\\spad{+2}.777777777777777D0*XC(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(6,{}3)=(0.2220446049250313D-15*XC(2)\\spad{-1}.0D0)/(\\spad{XC}(3)\\spad{**2+3}.333333\\spad{\\br} \\tab{4}&333333333D0*XC(2)\\spad{*XC}(3)\\spad{+2}.777777777777777D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(7,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(7,{}2)=((\\spad{-0}.5551115123125783D-16*XC(3))\\spad{-1}.285714285714286D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{**2+2}.571428571428571D0*XC(2)\\spad{*XC}(3)\\spad{+1}.653061224489796D0*XC(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(7,{}3)=(0.5551115123125783D-16*XC(2)\\spad{-1}.0D0)/(\\spad{XC}(3)\\spad{**2+2}.571428\\spad{\\br} \\tab{4}&571428571D0*XC(2)\\spad{*XC}(3)\\spad{+1}.653061224489796D0*XC(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(8,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(8,{}2)=-1.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(8,{}3)=-1.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(9,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(9,{}2)=-1.285714285714286D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)*\\spad{\\br} \\tab{4}\\spad{&*2})\\spad{\\br} \\tab{5}FJACC(9,{}3)=-1.285714285714286D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)*\\spad{\\br} \\tab{4}\\spad{&*2})\\spad{\\br} \\tab{5}FJACC(10,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(10,{}2)=-1.666666666666667D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(10,{}3)=-1.666666666666667D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(11,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(11,{}2)=-2.2D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(11,{}3)=-2.2D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(12,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(12,{}2)=-3.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(12,{}3)=-3.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(13,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(13,{}2)=-4.333333333333333D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(13,{}3)=-4.333333333333333D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{\\br} \\tab{4}\\spad{&**2})\\spad{\\br} \\tab{5}FJACC(14,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(14,{}2)=-7.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(14,{}3)=-7.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(15,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}FJACC(15,{}2)=-15.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}FJACC(15,{}3)=-15.0D0/(\\spad{XC}(3)\\spad{**2+2}.0D0*XC(2)\\spad{*XC}(3)\\spad{+XC}(2)\\spad{**2})\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -3986) -((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-69 -1337) +((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{x}) and turn it into a Fortran Function like the following: \\blankline \\tab{5}DOUBLE PRECISION FUNCTION \\spad{F}(\\spad{X})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}\\spad{\\br} \\tab{5}F=DSIN(\\spad{X})\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -3986) -((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-70 -1337) +((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example: \\blankline \\tab{5}SUBROUTINE QPHESS(\\spad{N},{}NROWH,{}NCOLH,{}JTHCOL,{}HESS,{}\\spad{X},{}\\spad{HX})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{HX}(\\spad{N}),{}\\spad{X}(\\spad{N}),{}HESS(NROWH,{}NCOLH)\\spad{\\br} \\tab{5}INTEGER JTHCOL,{}\\spad{N},{}NROWH,{}NCOLH\\spad{\\br} \\tab{5}\\spad{HX}(1)\\spad{=2}.0D0*X(1)\\spad{\\br} \\tab{5}\\spad{HX}(2)\\spad{=2}.0D0*X(2)\\spad{\\br} \\tab{5}\\spad{HX}(3)\\spad{=2}.0D0*X(4)\\spad{+2}.0D0*X(3)\\spad{\\br} \\tab{5}\\spad{HX}(4)\\spad{=2}.0D0*X(4)\\spad{+2}.0D0*X(3)\\spad{\\br} \\tab{5}\\spad{HX}(5)\\spad{=2}.0D0*X(5)\\spad{\\br} \\tab{5}\\spad{HX}(6)=(\\spad{-2}.0D0*X(7))+(\\spad{-2}.0D0*X(6))\\spad{\\br} \\tab{5}\\spad{HX}(7)=(\\spad{-2}.0D0*X(7))+(\\spad{-2}.0D0*X(6))\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -3986) -((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-71 -1337) +((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine e04jaf),{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{FUNCT1}(\\spad{N},{}\\spad{XC},{}\\spad{FC})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{FC},{}\\spad{XC}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}\\spad{FC=10}.0D0*XC(4)**4+(\\spad{-40}.0D0*XC(1)\\spad{*XC}(4)\\spad{**3})+(60.0D0*XC(1)\\spad{**2+5}\\spad{\\br} \\tab{4}&.0D0)\\spad{*XC}(4)**2+((\\spad{-10}.0D0*XC(3))+(\\spad{-40}.0D0*XC(1)\\spad{**3}))\\spad{*XC}(4)\\spad{+16}.0D0*X\\spad{\\br} \\tab{4}\\spad{&C}(3)**4+(\\spad{-32}.0D0*XC(2)\\spad{*XC}(3)\\spad{**3})+(24.0D0*XC(2)\\spad{**2+5}.0D0)\\spad{*XC}(3)**2+\\spad{\\br} \\tab{4}&(\\spad{-8}.0D0*XC(2)**3*XC(3))\\spad{+XC}(2)\\spad{**4+100}.0D0*XC(2)\\spad{**2+20}.0D0*XC(1)\\spad{*XC}(\\spad{\\br} \\tab{4}\\spad{&2})\\spad{+10}.0D0*XC(1)**4+XC(1)\\spad{**2}\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spadtype{FortranExpression} and turns it into an ASP. coerce(\\spad{f}) takes an object from the appropriate instantiation of"))) NIL NIL -(-65 -3986) -((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) +(-72 -1337) +((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine f02fjf ,{}for example: \\blankline \\tab{5}FUNCTION DOT(IFLAG,{}\\spad{N},{}\\spad{Z},{}\\spad{W},{}RWORK,{}LRWORK,{}IWORK,{}LIWORK)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{W}(\\spad{N}),{}\\spad{Z}(\\spad{N}),{}RWORK(LRWORK)\\spad{\\br} \\tab{5}INTEGER \\spad{N},{}LIWORK,{}IFLAG,{}LRWORK,{}IWORK(LIWORK)\\spad{\\br} \\tab{5}DOT=(\\spad{W}(16)+(\\spad{-0}.5D0*W(15)))\\spad{*Z}(16)+((\\spad{-0}.5D0*W(16))\\spad{+W}(15)+(\\spad{-0}.5D0*W(1\\spad{\\br} \\tab{4}\\spad{&4})))\\spad{*Z}(15)+((\\spad{-0}.5D0*W(15))\\spad{+W}(14)+(\\spad{-0}.5D0*W(13)))\\spad{*Z}(14)+((\\spad{-0}.5D0*W(\\spad{\\br} \\tab{4}\\spad{&14}))\\spad{+W}(13)+(\\spad{-0}.5D0*W(12)))\\spad{*Z}(13)+((\\spad{-0}.5D0*W(13))\\spad{+W}(12)+(\\spad{-0}.5D0*W(1\\spad{\\br} \\tab{4}\\spad{&1})))\\spad{*Z}(12)+((\\spad{-0}.5D0*W(12))\\spad{+W}(11)+(\\spad{-0}.5D0*W(10)))\\spad{*Z}(11)+((\\spad{-0}.5D0*W(\\spad{\\br} \\tab{4}\\spad{&11}))\\spad{+W}(10)+(\\spad{-0}.5D0*W(9)))\\spad{*Z}(10)+((\\spad{-0}.5D0*W(10))\\spad{+W}(9)+(\\spad{-0}.5D0*W(8))\\spad{\\br} \\tab{4}&)\\spad{*Z}(9)+((\\spad{-0}.5D0*W(9))\\spad{+W}(8)+(\\spad{-0}.5D0*W(7)))\\spad{*Z}(8)+((\\spad{-0}.5D0*W(8))\\spad{+W}(7)\\spad{\\br} \\tab{4}\\spad{&+}(\\spad{-0}.5D0*W(6)))\\spad{*Z}(7)+((\\spad{-0}.5D0*W(7))\\spad{+W}(6)+(\\spad{-0}.5D0*W(5)))\\spad{*Z}(6)+((\\spad{-0}.\\spad{\\br} \\tab{4}&5D0*W(6))\\spad{+W}(5)+(\\spad{-0}.5D0*W(4)))\\spad{*Z}(5)+((\\spad{-0}.5D0*W(5))\\spad{+W}(4)+(\\spad{-0}.5D0*W(3\\spad{\\br} \\tab{4}&)))\\spad{*Z}(4)+((\\spad{-0}.5D0*W(4))\\spad{+W}(3)+(\\spad{-0}.5D0*W(2)))\\spad{*Z}(3)+((\\spad{-0}.5D0*W(3))\\spad{+W}(\\spad{\\br} \\tab{4}\\spad{&2})+(\\spad{-0}.5D0*W(1)))\\spad{*Z}(2)+((\\spad{-0}.5D0*W(2))\\spad{+W}(1))\\spad{*Z}(1)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END"))) NIL NIL -(-66 -3986) -((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) +(-73 -1337) +((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine f02fjf,{} for example: \\blankline \\tab{5}SUBROUTINE IMAGE(IFLAG,{}\\spad{N},{}\\spad{Z},{}\\spad{W},{}RWORK,{}LRWORK,{}IWORK,{}LIWORK)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{Z}(\\spad{N}),{}\\spad{W}(\\spad{N}),{}IWORK(LRWORK),{}RWORK(LRWORK)\\spad{\\br} \\tab{5}INTEGER \\spad{N},{}LIWORK,{}IFLAG,{}LRWORK\\spad{\\br} \\tab{5}\\spad{W}(1)\\spad{=0}.01707454969713436D0*Z(16)\\spad{+0}.001747395874954051D0*Z(15)\\spad{+0}.00\\spad{\\br} \\tab{4}&2106973900813502D0*Z(14)\\spad{+0}.002957434991769087D0*Z(13)+(\\spad{-0}.00700554\\spad{\\br} \\tab{4}&0882865317D0*Z(12))+(\\spad{-0}.01219194009813166D0*Z(11))\\spad{+0}.0037230647365\\spad{\\br} \\tab{4}&3087D0*Z(10)\\spad{+0}.04932374658377151D0*Z(9)+(\\spad{-0}.03586220812223305D0*Z(\\spad{\\br} \\tab{4}\\spad{&8}))+(\\spad{-0}.04723268012114625D0*Z(7))+(\\spad{-0}.02434652144032987D0*Z(6))\\spad{+0}.\\spad{\\br} \\tab{4}&2264766947290192D0*Z(5)+(\\spad{-0}.1385343580686922D0*Z(4))+(\\spad{-0}.116530050\\spad{\\br} \\tab{4}&8238904D0*Z(3))+(\\spad{-0}.2803531651057233D0*Z(2))\\spad{+1}.019463911841327D0*Z\\spad{\\br} \\tab{4}&(1)\\spad{\\br} \\tab{5}\\spad{W}(2)\\spad{=0}.0227345011107737D0*Z(16)\\spad{+0}.008812321197398072D0*Z(15)\\spad{+0}.010\\spad{\\br} \\tab{4}&94012210519586D0*Z(14)+(\\spad{-0}.01764072463999744D0*Z(13))+(\\spad{-0}.01357136\\spad{\\br} \\tab{4}&72105995D0*Z(12))\\spad{+0}.00157466157362272D0*Z(11)\\spad{+0}.05258889186338282D\\spad{\\br} \\tab{4}&0*Z(10)+(\\spad{-0}.01981532388243379D0*Z(9))+(\\spad{-0}.06095390688679697D0*Z(8)\\spad{\\br} \\tab{4}&)+(\\spad{-0}.04153119955569051D0*Z(7))\\spad{+0}.2176561076571465D0*Z(6)+(\\spad{-0}.0532\\spad{\\br} \\tab{4}&5555586632358D0*Z(5))+(\\spad{-0}.1688977368984641D0*Z(4))+(\\spad{-0}.32440166056\\spad{\\br} \\tab{4}&67343D0*Z(3))\\spad{+0}.9128222941872173D0*Z(2)+(\\spad{-0}.2419652703415429D0*Z(1\\spad{\\br} \\tab{4}&))\\spad{\\br} \\tab{5}\\spad{W}(3)\\spad{=0}.03371198197190302D0*Z(16)\\spad{+0}.02021603150122265D0*Z(15)+(\\spad{-0}.0\\spad{\\br} \\tab{4}&06607305534689702D0*Z(14))+(\\spad{-0}.03032392238968179D0*Z(13))\\spad{+0}.002033\\spad{\\br} \\tab{4}&305231024948D0*Z(12)\\spad{+0}.05375944956767728D0*Z(11)+(\\spad{-0}.0163213312502\\spad{\\br} \\tab{4}&9967D0*Z(10))+(\\spad{-0}.05483186562035512D0*Z(9))+(\\spad{-0}.04901428822579872D\\spad{\\br} \\tab{4}&0*Z(8))\\spad{+0}.2091097927887612D0*Z(7)+(\\spad{-0}.05760560341383113D0*Z(6))+(-\\spad{\\br} \\tab{4}\\spad{&0}.1236679206156403D0*Z(5))+(\\spad{-0}.3523683853026259D0*Z(4))\\spad{+0}.88929961\\spad{\\br} \\tab{4}&32269974D0*Z(3)+(\\spad{-0}.2995429545781457D0*Z(2))+(\\spad{-0}.02986582812574917\\spad{\\br} \\tab{4}&D0*Z(1))\\spad{\\br} \\tab{5}\\spad{W}(4)\\spad{=0}.05141563713660119D0*Z(16)\\spad{+0}.005239165960779299D0*Z(15)+(\\spad{-0}.\\spad{\\br} \\tab{4}&01623427735779699D0*Z(14))+(\\spad{-0}.01965809746040371D0*Z(13))\\spad{+0}.054688\\spad{\\br} \\tab{4}&97337339577D0*Z(12)+(\\spad{-0}.014224695935687D0*Z(11))+(\\spad{-0}.0505181779315\\spad{\\br} \\tab{4}&6355D0*Z(10))+(\\spad{-0}.04353074206076491D0*Z(9))\\spad{+0}.2012230497530726D0*Z\\spad{\\br} \\tab{4}&(8)+(\\spad{-0}.06630874514535952D0*Z(7))+(\\spad{-0}.1280829963720053D0*Z(6))+(\\spad{-0}\\spad{\\br} \\tab{4}&.305169742604165D0*Z(5))\\spad{+0}.8600427128450191D0*Z(4)+(\\spad{-0}.32415033802\\spad{\\br} \\tab{4}&68184D0*Z(3))+(\\spad{-0}.09033531980693314D0*Z(2))\\spad{+0}.09089205517109111D0*\\spad{\\br} \\tab{4}\\spad{&Z}(1)\\spad{\\br} \\tab{5}\\spad{W}(5)\\spad{=0}.04556369767776375D0*Z(16)+(\\spad{-0}.001822737697581869D0*Z(15))+(\\spad{\\br} \\tab{4}&-0.002512226501941856D0*Z(14))\\spad{+0}.02947046460707379D0*Z(13)+(\\spad{-0}.014\\spad{\\br} \\tab{4}&45079632086177D0*Z(12))+(\\spad{-0}.05034242196614937D0*Z(11))+(\\spad{-0}.0376966\\spad{\\br} \\tab{4}&3291725935D0*Z(10))\\spad{+0}.2171103102175198D0*Z(9)+(\\spad{-0}.0824949256021352\\spad{\\br} \\tab{4}&4D0*Z(8))+(\\spad{-0}.1473995209288945D0*Z(7))+(\\spad{-0}.315042193418466D0*Z(6))\\spad{\\br} \\tab{4}\\spad{&+0}.9591623347824002D0*Z(5)+(\\spad{-0}.3852396953763045D0*Z(4))+(\\spad{-0}.141718\\spad{\\br} \\tab{4}&5427288274D0*Z(3))+(\\spad{-0}.03423495461011043D0*Z(2))\\spad{+0}.319820917706851\\spad{\\br} \\tab{4}&6D0*Z(1)\\spad{\\br} \\tab{5}\\spad{W}(6)\\spad{=0}.04015147277405744D0*Z(16)\\spad{+0}.01328585741341559D0*Z(15)\\spad{+0}.048\\spad{\\br} \\tab{4}&26082005465965D0*Z(14)+(\\spad{-0}.04319641116207706D0*Z(13))+(\\spad{-0}.04931323\\spad{\\br} \\tab{4}&319055762D0*Z(12))+(\\spad{-0}.03526886317505474D0*Z(11))\\spad{+0}.22295383396730\\spad{\\br} \\tab{4}&01D0*Z(10)+(\\spad{-0}.07375317649315155D0*Z(9))+(\\spad{-0}.1589391311991561D0*Z(\\spad{\\br} \\tab{4}\\spad{&8}))+(\\spad{-0}.328001910890377D0*Z(7))\\spad{+0}.952576555482747D0*Z(6)+(\\spad{-0}.31583\\spad{\\br} \\tab{4}&09975786731D0*Z(5))+(\\spad{-0}.1846882042225383D0*Z(4))+(\\spad{-0}.0703762046700\\spad{\\br} \\tab{4}&4427D0*Z(3))\\spad{+0}.2311852964327382D0*Z(2)\\spad{+0}.04254083491825025D0*Z(1)\\spad{\\br} \\tab{5}\\spad{W}(7)\\spad{=0}.06069778964023718D0*Z(16)\\spad{+0}.06681263884671322D0*Z(15)+(\\spad{-0}.0\\spad{\\br} \\tab{4}&2113506688615768D0*Z(14))+(\\spad{-0}.083996867458326D0*Z(13))+(\\spad{-0}.0329843\\spad{\\br} \\tab{4}&8523869648D0*Z(12))\\spad{+0}.2276878326327734D0*Z(11)+(\\spad{-0}.067356038933017\\spad{\\br} \\tab{4}&95D0*Z(10))+(\\spad{-0}.1559813965382218D0*Z(9))+(\\spad{-0}.3363262957694705D0*Z(\\spad{\\br} \\tab{4}\\spad{&8}))\\spad{+0}.9442791158560948D0*Z(7)+(\\spad{-0}.3199955249404657D0*Z(6))+(\\spad{-0}.136\\spad{\\br} \\tab{4}&2463839920727D0*Z(5))+(\\spad{-0}.1006185171570586D0*Z(4))\\spad{+0}.2057504515015\\spad{\\br} \\tab{4}&423D0*Z(3)+(\\spad{-0}.02065879269286707D0*Z(2))\\spad{+0}.03160990266745513D0*Z(1\\spad{\\br} \\tab{4}&)\\spad{\\br} \\tab{5}\\spad{W}(8)\\spad{=0}.126386868896738D0*Z(16)\\spad{+0}.002563370039476418D0*Z(15)+(\\spad{-0}.05\\spad{\\br} \\tab{4}&581757739455641D0*Z(14))+(\\spad{-0}.07777893205900685D0*Z(13))\\spad{+0}.23117338\\spad{\\br} \\tab{4}&45834199D0*Z(12)+(\\spad{-0}.06031581134427592D0*Z(11))+(\\spad{-0}.14805474755869\\spad{\\br} \\tab{4}&52D0*Z(10))+(\\spad{-0}.3364014128402243D0*Z(9))\\spad{+0}.9364014128402244D0*Z(8)\\spad{\\br} \\tab{4}\\spad{&+}(\\spad{-0}.3269452524413048D0*Z(7))+(\\spad{-0}.1396841886557241D0*Z(6))+(\\spad{-0}.056\\spad{\\br} \\tab{4}&1733845834199D0*Z(5))\\spad{+0}.1777789320590069D0*Z(4)+(\\spad{-0}.04418242260544\\spad{\\br} \\tab{4}&359D0*Z(3))+(\\spad{-0}.02756337003947642D0*Z(2))\\spad{+0}.07361313110326199D0*Z(\\spad{\\br} \\tab{4}\\spad{&1})\\spad{\\br} \\tab{5}\\spad{W}(9)\\spad{=0}.07361313110326199D0*Z(16)+(\\spad{-0}.02756337003947642D0*Z(15))+(-\\spad{\\br} \\tab{4}\\spad{&0}.04418242260544359D0*Z(14))\\spad{+0}.1777789320590069D0*Z(13)+(\\spad{-0}.056173\\spad{\\br} \\tab{4}&3845834199D0*Z(12))+(\\spad{-0}.1396841886557241D0*Z(11))+(\\spad{-0}.326945252441\\spad{\\br} \\tab{4}&3048D0*Z(10))\\spad{+0}.9364014128402244D0*Z(9)+(\\spad{-0}.3364014128402243D0*Z(8\\spad{\\br} \\tab{4}&))+(\\spad{-0}.1480547475586952D0*Z(7))+(\\spad{-0}.06031581134427592D0*Z(6))\\spad{+0}.23\\spad{\\br} \\tab{4}&11733845834199D0*Z(5)+(\\spad{-0}.07777893205900685D0*Z(4))+(\\spad{-0}.0558175773\\spad{\\br} \\tab{4}&9455641D0*Z(3))\\spad{+0}.002563370039476418D0*Z(2)\\spad{+0}.126386868896738D0*Z(\\spad{\\br} \\tab{4}\\spad{&1})\\spad{\\br} \\tab{5}\\spad{W}(10)\\spad{=0}.03160990266745513D0*Z(16)+(\\spad{-0}.02065879269286707D0*Z(15))\\spad{+0}\\spad{\\br} \\tab{4}&.2057504515015423D0*Z(14)+(\\spad{-0}.1006185171570586D0*Z(13))+(\\spad{-0}.136246\\spad{\\br} \\tab{4}&3839920727D0*Z(12))+(\\spad{-0}.3199955249404657D0*Z(11))\\spad{+0}.94427911585609\\spad{\\br} \\tab{4}&48D0*Z(10)+(\\spad{-0}.3363262957694705D0*Z(9))+(\\spad{-0}.1559813965382218D0*Z(8\\spad{\\br} \\tab{4}&))+(\\spad{-0}.06735603893301795D0*Z(7))\\spad{+0}.2276878326327734D0*Z(6)+(\\spad{-0}.032\\spad{\\br} \\tab{4}&98438523869648D0*Z(5))+(\\spad{-0}.083996867458326D0*Z(4))+(\\spad{-0}.02113506688\\spad{\\br} \\tab{4}&615768D0*Z(3))\\spad{+0}.06681263884671322D0*Z(2)\\spad{+0}.06069778964023718D0*Z(\\spad{\\br} \\tab{4}\\spad{&1})\\spad{\\br} \\tab{5}\\spad{W}(11)\\spad{=0}.04254083491825025D0*Z(16)\\spad{+0}.2311852964327382D0*Z(15)+(\\spad{-0}.0\\spad{\\br} \\tab{4}&7037620467004427D0*Z(14))+(\\spad{-0}.1846882042225383D0*Z(13))+(\\spad{-0}.315830\\spad{\\br} \\tab{4}&9975786731D0*Z(12))\\spad{+0}.952576555482747D0*Z(11)+(\\spad{-0}.328001910890377D\\spad{\\br} \\tab{4}&0*Z(10))+(\\spad{-0}.1589391311991561D0*Z(9))+(\\spad{-0}.07375317649315155D0*Z(8)\\spad{\\br} \\tab{4}&)\\spad{+0}.2229538339673001D0*Z(7)+(\\spad{-0}.03526886317505474D0*Z(6))+(\\spad{-0}.0493\\spad{\\br} \\tab{4}&1323319055762D0*Z(5))+(\\spad{-0}.04319641116207706D0*Z(4))\\spad{+0}.048260820054\\spad{\\br} \\tab{4}&65965D0*Z(3)\\spad{+0}.01328585741341559D0*Z(2)\\spad{+0}.04015147277405744D0*Z(1)\\spad{\\br} \\tab{5}\\spad{W}(12)\\spad{=0}.3198209177068516D0*Z(16)+(\\spad{-0}.03423495461011043D0*Z(15))+(-\\spad{\\br} \\tab{4}\\spad{&0}.1417185427288274D0*Z(14))+(\\spad{-0}.3852396953763045D0*Z(13))\\spad{+0}.959162\\spad{\\br} \\tab{4}&3347824002D0*Z(12)+(\\spad{-0}.315042193418466D0*Z(11))+(\\spad{-0}.14739952092889\\spad{\\br} \\tab{4}&45D0*Z(10))+(\\spad{-0}.08249492560213524D0*Z(9))\\spad{+0}.2171103102175198D0*Z(8\\spad{\\br} \\tab{4}&)+(\\spad{-0}.03769663291725935D0*Z(7))+(\\spad{-0}.05034242196614937D0*Z(6))+(\\spad{-0}.\\spad{\\br} \\tab{4}&01445079632086177D0*Z(5))\\spad{+0}.02947046460707379D0*Z(4)+(\\spad{-0}.002512226\\spad{\\br} \\tab{4}&501941856D0*Z(3))+(\\spad{-0}.001822737697581869D0*Z(2))\\spad{+0}.045563697677763\\spad{\\br} \\tab{4}&75D0*Z(1)\\spad{\\br} \\tab{5}\\spad{W}(13)\\spad{=0}.09089205517109111D0*Z(16)+(\\spad{-0}.09033531980693314D0*Z(15))+(\\spad{\\br} \\tab{4}&-0.3241503380268184D0*Z(14))\\spad{+0}.8600427128450191D0*Z(13)+(\\spad{-0}.305169\\spad{\\br} \\tab{4}&742604165D0*Z(12))+(\\spad{-0}.1280829963720053D0*Z(11))+(\\spad{-0}.0663087451453\\spad{\\br} \\tab{4}&5952D0*Z(10))\\spad{+0}.2012230497530726D0*Z(9)+(\\spad{-0}.04353074206076491D0*Z(\\spad{\\br} \\tab{4}\\spad{&8}))+(\\spad{-0}.05051817793156355D0*Z(7))+(\\spad{-0}.014224695935687D0*Z(6))\\spad{+0}.05\\spad{\\br} \\tab{4}&468897337339577D0*Z(5)+(\\spad{-0}.01965809746040371D0*Z(4))+(\\spad{-0}.016234277\\spad{\\br} \\tab{4}&35779699D0*Z(3))\\spad{+0}.005239165960779299D0*Z(2)\\spad{+0}.05141563713660119D0\\spad{\\br} \\tab{4}\\spad{&*Z}(1)\\spad{\\br} \\tab{5}\\spad{W}(14)=(\\spad{-0}.02986582812574917D0*Z(16))+(\\spad{-0}.2995429545781457D0*Z(15))\\spad{\\br} \\tab{4}\\spad{&+0}.8892996132269974D0*Z(14)+(\\spad{-0}.3523683853026259D0*Z(13))+(\\spad{-0}.1236\\spad{\\br} \\tab{4}&679206156403D0*Z(12))+(\\spad{-0}.05760560341383113D0*Z(11))\\spad{+0}.20910979278\\spad{\\br} \\tab{4}&87612D0*Z(10)+(\\spad{-0}.04901428822579872D0*Z(9))+(\\spad{-0}.05483186562035512D\\spad{\\br} \\tab{4}&0*Z(8))+(\\spad{-0}.01632133125029967D0*Z(7))\\spad{+0}.05375944956767728D0*Z(6)\\spad{+0}\\spad{\\br} \\tab{4}&.002033305231024948D0*Z(5)+(\\spad{-0}.03032392238968179D0*Z(4))+(\\spad{-0}.00660\\spad{\\br} \\tab{4}&7305534689702D0*Z(3))\\spad{+0}.02021603150122265D0*Z(2)\\spad{+0}.033711981971903\\spad{\\br} \\tab{4}&02D0*Z(1)\\spad{\\br} \\tab{5}\\spad{W}(15)=(\\spad{-0}.2419652703415429D0*Z(16))\\spad{+0}.9128222941872173D0*Z(15)+(\\spad{-0}\\spad{\\br} \\tab{4}&.3244016605667343D0*Z(14))+(\\spad{-0}.1688977368984641D0*Z(13))+(\\spad{-0}.05325\\spad{\\br} \\tab{4}&555586632358D0*Z(12))\\spad{+0}.2176561076571465D0*Z(11)+(\\spad{-0}.0415311995556\\spad{\\br} \\tab{4}&9051D0*Z(10))+(\\spad{-0}.06095390688679697D0*Z(9))+(\\spad{-0}.01981532388243379D\\spad{\\br} \\tab{4}&0*Z(8))\\spad{+0}.05258889186338282D0*Z(7)\\spad{+0}.00157466157362272D0*Z(6)+(\\spad{-0}.\\spad{\\br} \\tab{4}&0135713672105995D0*Z(5))+(\\spad{-0}.01764072463999744D0*Z(4))\\spad{+0}.010940122\\spad{\\br} \\tab{4}&10519586D0*Z(3)\\spad{+0}.008812321197398072D0*Z(2)\\spad{+0}.0227345011107737D0*Z\\spad{\\br} \\tab{4}&(1)\\spad{\\br} \\tab{5}\\spad{W}(16)\\spad{=1}.019463911841327D0*Z(16)+(\\spad{-0}.2803531651057233D0*Z(15))+(\\spad{-0}.\\spad{\\br} \\tab{4}&1165300508238904D0*Z(14))+(\\spad{-0}.1385343580686922D0*Z(13))\\spad{+0}.22647669\\spad{\\br} \\tab{4}&47290192D0*Z(12)+(\\spad{-0}.02434652144032987D0*Z(11))+(\\spad{-0}.04723268012114\\spad{\\br} \\tab{4}&625D0*Z(10))+(\\spad{-0}.03586220812223305D0*Z(9))\\spad{+0}.04932374658377151D0*Z\\spad{\\br} \\tab{4}&(8)\\spad{+0}.00372306473653087D0*Z(7)+(\\spad{-0}.01219194009813166D0*Z(6))+(\\spad{-0}.0\\spad{\\br} \\tab{4}&07005540882865317D0*Z(5))\\spad{+0}.002957434991769087D0*Z(4)\\spad{+0}.0021069739\\spad{\\br} \\tab{4}&00813502D0*Z(3)\\spad{+0}.001747395874954051D0*Z(2)\\spad{+0}.01707454969713436D0*\\spad{\\br} \\tab{4}\\spad{&Z}(1)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br}"))) NIL NIL -(-67 -3986) -((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) +(-74 -1337) +((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine f02fjf,{} for example: \\blankline \\tab{5}SUBROUTINE MONIT(ISTATE,{}NEXTIT,{}NEVALS,{}NEVECS,{}\\spad{K},{}\\spad{F},{}\\spad{D})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{D}(\\spad{K}),{}\\spad{F}(\\spad{K})\\spad{\\br} \\tab{5}INTEGER \\spad{K},{}NEXTIT,{}NEVALS,{}NVECS,{}ISTATE\\spad{\\br} \\tab{5}CALL F02FJZ(ISTATE,{}NEXTIT,{}NEVALS,{}NEVECS,{}\\spad{K},{}\\spad{F},{}\\spad{D})\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -3986) -((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) +(-75 -1337) +((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine f04qaf,{} for example: \\blankline \\tab{5}SUBROUTINE APROD(MODE,{}\\spad{M},{}\\spad{N},{}\\spad{X},{}\\spad{Y},{}RWORK,{}LRWORK,{}IWORK,{}LIWORK)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}(\\spad{N}),{}\\spad{Y}(\\spad{M}),{}RWORK(LRWORK)\\spad{\\br} \\tab{5}INTEGER \\spad{M},{}\\spad{N},{}LIWORK,{}IFAIL,{}LRWORK,{}IWORK(LIWORK),{}MODE\\spad{\\br} \\tab{5}DOUBLE PRECISION A(5,{}5)\\spad{\\br} \\tab{5}EXTERNAL F06PAF\\spad{\\br} \\tab{5}A(1,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}A(1,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(1,{}4)=-1.0D0\\spad{\\br} \\tab{5}A(1,{}5)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(2,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}A(2,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(2,{}4)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(2,{}5)=-1.0D0\\spad{\\br} \\tab{5}A(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(3,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(3,{}3)\\spad{=1}.0D0\\spad{\\br} \\tab{5}A(3,{}4)=-1.0D0\\spad{\\br} \\tab{5}A(3,{}5)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(4,{}1)=-1.0D0\\spad{\\br} \\tab{5}A(4,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(4,{}3)=-1.0D0\\spad{\\br} \\tab{5}A(4,{}4)\\spad{=4}.0D0\\spad{\\br} \\tab{5}A(4,{}5)=-1.0D0\\spad{\\br} \\tab{5}A(5,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(5,{}2)=-1.0D0\\spad{\\br} \\tab{5}A(5,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}A(5,{}4)=-1.0D0\\spad{\\br} \\tab{5}A(5,{}5)\\spad{=4}.0D0\\spad{\\br} \\tab{5}IF(MODE.EQ.1)THEN\\spad{\\br} \\tab{7}CALL F06PAF(\\spad{'N'},{}\\spad{M},{}\\spad{N},{}1.0D0,{}A,{}\\spad{M},{}\\spad{X},{}1,{}1.0D0,{}\\spad{Y},{}1)\\spad{\\br} \\tab{5}ELSEIF(MODE.EQ.2)THEN\\spad{\\br} \\tab{7}CALL F06PAF(\\spad{'T'},{}\\spad{M},{}\\spad{N},{}1.0D0,{}A,{}\\spad{M},{}\\spad{Y},{}1,{}1.0D0,{}\\spad{X},{}1)\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END"))) NIL NIL -(-69 -3986) -((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-76 -1337) +((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine d02ejf,{} for example: \\blankline \\tab{5}SUBROUTINE PEDERV(\\spad{X},{}\\spad{Y},{}\\spad{PW})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X},{}\\spad{Y}(*)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{PW}(3,{}3)\\spad{\\br} \\tab{5}\\spad{PW}(1,{}1)=-0.03999999999999999D0\\spad{\\br} \\tab{5}\\spad{PW}(1,{}2)\\spad{=10000}.0D0*Y(3)\\spad{\\br} \\tab{5}\\spad{PW}(1,{}3)\\spad{=10000}.0D0*Y(2)\\spad{\\br} \\tab{5}\\spad{PW}(2,{}1)\\spad{=0}.03999999999999999D0\\spad{\\br} \\tab{5}\\spad{PW}(2,{}2)=(\\spad{-10000}.0D0*Y(3))+(\\spad{-60000000}.0D0*Y(2))\\spad{\\br} \\tab{5}\\spad{PW}(2,{}3)=-10000.0D0*Y(2)\\spad{\\br} \\tab{5}\\spad{PW}(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{PW}(3,{}2)\\spad{=60000000}.0D0*Y(2)\\spad{\\br} \\tab{5}\\spad{PW}(3,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -3986) -((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) +(-77 -1337) +((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine d02kef. The code is a dummy ASP: \\blankline \\tab{5}SUBROUTINE REPORT(\\spad{X},{}\\spad{V},{}JINT)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{V}(3),{}\\spad{X}\\spad{\\br} \\tab{5}INTEGER JINT\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -3986) -((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) +(-78 -1337) +((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine f04mbf,{} for example: \\blankline \\tab{5}SUBROUTINE MSOLVE(IFLAG,{}\\spad{N},{}\\spad{X},{}\\spad{Y},{}RWORK,{}LRWORK,{}IWORK,{}LIWORK)\\spad{\\br} \\tab{5}DOUBLE PRECISION RWORK(LRWORK),{}\\spad{X}(\\spad{N}),{}\\spad{Y}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{I},{}\\spad{J},{}\\spad{N},{}LIWORK,{}IFLAG,{}LRWORK,{}IWORK(LIWORK)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{W1}(3),{}\\spad{W2}(3),{}\\spad{MS}(3,{}3)\\spad{\\br} \\tab{5}IFLAG=-1\\spad{\\br} \\tab{5}\\spad{MS}(1,{}1)\\spad{=2}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(1,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(2,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(2,{}2)\\spad{=2}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(2,{}3)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(3,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{MS}(3,{}3)\\spad{=2}.0D0\\spad{\\br} \\tab{5}CALL F04ASF(\\spad{MS},{}\\spad{N},{}\\spad{X},{}\\spad{N},{}\\spad{Y},{}\\spad{W1},{}\\spad{W2},{}IFLAG)\\spad{\\br} \\tab{5}IFLAG=-IFLAG\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END"))) NIL NIL -(-72 -3986) -((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-79 -1337) +((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines c05pbf,{} c05pcf,{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{FCN}(\\spad{N},{}\\spad{X},{}FVEC,{}FJAC,{}LDFJAC,{}IFLAG)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}(\\spad{N}),{}FVEC(\\spad{N}),{}FJAC(LDFJAC,{}\\spad{N})\\spad{\\br} \\tab{5}INTEGER LDFJAC,{}\\spad{N},{}IFLAG\\spad{\\br} \\tab{5}IF(IFLAG.EQ.1)THEN\\spad{\\br} \\tab{7}FVEC(1)=(\\spad{-1}.0D0*X(2))\\spad{+X}(1)\\spad{\\br} \\tab{7}FVEC(2)=(\\spad{-1}.0D0*X(3))\\spad{+2}.0D0*X(2)\\spad{\\br} \\tab{7}FVEC(3)\\spad{=3}.0D0*X(3)\\spad{\\br} \\tab{5}ELSEIF(IFLAG.EQ.2)THEN\\spad{\\br} \\tab{7}FJAC(1,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{7}FJAC(1,{}2)=-1.0D0\\spad{\\br} \\tab{7}FJAC(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{7}FJAC(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{7}FJAC(2,{}2)\\spad{=2}.0D0\\spad{\\br} \\tab{7}FJAC(2,{}3)=-1.0D0\\spad{\\br} \\tab{7}FJAC(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{7}FJAC(3,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{7}FJAC(3,{}3)\\spad{=3}.0D0\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-73 -3986) -((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-80 |nameOne| |nameTwo| |nameThree|) +((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 ASPs,{} needed for NAG routines d02raf and d02saf in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{FCN}(\\spad{X},{}EPS,{}\\spad{Y},{}\\spad{F},{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}\\spad{F}(\\spad{N}),{}\\spad{X},{}\\spad{Y}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}\\spad{F}(1)\\spad{=Y}(2)\\spad{\\br} \\tab{5}\\spad{F}(2)\\spad{=Y}(3)\\spad{\\br} \\tab{5}\\spad{F}(3)=(\\spad{-1}.0D0*Y(1)\\spad{*Y}(3))\\spad{+2}.0D0*EPS*Y(2)**2+(\\spad{-2}.0D0*EPS)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br} \\tab{5}SUBROUTINE JACOBF(\\spad{X},{}EPS,{}\\spad{Y},{}\\spad{F},{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}\\spad{F}(\\spad{N},{}\\spad{N}),{}\\spad{X},{}\\spad{Y}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}\\spad{F}(1,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(1,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{F}(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2,{}3)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{F}(3,{}1)=-1.0D0*Y(3)\\spad{\\br} \\tab{5}\\spad{F}(3,{}2)\\spad{=4}.0D0*EPS*Y(2)\\spad{\\br} \\tab{5}\\spad{F}(3,{}3)=-1.0D0*Y(1)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br} \\tab{5}SUBROUTINE JACEPS(\\spad{X},{}EPS,{}\\spad{Y},{}\\spad{F},{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}\\spad{F}(\\spad{N}),{}\\spad{X},{}\\spad{Y}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}\\spad{F}(1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(3)\\spad{=2}.0D0*Y(2)\\spad{**2}-2.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-74 |nameOne| |nameTwo| |nameThree|) -((|constructor| (NIL "\\spadtype{Asp41} produces Fortran for Type 41 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE FCN(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=Y(2) F(2)=Y(3) F(3)=(-1.0D0*Y(1)*Y(3))+2.0D0*EPS*Y(2)**2+(-2.0D0*EPS) RETURN END SUBROUTINE JACOBF(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N,N),X,Y(N) INTEGER N F(1,1)=0.0D0 F(1,2)=1.0D0 F(1,3)=0.0D0 F(2,1)=0.0D0 F(2,2)=0.0D0 F(2,3)=1.0D0 F(3,1)=-1.0D0*Y(3) F(3,2)=4.0D0*EPS*Y(2) F(3,3)=-1.0D0*Y(1) RETURN END SUBROUTINE JACEPS(X,EPS,Y,F,N) DOUBLE PRECISION EPS,F(N),X,Y(N) INTEGER N F(1)=0.0D0 F(2)=0.0D0 F(3)=2.0D0*Y(2)**2-2.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE EPS)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-81 |nameOne| |nameTwo| |nameThree|) +((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines d02raf and d02saf in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{G}(EPS,{}YA,{}\\spad{YB},{}\\spad{BC},{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}YA(\\spad{N}),{}\\spad{YB}(\\spad{N}),{}\\spad{BC}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}\\spad{BC}(1)=YA(1)\\spad{\\br} \\tab{5}\\spad{BC}(2)=YA(2)\\spad{\\br} \\tab{5}\\spad{BC}(3)\\spad{=YB}(2)\\spad{-1}.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br} \\tab{5}SUBROUTINE JACOBG(EPS,{}YA,{}\\spad{YB},{}AJ,{}\\spad{BJ},{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}YA(\\spad{N}),{}AJ(\\spad{N},{}\\spad{N}),{}\\spad{BJ}(\\spad{N},{}\\spad{N}),{}\\spad{YB}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}AJ(1,{}1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}AJ(1,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(2,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}AJ(2,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(3,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}AJ(3,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(1,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(1,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(2,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(2,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(3,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(3,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{BJ}(3,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END\\spad{\\br} \\tab{5}SUBROUTINE JACGEP(EPS,{}YA,{}\\spad{YB},{}BCEP,{}\\spad{N})\\spad{\\br} \\tab{5}DOUBLE PRECISION EPS,{}YA(\\spad{N}),{}\\spad{YB}(\\spad{N}),{}BCEP(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{N}\\spad{\\br} \\tab{5}BCEP(1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}BCEP(2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}BCEP(3)\\spad{=0}.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 |nameOne| |nameTwo| |nameThree|) -((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-82 -1337) +((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines e04dgf,{} e04ucf,{} for example: \\blankline \\tab{5}SUBROUTINE OBJFUN(MODE,{}\\spad{N},{}\\spad{X},{}OBJF,{}OBJGRD,{}NSTATE,{}IUSER,{}USER)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}(\\spad{N}),{}OBJF,{}OBJGRD(\\spad{N}),{}USER(*)\\spad{\\br} \\tab{5}INTEGER \\spad{N},{}IUSER(*),{}MODE,{}NSTATE\\spad{\\br} \\tab{5}OBJF=X(4)\\spad{*X}(9)+((\\spad{-1}.0D0*X(5))\\spad{+X}(3))\\spad{*X}(8)+((\\spad{-1}.0D0*X(3))\\spad{+X}(1))\\spad{*X}(7)\\spad{\\br} \\tab{4}\\spad{&+}(\\spad{-1}.0D0*X(2)\\spad{*X}(6))\\spad{\\br} \\tab{5}OBJGRD(1)\\spad{=X}(7)\\spad{\\br} \\tab{5}OBJGRD(2)=-1.0D0*X(6)\\spad{\\br} \\tab{5}OBJGRD(3)\\spad{=X}(8)+(\\spad{-1}.0D0*X(7))\\spad{\\br} \\tab{5}OBJGRD(4)\\spad{=X}(9)\\spad{\\br} \\tab{5}OBJGRD(5)=-1.0D0*X(8)\\spad{\\br} \\tab{5}OBJGRD(6)=-1.0D0*X(2)\\spad{\\br} \\tab{5}OBJGRD(7)=(\\spad{-1}.0D0*X(3))\\spad{+X}(1)\\spad{\\br} \\tab{5}OBJGRD(8)=(\\spad{-1}.0D0*X(5))\\spad{+X}(3)\\spad{\\br} \\tab{5}OBJGRD(9)\\spad{=X}(4)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -3986) -((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-83 -1337) +((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form: \\blankline \\tab{5}DOUBLE PRECISION FUNCTION FUNCTN(NDIM,{}\\spad{X})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}(NDIM)\\spad{\\br} \\tab{5}INTEGER NDIM\\spad{\\br} \\tab{5}FUNCTN=(4.0D0*X(1)\\spad{*X}(3)**2*DEXP(2.0D0*X(1)\\spad{*X}(3)))/(\\spad{X}(4)**2+(2.0D0*\\spad{\\br} \\tab{4}\\spad{&X}(2)\\spad{+2}.0D0)\\spad{*X}(4)\\spad{+X}(2)\\spad{**2+2}.0D0*X(2)\\spad{+1}.0D0)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -3986) -((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-84 -1337) +((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine e04fdf,{} for example: \\blankline \\tab{5}SUBROUTINE \\spad{LSFUN1}(\\spad{M},{}\\spad{N},{}\\spad{XC},{}FVECC)\\spad{\\br} \\tab{5}DOUBLE PRECISION FVECC(\\spad{M}),{}\\spad{XC}(\\spad{N})\\spad{\\br} \\tab{5}INTEGER \\spad{I},{}\\spad{M},{}\\spad{N}\\spad{\\br} \\tab{5}FVECC(1)=((\\spad{XC}(1)\\spad{-2}.4D0)\\spad{*XC}(3)+(15.0D0*XC(1)\\spad{-36}.0D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{\\br} \\tab{4}\\spad{&XC}(3)\\spad{+15}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(2)=((\\spad{XC}(1)\\spad{-2}.8D0)\\spad{*XC}(3)+(7.0D0*XC(1)\\spad{-19}.6D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{X}\\spad{\\br} \\tab{4}\\spad{&C}(3)\\spad{+7}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(3)=((\\spad{XC}(1)\\spad{-3}.2D0)\\spad{*XC}(3)+(4.333333333333333D0*XC(1)\\spad{-13}.866666\\spad{\\br} \\tab{4}\\spad{&66666667D0})\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+4}.333333333333333D0*XC(2))\\spad{\\br} \\tab{5}FVECC(4)=((\\spad{XC}(1)\\spad{-3}.5D0)\\spad{*XC}(3)+(3.0D0*XC(1)\\spad{-10}.5D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{X}\\spad{\\br} \\tab{4}\\spad{&C}(3)\\spad{+3}.0D0*XC(2))\\spad{\\br} \\tab{5}FVECC(5)=((\\spad{XC}(1)\\spad{-3}.9D0)\\spad{*XC}(3)+(2.2D0*XC(1)\\spad{-8}.579999999999998D0)\\spad{*XC}\\spad{\\br} \\tab{4}&(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+2}.2D0*XC(2))\\spad{\\br} \\tab{5}FVECC(6)=((\\spad{XC}(1)\\spad{-4}.199999999999999D0)\\spad{*XC}(3)+(1.666666666666667D0*X\\spad{\\br} \\tab{4}\\spad{&C}(1)\\spad{-7}.0D0)\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+1}.666666666666667D0*XC(2))\\spad{\\br} \\tab{5}FVECC(7)=((\\spad{XC}(1)\\spad{-4}.5D0)\\spad{*XC}(3)+(1.285714285714286D0*XC(1)\\spad{-5}.7857142\\spad{\\br} \\tab{4}\\spad{&85714286D0})\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+1}.285714285714286D0*XC(2))\\spad{\\br} \\tab{5}FVECC(8)=((\\spad{XC}(1)\\spad{-4}.899999999999999D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-4}.8999999999999\\spad{\\br} \\tab{4}\\spad{&99D0})\\spad{*XC}(2)\\spad{+1}.0D0)/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(9)=((\\spad{XC}(1)\\spad{-4}.699999999999999D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-4}.6999999999999\\spad{\\br} \\tab{4}\\spad{&99D0})\\spad{*XC}(2)\\spad{+1}.285714285714286D0)/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(10)=((\\spad{XC}(1)\\spad{-6}.8D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-6}.8D0)\\spad{*XC}(2)\\spad{+1}.6666666666666\\spad{\\br} \\tab{4}\\spad{&67D0})/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(11)=((\\spad{XC}(1)\\spad{-8}.299999999999999D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-8}.299999999999\\spad{\\br} \\tab{4}\\spad{&999D0})\\spad{*XC}(2)\\spad{+2}.2D0)/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(12)=((\\spad{XC}(1)\\spad{-10}.6D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-10}.6D0)\\spad{*XC}(2)\\spad{+3}.0D0)/(\\spad{XC}(3)\\spad{\\br} \\tab{4}&+XC(2))\\spad{\\br} \\tab{5}FVECC(13)=((\\spad{XC}(1)\\spad{-1}.34D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-1}.34D0)\\spad{*XC}(2)\\spad{+4}.33333333333\\spad{\\br} \\tab{4}\\spad{&3333D0})/(\\spad{XC}(3)\\spad{+XC}(2))\\spad{\\br} \\tab{5}FVECC(14)=((\\spad{XC}(1)\\spad{-2}.1D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-2}.1D0)\\spad{*XC}(2)\\spad{+7}.0D0)/(\\spad{XC}(3)\\spad{+X}\\spad{\\br} \\tab{4}\\spad{&C}(2))\\spad{\\br} \\tab{5}FVECC(15)=((\\spad{XC}(1)\\spad{-4}.39D0)\\spad{*XC}(3)+(\\spad{XC}(1)\\spad{-4}.39D0)\\spad{*XC}(2)\\spad{+15}.0D0)/(\\spad{XC}(3\\spad{\\br} \\tab{4}&)\\spad{+XC}(2))\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -3986) -((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-85 -1337) +((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines e04dgf and e04ucf,{} for example: \\blankline \\tab{5}SUBROUTINE CONFUN(MODE,{}NCNLN,{}\\spad{N},{}NROWJ,{}NEEDC,{}\\spad{X},{}\\spad{C},{}CJAC,{}NSTATE,{}IUSER\\spad{\\br} \\tab{4}&,{}USER)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{C}(NCNLN),{}\\spad{X}(\\spad{N}),{}CJAC(NROWJ,{}\\spad{N}),{}USER(*)\\spad{\\br} \\tab{5}INTEGER \\spad{N},{}IUSER(*),{}NEEDC(NCNLN),{}NROWJ,{}MODE,{}NCNLN,{}NSTATE\\spad{\\br} \\tab{5}IF(NEEDC(1).\\spad{GT}.0)THEN\\spad{\\br} \\tab{7}\\spad{C}(1)\\spad{=X}(6)**2+X(1)\\spad{**2}\\spad{\\br} \\tab{7}CJAC(1,{}1)\\spad{=2}.0D0*X(1)\\spad{\\br} \\tab{7}CJAC(1,{}2)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(1,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(1,{}4)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(1,{}5)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(1,{}6)\\spad{=2}.0D0*X(6)\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}IF(NEEDC(2).\\spad{GT}.0)THEN\\spad{\\br} \\tab{7}\\spad{C}(2)\\spad{=X}(2)**2+(\\spad{-2}.0D0*X(1)\\spad{*X}(2))\\spad{+X}(1)\\spad{**2}\\spad{\\br} \\tab{7}CJAC(2,{}1)=(\\spad{-2}.0D0*X(2))\\spad{+2}.0D0*X(1)\\spad{\\br} \\tab{7}CJAC(2,{}2)\\spad{=2}.0D0*X(2)+(\\spad{-2}.0D0*X(1))\\spad{\\br} \\tab{7}CJAC(2,{}3)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(2,{}4)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(2,{}5)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(2,{}6)\\spad{=0}.0D0\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}IF(NEEDC(3).\\spad{GT}.0)THEN\\spad{\\br} \\tab{7}\\spad{C}(3)\\spad{=X}(3)**2+(\\spad{-2}.0D0*X(1)\\spad{*X}(3))\\spad{+X}(2)**2+X(1)\\spad{**2}\\spad{\\br} \\tab{7}CJAC(3,{}1)=(\\spad{-2}.0D0*X(3))\\spad{+2}.0D0*X(1)\\spad{\\br} \\tab{7}CJAC(3,{}2)\\spad{=2}.0D0*X(2)\\spad{\\br} \\tab{7}CJAC(3,{}3)\\spad{=2}.0D0*X(3)+(\\spad{-2}.0D0*X(1))\\spad{\\br} \\tab{7}CJAC(3,{}4)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(3,{}5)\\spad{=0}.0D0\\spad{\\br} \\tab{7}CJAC(3,{}6)\\spad{=0}.0D0\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -3986) -((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-86 -1337) +((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines c05nbf,{} c05ncf. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like: \\blankline \\tab{5}SUBROUTINE \\spad{FCN}(\\spad{N},{}\\spad{X},{}FVEC,{}IFLAG) \\tab{5}DOUBLE PRECISION \\spad{X}(\\spad{N}),{}FVEC(\\spad{N}) \\tab{5}INTEGER \\spad{N},{}IFLAG \\tab{5}FVEC(1)=(\\spad{-2}.0D0*X(2))+(\\spad{-2}.0D0*X(1)\\spad{**2})\\spad{+3}.0D0*X(1)\\spad{+1}.0D0 \\tab{5}FVEC(2)=(\\spad{-2}.0D0*X(3))+(\\spad{-2}.0D0*X(2)\\spad{**2})\\spad{+3}.0D0*X(2)+(\\spad{-1}.0D0*X(1))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(3)=(\\spad{-2}.0D0*X(4))+(\\spad{-2}.0D0*X(3)\\spad{**2})\\spad{+3}.0D0*X(3)+(\\spad{-1}.0D0*X(2))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(4)=(\\spad{-2}.0D0*X(5))+(\\spad{-2}.0D0*X(4)\\spad{**2})\\spad{+3}.0D0*X(4)+(\\spad{-1}.0D0*X(3))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(5)=(\\spad{-2}.0D0*X(6))+(\\spad{-2}.0D0*X(5)\\spad{**2})\\spad{+3}.0D0*X(5)+(\\spad{-1}.0D0*X(4))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(6)=(\\spad{-2}.0D0*X(7))+(\\spad{-2}.0D0*X(6)\\spad{**2})\\spad{+3}.0D0*X(6)+(\\spad{-1}.0D0*X(5))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(7)=(\\spad{-2}.0D0*X(8))+(\\spad{-2}.0D0*X(7)\\spad{**2})\\spad{+3}.0D0*X(7)+(\\spad{-1}.0D0*X(6))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(8)=(\\spad{-2}.0D0*X(9))+(\\spad{-2}.0D0*X(8)\\spad{**2})\\spad{+3}.0D0*X(8)+(\\spad{-1}.0D0*X(7))\\spad{+1}. \\tab{4}\\spad{&0D0} \\tab{5}FVEC(9)=(\\spad{-2}.0D0*X(9)\\spad{**2})\\spad{+3}.0D0*X(9)+(\\spad{-1}.0D0*X(8))\\spad{+1}.0D0 \\tab{5}RETURN \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -3986) -((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-87 -1337) +((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine d03eef,{} for example: \\blankline \\tab{5}SUBROUTINE PDEF(\\spad{X},{}\\spad{Y},{}ALPHA,{}BETA,{}GAMMA,{}DELTA,{}EPSOLN,{}PHI,{}PSI)\\spad{\\br} \\tab{5}DOUBLE PRECISION ALPHA,{}EPSOLN,{}PHI,{}\\spad{X},{}\\spad{Y},{}BETA,{}DELTA,{}GAMMA,{}PSI\\spad{\\br} \\tab{5}ALPHA=DSIN(\\spad{X})\\spad{\\br} \\tab{5}BETA=Y\\spad{\\br} \\tab{5}GAMMA=X*Y\\spad{\\br} \\tab{5}DELTA=DCOS(\\spad{X})*DSIN(\\spad{Y})\\spad{\\br} \\tab{5}EPSOLN=Y+X\\spad{\\br} \\tab{5}PHI=X\\spad{\\br} \\tab{5}PSI=Y\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -3986) -((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-88 -1337) +((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine d03eef,{} for example: \\blankline \\tab{5} SUBROUTINE BNDY(\\spad{X},{}\\spad{Y},{}A,{}\\spad{B},{}\\spad{C},{}IBND)\\spad{\\br} \\tab{5} DOUBLE PRECISION A,{}\\spad{B},{}\\spad{C},{}\\spad{X},{}\\spad{Y}\\spad{\\br} \\tab{5} INTEGER IBND\\spad{\\br} \\tab{5} IF(IBND.EQ.0)THEN\\spad{\\br} \\tab{7} \\spad{A=0}.0D0\\spad{\\br} \\tab{7} \\spad{B=1}.0D0\\spad{\\br} \\tab{7} \\spad{C=}-1.0D0*DSIN(\\spad{X})\\spad{\\br} \\tab{5} ELSEIF(IBND.EQ.1)THEN\\spad{\\br} \\tab{7} \\spad{A=1}.0D0\\spad{\\br} \\tab{7} \\spad{B=0}.0D0\\spad{\\br} \\tab{7} C=DSIN(\\spad{X})*DSIN(\\spad{Y})\\spad{\\br} \\tab{5} ELSEIF(IBND.EQ.2)THEN\\spad{\\br} \\tab{7} \\spad{A=1}.0D0\\spad{\\br} \\tab{7} \\spad{B=0}.0D0\\spad{\\br} \\tab{7} C=DSIN(\\spad{X})*DSIN(\\spad{Y})\\spad{\\br} \\tab{5} ELSEIF(IBND.EQ.3)THEN\\spad{\\br} \\tab{7} \\spad{A=0}.0D0\\spad{\\br} \\tab{7} \\spad{B=1}.0D0\\spad{\\br} \\tab{7} \\spad{C=}-1.0D0*DSIN(\\spad{Y})\\spad{\\br} \\tab{5} ENDIF\\spad{\\br} \\tab{5} END")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -3986) -((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-89 -1337) +((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine d02gbf,{} for example: \\blankline \\tab{5}SUBROUTINE FCNF(\\spad{X},{}\\spad{F})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X}\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{F}(2,{}2)\\spad{\\br} \\tab{5}\\spad{F}(1,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(1,{}2)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2,{}1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{F}(2,{}2)=-10.0D0\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -3986) -((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-90 -1337) +((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine d02gbf,{} for example: \\blankline \\tab{5}SUBROUTINE FCNG(\\spad{X},{}\\spad{G})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{G}(*),{}\\spad{X}\\spad{\\br} \\tab{5}\\spad{G}(1)\\spad{=0}.0D0\\spad{\\br} \\tab{5}\\spad{G}(2)\\spad{=0}.0D0\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -3986) -((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-91 -1337) +((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines d02bbf,{} d02gaf. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like: \\blankline \\tab{5}SUBROUTINE \\spad{FCN}(\\spad{X},{}\\spad{Z},{}\\spad{F})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{F}(*),{}\\spad{X},{}\\spad{Z}(*)\\spad{\\br} \\tab{5}\\spad{F}(1)=DTAN(\\spad{Z}(3))\\spad{\\br} \\tab{5}\\spad{F}(2)=((\\spad{-0}.03199999999999999D0*DCOS(\\spad{Z}(3))*DTAN(\\spad{Z}(3)))+(\\spad{-0}.02D0*Z(2)\\spad{\\br} \\tab{4}\\spad{&**2}))/(\\spad{Z}(2)*DCOS(\\spad{Z}(3)))\\spad{\\br} \\tab{5}\\spad{F}(3)=-0.03199999999999999D0/(\\spad{X*Z}(2)\\spad{**2})\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -3986) -((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) +(-92 -1337) +((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine d02kef,{} for example: \\blankline \\tab{5}SUBROUTINE BDYVAL(\\spad{XL},{}\\spad{XR},{}ELAM,{}\\spad{YL},{}\\spad{YR})\\spad{\\br} \\tab{5}DOUBLE PRECISION ELAM,{}\\spad{XL},{}\\spad{YL}(3),{}\\spad{XR},{}\\spad{YR}(3)\\spad{\\br} \\tab{5}\\spad{YL}(1)\\spad{=XL}\\spad{\\br} \\tab{5}\\spad{YL}(2)\\spad{=2}.0D0\\spad{\\br} \\tab{5}\\spad{YR}(1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}\\spad{YR}(2)=-1.0D0*DSQRT(\\spad{XR+}(\\spad{-1}.0D0*ELAM))\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -3986) -((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) +(-93 -1337) +((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine d02bbf. This ASP prints intermediate values of the computed solution of an ODE and might look like: \\blankline \\tab{5}SUBROUTINE OUTPUT(XSOL,{}\\spad{Y},{}COUNT,{}\\spad{M},{}\\spad{N},{}RESULT,{}FORWRD)\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{Y}(\\spad{N}),{}RESULT(\\spad{M},{}\\spad{N}),{}XSOL\\spad{\\br} \\tab{5}INTEGER \\spad{M},{}\\spad{N},{}COUNT\\spad{\\br} \\tab{5}LOGICAL FORWRD\\spad{\\br} \\tab{5}DOUBLE PRECISION X02ALF,{}POINTS(8)\\spad{\\br} \\tab{5}EXTERNAL X02ALF\\spad{\\br} \\tab{5}INTEGER \\spad{I}\\spad{\\br} \\tab{5}POINTS(1)\\spad{=1}.0D0\\spad{\\br} \\tab{5}POINTS(2)\\spad{=2}.0D0\\spad{\\br} \\tab{5}POINTS(3)\\spad{=3}.0D0\\spad{\\br} \\tab{5}POINTS(4)\\spad{=4}.0D0\\spad{\\br} \\tab{5}POINTS(5)\\spad{=5}.0D0\\spad{\\br} \\tab{5}POINTS(6)\\spad{=6}.0D0\\spad{\\br} \\tab{5}POINTS(7)\\spad{=7}.0D0\\spad{\\br} \\tab{5}POINTS(8)\\spad{=8}.0D0\\spad{\\br} \\tab{5}\\spad{COUNT=COUNT+1}\\spad{\\br} \\tab{5}DO 25001 \\spad{I=1},{}\\spad{N}\\spad{\\br} \\tab{7} RESULT(COUNT,{}\\spad{I})\\spad{=Y}(\\spad{I})\\spad{\\br} 25001 CONTINUE\\spad{\\br} \\tab{5}IF(COUNT.EQ.\\spad{M})THEN\\spad{\\br} \\tab{7}IF(FORWRD)THEN\\spad{\\br} \\tab{9}XSOL=X02ALF()\\spad{\\br} \\tab{7}ELSE\\spad{\\br} \\tab{9}XSOL=-X02ALF()\\spad{\\br} \\tab{7}ENDIF\\spad{\\br} \\tab{5}ELSE\\spad{\\br} \\tab{7} XSOL=POINTS(COUNT)\\spad{\\br} \\tab{5}ENDIF\\spad{\\br} \\tab{5}END"))) NIL NIL -(-87 -3986) -((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) +(-94 -1337) +((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines d02bhf,{} d02cjf,{} d02ejf. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example: \\blankline \\tab{5}DOUBLE PRECISION FUNCTION \\spad{G}(\\spad{X},{}\\spad{Y})\\spad{\\br} \\tab{5}DOUBLE PRECISION \\spad{X},{}\\spad{Y}(*)\\spad{\\br} \\tab{5}G=X+Y(1)\\spad{\\br} \\tab{5}RETURN\\spad{\\br} \\tab{5}END \\blankline If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-88 R L) +(-95 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op,{} m)} returns \\spad{[w,{} eq,{} lw,{} lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,{}...,{}A_n]} such that if \\spad{y = [y_1,{}...,{}y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',{}y_j'',{}...,{}y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}\\spad{'s}.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op,{} m)} returns \\spad{[M,{}w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) NIL -((|HasCategory| |#1| (QUOTE (-331)))) -(-89 S) -((|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-90 S) +((|HasCategory| |#1| (QUOTE (-359)))) +(-96 S) +((|constructor| (NIL "A stack represented as a flexible array.")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} member?(3,{}a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} count(4,{}a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} count(\\spad{x+}->(\\spad{x>2}),{}a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} any?(\\spad{x+}->(\\spad{x=4}),{}a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} every?(\\spad{x+}->(\\spad{x=4}),{}a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} b:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} map!(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} map(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} eq?(a,{}\\spad{b})")) (|copy| (($ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()\\$ArrayStack(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()\\$(ArrayStack INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,{}2,{}3,{}4,{}5])\\$ArrayStack(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} size?(a,{}5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} more?(a,{}9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} less?(a,{}9)")) (|depth| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} depth a")) (|top| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} top a")) (|inspect| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} insert!(8,{}a) \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} push!(9,{}a) \\spad{X} a")) (|extract!| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} extract! a \\spad{X} a")) (|pop!| ((|#1| $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5] \\spad{X} pop! a \\spad{X} a")) (|arrayStack| (($ (|List| |#1|)) "\\indented{1}{arrayStack([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) creates an array stack with first (top)} \\indented{1}{element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.} \\blankline \\spad{E} c:ArrayStack INT:= arrayStack [1,{}2,{}3,{}4,{}5]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-97 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL NIL -(-91) +(-98) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL NIL -(-92) -((|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4167 . T)) +(-99) +((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved.")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) +((-4505 . T)) NIL -(-93) -((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} imples \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4167 . T) ((-4169 "*") . T) (-4168 . T) (-4164 . T) (-4162 . T) (-4161 . T) (-4160 . T) (-4165 . T) (-4159 . T) (-4158 . T) (-4157 . T) (-4156 . T) (-4155 . T) (-4163 . T) (-4166 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4154 . T)) +(-100) +((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\".")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) +((-4505 . T) ((-4507 "*") . T) (-4506 . T) (-4502 . T) (-4500 . T) (-4499 . T) (-4498 . T) (-4503 . T) (-4497 . T) (-4496 . T) (-4495 . T) (-4494 . T) (-4493 . T) (-4501 . T) (-4504 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4492 . T) (-2550 . T)) NIL -(-94 R) +(-101 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4164 . T)) +((-4502 . T)) +NIL +(-102) +((|constructor| (NIL "This package provides a functions to support a web server for the new Axiom Browser functions."))) +NIL NIL -(-95 R UP) +(-103 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) NIL NIL -(-96 S) +(-104 S) ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) NIL NIL -(-97) +(-105) ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) NIL NIL -(-98 S) -((|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-99 R UP M |Row| |Col|) +(-106 S) +((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\indented{1}{mapDown!(\\spad{t},{}\\spad{p},{}\\spad{f}) returns \\spad{t} after traversing \\spad{t} in \"preorder\"} \\indented{1}{(node then left then right) fashion replacing the successive} \\indented{1}{interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and} \\indented{1}{right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}.} \\indented{1}{Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left} \\indented{1}{and right subtrees of \\spad{t},{} is evaluated producing two values} \\indented{1}{\\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)}} \\indented{1}{are evaluated.} \\blankline \\spad{X} T1:=BalancedBinaryTree Integer \\spad{X} t2:=balancedBinaryTree(4,{} 0)\\$\\spad{T1} \\spad{X} setleaves!(\\spad{t2},{}[1,{}2,{}3,{}4]::List(Integer)) \\spad{X} \\spad{adder3}(i:Integer,{}j:Integer,{}k:Integer):List Integer \\spad{==} [i+j,{}\\spad{j+k}] \\spad{X} mapDown!(\\spad{t2},{}4::INT,{}\\spad{adder3}) \\spad{X} \\spad{t2}") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\indented{1}{mapDown!(\\spad{t},{}\\spad{p},{}\\spad{f}) returns \\spad{t} after traversing \\spad{t} in \"preorder\"} \\indented{1}{(node then left then right) fashion replacing the successive} \\indented{1}{interior nodes as follows. The root value \\spad{x} is} \\indented{1}{replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and} \\indented{1}{mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees} \\indented{1}{\\spad{l} and \\spad{r} of \\spad{t}.} \\blankline \\spad{X} T1:=BalancedBinaryTree Integer \\spad{X} t2:=balancedBinaryTree(4,{} 0)\\$\\spad{T1} \\spad{X} setleaves!(\\spad{t2},{}[1,{}2,{}3,{}4]::List(Integer)) \\spad{X} adder(i:Integer,{}j:Integer):Integer \\spad{==} i+j \\spad{X} mapDown!(\\spad{t2},{}4::INT,{}adder) \\spad{X} \\spad{t2}")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\indented{1}{mapUp!(\\spad{t},{}\\spad{t1},{}\\spad{f}) traverses balanced binary tree \\spad{t} in an \"endorder\"} \\indented{1}{(left then right then node) fashion returning \\spad{t} with the value} \\indented{1}{at each successive interior node of \\spad{t} replaced by} \\indented{1}{\\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate} \\indented{1}{left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the} \\indented{1}{corresponding nodes of a balanced binary tree \\spad{t1},{} of identical} \\indented{1}{shape at \\spad{t}.} \\blankline \\spad{X} T1:=BalancedBinaryTree Integer \\spad{X} t2:=balancedBinaryTree(4,{} 0)\\$\\spad{T1} \\spad{X} setleaves!(\\spad{t2},{}[1,{}2,{}3,{}4]::List(Integer)) \\spad{X} \\spad{adder4}(i:INT,{}j:INT,{}k:INT,{}l:INT):INT \\spad{==} i+j+k+l \\spad{X} mapUp!(\\spad{t2},{}\\spad{t2},{}\\spad{adder4}) \\spad{X} \\spad{t2}") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\indented{1}{mapUp!(\\spad{t},{}\\spad{f}) traverses balanced binary tree \\spad{t} in an \"endorder\"} \\indented{1}{(left then right then node) fashion returning \\spad{t} with the value} \\indented{1}{at each successive interior node of \\spad{t} replaced by} \\indented{1}{\\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate} \\indented{1}{left and right nodes.} \\blankline \\spad{X} T1:=BalancedBinaryTree Integer \\spad{X} t2:=balancedBinaryTree(4,{} 0)\\$\\spad{T1} \\spad{X} setleaves!(\\spad{t2},{}[1,{}2,{}3,{}4]::List(Integer)) \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} mapUp!(\\spad{t2},{}adder) \\spad{X} \\spad{t2}")) (|setleaves!| (($ $ (|List| |#1|)) "\\indented{1}{setleaves!(\\spad{t},{} \\spad{ls}) sets the leaves of \\spad{t} in left-to-right order} \\indented{1}{to the elements of \\spad{ls}.} \\blankline \\spad{X} t1:=balancedBinaryTree(4,{} 0) \\spad{X} setleaves!(\\spad{t1},{}[1,{}2,{}3,{}4])")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\indented{1}{balancedBinaryTree(\\spad{n},{} \\spad{s}) creates a balanced binary tree with} \\indented{1}{\\spad{n} nodes each with value \\spad{s}.} \\blankline \\spad{X} balancedBinaryTree(4,{} 0)"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-107 R) +((|constructor| (NIL "Provide linear,{} quadratic,{} and cubic spline bezier curves")) (|cubicBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\indented{1}{A cubic Bezier curve is a simple interpolation between the} \\indented{1}{starting point,{} a left-middle point,{},{} a right-middle point,{}} \\indented{1}{and the ending point based on a parameter \\spad{t}.} \\indented{1}{Given a start point a=[\\spad{x1},{}\\spad{y1}],{} the left-middle point \\spad{b=}[\\spad{x2},{}\\spad{y2}],{}} \\indented{1}{the right-middle point \\spad{c=}[\\spad{x3},{}\\spad{y3}] and an endpoint \\spad{d=}[\\spad{x4},{}\\spad{y4}]} \\indented{1}{\\spad{f}(\\spad{t}) \\spad{==} [(1-\\spad{t})\\spad{^3} \\spad{x1} + 3t(1-\\spad{t})\\spad{^2} \\spad{x2} + 3t^2 (1-\\spad{t}) \\spad{x3} + \\spad{t^3} \\spad{x4},{}} \\indented{10}{(1-\\spad{t})\\spad{^3} \\spad{y1} + 3t(1-\\spad{t})\\spad{^2} \\spad{y2} + 3t^2 (1-\\spad{t}) \\spad{y3} + \\spad{t^3} \\spad{y4}]} \\blankline \\spad{X} n:=cubicBezier([2.0,{}2.0],{}[2.0,{}4.0],{}[6.0,{}4.0],{}[6.0,{}2.0]) \\spad{X} [\\spad{n}(\\spad{t/10}.0) for \\spad{t} in 0..10 by 1]")) (|quadraticBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\indented{1}{A quadratic Bezier curve is a simple interpolation between the} \\indented{1}{starting point,{} a middle point,{} and the ending point based on} \\indented{1}{a parameter \\spad{t}.} \\indented{1}{Given a start point a=[\\spad{x1},{}\\spad{y1}],{} a middle point \\spad{b=}[\\spad{x2},{}\\spad{y2}],{}} \\indented{1}{and an endpoint \\spad{c=}[\\spad{x3},{}\\spad{y3}]} \\indented{1}{\\spad{f}(\\spad{t}) \\spad{==} [(1-\\spad{t})\\spad{^2} \\spad{x1} + 2t(1-\\spad{t}) \\spad{x2} + \\spad{t^2} \\spad{x3},{}} \\indented{10}{(1-\\spad{t})\\spad{^2} \\spad{y1} + 2t(1-\\spad{t}) \\spad{y2} + \\spad{t^2} \\spad{y3}]} \\blankline \\spad{X} n:=quadraticBezier([2.0,{}2.0],{}[4.0,{}4.0],{}[6.0,{}2.0]) \\spad{X} [\\spad{n}(\\spad{t/10}.0) for \\spad{t} in 0..10 by 1]")) (|linearBezier| (((|Mapping| (|List| |#1|) |#1|) (|List| |#1|) (|List| |#1|)) "\\indented{1}{A linear Bezier curve is a simple interpolation between the} \\indented{1}{starting point and the ending point based on a parameter \\spad{t}.} \\indented{1}{Given a start point a=[\\spad{x1},{}\\spad{y1}] and an endpoint \\spad{b=}[\\spad{x2},{}\\spad{y2}]} \\indented{1}{\\spad{f}(\\spad{t}) \\spad{==} [(1-\\spad{t})\\spad{*x1} + \\spad{t*x2},{} (1-\\spad{t})\\spad{*y1} + \\spad{t*y2}]} \\blankline \\spad{X} n:=linearBezier([2.0,{}2.0],{}[4.0,{}4.0]) \\spad{X} [\\spad{n}(\\spad{t/10}.0) for \\spad{t} in 0..10 by 1]"))) +NIL +NIL +(-108 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4169 "*")))) -(-100) -((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4167 . T)) +((|HasAttribute| |#1| (QUOTE (-4507 "*")))) +(-109) +((|constructor| (NIL "A Domain which implements a table containing details of points at which particular functions have evaluation problems.")) (|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) +((-4505 . T)) NIL -(-101 A S) -((|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) +(-110 A S) +((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) NIL NIL -(-102 S) -((|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4168 . T) (-2951 . T)) +(-111 S) +((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) +((-4506 . T) (-2537 . T)) NIL -(-103) -((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-501) (QUOTE (-830))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-501) (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-134))) (|HasCategory| (-501) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-501) (QUOTE (-933))) (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-1046))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-501) (QUOTE (-206))) (|HasCategory| (-501) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-501) (LIST (QUOTE -476) (QUOTE (-1070)) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -278) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -256) (QUOTE (-501)) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-276))) (|HasCategory| (-501) (QUOTE (-500))) (|HasCategory| (-501) (QUOTE (-777))) (-1405 (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (QUOTE (-777)))) (|HasCategory| (-501) (LIST (QUOTE -577) (QUOTE (-501)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (|HasCategory| (-501) (QUOTE (-132))))) -(-104) +(-112) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\indented{1}{binary(\\spad{r}) converts a rational number to a binary expansion.} \\blankline \\spad{X} binary(22/7)")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-560) (QUOTE (-896))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-560) (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-148))) (|HasCategory| (-560) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-560) (QUOTE (-1013))) (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1128))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-221))) (|HasCategory| (-560) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-560) (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -276) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-296))) (|HasCategory| (-560) (QUOTE (-542))) (|HasCategory| (-560) (QUOTE (-834))) (-2318 (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (QUOTE (-834)))) (|HasCategory| (-560) (LIST (QUOTE -622) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (|HasCategory| (-560) (QUOTE (-146))))) +(-113) ((|constructor| (NIL "This domain provides an implementation of binary files. Data is accessed one byte at a time as a small integer.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "\\spad{position!(f,{} i)} sets the current byte-position to \\spad{i}.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{f}.")) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-105) +(-114) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| (-107) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-107) (QUOTE (-777))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| (-107) (QUOTE (-1001))) (-12 (|HasCategory| (-107) (LIST (QUOTE -278) (QUOTE (-107)))) (|HasCategory| (-107) (QUOTE (-1001))))) -(-106 R S) -((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4162 . T) (-4161 . T)) +((-4506 . T) (-4505 . T)) +((|HasCategory| (-121) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-121) (QUOTE (-834))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| (-121) (QUOTE (-1082))) (-12 (|HasCategory| (-121) (LIST (QUOTE -298) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1082))))) +(-115) +((|constructor| (NIL "This package provides an interface to the Blas library (level 1)")) (|dcopy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\indented{1}{dcopy(\\spad{n},{}\\spad{x},{}incx,{}\\spad{y},{}incy) copies \\spad{y} from \\spad{x}} \\indented{1}{for each of the chosen elements of the vectors \\spad{x} and \\spad{y}} \\indented{1}{Note that the vector \\spad{y} is modified with the results.} \\blankline \\spad{X} x:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0,{}4.0,{}5.0,{}6.0]] \\spad{X} y:PRIMARR(DFLOAT)\\spad{:=}[[0.0,{}0.0,{}0.0,{}0.0,{}0.0,{}0.0]] \\spad{X} dcopy(6,{}\\spad{x},{}1,{}\\spad{y},{}1) \\spad{X} \\spad{y} \\spad{X} m:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0]] \\spad{X} n:PRIMARR(DFLOAT)\\spad{:=}[[0.0,{}0.0,{}0.0,{}0.0,{}0.0,{}0.0]] \\spad{X} dcopy(3,{}\\spad{m},{}1,{}\\spad{n},{}2) \\spad{X} \\spad{n}")) (|daxpy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\indented{1}{daxpy(\\spad{n},{}da,{}\\spad{x},{}incx,{}\\spad{y},{}incy) computes a \\spad{y} = a*x + \\spad{y}} \\indented{1}{for each of the chosen elements of the vectors \\spad{x} and \\spad{y}} \\indented{1}{and a constant multiplier a} \\indented{1}{Note that the vector \\spad{y} is modified with the results.} \\blankline \\spad{X} x:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0,{}4.0,{}5.0,{}6.0]] \\spad{X} y:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0,{}4.0,{}5.0,{}6.0]] \\spad{X} daxpy(6,{}2.0,{}\\spad{x},{}1,{}\\spad{y},{}1) \\spad{X} \\spad{y} \\spad{X} m:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0]] \\spad{X} n:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0,{}4.0,{}5.0,{}6.0]] \\spad{X} daxpy(3,{}\\spad{-2}.0,{}\\spad{m},{}1,{}\\spad{n},{}2) \\spad{X} \\spad{n}")) (|dasum| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\indented{1}{dasum(\\spad{n},{}array,{}incx) computes the sum of \\spad{n} elements in array} \\indented{1}{using a stride of incx} \\blankline \\spad{X} dx:PRIMARR(DFLOAT)\\spad{:=}[[1.0,{}2.0,{}3.0,{}4.0,{}5.0,{}6.0]] \\spad{X} dasum(6,{}\\spad{dx},{}1) \\spad{X} dasum(3,{}\\spad{dx},{}2)")) (|dcabs1| (((|DoubleFloat|) (|Complex| (|DoubleFloat|))) "\\indented{1}{\\spad{dcabs1}(\\spad{z}) computes (+ (abs (realpart \\spad{z})) (abs (imagpart \\spad{z})))} \\blankline \\spad{X} t1:Complex DoubleFloat \\spad{:=} complex(1.0,{}0) \\spad{X} dcabs(\\spad{t1})"))) NIL -(-107) -((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,{}b)} returns the logical implication of Boolean \\spad{a} and \\spad{b}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical inclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of Boolean \\spad{a} and \\spad{b}.")) (|not| (($ $) "\\spad{not n} returns the negation of \\spad{n}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL +(-116) +((|constructor| (NIL "This domain is part of the PAFF package"))) +((|HamburgerNoether| . T)) NIL -(-108) -((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1} and \\spad{op2} should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) +(-117) NIL NIL -(-109 A) +NIL +(-118) +((|constructor| (NIL "This domain is part of the PAFF package"))) +((|QuadraticTransform| . T)) +NIL +(-119 K |symb| |PolyRing| E BLMET) +((|constructor| (NIL "The following is part of the PAFF package")) (|stepBlowUp| (((|Record| (|:| |mult| (|NonNegativeInteger|)) (|:| |subMult| (|NonNegativeInteger|)) (|:| |blUpRec| (|List| (|Record| (|:| |recTransStr| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|)) (|:| |recPoint| (|AffinePlane| |#1|)) (|:| |recChart| |#5|) (|:| |definingExtension| |#1|))))) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) |#5| |#1|) "\\spad{stepBlowUp(pol,{}pt,{}n)} blow-up the point \\spad{pt} on the curve defined by \\spad{pol} in the affine neighbourhood specified by \\spad{n}.")) (|quadTransform| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|NonNegativeInteger|) |#5|) "\\spad{quadTransform(pol,{}n,{}chart)} apply the quadratique transformation to \\spad{pol} specified by \\spad{chart} has in quadTransform(\\spad{pol},{}\\spad{chart}) and extract x**n to it,{} where \\spad{x} is the variable specified by the first integer in \\spad{chart} (blow-up exceptional coordinate).")) (|applyTransform| ((|#3| |#3| |#5|) "quadTransform(pol,{}chart) apply the quadratique transformation to pol specified by chart which consist of 3 integers. The last one indicates which varibles is set to 1,{} the first on indicates which variable remains unchange,{} and the second one indicates which variable oon which the transformation is applied. For example,{} [2,{}3,{}1] correspond to the following: \\spad{x} \\spad{->} 1,{} \\spad{y} \\spad{->} \\spad{y},{} \\spad{z} \\spad{->} \\spad{yz} (here the variable are [\\spad{x},{}\\spad{y},{}\\spad{z}] in BlUpRing)."))) +NIL +NIL +(-120 R S) +((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline Axiom\\spad{\\br} \\tab{5}\\spad{ r*(x*s) = (r*x)*s }")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) +((-4500 . T) (-4499 . T)) +NIL +(-121) +((|constructor| (NIL "\\spadtype{Boolean} is the elementary logic with 2 values: \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,{}b)} returns the logical implication of Boolean \\spad{a} and \\spad{b}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive or of Boolean \\spad{a} and \\spad{b}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical inclusive or of Boolean \\spad{a} and \\spad{b}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical and of Boolean \\spad{a} and \\spad{b}.")) (|not| (($ $) "\\spad{not n} returns the negation of \\spad{n}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) +NIL +NIL +(-122 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-777)))) -(-110 -2958 UP) +((|HasCategory| |#1| (QUOTE (-834)))) +(-123) +((|constructor| (NIL "Basic system operators. A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1} and \\spad{op2} should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) +NIL +NIL +(-124 -1333 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL -(-111 |p|) +(-125 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-112 |p|) +(-126 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-111 |#1|) (QUOTE (-830))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-111 |#1|) (QUOTE (-933))) (|HasCategory| (-111 |#1|) (QUOTE (-750))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-111 |#1|) (QUOTE (-1046))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-111 |#1|) (QUOTE (-206))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -476) (QUOTE (-1070)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -278) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -256) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-276))) (|HasCategory| (-111 |#1|) (QUOTE (-500))) (|HasCategory| (-111 |#1|) (QUOTE (-777))) (-1405 (|HasCategory| (-111 |#1|) (QUOTE (-750))) (|HasCategory| (-111 |#1|) (QUOTE (-777)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-830)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) -(-113 A S) -((|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-125 |#1|) (QUOTE (-896))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-125 |#1|) (QUOTE (-146))) (|HasCategory| (-125 |#1|) (QUOTE (-148))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-125 |#1|) (QUOTE (-1013))) (|HasCategory| (-125 |#1|) (QUOTE (-807))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-125 |#1|) (QUOTE (-1128))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-125 |#1|) (QUOTE (-221))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -515) (QUOTE (-1153)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -276) (LIST (QUOTE -125) (|devaluate| |#1|)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (QUOTE (-296))) (|HasCategory| (-125 |#1|) (QUOTE (-542))) (|HasCategory| (-125 |#1|) (QUOTE (-834))) (-2318 (|HasCategory| (-125 |#1|) (QUOTE (-807))) (|HasCategory| (-125 |#1|) (QUOTE (-834)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-125 |#1|) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-125 |#1|) (QUOTE (-896)))) (|HasCategory| (-125 |#1|) (QUOTE (-146))))) +(-127 A S) +((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4168))) -(-114 S) -((|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2951 . T)) +((|HasAttribute| |#1| (QUOTE -4506))) +(-128 S) +((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) +((-2537 . T)) NIL -(-115 UP) -((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) +(-129 UP) +((|constructor| (NIL "This package has no description")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) NIL NIL -(-116 S) -((|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-117 S) -((|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) +(-130 S) +((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\indented{1}{split(\\spad{x},{}\\spad{b}) splits binary tree \\spad{b} into two trees,{} one with elements} \\indented{1}{greater than \\spad{x},{} the other with elements less than \\spad{x}.} \\blankline \\spad{X} t1:=binarySearchTree [1,{}2,{}3,{}4] \\spad{X} split(3,{}\\spad{t1})")) (|insertRoot!| (($ |#1| $) "\\indented{1}{insertRoot!(\\spad{x},{}\\spad{b}) inserts element \\spad{x} as a root of binary search tree \\spad{b}.} \\blankline \\spad{X} t1:=binarySearchTree [1,{}2,{}3,{}4] \\spad{X} insertRoot!(5,{}\\spad{t1})")) (|insert!| (($ |#1| $) "\\indented{1}{insert!(\\spad{x},{}\\spad{b}) inserts element \\spad{x} as leaves into binary search tree \\spad{b}.} \\blankline \\spad{X} t1:=binarySearchTree [1,{}2,{}3,{}4] \\spad{X} insert!(5,{}\\spad{t1})")) (|binarySearchTree| (($ (|List| |#1|)) "\\indented{1}{binarySearchTree(\\spad{l}) is not documented} \\blankline \\spad{X} binarySearchTree [1,{}2,{}3,{}4]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-131 S) +((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical and of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical not of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL -(-118) -((|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-132) +((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical and of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical not of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{\\spad{b}}."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-119 A S) -((|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) +(-133 A S) +((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) NIL NIL -(-120 S) -((|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-134 S) +((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-121 S) -((|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-122 S) -((|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-123) -((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) +(-135 S) +((|constructor| (NIL "BinaryTournament creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")) (|insert!| (($ |#1| $) "\\indented{1}{insert!(\\spad{x},{}\\spad{b}) inserts element \\spad{x} as leaves into binary tournament \\spad{b}.} \\blankline \\spad{X} t1:=binaryTournament [1,{}2,{}3,{}4] \\spad{X} insert!(5,{}\\spad{t1}) \\spad{X} \\spad{t1}")) (|binaryTournament| (($ (|List| |#1|)) "\\indented{1}{binaryTournament(\\spad{ls}) creates a binary tournament with the} \\indented{1}{elements of \\spad{ls} as values at the nodes.} \\blankline \\spad{X} binaryTournament [1,{}2,{}3,{}4]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-136 S) +((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\indented{1}{binaryTree(\\spad{l},{}\\spad{v},{}\\spad{r}) creates a binary tree with} \\indented{1}{value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.} \\blankline \\spad{X} t1:=binaryTree([1,{}2,{}3]) \\spad{X} t2:=binaryTree([4,{}5,{}6]) \\spad{X} binaryTree(\\spad{t1},{}[7,{}8,{}9],{}\\spad{t2})") (($ |#1|) "\\indented{1}{binaryTree(\\spad{v}) is an non-empty binary tree} \\indented{1}{with value \\spad{v},{} and left and right empty.} \\blankline \\spad{X} t1:=binaryTree([1,{}2,{}3])"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-137) +((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\tab{5}\\spad{ a+b = a+c => b=c }.\\spad{\\br} This is formalised by the partial subtraction operator,{} which satisfies the Axioms\\spad{\\br} \\tab{5}\\spad{c = a+b <=> c-b = a}")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL NIL -(-124) +(-138) ((|constructor| (NIL "A cachable set is a set whose elements keep an integer as part of their structure.")) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) "\\spad{setPosition(x,{} n)} associates the integer \\spad{n} to \\spad{x}.")) (|position| (((|NonNegativeInteger|) $) "\\spad{position(x)} returns the integer \\spad{n} associated to \\spad{x}."))) NIL NIL -(-125) -((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4169 "*") . T)) +(-139) +((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then\\spad{\\br} \\tab{5}\\spad{x+y = \\#(X+Y)} \\tab{5}disjoint union\\spad{\\br} \\tab{5}\\spad{x-y = \\#(X-Y)} \\tab{5}relative complement\\spad{\\br} \\tab{5}\\spad{x*y = \\#(X*Y)} \\tab{5}cartesian product\\spad{\\br} \\tab{5}\\spad{x**y = \\#(X**Y)} \\tab{4}\\spad{X**Y = g| g:Y->X} \\blankline The non-negative integers have a natural construction as cardinals\\spad{\\br} \\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}. \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\spad{\\br} \\spad{2**Aleph i = Aleph(i+1)} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are\\spad{\\br} \\tab{5}\\spad{a = \\#Z} \\tab{5}countable infinity\\spad{\\br} \\tab{5}\\spad{c = \\#R} \\tab{5}the continuum\\spad{\\br} \\tab{5}\\spad{f = \\# g | g:[0,{}1]->R\\} \\blankline In this domain,{} these values are obtained using\\br \\tab{5}\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\indented{1}{generalizedContinuumHypothesisAssumed(bool)} \\indented{1}{is used to dictate whether the hypothesis is to be assumed.} \\blankline \\spad{X} generalizedContinuumHypothesisAssumed \\spad{true} \\spad{X} a:=Aleph 0 \\spad{X} c:=2**a \\spad{X} f:=2**c")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\indented{1}{generalizedContinuumHypothesisAssumed?()} \\indented{1}{tests if the hypothesis is currently assumed.} \\blankline \\spad{X} generalizedContinuumHypothesisAssumed?")) (|countable?| (((|Boolean|) $) "\\indented{1}{countable?(\\spad{a}) determines} \\indented{1}{whether \\spad{a} is a countable cardinal,{}} \\indented{1}{\\spadignore{i.e.} an integer or \\spad{Aleph 0}.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} countable? \\spad{c2} \\spad{X} A0:=Aleph 0 \\spad{X} countable? \\spad{A0} \\spad{X} A1:=Aleph 1 \\spad{X} countable? \\spad{A1}")) (|finite?| (((|Boolean|) $) "\\indented{1}{finite?(\\spad{a}) determines whether} \\indented{1}{\\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} finite? \\spad{c2} \\spad{X} A0:=Aleph 0 \\spad{X} finite? \\spad{A0}")) (|Aleph| (($ (|NonNegativeInteger|)) "\\indented{1}{Aleph(\\spad{n}) provides the named (infinite) cardinal number.} \\blankline \\spad{X} A0:=Aleph 0")) (** (($ $ $) "\\indented{1}{\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined} \\indented{2}{as \\spad{\\{g| g:Y->X\\}}.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} \\spad{c2**c2} \\spad{X} A1:=Aleph 1 \\spad{X} \\spad{A1**c2} \\spad{X} generalizedContinuumHypothesisAssumed \\spad{true} \\spad{X} \\spad{A1**A1}")) (- (((|Union| $ "failed") $ $) "\\indented{1}{\\spad{x - y} returns an element \\spad{z} such that} \\indented{1}{\\spad{z+y=x} or \"failed\" if no such element exists.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} \\spad{c2}-\\spad{c2} \\spad{X} A1:=Aleph 1 \\spad{X} \\spad{A1}-\\spad{c2}")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) +(((-4507 "*") . T)) NIL -(-126 |minix| -2742 R) -((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\^= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) +(-140 |minix| -2050 S T$) +((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-127 |minix| -2742 S T$) -((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) +(-141 |minix| -2050 R) +((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\indented{1}{ravel(\\spad{t}) produces a list of components from a tensor such that} \\indented{3}{\\spad{unravel(ravel(t)) = t}.} \\blankline \\spad{X} n:SquareMatrix(2,{}Integer):=matrix [[2,{}3],{}[0,{}1]] \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=n} \\spad{X} ravel \\spad{tn}")) (|leviCivitaSymbol| (($) "\\indented{1}{leviCivitaSymbol() is the rank \\spad{dim} tensor defined by} \\indented{1}{\\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1}} \\indented{1}{if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation} \\indented{1}{of \\spad{minix,{}...,{}minix+dim-1}.} \\blankline \\spad{X} lcs:CartesianTensor(1,{}2,{}Integer):=leviCivitaSymbol()")) (|kroneckerDelta| (($) "\\indented{1}{kroneckerDelta() is the rank 2 tensor defined by} \\indented{4}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{7}{\\spad{= 1\\space{2}if i = j}} \\indented{7}{\\spad{= 0 if\\space{2}i \\^= j}} \\blankline \\spad{X} delta:CartesianTensor(1,{}2,{}Integer):=kroneckerDelta()")) (|reindex| (($ $ (|List| (|Integer|))) "\\indented{1}{reindex(\\spad{t},{}[\\spad{i1},{}...,{}idim]) permutes the indices of \\spad{t}.} \\indented{1}{For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])}} \\indented{1}{for a rank 4 tensor \\spad{t},{}} \\indented{1}{then \\spad{r} is the rank for tensor given by} \\indented{5}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.} \\blankline \\spad{X} n:SquareMatrix(2,{}Integer):=matrix [[2,{}3],{}[0,{}1]] \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=n} \\spad{X} p:=product(\\spad{tn},{}\\spad{tn}) \\spad{X} reindex(\\spad{p},{}[4,{}3,{}2,{}1])")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{transpose(\\spad{t},{}\\spad{i},{}\\spad{j}) exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th} \\indented{1}{indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)}} \\indented{1}{for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor} \\indented{1}{given by} \\indented{5}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tm},{}\\spad{tm}] \\spad{X} transpose(\\spad{tn},{}1,{}2)") (($ $) "\\indented{1}{transpose(\\spad{t}) exchanges the first and last indices of \\spad{t}.} \\indented{1}{For example,{} if \\spad{r = transpose(t)} for a rank 4} \\indented{1}{tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by} \\indented{5}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} Tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} transpose(\\spad{Tm})")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{contract(\\spad{t},{}\\spad{i},{}\\spad{j}) is the contraction of tensor \\spad{t} which} \\indented{1}{sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices.} \\indented{1}{For example,{}\\space{2}if} \\indented{1}{\\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then} \\indented{1}{\\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by} \\indented{5}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} Tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} v:DirectProduct(2,{}Integer):=directProduct [3,{}4] \\spad{X} Tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} Tmv:=contract(\\spad{Tm},{}2,{}1)") (($ $ (|Integer|) $ (|Integer|)) "\\indented{1}{contract(\\spad{t},{}\\spad{i},{}\\spad{s},{}\\spad{j}) is the inner product of tenors \\spad{s} and \\spad{t}} \\indented{1}{which sums along the \\spad{k1}\\spad{-}th index of} \\indented{1}{\\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}.} \\indented{1}{For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors} \\indented{1}{rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is} \\indented{1}{the rank 4 \\spad{(= 3 + 3 - 2)} tensor\\space{2}given by} \\indented{5}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} Tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} v:DirectProduct(2,{}Integer):=directProduct [3,{}4] \\spad{X} Tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} Tmv:=contract(\\spad{Tm},{}2,{}\\spad{Tv},{}1)")) (* (($ $ $) "\\indented{1}{\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts} \\indented{1}{the last index of \\spad{s} with the first index of \\spad{t},{} that is,{}} \\indented{5}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{5}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} \\indented{1}{This is compatible with the use of \\spad{M*v} to denote} \\indented{1}{the matrix-vector inner product.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} Tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} v:DirectProduct(2,{}Integer):=directProduct [3,{}4] \\spad{X} Tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} Tm*Tv")) (|product| (($ $ $) "\\indented{1}{product(\\spad{s},{}\\spad{t}) is the outer product of the tensors \\spad{s} and \\spad{t}.} \\indented{1}{For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors} \\indented{1}{\\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by} \\indented{5}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.} \\blankline \\spad{X} m:SquareMatrix(2,{}Integer):=matrix [[1,{}2],{}[4,{}5]] \\spad{X} Tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=m} \\spad{X} n:SquareMatrix(2,{}Integer):=matrix [[2,{}3],{}[0,{}1]] \\spad{X} Tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=n} \\spad{X} Tmn:=product(\\spad{Tm},{}\\spad{Tn})")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\indented{1}{elt(\\spad{t},{}[\\spad{i1},{}...,{}iN]) gives a component of a rank \\spad{N} tensor.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tv},{}\\spad{tv}] \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tm},{}\\spad{tm}] \\spad{X} tp:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tn},{}\\spad{tn}] \\spad{X} tq:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tp},{}\\spad{tp}] \\spad{X} elt(\\spad{tq},{}[2,{}2,{}2,{}2,{}2])") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{elt(\\spad{t},{}\\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{l}) gives a component of a rank 4 tensor.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tv},{}\\spad{tv}] \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tm},{}\\spad{tm}] \\spad{X} tp:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tn},{}\\spad{tn}] \\spad{X} elt(\\spad{tp},{}2,{}2,{}2,{}2) \\spad{X} \\spad{tp}[2,{}2,{}2,{}2]") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{elt(\\spad{t},{}\\spad{i},{}\\spad{j},{}\\spad{k}) gives a component of a rank 3 tensor.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tv},{}\\spad{tv}] \\spad{X} tn:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tm},{}\\spad{tm}] \\spad{X} elt(\\spad{tn},{}2,{}2,{}2) \\spad{X} \\spad{tn}[2,{}2,{}2]") ((|#3| $ (|Integer|) (|Integer|)) "\\indented{1}{elt(\\spad{t},{}\\spad{i},{}\\spad{j}) gives a component of a rank 2 tensor.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tv},{}\\spad{tv}] \\spad{X} elt(\\spad{tm},{}2,{}2) \\spad{X} \\spad{tm}[2,{}2]") ((|#3| $ (|Integer|)) "\\indented{1}{elt(\\spad{t},{}\\spad{i}) gives a component of a rank 1 tensor.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} elt(\\spad{tv},{}2) \\spad{X} \\spad{tv}[2]") ((|#3| $) "\\indented{1}{elt(\\spad{t}) gives the component of a rank 0 tensor.} \\blankline \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=8} \\spad{X} elt(\\spad{tv}) \\spad{X} \\spad{tv}[]")) (|rank| (((|NonNegativeInteger|) $) "\\indented{1}{rank(\\spad{t}) returns the tensorial rank of \\spad{t} (that is,{} the} \\indented{1}{number of indices).\\space{2}This is the same as the graded module} \\indented{1}{degree.} \\blankline \\spad{X} CT:=CARTEN(1,{}2,{}Integer) \\spad{X} \\spad{t0:CT:=8} \\spad{X} rank \\spad{t0}")) (|coerce| (($ (|List| $)) "\\indented{1}{coerce([\\spad{t_1},{}...,{}t_dim]) allows tensors to be constructed} \\indented{1}{using lists.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v} \\spad{X} tm:CartesianTensor(1,{}2,{}Integer)\\spad{:=}[\\spad{tv},{}\\spad{tv}]") (($ (|List| |#3|)) "\\indented{1}{coerce([\\spad{r_1},{}...,{}r_dim]) allows tensors to be constructed} \\indented{1}{using lists.} \\blankline \\spad{X} \\spad{v:=}[2,{}3] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v}") (($ (|SquareMatrix| |#2| |#3|)) "\\indented{1}{coerce(\\spad{m}) views a matrix as a rank 2 tensor.} \\blankline \\spad{X} v:SquareMatrix(2,{}Integer)\\spad{:=}[[1,{}2],{}[3,{}4]] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v}") (($ (|DirectProduct| |#2| |#3|)) "\\indented{1}{coerce(\\spad{v}) views a vector as a rank 1 tensor.} \\blankline \\spad{X} v:DirectProduct(2,{}Integer):=directProduct [3,{}4] \\spad{X} tv:CartesianTensor(1,{}2,{}Integer)\\spad{:=v}"))) NIL NIL -(-128) -((|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4167 . T) (-4157 . T) (-4168 . T)) -((|HasCategory| (-131) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-131) (QUOTE (-336))) (|HasCategory| (-131) (QUOTE (-777))) (|HasCategory| (-131) (QUOTE (-1001))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-336)))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))))) -(-129 R Q A) +(-142) +((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which alphanumeric? is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which alphabetic? is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which lowerCase? is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which upperCase? is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which hexDigit? is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which digit? is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) +((-4505 . T) (-4495 . T) (-4506 . T)) +((|HasCategory| (-145) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-145) (QUOTE (-364))) (|HasCategory| (-145) (QUOTE (-834))) (|HasCategory| (-145) (QUOTE (-1082))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-364)))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))))) +(-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-130) -((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n,{} m)} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note: \\spad{permutation(n,{}m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note: \\spad{n! = n (n-1)! when n > 0}; also,{} \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}r)} returns the \\spad{(n,{}r)} binomial coefficient (often denoted in the literature by \\spad{C(n,{}r)}). Note: \\spad{C(n,{}r) = n!/(r!(n-r)!)} where \\spad{n >= r >= 0}."))) +(-144) +((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n,{} m)} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note that \\spad{permutation(n,{}m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note that \\spad{n! = n (n-1)! when n > 0}; also,{} \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\indented{1}{binomial(\\spad{n},{}\\spad{r}) returns the \\spad{(n,{}r)} binomial coefficient} \\indented{1}{(often denoted in the literature by \\spad{C(n,{}r)}).} \\indented{1}{Note that \\spad{C(n,{}r) = n!/(r!(n-r)!)} where \\spad{n >= r >= 0}.} \\blankline \\spad{X} [binomial(5,{}\\spad{i}) for \\spad{i} in 0..5]"))) NIL NIL -(-131) -((|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape()} provides the escape character,{} \\spad{_},{} which is used to allow quotes and other characters {\\em within} strings.")) (|quote| (($) "\\spad{quote()} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space()} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|Integer|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|Integer|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}."))) +(-145) +((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\indented{1}{alphanumeric?(\\spad{c}) tests if \\spad{c} is either a letter or number,{}} \\indented{1}{\\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [alphanumeric? \\spad{c} for \\spad{c} in chars]")) (|lowerCase?| (((|Boolean|) $) "\\indented{1}{lowerCase?(\\spad{c}) tests if \\spad{c} is an lower case letter,{}} \\indented{1}{\\spadignore{i.e.} one of a..\\spad{z}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [lowerCase? \\spad{c} for \\spad{c} in chars]")) (|upperCase?| (((|Boolean|) $) "\\indented{1}{upperCase?(\\spad{c}) tests if \\spad{c} is an upper case letter,{}} \\indented{1}{\\spadignore{i.e.} one of A..\\spad{Z}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [upperCase? \\spad{c} for \\spad{c} in chars]")) (|alphabetic?| (((|Boolean|) $) "\\indented{1}{alphabetic?(\\spad{c}) tests if \\spad{c} is a letter,{}} \\indented{1}{\\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [alphabetic? \\spad{c} for \\spad{c} in chars]")) (|hexDigit?| (((|Boolean|) $) "\\indented{1}{hexDigit?(\\spad{c}) tests if \\spad{c} is a hexadecimal numeral,{}} \\indented{1}{\\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [hexDigit? \\spad{c} for \\spad{c} in chars]")) (|digit?| (((|Boolean|) $) "\\indented{1}{digit?(\\spad{c}) tests if \\spad{c} is a digit character,{}} \\indented{1}{\\spadignore{i.e.} one of 0..9.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [digit? \\spad{c} for \\spad{c} in chars]")) (|lowerCase| (($ $) "\\indented{1}{lowerCase(\\spad{c}) converts an upper case letter to the corresponding} \\indented{1}{lower case letter.\\space{2}If \\spad{c} is not an upper case letter,{} then} \\indented{1}{it is returned unchanged.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [lowerCase \\spad{c} for \\spad{c} in chars]")) (|upperCase| (($ $) "\\indented{1}{upperCase(\\spad{c}) converts a lower case letter to the corresponding} \\indented{1}{upper case letter.\\space{2}If \\spad{c} is not a lower case letter,{} then} \\indented{1}{it is returned unchanged.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [upperCase \\spad{c} for \\spad{c} in chars]")) (|escape| (($) "\\indented{1}{escape() provides the escape character,{} \\spad{_},{} which} \\indented{1}{is used to allow quotes and other characters within} \\indented{1}{strings.} \\blankline \\spad{X} escape()")) (|quote| (($) "\\indented{1}{quote() provides the string quote character,{} \\spad{\"}.} \\blankline \\spad{X} quote()")) (|space| (($) "\\indented{1}{space() provides the blank character.} \\blankline \\spad{X} space()")) (|char| (($ (|String|)) "\\indented{1}{char(\\spad{s}) provides a character from a string \\spad{s} of length one.} \\blankline \\spad{X} [char \\spad{c} for \\spad{c} in [\"a\",{}\"A\",{}\\spad{\"X\"},{}\\spad{\"8\"},{}\\spad{\"+\"}]]") (($ (|Integer|)) "\\indented{1}{char(\\spad{i}) provides a character corresponding to the integer} \\indented{1}{code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.} \\blankline \\spad{X} [char \\spad{c} for \\spad{c} in [97,{}65,{}88,{}56,{}43]]")) (|ord| (((|Integer|) $) "\\indented{1}{ord(\\spad{c}) provides an integral code corresponding to the} \\indented{1}{character \\spad{c}.\\space{2}It is always \\spad{true} that \\spad{char ord c = c}.} \\blankline \\spad{X} chars \\spad{:=} [char \"a\",{} char \"A\",{} char \\spad{\"X\"},{} char \\spad{\"8\"},{} char \\spad{\"+\"}] \\spad{X} [ord \\spad{c} for \\spad{c} in chars]"))) NIL NIL -(-132) +(-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4164 . T)) +((-4502 . T)) NIL -(-133 R) +(-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) NIL NIL -(-134) +(-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4164 . T)) +((-4502 . T)) NIL -(-135 -2958 UP UPUP) +(-149 -1333 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL -(-136 R CR) -((|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} where (\\spad{fi} relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g} = sum \\spad{ai} prod \\spad{fj} (\\spad{j} \\spad{\\=} \\spad{i}) or equivalently g/prod \\spad{fj} = sum (ai/fi) or returns \"failed\" if no such list exists"))) +(-150 R CR) +((|constructor| (NIL "This package provides the generalized euclidean algorithm which is needed as the basic step for factoring polynomials.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} where (\\spad{fi} relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g} = sum \\spad{ai} prod \\spad{fj} (\\spad{j} \\spad{\\=} \\spad{i}) or equivalently g/prod \\spad{fj} = sum (ai/fi) or returns \"failed\" if no such list exists"))) NIL NIL -(-137 A S) -((|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) +(-151 A S) +((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note that \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note that \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note that \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\indented{1}{reduce(\\spad{f},{}\\spad{u}) reduces the binary operation \\spad{f} across \\spad{u}. For example,{}} \\indented{1}{if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})}} \\indented{1}{returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}.} \\indented{1}{Note that if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}.} \\indented{1}{Error: if \\spad{u} is empty.} \\blankline \\spad{C} )clear all \\spad{X} reduce(+,{}[\\spad{C}[\\spad{i}]*x**i for \\spad{i} in 1..5])")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasAttribute| |#1| (QUOTE -4167))) -(-138 S) -((|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2951 . T)) +((|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasAttribute| |#1| (QUOTE -4505))) +(-152 S) +((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note that \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note that \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note that \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\indented{1}{reduce(\\spad{f},{}\\spad{u}) reduces the binary operation \\spad{f} across \\spad{u}. For example,{}} \\indented{1}{if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})}} \\indented{1}{returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}.} \\indented{1}{Note that if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}.} \\indented{1}{Error: if \\spad{u} is empty.} \\blankline \\spad{C} )clear all \\spad{X} reduce(+,{}[\\spad{C}[\\spad{i}]*x**i for \\spad{i} in 1..5])")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) +((-2537 . T)) NIL -(-139 |n| K Q) -((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]} (\\spad{1<=i1= r >= 0}. This is the number of combinations of \\spad{n} objects taken \\spad{r} at a time."))) +(-158 I) +((|constructor| (NIL "The \\spadtype{IntegerCombinatoricFunctions} package provides some standard functions in combinatorics.")) (|stirling2| ((|#1| |#1| |#1|) "\\spad{stirling2(n,{}m)} returns the Stirling number of the second kind denoted \\spad{SS[n,{}m]}.")) (|stirling1| ((|#1| |#1| |#1|) "\\spad{stirling1(n,{}m)} returns the Stirling number of the first kind denoted \\spad{S[n,{}m]}.")) (|permutation| ((|#1| |#1| |#1|) "\\spad{permutation(n)} returns \\spad{!P(n,{}r) = n!/(n-r)!}. This is the number of permutations of \\spad{n} objects taken \\spad{r} at a time.")) (|partition| ((|#1| |#1|) "\\spad{partition(n)} returns the number of partitions of the integer \\spad{n}. This is the number of distinct ways that \\spad{n} can be written as a sum of positive integers.")) (|multinomial| ((|#1| |#1| (|List| |#1|)) "\\spad{multinomial(n,{}[m1,{}m2,{}...,{}mk])} returns the multinomial coefficient \\spad{n!/(m1! m2! ... mk!)}.")) (|factorial| ((|#1| |#1|) "\\spad{factorial(n)} returns \\spad{n!}. this is the product of all integers between 1 and \\spad{n} (inclusive). Note that \\spad{0!} is defined to be 1.")) (|binomial| ((|#1| |#1| |#1|) "\\indented{1}{\\spad{binomial(n,{}r)} returns the binomial coefficient} \\indented{1}{\\spad{C(n,{}r) = n!/(r! (n-r)!)},{} where \\spad{n >= r >= 0}.} \\indented{1}{This is the number of combinations of \\spad{n} objects taken \\spad{r} at a time.} \\blankline \\spad{X} [binomial(5,{}\\spad{i}) for \\spad{i} in 0..5]"))) NIL NIL -(-145) +(-159) ((|constructor| (NIL "CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.")) (|product| (($ $ (|SegmentBinding| $)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") (($ $ (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| (($ $ (|SegmentBinding| $)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") (($ $ (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| (($ $ (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") (($ $) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials."))) NIL NIL -(-146) -((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) +(-160) +((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} is not documented") (($ (|Integer|)) "\\spad{mkcomm(i)} is not documented"))) NIL NIL -(-147) +(-161) ((|constructor| (NIL "This package exports the elementary operators,{} with some semantics already attached to them. The semantics that is attached here is not dependent on the set in which the operators will be applied.")) (|operator| (((|BasicOperator|) (|Symbol|)) "\\spad{operator(s)} returns an operator with name \\spad{s},{} with the appropriate semantics if \\spad{s} is known. If \\spad{s} is not known,{} the result has no semantics."))) NIL NIL -(-148 R UP UPUP) +(-162 R UP UPUP) ((|constructor| (NIL "A package for swapping the order of two variables in a tower of two UnivariatePolynomialCategory extensions.")) (|swap| ((|#3| |#3|) "\\spad{swap(p(x,{}y))} returns \\spad{p}(\\spad{y},{}\\spad{x})."))) NIL NIL -(-149 S R) -((|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) +(-163 S R) +((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-967))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-331))) (|HasAttribute| |#2| (QUOTE -4163)) (|HasAttribute| |#2| (QUOTE -4166)) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-777)))) -(-150 R) -((|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4160 -1405 (|has| |#1| (-508)) (-12 (|has| |#1| (-276)) (|has| |#1| (-830)))) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4163 |has| |#1| (-6 -4163)) (-4166 |has| |#1| (-6 -4166)) (-1976 . T) (-2951 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . 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NIL +(-167 R) +((|constructor| (NIL "\\spadtype{Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) +((-4498 -2318 (|has| |#1| (-550)) (-12 (|has| |#1| (-296)) (|has| |#1| (-896)))) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4501 |has| |#1| (-6 -4501)) (-4504 |has| |#1| (-6 -4504)) (-2556 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1173))) (-12 (|HasCategory| |#1| (QUOTE (-994))) (|HasCategory| |#1| (QUOTE (-1173)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST 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(-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1173))))) (-12 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-359))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-896))))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-896))))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-359)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasAttribute| |#1| (QUOTE -4501)) (|HasAttribute| |#1| (QUOTE -4504)) (-12 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(((|Boolean|) $ (|Boolean|)) "\\spad{close(x,{}b)} \\undocumented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} \\undocumented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented"))) +(-169) +((|constructor| (NIL "This domain implements some global properties of subspaces.")) (|copy| (($ $) "\\spad{copy(x)} is not documented")) (|solid| (((|Boolean|) $ (|Boolean|)) "\\spad{solid(x,{}b)} is not documented")) (|close| (((|Boolean|) $ (|Boolean|)) "\\spad{close(x,{}b)} is not documented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} is not documented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} is not documented")) (|new| (($) "\\spad{new()} is not documented"))) NIL NIL -(-156) -((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-170) +((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) +(((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-157 R) -((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4169 "*") . T) (-4160 . T) (-4165 . T) (-4159 . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-171 R) +((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general continued fractions. This version is not restricted to simple,{} finite fractions and uses the \\spadtype{Stream} as a representation. The arithmetic functions assume that the approximants alternate below/above the convergence point. This is enforced by ensuring the partial numerators and partial denominators are greater than 0 in the Euclidean domain view of \\spad{R} (\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) +(((-4507 "*") . T) (-4498 . T) (-4503 . T) (-4497 . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-158 R) +(-172 R) ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,{}b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,{}b)} is a function which will map the point \\spad{(lambda,{}mu,{}nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) NIL NIL -(-159 R |PolR| E) +(-173 R |PolR| E) ((|constructor| (NIL "This package implements characteristicPolynomials for monogenic algebras using resultants")) (|characteristicPolynomial| ((|#2| |#3|) "\\spad{characteristicPolynomial(e)} returns the characteristic polynomial of \\spad{e} using resultants"))) NIL NIL -(-160 R S CS) -((|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) +(-174 R S CS) +((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-866 |#2|) (LIST (QUOTE -806) (|devaluate| |#1|)))) -(-161 R) -((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) +((|HasCategory| (-945 |#2|) (LIST (QUOTE -873) (|devaluate| |#1|)))) +(-175 R) +((|constructor| (NIL "This package has no documentation")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL NIL -(-162 R UP) -((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken\\spad{'s} idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see \\spadfunFrom{digits}{Float}) is not increased when this is necessary to avoid rounding errors. Hence it is the user\\spad{'s} responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage\\spad{'s} variant of Graeffe\\spad{'s} method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in {\\em factors} which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being {\\em 10 ** (-3)} to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal {\\em globalDigits} is set to {\\em ceiling(1/r)**2*10} being {\\em 10**7} by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is {\\em coeffient of \\spad{x**(n-1)}} divided by {\\em n times coefficient of \\spad{x**n}}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em 1+globalEps},{} where {\\em globalEps} is the internal error bound,{} which can be set by {\\em setErrorBound}.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,{}errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly,{} eps)} determines a start polynomial {\\em start}\\\\ by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,{}eps,{}info)} determines a start polynomial {\\em start} by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If {\\em info} is {\\em true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note: this function depends on \\spadfunFrom{abs}{Complex}.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost {\\em globalEps},{} the internal error bound,{} which can be set by {\\em setErrorBound}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p,{} eps)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p,{} eps,{} info)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization. If {\\em info} is {\\em true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If {\\em info} is {\\em true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p,{} eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by {\\em eps}.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant {\\em globalEps} which you may change by {\\em setErrorBound}."))) +(-176 R UP) +((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken\\spad{'s} idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see digits) is not increased when this is necessary to avoid rounding errors. Hence it is the user\\spad{'s} responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage\\spad{'s} variant of Graeffe\\spad{'s} method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in factors which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being 10 \\spad{**} (\\spad{-3}) to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal globalDigits is set to \\em ceiling(1/r)\\spad{**2*10} being 10**7 by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is coeffient of \\spad{x**(n-1)} divided by \\spad{n} times coefficient of \\spad{x**n}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of 1+globalEps,{} where globalEps is the internal error bound,{} which can be set by setErrorBound.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,{}errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of \\spad{errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly,{} eps)} determines a start polynomial start by using \"startPolynomial then it increases the exponent \\spad{n} of start \\spad{**} \\spad{n} mod \\spad{poly} to get an approximate factor of \\spad{poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,{}eps,{}info)} determines a start polynomial start by using \"startPolynomial then it increases the exponent \\spad{n} of start \\spad{**} \\spad{n} mod \\spad{poly} to get an approximate factor of \\spad{poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If \\spad{info} is \\spad{true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note that this function depends on abs.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost globalEps,{} the internal error bound,{} which can be set by setErrorBound. An overall error bound \\spad{eps0} is determined and iterated tree-like calls to pleskenSplit are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p,{} eps)} tries to factor \\spad{p} into linear factors with error atmost eps. An overall error bound \\spad{eps0} is determined and iterated tree-like calls to pleskenSplit are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p,{} eps,{} info)} tries to factor \\spad{p} into linear factors with error atmost \\spad{eps}. An overall error bound \\spad{eps0} is determined and iterated tree-like calls to pleskenSplit are used to get the factorization. If info is \\spad{true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial \\spad{tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial \\spad{tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If info is \\spad{true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p,{} eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by eps.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant globalEps which you may change by setErrorBound."))) NIL NIL -(-163 S ST) -((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) +(-177 S ST) +((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\indented{1}{computeCycleEntry(\\spad{x},{}cycElt),{} where cycElt is a pointer to a} \\indented{1}{node in the cyclic part of the cyclic stream \\spad{x},{} returns a} \\indented{1}{pointer to the first node in the cycle} \\blankline \\spad{X} p:=repeating([1,{}2,{}3]) \\spad{X} q:=cons(4,{}\\spad{p}) \\spad{X} computeCycleEntry(\\spad{q},{}cycleElt(\\spad{q}))")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\indented{1}{computeCycleLength(\\spad{s}) returns the length of the cycle of a} \\indented{1}{cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the} \\indented{1}{cyclic part of \\spad{t}.} \\blankline \\spad{X} p:=repeating([1,{}2,{}3]) \\spad{X} q:=cons(4,{}\\spad{p}) \\spad{X} computeCycleLength(cycleElt(\\spad{q}))")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\indented{1}{cycleElt(\\spad{s}) returns a pointer to a node in the cycle if the stream} \\indented{1}{\\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic} \\blankline \\spad{X} p:=repeating([1,{}2,{}3]) \\spad{X} q:=cons(4,{}\\spad{p}) \\spad{X} cycleElt \\spad{q} \\spad{X} \\spad{r:=}[1,{}2,{}3]::Stream(Integer) \\spad{X} cycleElt \\spad{r}"))) NIL NIL -(-164 R -2958) +(-178 R -1333) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-165 R) -((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}"))) -NIL -NIL -(-166) -((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,{}li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) "\\spad{SFunction(\\spad{li})} is the \\spad{S}-function of the partition \\spad{\\spad{li}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,{}s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) -NIL -NIL -(-167) -((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}"))) -NIL -NIL -(-168) -((|changeName| (((|Result|) (|Symbol|) (|Symbol|) (|Result|)) "\\spad{changeName(s,{}t,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to \\axiom{\\spad{t}}.")) (|commaSeparate| (((|String|) (|List| (|String|))) "\\spad{commaSeparate(l)} produces a comma separated string from a list of strings.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{singularitiesOf(args)} returns a list of potential singularities of the function within the given range")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function if it can be retracted to \\axiomType{Polynomial DoubleFloat}.")) (|functionIsOscillatory| (((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsOscillatory(a)} tests whether the function \\spad{a.fn} has many zeros of its derivative.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(x)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{x}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(x)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{x}}")) (|functionIsContinuousAtEndPoints| (((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsContinuousAtEndPoints(args)} uses power series limits to check for problems at the end points of the range of \\spad{args}.")) (|rangeIsFinite| (((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{rangeIsFinite(args)} tests the endpoints of \\spad{args.range} for infinite end points."))) +(-179 R) +((|constructor| (NIL "CoerceVectorMatrixPackage is an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}"))) NIL NIL -(-169) -NIL -NIL -NIL -(-170) -NIL -NIL -NIL -(-171) -NIL -NIL -NIL -(-172) -NIL +(-180) +((|constructor| (NIL "Polya-Redfield enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,{}li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) "\\spad{SFunction(\\spad{li})} is the \\spad{S}-function of the partition \\spad{\\spad{li}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,{}s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) NIL NIL -(-173) +(-181) +((|constructor| (NIL "This package has no description")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}"))) NIL NIL +(-182) +((|constructor| (NIL "\\axiomType{d01AgentsPackage} is a package of numerical agents to be used to investigate attributes of an input function so as to decide the \\axiomFun{measure} of an appropriate numerical integration routine. It contains functions \\axiomFun{rangeIsFinite} to test the input range and \\axiomFun{functionIsContinuousAtEndPoints} to check for continuity at the end points of the range.")) (|changeName| (((|Result|) (|Symbol|) (|Symbol|) (|Result|)) "\\spad{changeName(s,{}t,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to \\axiom{\\spad{t}}.")) (|commaSeparate| (((|String|) (|List| (|String|))) "\\spad{commaSeparate(l)} produces a comma separated string from a list of strings.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{singularitiesOf(args)} returns a list of potential singularities of the function within the given range")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function if it can be retracted to \\axiomType{Polynomial DoubleFloat}.")) (|functionIsOscillatory| (((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsOscillatory(a)} tests whether the function \\spad{a.fn} has many zeros of its derivative.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(x)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{x}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(x)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{x}}")) (|functionIsContinuousAtEndPoints| (((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsContinuousAtEndPoints(args)} uses power series limits to check for problems at the end points of the range of \\spad{args}.")) (|rangeIsFinite| (((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{rangeIsFinite(args)} tests the endpoints of \\spad{args.range} for infinite end points."))) NIL -(-174) NIL +(-183) +((|constructor| (NIL "\\axiomType{d01ajfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AJF,{} a general numerical integration routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AJF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL -(-175) +(-184) +((|constructor| (NIL "\\axiomType{d01akfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AKF,{} a numerical integration routine which is is suitable for oscillating,{} non-singular functions. The function \\axiomFun{measure} measures the usefulness of the routine D01AKF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL +(-185) +((|constructor| (NIL "\\axiomType{d01alfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ALF,{} a general numerical integration routine which can handle a list of singularities. The function \\axiomFun{measure} measures the usefulness of the routine D01ALF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL -(-176) NIL +(-186) +((|constructor| (NIL "\\axiomType{d01amfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AMF,{} a general numerical integration routine which can handle infinite or semi-infinite range of the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AMF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL -(-177) +(-187) +((|constructor| (NIL "\\axiomType{d01anfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ANF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}). The function \\axiomFun{measure} measures the usefulness of the routine D01ANF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL +(-188) +((|constructor| (NIL "\\axiomType{d01apfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01APF,{} a general numerical integration routine which can handle end point singularities of the algebraico-logarithmic form \\spad{w}(\\spad{x}) = (\\spad{x}-a)\\spad{^c} * (\\spad{b}-\\spad{x})\\spad{^d}. The function \\axiomFun{measure} measures the usefulness of the routine D01APF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL -(-178) NIL +(-189) +((|constructor| (NIL "\\axiomType{d01aqfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AQF,{} a general numerical integration routine which can solve an integral of the form /home/bjd/Axiom/anna/hypertex/bitmaps/d01aqf.\\spad{xbm} The function \\axiomFun{measure} measures the usefulness of the routine D01AQF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL -(-179) +(-190) +((|constructor| (NIL "\\axiomType{d01asfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ASF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}) on an semi-infinite range. The function \\axiomFun{measure} measures the usefulness of the routine D01ASF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL NIL +(-191) +((|constructor| (NIL "\\axiomType{d01fcfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01FCF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL -(-180) -((|exprHasLogarithmicWeights| (((|Integer|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasLogarithmicWeights} looks for logarithmic weights giving rise to singularities of the function at the end-points.")) (|exprHasAlgebraicWeight| (((|Union| (|List| (|DoubleFloat|)) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasAlgebraicWeight} looks for algebraic weights giving rise to singularities of the function at the end-points.")) (|exprHasWeightCosWXorSinWX| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |w| (|DoubleFloat|))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasWeightCosWXorSinWX} looks for trigonometric weights in an expression of the form \\axiom{cos \\omega \\spad{x}} or \\axiom{sin \\omega \\spad{x}},{} returning the value of \\omega (\\notequal 1) and the operator."))) NIL +(-192) +((|constructor| (NIL "\\axiomType{d01gbfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01GBF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}."))) NIL -(-181) -((|intermediateResultsIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{intermediateResultsIF(o)} returns a value corresponding to the required number of intermediate results required and,{} therefore,{} an indication of how much this would affect the step-length of the calculation. It returns a value in the range [0,{}1].")) (|accuracyIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{accuracyIF(o)} returns the intensity value of the accuracy requirements of the input ODE. A request of accuracy of 10^-6 corresponds to the neutral intensity. It returns a value in the range [0,{}1].")) (|expenseOfEvaluationIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{expenseOfEvaluationIF(o)} returns the intensity value of the cost of evaluating the input ODE. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].\\newline\\indent{20} 400 ``operation units\\spad{''} \\spad{->} 0.75 \\newline 200 ``operation units\\spad{''} \\spad{->} 0.5 \\newline 83 ``operation units\\spad{''} \\spad{->} 0.25 \\newline\\indent{15} exponentiation = 4 units ,{} function calls = 10 units.")) (|systemSizeIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{systemSizeIF(ode)} returns the intensity value of the size of the system of ODEs. 20 equations corresponds to the neutral value. It returns a value in the range [0,{}1].")) (|stiffnessAndStabilityOfODEIF| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityOfODEIF(ode)} calculates the intensity values of stiffness of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian). \\blankline It returns two values in the range [0,{}1].")) (|stiffnessAndStabilityFactor| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityFactor(me)} calculates the stability and stiffness factor of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian).")) (|eval| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Matrix| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{eval(mat,{}symbols,{}values)} evaluates a multivariable matrix at given \\spad{values} for each of a list of variables")) (|jacobian| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|))) "\\spad{jacobian(v,{}w)} is a local function to make a jacobian matrix")) (|sparsityIF| (((|Float|) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{sparsityIF(m)} calculates the sparsity of a jacobian matrix")) (|combineFeatureCompatibility| (((|Float|) (|Float|) (|List| (|Float|))) "\\spad{combineFeatureCompatibility(C1,{}L)} is for interacting attributes") (((|Float|) (|Float|) (|Float|)) "\\spad{combineFeatureCompatibility(C1,{}C2)} is for interacting attributes"))) NIL +(-193) NIL -(-182) NIL NIL +(-194) +((|constructor| (NIL "\\axiom{d01WeightsPackage} is a package for functions used to investigate whether a function can be divided into a simpler function and a weight function. The types of weights investigated are those giving rise to end-point singularities of the algebraico-logarithmic type,{} and trigonometric weights.")) (|exprHasLogarithmicWeights| (((|Integer|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasLogarithmicWeights} looks for logarithmic weights giving rise to singularities of the function at the end-points.")) (|exprHasAlgebraicWeight| (((|Union| (|List| (|DoubleFloat|)) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasAlgebraicWeight} looks for algebraic weights giving rise to singularities of the function at the end-points.")) (|exprHasWeightCosWXorSinWX| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |w| (|DoubleFloat|))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasWeightCosWXorSinWX} looks for trigonometric weights in an expression of the form \\axiom{cos \\omega \\spad{x}} or \\axiom{sin \\omega \\spad{x}},{} returning the value of \\omega (\\notequal 1) and the operator."))) NIL -(-183) NIL +(-195) +((|constructor| (NIL "\\axiom{d02AgentsPackage} contains a set of computational agents for use with Ordinary Differential Equation solvers.")) (|intermediateResultsIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{intermediateResultsIF(o)} returns a value corresponding to the required number of intermediate results required and,{} therefore,{} an indication of how much this would affect the step-length of the calculation. It returns a value in the range [0,{}1].")) (|accuracyIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{accuracyIF(o)} returns the intensity value of the accuracy requirements of the input ODE. A request of accuracy of 10^-6 corresponds to the neutral intensity. It returns a value in the range [0,{}1].")) (|expenseOfEvaluationIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{expenseOfEvaluationIF(o)} returns the intensity value of the cost of evaluating the input ODE. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].\\indent{20} 400 ``operation units\\spad{''} \\spad{->} 0.75 200 ``operation units\\spad{''} \\spad{->} 0.5 83 ``operation units\\spad{''} \\spad{->} 0.25 \\indent{15} exponentiation = 4 units ,{} function calls = 10 units.")) (|systemSizeIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{systemSizeIF(ode)} returns the intensity value of the size of the system of ODEs. 20 equations corresponds to the neutral value. It returns a value in the range [0,{}1].")) (|stiffnessAndStabilityOfODEIF| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityOfODEIF(ode)} calculates the intensity values of stiffness of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian). \\blankline It returns two values in the range [0,{}1].")) (|stiffnessAndStabilityFactor| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityFactor(me)} calculates the stability and stiffness factor of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian).")) (|eval| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Matrix| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{eval(mat,{}symbols,{}values)} evaluates a multivariable matrix at given \\spad{values} for each of a list of variables")) (|jacobian| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|))) "\\spad{jacobian(v,{}w)} is a local function to make a jacobian matrix")) (|sparsityIF| (((|Float|) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{sparsityIF(m)} calculates the sparsity of a jacobian matrix")) (|combineFeatureCompatibility| (((|Float|) (|Float|) (|List| (|Float|))) "\\spad{combineFeatureCompatibility(C1,{}L)} is for interacting attributes") (((|Float|) (|Float|) (|Float|)) "\\spad{combineFeatureCompatibility(C1,{}C2)} is for interacting attributes"))) NIL NIL -(-184) +(-196) +((|constructor| (NIL "\\axiomType{d02bbfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BBF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BBF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL +(-197) +((|constructor| (NIL "\\axiomType{d02bhfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BHF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BHF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL -(-185) NIL +(-198) +((|constructor| (NIL "\\axiomType{d02cjfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02CJF,{} a ODE routine which uses an Adams-Moulton-Bashworth method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02CJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-186) -((|elliptic?| (((|Boolean|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{elliptic?(r)} \\undocumented{}")) (|central?| (((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{central?(f,{}g,{}l)} \\undocumented{}")) (|subscriptedVariables| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{subscriptedVariables(e)} \\undocumented{}")) (|varList| (((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|)) "\\spad{varList(s,{}n)} \\undocumented{}"))) +(-199) +((|constructor| (NIL "\\axiomType{d02ejfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02EJF,{} a ODE routine which uses a backward differentiation formulae method to handle a stiff system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02EJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-187) +(-200) +((|constructor| (NIL "\\axiom{d03AgentsPackage} contains a set of computational agents for use with Partial Differential Equation solvers.")) (|elliptic?| (((|Boolean|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{elliptic?(r)} \\undocumented{}")) (|central?| (((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{central?(f,{}g,{}l)} \\undocumented{}")) (|subscriptedVariables| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{subscriptedVariables(e)} \\undocumented{}")) (|varList| (((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|)) "\\spad{varList(s,{}n)} \\undocumented{}"))) NIL NIL +(-201) +((|constructor| (NIL "\\axiomType{d03eefAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routines D03EEF/D03EDF."))) NIL -(-188) NIL +(-202) +((|constructor| (NIL "\\axiomType{d03fafAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routine D03FAF."))) NIL NIL -(-189 S) -((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) +(-203 S) +((|constructor| (NIL "This domain implements a simple view of a database whose fields are indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-190 -2958 UP UPUP R) +(-204 -1333 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-191 -2958 FP) -((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) +(-205 -1333 FP) +((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of u**(2**i) for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by separateDegrees and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL -(-192) +(-206) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-501) (QUOTE (-830))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-501) (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-134))) (|HasCategory| (-501) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-501) (QUOTE (-933))) (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-1046))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-501) (QUOTE (-206))) (|HasCategory| (-501) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-501) (LIST (QUOTE -476) (QUOTE (-1070)) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -278) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -256) (QUOTE (-501)) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-276))) (|HasCategory| (-501) (QUOTE (-500))) (|HasCategory| (-501) (QUOTE (-777))) (-1405 (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (QUOTE (-777)))) (|HasCategory| (-501) (LIST (QUOTE -577) (QUOTE (-501)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (|HasCategory| (-501) (QUOTE (-132))))) -(-193 R -2958) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-560) (QUOTE (-896))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-560) (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-148))) (|HasCategory| (-560) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-560) (QUOTE (-1013))) (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1128))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-221))) (|HasCategory| (-560) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-560) (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -276) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-296))) (|HasCategory| (-560) (QUOTE (-542))) (|HasCategory| (-560) (QUOTE (-834))) (-2318 (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (QUOTE (-834)))) (|HasCategory| (-560) (LIST (QUOTE -622) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (|HasCategory| (-560) (QUOTE (-146))))) +(-207 R -1333) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL -(-194 R) -((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) +(-208 R) +((|constructor| (NIL "Definite integration of rational functions. \\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL -(-195 R1 R2) -((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,{}n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) +(-209 R1 R2) +((|constructor| (NIL "This package has no description")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,{}n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) NIL NIL -(-196 S) -((|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-197 |CoefRing| |listIndVar|) +(-210 S) +((|constructor| (NIL "Linked list implementation of a Dequeue")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} member?(3,{}a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} count(4,{}a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} count(\\spad{x+}->(\\spad{x>2}),{}a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} any?(\\spad{x+}->(\\spad{x=4}),{}a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} every?(\\spad{x+}->(\\spad{x=4}),{}a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} b:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} map!(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|top!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} top! a \\spad{X} a")) (|reverse!| (($ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} reverse! a \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} push! a \\spad{X} a")) (|pop!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} pop! a \\spad{X} a")) (|insertTop!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} insertTop! a \\spad{X} a")) (|insertBottom!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} insertBottom! a \\spad{X} a")) (|extractTop!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} extractTop! a \\spad{X} a")) (|extractBottom!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} extractBottom! a \\spad{X} a")) (|bottom!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} bottom! a \\spad{X} a")) (|top| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} top a")) (|height| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} height a")) (|depth| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} depth a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} map(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} eq?(a,{}\\spad{b})")) (|copy| (($ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()\\$Dequeue(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()\\$(Dequeue INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,{}2,{}3,{}4,{}5])\\$Dequeue(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} size?(a,{}5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} more?(a,{}9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} less?(a,{}9)")) (|length| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} length a")) (|rotate!| (($ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} rotate! a")) (|back| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} back a")) (|front| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} front a")) (|inspect| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} insert! (8,{}a) \\spad{X} a")) (|enqueue!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} enqueue! (9,{}a) \\spad{X} a")) (|extract!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} extract! a \\spad{X} a")) (|dequeue!| ((|#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5] \\spad{X} dequeue! a \\spad{X} a")) (|dequeue| (($) "\\blankline \\spad{X} a:Dequeue INT:= dequeue ()") (($ (|List| |#1|)) "\\indented{1}{dequeue([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) creates a dequeue with first (top or front)} \\indented{1}{element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.} \\blankline \\spad{E} g:Dequeue INT:= dequeue [1,{}2,{}3,{}4,{}5]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-211 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4164 . T)) +((-4502 . T)) NIL -(-198 R -2958) +(-212 R -1333) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL -(-199) -((|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2391 . T) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-200) -((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) -NIL +(-213) +((|constructor| (NIL "\\spadtype{DoubleFloat} is intended to make accessible hardware floating point arithmetic in Axiom,{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spad{++} +,{} *,{} / and possibly also the sqrt operation. The operations exp,{} log,{} sin,{} cos,{} atan are normally coded in software based on minimax polynomial/rational approximations. \\blankline Some general comments about the accuracy of the operations: the operations +,{} *,{} / and sqrt are expected to be fully accurate. The operations exp,{} log,{} sin,{} cos and atan are not expected to be fully accurate. In particular,{} sin and cos will lose all precision for large arguments. \\blankline The Float domain provides an alternative to the DoubleFloat domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as erf,{} the error function in addition to the elementary functions. The disadvantage of Float is that it is much more expensive than small floats when the latter can be used.")) (|integerDecode| (((|List| (|Integer|)) $) "\\indented{1}{integerDecode(\\spad{x}) returns the multiple values of the\\space{2}common} \\indented{1}{lisp integer-decode-float function.} \\indented{1}{See Steele,{} ISBN 0-13-152414-3 \\spad{p354}. This function can be used} \\indented{1}{to ensure that the results are bit-exact and do not depend on} \\indented{1}{the binary-to-decimal conversions.} \\blankline \\spad{X} a:DFLOAT:=-1.0/3.0 \\spad{X} integerDecode a")) (|machineFraction| (((|Fraction| (|Integer|)) $) "\\indented{1}{machineFraction(\\spad{x}) returns a bit-exact fraction of the machine} \\indented{1}{floating point number using the common lisp integer-decode-float} \\indented{1}{function. See Steele,{} ISBN 0-13-152414-3 \\spad{p354}} \\indented{1}{This function can be used to print results which do not depend} \\indented{1}{on binary-to-decimal conversions} \\blankline \\spad{X} a:DFLOAT:=-1.0/3.0 \\spad{X} machineFraction a")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-2550 . T) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-201 A S) +(-214) +((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the second kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note that the default implementation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the second kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note that the default implementation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note that the default implementation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note that the default implementation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Ei6| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei6} is the first approximation of \\spad{Ei} where the result is \\spad{x*}\\%e^-x*Ei(\\spad{x}) from 32 to infinity (preserves digits)")) (|Ei5| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei5} is the first approximation of \\spad{Ei} where the result is \\spad{x*}\\%e^-x*Ei(\\spad{x}) from 12 to 32 (preserves digits)")) (|Ei4| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei4} is the first approximation of \\spad{Ei} where the result is \\spad{x*}\\%e^-x*Ei(\\spad{x}) from 4 to 12 (preserves digits)")) (|Ei3| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei3} is the first approximation of \\spad{Ei} where the result is (\\spad{Ei}(\\spad{x})-log \\spad{|x|} - gamma)\\spad{/x} from \\spad{-4} to 4 (preserves digits)")) (|Ei2| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei2} is the first approximation of \\spad{Ei} where the result is \\spad{x*}\\%e^-x*Ei(\\spad{x}) from \\spad{-10} to \\spad{-4} (preserves digits)")) (|Ei1| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei1} is the first approximation of \\spad{Ei} where the result is \\spad{x*}\\%e^-x*Ei(\\spad{x}) from -infinity to \\spad{-10} (preserves digits)")) (|Ei| (((|OnePointCompletion| (|DoubleFloat|)) (|OnePointCompletion| (|DoubleFloat|))) "\\spad{Ei} is the Exponential Integral function This is computed using a 6 part piecewise approximation. DoubleFloat can only preserve about 16 digits but the Chebyshev approximation used can give 30 digits.")) (|En| (((|OnePointCompletion| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|)) "\\spad{En(n,{}x)} is the \\spad{n}th Exponential Integral Function")) (E1 (((|OnePointCompletion| (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{E1(x)} is the Exponential Integral function The current implementation is a piecewise approximation involving one poly from \\spad{-4}..4 and a second poly for \\spad{x} > 4")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) NIL NIL +(-215 R) +((|constructor| (NIL "4x4 Matrices for coordinate transformations\\spad{\\br} This package contains functions to create 4x4 matrices useful for rotating and transforming coordinate systems. These matrices are useful for graphics and robotics. (Reference: Robot Manipulators Richard Paul MIT Press 1981) \\blankline A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:\\spad{\\br} \\tab{5}\\spad{nx ox ax px}\\spad{\\br} \\tab{5}\\spad{ny oy ay py}\\spad{\\br} \\tab{5}\\spad{nz oz az pz}\\spad{\\br} \\tab{5}\\spad{0 0 0 1}\\spad{\\br} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(x,{}y,{}z)} returns a dhmatrix for translation by \\spad{x},{} \\spad{y},{} and \\spad{z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{x},{} \\spad{y} and \\spad{z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{x} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4507 "*"))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359)))) +(-216 A S) +((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL -(-202 S) NIL -((-4168 . T) (-2951 . T)) +(-217 S) +((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) +((-4506 . T) (-2537 . T)) NIL -(-203 S R) +(-218 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206)))) -(-204 R) +((|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221)))) +(-219 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4164 . T)) +((-4502 . T)) NIL -(-205 S) -((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) +(-220 S) +((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\\spad{\\br} \\tab{5}\\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) NIL NIL -(-206) -((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4164 . T)) -NIL -(-207 A S) -((|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) +(-221) +((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\\spad{\\br} \\tab{5}\\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) +((-4502 . T)) NIL -((|HasAttribute| |#1| (QUOTE -4167))) -(-208 S) -((|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4168 . T) (-2951 . T)) +(-222 A S) +((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -(-209) -((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) +((|HasAttribute| |#1| (QUOTE -4505))) +(-223 S) +((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) +((-4506 . T) (-2537 . T)) NIL +(-224) +((|constructor| (NIL "Any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets:\\spad{\\br} \\tab{5}1. all minimal inhomogeneous solutions\\spad{\\br} \\tab{5}2. all minimal homogeneous solutions\\spad{\\br} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL -(-210 S -2742 R) -((* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-331))) (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (QUOTE (-775))) (|HasAttribute| |#3| (QUOTE -4164)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-336))) (|HasCategory| |#3| (QUOTE (-657))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-959))) (|HasCategory| |#3| (QUOTE (-1001)))) -(-211 -2742 R) -((* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4161 |has| |#2| (-959)) (-4162 |has| |#2| (-959)) (-4164 |has| |#2| (-6 -4164)) ((-4169 "*") |has| |#2| (-156)) (-4167 . T) (-2951 . T)) +(-225 S -2050 R) +((|constructor| (NIL "This category represents a finite cartesian product of a given type. Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -(-212 -2742 R) +((|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (QUOTE (-780))) (|HasCategory| |#3| (QUOTE (-832))) (|HasAttribute| |#3| (QUOTE -4502)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-364))) (|HasCategory| |#3| (QUOTE (-708))) (|HasCategory| |#3| (QUOTE (-137))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1082)))) +(-226 -2050 R) +((|constructor| (NIL "This category represents a finite cartesian product of a given type. Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) +((-4499 |has| |#2| (-1039)) (-4500 |has| |#2| (-1039)) (-4502 |has| |#2| (-6 -4502)) ((-4507 "*") |has| |#2| (-170)) (-4505 . T) (-2537 . T)) NIL -((-4161 |has| |#2| (-959)) (-4162 |has| |#2| (-959)) (-4164 |has| |#2| (-6 -4164)) ((-4169 "*") |has| |#2| (-156)) (-4167 . T)) -((|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-775))) (-1405 (|HasCategory| |#2| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-775)))) (|HasCategory| |#2| (QUOTE (-156))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-959)))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-331)))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-959)))) (|HasCategory| |#2| (QUOTE (-336))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206))) (-1405 (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-206))) (|HasCategory| |#2| (QUOTE (-331))) 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(|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1082))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-170)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-221)))) (-12 (|HasCategory| |#2| (LIST (QUOTE 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL NIL -(-215 S) +(-230 S) +((|constructor| (NIL "This category exports the function for domains")) (|divOfPole| (($ $) "\\spad{divOfPole(d)} returns the negative part of \\spad{d}.")) (|divOfZero| (($ $) "\\spad{divOfZero(d)} returns the positive part of \\spad{d}.")) (|suppOfPole| (((|List| |#1|) $) "suppOfZero(\\spad{d}) returns the elements of the support of \\spad{d} that have a negative coefficient.")) (|suppOfZero| (((|List| |#1|) $) "\\spad{suppOfZero(d)} returns the elements of the support of \\spad{d} that have a positive coefficient.")) (|supp| (((|List| |#1|) $) "\\spad{supp(d)} returns the support of the divisor \\spad{d}.")) (|effective?| (((|Boolean|) $) "\\spad{effective?(d)} returns \\spad{true} if \\spad{d} \\spad{>=} 0.")) (|concat| (($ $ $) "\\spad{concat(a,{}b)} concats the divisor a and \\spad{b} without collecting the duplicative points.")) (|collect| (($ $) "\\spad{collect collects} the duplicative points in the divisor.")) (|split| (((|List| $) $) "\\spad{split(d)} splits the divisor \\spad{d}. For example,{} split( 2 \\spad{p1} + 3p2 ) returns the list [ 2 \\spad{p1},{} 3 \\spad{p2} ].")) (|degree| (((|Integer|) $) "\\spad{degree(d)} returns the degree of the divisor \\spad{d}"))) +((-4500 . T) (-4499 . T)) +NIL +(-231 S) +((|constructor| (NIL "The following is part of the PAFF package"))) +((-4500 . T) (-4499 . T)) +((|HasCategory| (-560) (QUOTE (-779)))) +(-232 S) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) NIL NIL -(-216) +(-233) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4160 . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-217 S) -((|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2951 . T)) +(-234 S) +((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note that \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note that \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) +((-2537 . T)) NIL -(-218 S) +(-235 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-219 M) -((|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-236 M) +((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note that this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL -(-220 |vl| R) -((|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4169 "*") |has| |#2| (-156)) (-4160 |has| |#2| (-508)) (-4165 |has| |#2| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . 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(|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) 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(|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-1153))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-170)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-221)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-359)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-364)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-708)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-780)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-832)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))))) +(-240 A R S V E) +((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates.")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note that an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note that In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note that In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL -((|HasCategory| |#2| (QUOTE (-206)))) -(-224 R S V E) -((|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-221)))) +(-241 R S V E) +((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates.")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note that an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note that In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note that In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-225 S) -((|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-242 S) +((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note that \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-226 |Ex|) -((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) -NIL -NIL -(-227) +(-243) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-228 R |Ex|) +(-244 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-229) -((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) -NIL -NIL -(-230 R) -((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) -NIL +(-245) +((|constructor| (NIL "\\axiomType{DrawComplex} provides some facilities for drawing complex functions.")) (|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel. Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value. Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL -(-231) -((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL +(-246 R) +((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}. Note that this package is meant for internal use only.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) NIL -(-232) -((|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) NIL +(-247 |Ex|) +((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL -(-233) -((|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL +(-248) +((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{x} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL -(-234 S) -((|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL +(-249) +((|constructor| (NIL "This package has no description")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) NIL -(-235 R S V) NIL -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#3| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#3| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#3| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#3| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#1| (QUOTE -4165)) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-236 A S) -((|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) +(-250 S) +((|constructor| (NIL "This package has no description")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) NIL NIL -(-237 S) -((|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) +(-251) +((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) NIL NIL -(-238) -((|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,{}n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\axiom{\\spad{l}}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,{}n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,{}b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}."))) +(-252 R S V) +((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#3| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#3| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#3| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-253 S) +((|tree| (($ (|List| |#1|)) "\\spad{tree(l)} creates a chain tree from the list \\spad{l}") (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL +(-254 S) +((|constructor| (NIL "This category is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(\\spad{b}).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when \\spad{true},{} a coerce to OutputForm yields the full output of \\spad{tr},{} otherwise encode(\\spad{tr}) is output (see encode function). The default is \\spad{false}.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput).")) (|encode| (((|String|) $) "\\spad{encode(t)} returns a string indicating the \"shape\" of the tree"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-255 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +((|constructor| (NIL "\\indented{1}{The following is all the categories,{} domains and package} used for the desingularisation be means of monoidal transformation (Blowing-up)")) (|genusTreeNeg| (((|Integer|) (|NonNegativeInteger|) (|List| |#10|)) "\\spad{genusTreeNeg(n,{}listOfTrees)} computes the \"genus\" of a curve that may be not absolutly irreducible,{} where \\spad{n} is the degree of a polynomial pol defining the curve and \\spad{listOfTrees} is all the desingularisation trees at all singular points on the curve defined by pol. A \"negative\" genus means that the curve is reducible \\spad{!!}.")) (|genusTree| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|List| |#10|)) "\\spad{genusTree(n,{}listOfTrees)} computes the genus of a curve,{} where \\spad{n} is the degree of a polynomial pol defining the curve and \\spad{listOfTrees} is all the desingularisation trees at all singular points on the curve defined by pol.")) (|genusNeg| (((|Integer|) |#3|) "\\spad{genusNeg(pol)} computes the \"genus\" of a curve that may be not absolutly irreducible. A \"negative\" genus means that the curve is reducible \\spad{!!}.")) (|genus| (((|NonNegativeInteger|) |#3|) "\\spad{genus(pol)} computes the genus of the curve defined by \\spad{pol}.")) (|initializeParamOfPlaces| (((|Void|) |#10| (|List| |#3|)) "initParLocLeaves(\\spad{tr},{}listOfFnc) initialize the local parametrization at places corresponding to the leaves of \\spad{tr} according to the given list of functions in listOfFnc.") (((|Void|) |#10|) "initParLocLeaves(\\spad{tr}) initialize the local parametrization at places corresponding to the leaves of \\spad{tr}.")) (|initParLocLeaves| (((|Void|) |#10|) "\\spad{initParLocLeaves(tr)} initialize the local parametrization at simple points corresponding to the leaves of \\spad{tr}.")) (|fullParamInit| (((|Void|) |#10|) "\\spad{fullParamInit(tr)} initialize the local parametrization at all places (leaves of \\spad{tr}),{} computes the local exceptional divisor at each infinytly close points in the tree. This function is equivalent to the following called: initParLocLeaves(\\spad{tr}) initializeParamOfPlaces(\\spad{tr}) blowUpWithExcpDiv(\\spad{tr})")) (|desingTree| (((|List| |#10|) |#3|) "\\spad{desingTree(pol)} returns all the desingularisation trees of all singular points on the curve defined by \\spad{pol}.")) (|desingTreeAtPoint| ((|#10| |#5| |#3|) "\\spad{desingTreeAtPoint(pt,{}pol)} computes the desingularisation tree at the point \\spad{pt} on the curve defined by \\spad{pol}. This function recursively compute the tree.")) (|adjunctionDivisor| ((|#8| |#10|) "\\spad{adjunctionDivisor(tr)} compute the local adjunction divisor of a desingularisation tree \\spad{tr} of a singular point.")) (|divisorAtDesingTree| ((|#8| |#3| |#10|) "\\spad{divisorAtDesingTree(f,{}tr)} computes the local divisor of \\spad{f} at a desingularisation tree \\spad{tr} of a singular point."))) NIL -(-239) NIL +(-256 A S) +((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note that in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL -(-240) +(-257 S) +((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note that in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL +(-258) +((|constructor| (NIL "\\axiomType{e04AgentsPackage} is a package of numerical agents to be used to investigate attributes of an input function so as to decide the \\axiomFun{measure} of an appropriate numerical optimization routine.")) (|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,{}n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\spad{l}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,{}n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,{}b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}."))) NIL -(-241) NIL +(-259) +((|constructor| (NIL "\\axiomType{e04dgfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04DGF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04DGF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-242) +(-260) +((|constructor| (NIL "\\axiomType{e04fdfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04FDF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04FDF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL +(-261) +((|constructor| (NIL "\\axiomType{e04gcfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04GCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04GCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL -(-243) NIL +(-262) +((|constructor| (NIL "\\axiomType{e04jafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04JAF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04JAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-244) +(-263) +((|constructor| (NIL "\\axiomType{e04mbfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04MBF,{} an optimization routine for Linear functions. The function \\axiomFun{measure} measures the usefulness of the routine E04MBF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL +(-264) +((|constructor| (NIL "\\axiomType{e04nafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04NAF,{} an optimization routine for Quadratic functions. The function \\axiomFun{measure} measures the usefulness of the routine E04NAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL -(-245) NIL +(-265) +((|constructor| (NIL "\\axiomType{e04ucfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04UCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04UCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-246) +(-266) ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-247 R -2958) +(-267 R -1333) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-248 R -2958) +(-268 R -1333) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL -(-249 |Coef| UTS ULS) -((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) +(-269 |Coef| UTS ULS) +((|constructor| (NIL "This package provides elementary functions on any Laurent series domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-331)))) -(-250 |Coef| ULS UPXS EFULS) -((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) +((|HasCategory| |#1| (QUOTE (-359)))) +(-270 |Coef| ULS UPXS EFULS) +((|constructor| (NIL "This package provides elementary functions on any Laurent series domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-331)))) -(-251 A S) -((|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) +((|HasCategory| |#1| (QUOTE (-359)))) +(-271 A S) +((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\indented{1}{delete!(\\spad{u},{}\\spad{i}) destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.} \\blankline \\spad{E} Data:=Record(age:Integer,{}gender:String) \\spad{E} a1:AssociationList(String,{}Data):=table() \\spad{E} \\spad{a1}.\"tim\":=[55,{}\"male\"]\\$Data \\spad{E} delete!(\\spad{a1},{}1)")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001)))) -(-252 S) -((|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4168 . T) (-2951 . T)) +((|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082)))) +(-272 S) +((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\indented{1}{delete!(\\spad{u},{}\\spad{i}) destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.} \\blankline \\spad{E} Data:=Record(age:Integer,{}gender:String) \\spad{E} a1:AssociationList(String,{}Data):=table() \\spad{E} \\spad{a1}.\"tim\":=[55,{}\"male\"]\\$Data \\spad{E} delete!(\\spad{a1},{}1)")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) +((-4506 . T) (-2537 . T)) NIL -(-253 S) +(-273 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-254) +(-274) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) NIL NIL -(-255 |Coef| UTS) +(-275 |Coef| UTS) ((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,{}c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,{}k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,{}k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,{}k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) NIL NIL -(-256 S |Index|) -((|elt| ((|#2| $ |#1|) "\\spad{elt(u,{}i)} (also written: \\spad{u} . \\spad{i}) returns the element of \\spad{u} indexed by \\spad{i}. Error: if \\spad{i} is not an index of \\spad{u}."))) +(-276 S |Index|) +((|constructor| (NIL "An eltable over domains \\spad{D} and \\spad{I} is a structure which can be viewed as a function from \\spad{D} to \\spad{I}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures like \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,{}i)} (also written: \\spad{u} . \\spad{i}) returns the element of \\spad{u} indexed by \\spad{i}. Error: if \\spad{i} is not an index of \\spad{u}."))) NIL NIL -(-257 S |Dom| |Im|) -((|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) +(-277 S |Dom| |Im|) +((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain Dom to an image domain Im.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4168))) -(-258 |Dom| |Im|) -((|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) +((|HasAttribute| |#1| (QUOTE -4506))) +(-278 |Dom| |Im|) +((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain Dom to an image domain Im.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-259 S R |Mod| -3220 -3216 |exactQuo|) -((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-279 S R |Mod| -2512 -2492 |exactQuo|) +((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} is not documented")) (|inv| (($ $) "\\spad{inv(x)} is not documented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} is not documented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} is not documented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} is not documented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} is not documented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} is not documented"))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-260) -((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4160 . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-280) +((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{ab=0 => a=0 or b=0} \\spad{--} known as noZeroDivisors\\spad{\\br} \\tab{5}\\spad{not(1=0)}")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) +((-4498 . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-261 R) +(-281 R) ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-262 S) -((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4164 -1405 (|has| |#1| (-959)) (|has| |#1| (-440))) (-4161 |has| |#1| (-959)) (-4162 |has| |#1| (-959))) -((|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-267))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-440)))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331)))) (|HasCategory| |#1| (QUOTE (-657))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-657)))) (|HasCategory| |#1| (QUOTE (-1012))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-21))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-657)))) (|HasCategory| |#1| (QUOTE (-25))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-263 S R) +(-282 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL -(-264 |Key| |Entry|) +(-283 S) +((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) +((-4502 -2318 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4499 |has| |#1| (-1039)) (-4500 |has| |#1| (-1039))) +((|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-291))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-471)))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-708))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-708)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-21))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-708)))) (|HasCategory| |#1| (QUOTE (-25))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-284 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001))))) -(-265) -((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082))))) +(-285) +((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function\\spad{\\br} \\tab{5}\\spad{f x == if x < 0 then error \"negative argument\" else x}\\spad{\\br} the call to error will actually be of the form\\spad{\\br} \\tab{5}\\spad{error(\"f\",{}\"negative argument\")}\\spad{\\br} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them):\\spad{\\br} \\spad{\\%l}\\tab{6}start a new line\\spad{\\br} \\spad{\\%b}\\tab{6}start printing in a bold font (where available)\\spad{\\br} \\spad{\\%d}\\tab{6}stop printing in a bold font (where available)\\spad{\\br} \\spad{\\%ceon}\\tab{3}start centering message lines\\spad{\\br} \\spad{\\%ceoff}\\tab{2}stop centering message lines\\spad{\\br} \\spad{\\%rjon}\\tab{3}start displaying lines \"ragged left\"\\spad{\\br} \\spad{\\%rjoff}\\tab{2}stop displaying lines \"ragged left\"\\spad{\\br} \\spad{\\%i}\\tab{6}indent following lines 3 additional spaces\\spad{\\br} \\spad{\\%u}\\tab{6}unindent following lines 3 additional spaces\\spad{\\br} \\spad{\\%xN}\\tab{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks) \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-266 S) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) +(-286 -1333 S) +((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) -(-267) -((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL +(-287 E -1333) +((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL -(-268 -2958 S) -((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL +(-288 A B) +((|constructor| (NIL "\\spad{ExpertSystemContinuityPackage1} exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) NIL -(-269 E -2958) -((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL +(-289) +((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) NIL -(-270) -((|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) NIL +(-290 S) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -(-271 A B) -((|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) +((|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) +(-291) +((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-272) -((|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) +(-292 R1) +((|constructor| (NIL "\\axiom{\\spad{ExpertSystemToolsPackage1}} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) NIL NIL -(-273 R1) -((|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) +(-293 R1 R2) +((|constructor| (NIL "\\axiom{\\spad{ExpertSystemToolsPackage2}} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping \\spad{f:R1} \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) NIL NIL -(-274 R1 R2) -((|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping \\spad{f:R1} \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) +(-294) +((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) NIL NIL -(-275 S) -((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) +(-295 S) +((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes\\spad{\\br} \\tab{5}multiplicativeValuation\\tab{5}Size(a*b)=Size(a)*Size(\\spad{b})\\spad{\\br} \\tab{5}additiveValuation\\tab{11}Size(a*b)=Size(a)+Size(\\spad{b})")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL NIL -(-276) -((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-296) +((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes\\spad{\\br} \\tab{5}multiplicativeValuation\\tab{5}Size(a*b)=Size(a)*Size(\\spad{b})\\spad{\\br} \\tab{5}additiveValuation\\tab{11}Size(a*b)=Size(a)+Size(\\spad{b})")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-277 S R) +(-297 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-278 R) +(-298 R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-279 -2958) -((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) +(-299 -1333) +((|constructor| (NIL "This package is to be used in conjuction with the CycleIndicators package. It provides an evaluation function for SymmetricPolynomials.")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL -(-280) -((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) +(-300) +((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note that It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL -(-281 R FE |var| |cen|) +(-301 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-750))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-1046))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-206))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -476) (QUOTE (-1070)) (LIST (QUOTE -1136) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -278) (LIST (QUOTE -1136) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (LIST (QUOTE -256) (LIST (QUOTE -1136) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1136) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-276))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-500))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-777))) (-1405 (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-750))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-777)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-830)))) (|HasCategory| (-1136 |#1| |#2| |#3| |#4|) (QUOTE (-132))))) -(-282 R) -((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4164 -1405 (-1280 (|has| |#1| (-959)) (|has| |#1| (-577 (-501)))) (-12 (|has| |#1| (-508)) (-1405 (-1280 (|has| |#1| (-959)) (|has| |#1| (-577 (-501)))) (|has| |#1| (-959)) (|has| |#1| (-440)))) (|has| |#1| (-959)) (|has| |#1| (-440))) (-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) ((-4169 "*") |has| |#1| (-508)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-508)) (-4159 |has| |#1| (-508))) -((|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-959))) (-1405 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-959)))) (-12 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-21))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-21)))) (|HasCategory| |#1| (QUOTE (-25))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-959)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-25)))) (|HasCategory| |#1| (QUOTE (-1012))) (-1405 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#1| (QUOTE (-1012)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-1012)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-959)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))))) (|HasCategory| $ (QUOTE (-959))) (|HasCategory| $ (LIST (QUOTE -950) (QUOTE (-501))))) -(-283 R S) -((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-896))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-1013))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-807))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-1128))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-221))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -515) (QUOTE (-1153)) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -298) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (LIST (QUOTE -276) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1221) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-296))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-542))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-834))) (-2318 (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-807))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-834)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-896)))) (|HasCategory| (-1221 |#1| |#2| |#3| |#4|) (QUOTE (-146))))) +(-302 R S) +((|constructor| (NIL "Lifting of maps to Expressions.")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) +NIL +NIL +(-303 R FE) +((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-284 R FE) -((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) +(-304 R) +((|constructor| (NIL "Top-level mathematical expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} is not documented")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} is not documented")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) is not documented")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) +((-4502 -2318 (-2256 (|has| |#1| (-1039)) (|has| |#1| (-622 (-560)))) (-12 (|has| |#1| (-550)) (-2318 (-2256 (|has| |#1| (-1039)) (|has| |#1| (-622 (-560)))) (|has| |#1| (-1039)) (|has| |#1| (-471)))) (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) ((-4507 "*") |has| |#1| (-550)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-550)) (-4497 |has| |#1| (-550))) +((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-1039))) (-2318 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-21))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-21)))) (|HasCategory| |#1| (QUOTE (-25))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-1039)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-25)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2318 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1029) (QUOTE (-560))))) +(-305 R -1333) +((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "seriesSolve([\\spad{eq1},{}...,{}eqn],{} [\\spad{y1},{}...,{}\\spad{yn}],{} \\spad{x} = a,{}[\\spad{y1} a = \\spad{b1},{}...,{} \\spad{yn} a = \\spad{bn}]) is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note that eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note that \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL -(-285 R -2958) -((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) +(-306 R -1333 UTSF UTSSUPF) +((|constructor| (NIL "This package has no description"))) NIL NIL -(-286) -((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) +(-307) +((|constructor| (NIL "Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) NIL NIL -(-287 FE |var| |cen|) +(-308 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|))))) (|HasCategory| (-375 (-501)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-288 M) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasCategory| (-403 (-560)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-309 K) +((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) +NIL +NIL +(-310 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL NIL -(-289 E OV R P) +(-311 K) +((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) +NIL +NIL +(-312 E OV R P) ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between \\spad{-k} and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,{}i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly,{} lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly,{} lvar,{} lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}."))) NIL NIL -(-290 S) +(-313 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| (-501) (QUOTE (-722)))) -(-291 S E) -((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\spad{\\^}\\spad{e1} ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) +((-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-560) (QUOTE (-779)))) +(-314 S E) +((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\indented{1}{size(\\spad{x}) returns the number of terms in \\spad{x}.} \\indented{1}{mapGen(\\spad{f},{} \\spad{a1}\\spad{\\^}\\spad{e1} ... an\\spad{\\^}en) returns} \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL NIL -(-292 S) +(-315 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-701) (QUOTE (-722)))) -(-293 S R E) +((|HasCategory| (-755) (QUOTE (-779)))) +(-316 E R1 A1 R2 A2) +((|constructor| (NIL "This package provides a mapping function for \\spadtype{FiniteAbelianMonoidRing} The packages defined in this file provide fast fraction free rational interpolation algorithms. (see \\spad{FAMR2},{} FFFG,{} FFFGF,{} NEWTON)")) (|map| ((|#5| (|Mapping| |#4| |#2|) |#3|) "\\spad{map}(\\spad{f},{} a) applies the map \\spad{f} to each coefficient in a. It is assumed that \\spad{f} maps 0 to 0"))) +NIL +NIL +(-317 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156)))) -(-294 R E) +((|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170)))) +(-318 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-295 S) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-296 S -2958) -((|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) +(-319 S) +((|constructor| (NIL "A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a} \\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-320 S -1333) +((|constructor| (NIL "FiniteAlgebraicExtensionField \\spad{F} is the category of fields which are finite algebraic extensions of the field \\spad{F}. If \\spad{F} is finite then any finite algebraic extension of \\spad{F} is finite,{} too. Let \\spad{K} be a finite algebraic extension of the finite field \\spad{F}. The exponentiation of elements of \\spad{K} defines a \\spad{Z}-module structure on the multiplicative group of \\spad{K}. The additive group of \\spad{K} becomes a module over the ring of polynomials over \\spad{F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over \\spad{F},{} \\spadignore{i.e.} for elements a from \\spad{K},{} \\spad{c},{}\\spad{d} from \\spad{F} and \\spad{f},{}\\spad{g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from \\spad{F}[\\spad{X}]: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is a**(q**k) where q=size()\\spad{\\$}\\spad{F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial \\spad{g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals a. If there is no such polynomial \\spad{g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial \\spad{g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals a.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial \\spad{g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over \\spad{F},{} \\spadignore{i.e.} for elements a from \\spad{\\$},{} \\spad{c},{}\\spad{d} form \\spad{F} and \\spad{f},{}\\spad{g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from \\spad{F}[\\spad{X}]: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is a**(q**k),{} where q=size()\\spad{\\$}\\spad{F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note that \\spad{trace(a,{}d)=reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note that norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL -((|HasCategory| |#2| (QUOTE (-336)))) -(-297 -2958) -((|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-364)))) +(-321 -1333) +((|constructor| (NIL "FiniteAlgebraicExtensionField \\spad{F} is the category of fields which are finite algebraic extensions of the field \\spad{F}. If \\spad{F} is finite then any finite algebraic extension of \\spad{F} is finite,{} too. Let \\spad{K} be a finite algebraic extension of the finite field \\spad{F}. The exponentiation of elements of \\spad{K} defines a \\spad{Z}-module structure on the multiplicative group of \\spad{K}. The additive group of \\spad{K} becomes a module over the ring of polynomials over \\spad{F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over \\spad{F},{} \\spadignore{i.e.} for elements a from \\spad{K},{} \\spad{c},{}\\spad{d} from \\spad{F} and \\spad{f},{}\\spad{g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from \\spad{F}[\\spad{X}]: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is a**(q**k) where q=size()\\spad{\\$}\\spad{F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial \\spad{g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals a. If there is no such polynomial \\spad{g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial \\spad{g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals a.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial \\spad{g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over \\spad{F},{} \\spadignore{i.e.} for elements a from \\spad{\\$},{} \\spad{c},{}\\spad{d} form \\spad{F} and \\spad{f},{}\\spad{g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from \\spad{F}[\\spad{X}]: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is a**(q**k),{} where q=size()\\spad{\\$}\\spad{F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note that \\spad{trace(a,{}d)=reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note that norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-298) +(-322) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) NIL NIL -(-299 E) -((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) +(-323 E) +((|constructor| (NIL "This domain creates kernels for use in Fourier series")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) NIL NIL -(-300) +(-324) ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables \\spad{I1},{} \\spad{I2},{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} \\spad{I1} and \\spad{I2}")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}"))) NIL NIL -(-301 -2958 UP UPUP R) -((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) -NIL -NIL -(-302 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) -((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) +(-325 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((|constructor| (NIL "Lift a map to finite divisors.")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-303 S -2958 UP UPUP R) +(-326 S -1333 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-304 -2958 UP UPUP R) +(-327 -1333 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-305 S R) +(-328 -1333 UP UPUP R) +((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over \\spad{K}[\\spad{x}]."))) +NIL +NIL +(-329 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -256) (|devaluate| |#2|) (|devaluate| |#2|)))) -(-306 R) +((|HasCategory| |#2| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -276) (|devaluate| |#2|) (|devaluate| |#2|)))) +(-330 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL -(-307 |basicSymbols| |subscriptedSymbols| R) -((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#3| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#3| (LIST (QUOTE -950) (QUOTE (-346)))) (|HasCategory| $ (QUOTE (-959))) (|HasCategory| $ (LIST (QUOTE -950) (QUOTE (-501))))) -(-308 |p| |n|) -((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-826 |#1|) (QUOTE (-134))) (|HasCategory| (-826 |#1|) (QUOTE (-336))) (|HasCategory| (-826 |#1|) (QUOTE (-132))) (-1405 (|HasCategory| (-826 |#1|) (QUOTE (-132))) (|HasCategory| (-826 |#1|) (QUOTE (-336))))) -(-309 S -2958 UP UPUP) -((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) +(-331 |basicSymbols| |subscriptedSymbols| R) +((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function \\spad{LOG10}")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} is not documented")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it is one of the given basic symbols or subscripted symbols which correspond to scalar and array parameters respectively.") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it is one of the given basic symbols or subscripted symbols which correspond to scalar and array parameters respectively.") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression checking that it contains no non-Fortran functions,{} and that it only contains the given basic symbols and subscripted symbols which correspond to scalar and array parameters respectively."))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#3| (LIST (QUOTE -1029) (QUOTE (-375)))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1029) (QUOTE (-560))))) +(-332 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL -((|HasCategory| |#2| (QUOTE (-336))) (|HasCategory| |#2| (QUOTE (-331)))) -(-310 -2958 UP UPUP) -((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4160 |has| (-375 |#2|) (-331)) (-4165 |has| (-375 |#2|) (-331)) (-4159 |has| (-375 |#2|) (-331)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) NIL -(-311 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) -((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) +(-333 S -1333 UP UPUP) +((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\indented{1}{rationalPoints() returns the list of all the affine} rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\indented{1}{inverseIntegralMatrixAtInfinity() returns \\spad{M} such} \\indented{1}{that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} inverseIntegralMatrixAtInfinity()\\$\\spad{R}")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\indented{1}{integralMatrixAtInfinity() returns \\spad{M} such that} \\indented{1}{\\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralMatrixAtInfinity()\\$\\spad{R}")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\indented{1}{inverseIntegralMatrix() returns \\spad{M} such that} \\indented{1}{\\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(w1,{}...,{}wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} inverseIntegralMatrix()\\$\\spad{R}")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\indented{1}{integralMatrix() returns \\spad{M} such that} \\indented{1}{\\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{}} \\indented{1}{where \\spad{(w1,{}...,{}wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralMatrix()\\$\\spad{R}")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\indented{1}{integralBasisAtInfinity() returns the local integral basis} \\indented{1}{at infinity} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralBasisAtInfinity()\\$\\spad{R}")) (|integralBasis| (((|Vector| $)) "\\indented{1}{integralBasis() returns the integral basis for the curve.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralBasis()\\$\\spad{R}")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\indented{1}{branchPointAtInfinity?() tests if there is a branch point} \\indented{1}{at infinity.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} branchPointAtInfinity?()\\$\\spad{R} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} branchPointAtInfinity?()\\$\\spad{R}")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\indented{1}{rationalPoint?(a,{} \\spad{b}) tests if \\spad{(x=a,{}y=b)} is on the curve.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} rationalPoint?(0,{}0)\\$\\spad{R} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} rationalPoint?(0,{}0)\\$\\spad{R2}")) (|absolutelyIrreducible?| (((|Boolean|)) "\\indented{1}{absolutelyIrreducible?() tests if the curve absolutely irreducible?} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} absolutelyIrreducible?()\\$\\spad{R2}")) (|genus| (((|NonNegativeInteger|)) "\\indented{1}{genus() returns the genus of one absolutely irreducible component} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} genus()\\$\\spad{R}")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\indented{1}{numberOfComponents() returns the number of absolutely irreducible} \\indented{1}{components.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} numberOfComponents()\\$\\spad{R}"))) +NIL +((|HasCategory| |#2| (QUOTE (-364))) (|HasCategory| |#2| (QUOTE (-359)))) +(-334 -1333 UP UPUP) +((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\indented{1}{rationalPoints() returns the list of all the affine} rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\indented{1}{inverseIntegralMatrixAtInfinity() returns \\spad{M} such} \\indented{1}{that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} inverseIntegralMatrixAtInfinity()\\$\\spad{R}")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\indented{1}{integralMatrixAtInfinity() returns \\spad{M} such that} \\indented{1}{\\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralMatrixAtInfinity()\\$\\spad{R}")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\indented{1}{inverseIntegralMatrix() returns \\spad{M} such that} \\indented{1}{\\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))}} \\indented{1}{where \\spad{(w1,{}...,{}wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} inverseIntegralMatrix()\\$\\spad{R}")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\indented{1}{integralMatrix() returns \\spad{M} such that} \\indented{1}{\\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{}} \\indented{1}{where \\spad{(w1,{}...,{}wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralMatrix()\\$\\spad{R}")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\indented{1}{integralBasisAtInfinity() returns the local integral basis} \\indented{1}{at infinity} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralBasisAtInfinity()\\$\\spad{R}")) (|integralBasis| (((|Vector| $)) "\\indented{1}{integralBasis() returns the integral basis for the curve.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} integralBasis()\\$\\spad{R}")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\indented{1}{branchPointAtInfinity?() tests if there is a branch point} \\indented{1}{at infinity.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} branchPointAtInfinity?()\\$\\spad{R} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} branchPointAtInfinity?()\\$\\spad{R}")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\indented{1}{rationalPoint?(a,{} \\spad{b}) tests if \\spad{(x=a,{}y=b)} is on the curve.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} rationalPoint?(0,{}0)\\$\\spad{R} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} rationalPoint?(0,{}0)\\$\\spad{R2}")) (|absolutelyIrreducible?| (((|Boolean|)) "\\indented{1}{absolutelyIrreducible?() tests if the curve absolutely irreducible?} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 2 * \\spad{x**2},{} 4) \\spad{X} absolutelyIrreducible?()\\$\\spad{R2}")) (|genus| (((|NonNegativeInteger|)) "\\indented{1}{genus() returns the genus of one absolutely irreducible component} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} genus()\\$\\spad{R}")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\indented{1}{numberOfComponents() returns the number of absolutely irreducible} \\indented{1}{components.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(\\spad{x},{} Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(\\spad{y},{} Fraction \\spad{P0}) \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT,{} \\spad{P0},{} \\spad{P1},{} 1 - \\spad{x**20},{} 20) \\spad{X} numberOfComponents()\\$\\spad{R}"))) +((-4498 |has| (-403 |#2|) (-359)) (-4503 |has| (-403 |#2|) (-359)) (-4497 |has| (-403 |#2|) (-359)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-335 |p| |extdeg|) +((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by createPrimitivePoly from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-897 |#1|) (QUOTE (-148))) (|HasCategory| (-897 |#1|) (QUOTE (-364))) (|HasCategory| (-897 |#1|) (QUOTE (-146))) (-2318 (|HasCategory| (-897 |#1|) (QUOTE (-146))) (|HasCategory| (-897 |#1|) (QUOTE (-364))))) +(-336 GF |defpol|) +((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field \\spad{GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial defpol,{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-337 GF |extdeg|) +((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field \\spad{GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by createPrimitivePoly from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-338 K |PolK|) +((|constructor| (NIL "Part of the package for Algebraic Function Fields in one variable (\\spad{PAFF}) It has been modified (very slitely) so that each time the \"factor\" function is used,{} the variable related to the size of the field over which the polynomial is factorized is reset. This is done in order to be used with a \"dynamic extension field\" which size is not fixed but set before calling the \"factor\" function and which is parse by side effect to this package via the function \"size\". See the local function \"initialize\" of this package."))) +NIL NIL +(-339 -2500 V VF) +((|constructor| (NIL "This package lifts the interpolation functions from \\spadtype{FractionFreeFastGaussian} to fractions. The packages defined in this file provide fast fraction free rational interpolation algorithms. (see \\spad{FAMR2},{} FFFG,{} FFFGF,{} NEWTON)")) (|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalInterpolation(l,{} CA,{} f,{} sumEta,{} maxEta)} applies generalInterpolation(\\spad{l},{} \\spad{CA},{} \\spad{f},{} eta) for all possible eta with maximal entry maxEta and sum of entries \\spad{sumEta}") (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{generalInterpolation(l,{} CA,{} f,{} eta)} performs Hermite-Pade approximation using the given action \\spad{CA} of polynomials on the elements of \\spad{f}. The result is guaranteed to be correct up to order |eta|-1. Given that eta is a \"normal\" point,{} the degrees on the diagonal are given by eta. The degrees of column \\spad{i} are in this case eta + \\spad{e}.\\spad{i} - [1,{}1,{}...,{}1],{} where the degree of zero is \\spad{-1}."))) NIL -(-312 |p| |extdeg|) -((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-826 |#1|) (QUOTE (-134))) (|HasCategory| (-826 |#1|) (QUOTE (-336))) (|HasCategory| (-826 |#1|) (QUOTE (-132))) (-1405 (|HasCategory| (-826 |#1|) (QUOTE (-132))) (|HasCategory| (-826 |#1|) (QUOTE (-336))))) -(-313 GF |defpol|) -((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-314 GF |extdeg|) -((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-315 GF) -((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL +(-340 -2500 V) +((|constructor| (NIL "This package implements the interpolation algorithm proposed in Beckermann,{} Bernhard and Labahn,{} George,{} Fraction-free computation of matrix rational interpolants and matrix GCDs,{} SIAM Journal on Matrix Analysis and Applications 22. The packages defined in this file provide fast fraction free rational interpolation algorithms. (see \\spad{FAMR2},{} FFFG,{} FFFGF,{} NEWTON)")) (|qShiftC| (((|List| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{qShiftC} gives the coefficients \\spad{c_}{\\spad{k},{}\\spad{k}} in the expansion \\spad{z} \\spad{g}(\\spad{x}) = sum_{\\spad{i=0}}\\spad{^k} \\spad{c_}{\\spad{k},{}\\spad{i}} \\spad{g}(\\spad{x}),{} where \\spad{z} acts on \\spad{g}(\\spad{x}) by shifting. In fact,{} the result is [1,{}\\spad{q},{}\\spad{q^2},{}...]")) (|qShiftAction| ((|#1| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{qShiftAction(q,{} k,{} l,{} g)} gives the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{g}(\\spad{x}),{} where \\spad{z*}(a+b*x+c*x^2+d*x^3+...) = (a+q*b*x+q^2*c*x^2+q^3*d*x^3+...). In terms of sequences,{} z*u(\\spad{n})=q^n*u(\\spad{n}).")) (|DiffC| (((|List| |#1|) (|NonNegativeInteger|)) "\\spad{DiffC} gives the coefficients \\spad{c_}{\\spad{k},{}\\spad{k}} in the expansion \\spad{z} \\spad{g}(\\spad{x}) = sum_{\\spad{i=0}}\\spad{^k} \\spad{c_}{\\spad{k},{}\\spad{i}} \\spad{g}(\\spad{x}),{} where \\spad{z} acts on \\spad{g}(\\spad{x}) by shifting. In fact,{} the result is [0,{}0,{}0,{}...]")) (|DiffAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{DiffAction(k,{} l,{} g)} gives the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{g}(\\spad{x}),{} where \\spad{z*}(a+b*x+c*x^2+d*x^3+...) = (a*x+b*x^2+c*x^3+...),{} \\spadignore{i.e.} multiplication with \\spad{x}.")) (|ShiftC| (((|List| |#1|) (|NonNegativeInteger|)) "\\spad{ShiftC} gives the coefficients \\spad{c_}{\\spad{k},{}\\spad{k}} in the expansion \\spad{z} \\spad{g}(\\spad{x}) = sum_{\\spad{i=0}}\\spad{^k} \\spad{c_}{\\spad{k},{}\\spad{i}} \\spad{g}(\\spad{x}),{} where \\spad{z} acts on \\spad{g}(\\spad{x}) by shifting. In fact,{} the result is [0,{}1,{}2,{}...]")) (|ShiftAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{ShiftAction(k,{} l,{} g)} gives the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{g}(\\spad{x}),{} where \\spad{z*(a+b*x+c*x^2+d*x^3+...) = (b*x+2*c*x^2+3*d*x^3+...)}. In terms of sequences,{} z*u(\\spad{n})=n*u(\\spad{n}).")) (|generalCoefficient| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalCoefficient(action,{} f,{} k,{} p)} gives the coefficient of \\spad{x^k} in \\spad{p}(\\spad{z})\\dot \\spad{f}(\\spad{x}),{} where the \\spad{action} of \\spad{z^l} on a polynomial in \\spad{x} is given by \\spad{action},{} \\spadignore{i.e.} \\spad{action}(\\spad{k},{} \\spad{l},{} \\spad{f}) should return the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{f}(\\spad{x}).")) (|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalInterpolation(C,{} CA,{} f,{} sumEta,{} maxEta)} applies \\spad{generalInterpolation(C,{} CA,{} f,{} eta)} for all possible \\spad{eta} with maximal entry \\spad{maxEta} and sum of entries at most \\spad{sumEta}. \\blankline The first argument \\spad{C} is the list of coefficients \\spad{c_}{\\spad{k},{}\\spad{k}} in the expansion \\spad{z} \\spad{g}(\\spad{x}) = sum_{\\spad{i=0}}\\spad{^k} \\spad{c_}{\\spad{k},{}\\spad{i}} \\spad{g}(\\spad{x}). \\blankline The second argument,{} \\spad{CA}(\\spad{k},{} \\spad{l},{} \\spad{f}),{} should return the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{f}(\\spad{x}).") (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{generalInterpolation(C,{} CA,{} f,{} eta)} performs Hermite-Pade approximation using the given action \\spad{CA} of polynomials on the elements of \\spad{f}. The result is guaranteed to be correct up to order |eta|-1. Given that eta is a \"normal\" point,{} the degrees on the diagonal are given by eta. The degrees of column \\spad{i} are in this case eta + \\spad{e}.\\spad{i} - [1,{}1,{}...,{}1],{} where the degree of zero is \\spad{-1}. \\blankline The first argument \\spad{C} is the list of coefficients \\spad{c_}{\\spad{k},{}\\spad{k}} in the expansion \\spad{z} \\spad{g}(\\spad{x}) = sum_{\\spad{i=0}}\\spad{^k} \\spad{c_}{\\spad{k},{}\\spad{i}} \\spad{g}(\\spad{x}). \\blankline The second argument,{} \\spad{CA}(\\spad{k},{} \\spad{l},{} \\spad{f}),{} should return the coefficient of \\spad{x^k} in \\spad{z^l} \\spad{f}(\\spad{x}).")) (|interpolate| (((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| (|Fraction| |#1|)) (|List| (|Fraction| |#1|)) (|NonNegativeInteger|)) "\\spad{interpolate(xlist,{} ylist,{} deg} returns the rational function with numerator degree \\spad{deg} that interpolates the given points using fraction free arithmetic.") (((|Fraction| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{interpolate(xlist,{} ylist,{} deg} returns the rational function with numerator degree at most \\spad{deg} and denominator degree at most \\spad{\\#xlist-deg-1} that interpolates the given points using fraction free arithmetic. Note that rational interpolation does not guarantee that all given points are interpolated correctly: unattainable points may make this impossible.")) (|fffg| (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) (|List| (|NonNegativeInteger|))) "\\spad{fffg} is the general algorithm as proposed by Beckermann and Labahn. \\blankline The first argument is the list of \\spad{c_}{\\spad{i},{}\\spad{i}}. These are the only values of \\spad{C} explicitely needed in \\spad{fffg}. \\blankline The second argument \\spad{c},{} computes \\spad{c_k}(\\spad{M}),{} \\spadignore{i.e.} \\spad{c_k}(.) is the dual basis of the vector space \\spad{V},{} but also knows about the special multiplication rule as descibed in Equation (2). Note that the information about \\spad{f} is therefore encoded in \\spad{c}. \\blankline The third argument is the vector of degree bounds \\spad{n},{} as introduced in Definition 2.1. In particular,{} the sum of the entries is the order of the Mahler system computed."))) NIL -(-316 F1 GF F2) -((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL +(-341 GF) +((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field \\spad{GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree \\spad{n} over \\spad{GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree \\spad{n} over \\spad{GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree \\spad{n} over \\spad{GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table \\spad{m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table \\spad{m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by \\spad{f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial \\spad{f}(\\spad{x}),{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by x**Z(\\spad{i}) = 1+x**i is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL -(-317 S) -((|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) NIL +(-342 F1 GF F2) +((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields \\spad{F1} and \\spad{F2},{} which both must be finite simple algebraic extensions of the finite ground field \\spad{GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from \\spad{F2} in \\spad{F1},{} where coerce is a field homomorphism between the fields extensions \\spad{F2} and \\spad{F1} both over ground field \\spad{GF} (the second argument to the package). Error: if the extension degree of \\spad{F2} doesn\\spad{'t} divide the extension degree of \\spad{F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from \\spad{F1} in \\spad{F2}. Thus coerce is a field homomorphism between the fields extensions \\spad{F1} and \\spad{F2} both over ground field \\spad{GF} (the second argument to the package). Error: if the extension degree of \\spad{F1} doesn\\spad{'t} divide the extension degree of \\spad{F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL -(-318) -((|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) NIL -(-319 R UP -2958) -((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) +(-343 S) +((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note that see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of a. Note that such a root is alway defined in finite fields."))) NIL NIL -(-320 |p| |extdeg|) -((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-826 |#1|) (QUOTE (-134))) (|HasCategory| (-826 |#1|) (QUOTE (-336))) (|HasCategory| (-826 |#1|) (QUOTE (-132))) (-1405 (|HasCategory| (-826 |#1|) (QUOTE (-132))) (|HasCategory| (-826 |#1|) (QUOTE (-336))))) -(-321 GF |uni|) -((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-322 GF |extdeg|) -((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-323 GF |defpol|) -((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-324 GF) -((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) +(-344) +((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note that see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of a. Note that such a root is alway defined in finite fields."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL +(-345 R UP -1333) +((|constructor| (NIL "Integral bases for function fields of dimension one In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL -(-325 -2958 GF) -((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) +NIL +(-346 |p| |extdeg|) +((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by createNormalPoly")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-897 |#1|) (QUOTE (-148))) (|HasCategory| (-897 |#1|) (QUOTE (-364))) (|HasCategory| (-897 |#1|) (QUOTE (-146))) (-2318 (|HasCategory| (-897 |#1|) (QUOTE (-146))) (|HasCategory| (-897 |#1|) (QUOTE (-364))))) +(-347 GF |uni|) +((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field \\spad{GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of \\spad{GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over \\spad{GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-348 GF |extdeg|) +((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field \\spad{GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by createNormalPoly from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-349 |p| |n|) +((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-897 |#1|) (QUOTE (-148))) (|HasCategory| (-897 |#1|) (QUOTE (-364))) (|HasCategory| (-897 |#1|) (QUOTE (-146))) (-2318 (|HasCategory| (-897 |#1|) (QUOTE (-146))) (|HasCategory| (-897 |#1|) (QUOTE (-364))))) +(-350 GF |defpol|) +((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field \\spad{GF} generated by the extension polynomial defpol which MUST be irreducible."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-351 -1333 GF) +((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field \\spad{GF} and an algebraic extension \\spad{F} of \\spad{GF},{} \\spadignore{e.g.} a zero of a polynomial over \\spad{GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of \\spad{F} over \\spad{GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over \\spad{F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) +NIL +NIL +(-352 GF) +((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field \\spad{GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of \\spad{GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field \\spad{GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field \\spad{GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the lookup of the coefficient of the term of degree \\spad{n}-1 of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g} or if lookup of the coefficient of the term of degree \\spad{n}-1 of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the lookup of the coefficient of the term of degree \\spad{n}-1 of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field \\spad{GF}. polynomial of degree \\spad{n} over the field \\spad{GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field \\spad{GF}. Note that this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field \\spad{GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field \\spad{GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field \\spad{GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field \\spad{GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field \\spad{GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field \\spad{GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-326 -2958 FP FPP) -((|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) +(-353 -1333 FP FPP) +((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-327 GF |n|) -((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-132))) (-1405 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-336))))) -(-328 R |ls|) -((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) +(-354 K |PolK|) +((|constructor| (NIL "Part of the package for Algebraic Function Fields in one variable (\\spad{PAFF})"))) NIL NIL -(-329 S) +(-355 GF |n|) +((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field \\spad{GF} of degree \\spad{n} generated by the extension polynomial constructed by createIrreduciblePoly from \\spadtype{FiniteFieldPolynomialPackage}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-146))) (-2318 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364))))) +(-356 R |ls|) +((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the FGLM algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the FGLM strategy is used,{} otherwise the Sugar strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the FGLM strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) +NIL +NIL +(-357 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4164 . T)) +((-4502 . T)) NIL -(-330 S) -((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) +(-358 S) +((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{a*(b/a) = b}\\spad{\\br} \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) NIL NIL -(-331) -((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-359) +((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{a*(b/a) = b}\\spad{\\br} \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-332 S) -((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) +(-360 |Name| S) +((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|flush| (((|Void|) $) "\\spad{flush(f)} makes sure that buffered data is written out")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL -(-333 |Name| S) -((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) +(-361 S) +((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-334 S R) -((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) +(-362 S R) +((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note that this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-508)))) -(-335 R) -((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4164 |has| |#1| (-508)) (-4162 . T) (-4161 . T)) +((|HasCategory| |#2| (QUOTE (-550)))) +(-363 R) +((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note that we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note that this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) +((-4502 |has| |#1| (-550)) (-4500 . T) (-4499 . T)) NIL -(-336) +(-364) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) NIL NIL -(-337 S R UP) -((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) +(-365 S R UP) +((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1+...+an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) NIL -((|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-331)))) -(-338 R UP) -((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-359)))) +(-366 R UP) +((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1+...+an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) +((-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-339 A S) -((|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) +(-367 S A R B) +((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note that third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) NIL -((|HasAttribute| |#1| (QUOTE -4168)) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001)))) -(-340 S) -((|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4167 . T) (-2951 . T)) NIL -(-341 S A R B) -((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) +(-368 A S) +((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note that \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note that \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL +((|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082)))) +(-369 S) +((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note that \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note that \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) +((-4505 . T) (-2537 . T)) NIL -(-342 |VarSet| R) -((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4162 . T) (-4161 . T)) +(-370 |VarSet| R) +((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}.")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4500 . T) (-4499 . T)) NIL -(-343 S V) -((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) +(-371 S V) +((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates. Sort package (in-place) for shallowlyMutable Finite Linear Aggregates")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) NIL NIL -(-344 S R) +(-372 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501))))) -(-345 R) +((|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560))))) +(-373 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4164 . T)) +((-4502 . T)) NIL -(-346) -((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\^= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4150 . T) (-4158 . T) (-2391 . T) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-374 |Par|) +((|constructor| (NIL "This is a package for the approximation of complex solutions for systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL -(-347 |Par|) -((|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL +(-375) +((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}base)} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * base ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-bits)}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The base of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary base,{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the base to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal base when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision\\spad{\\br} \\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )} \\spad{\\br} \\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}: \\spad{O(sqrt(n) n**2)}\\spad{\\br} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\^= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-4488 . T) (-4496 . T) (-2550 . T) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-348 |Par|) -((|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) +(-376 |Par|) +((|constructor| (NIL "This is a package for the approximation of real solutions for systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) NIL NIL -(-349 R S) +(-377 R S) +((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: XDistributedPolynomial,{} XRecursivePolynomial.")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) +((-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-170)))) +(-378 R |Basis|) +((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor.")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{listOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{listOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{listOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}")) (|listOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{listOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) +((-4500 . T) (-4499 . T)) +NIL +(-379) +((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) +((-2537 . T)) +NIL +(-380) +((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((-2537 . T)) +NIL +(-381 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-156)))) -(-350 R S) -((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-156)))) -(-351) -((|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2951 . T)) -NIL -(-352 R |Basis|) -((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4162 . T) (-4161 . T)) -NIL -(-353) -((|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2951 . T)) -NIL -(-354 S) +((-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-170)))) +(-382 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL -((|HasCategory| |#1| (QUOTE (-777)))) -(-355) -NIL -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#1| (QUOTE (-834)))) +(-383) +((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-356) +(-384) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL NIL -(-357) +(-385) ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,{}pref,{}e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,{}n,{}e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used.")) (|coerce| (((|String|) $) "\\spad{coerce(fn)} produces a string for a file name according to operating system-dependent conventions.") (($ (|String|)) "\\spad{coerce(s)} converts a string to a file name according to operating system-dependent conventions."))) NIL NIL -(-358 |n| |class| R) -((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4162 . T) (-4161 . T)) +(-386 |n| |class| R) +((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} is not documented")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} is not documented")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) +((-4500 . T) (-4499 . T)) NIL -(-359) +(-387) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-360 -2958 UP UPUP R) -((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) +(-388 -1333 UP UPUP R) +((|constructor| (NIL "Finds the order of a divisor over a finite field")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-361) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) +(-389 S) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) NIL NIL -(-362 S) -((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) +(-390) +((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) NIL NIL -(-363) -((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) +(-391) +((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) +((-2537 . T)) NIL +(-392) +((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((-2537 . T)) NIL -(-364) -((|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2951 . T)) +(-393) +((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL -(-365) -((|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2951 . T)) NIL -(-366 -3986 |returnType| |arguments| |symbols|) -((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) +(-394 -1337 |returnType| |arguments| |symbols|) +((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} is not documented") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} is not documented") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} is not documented") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} is not documented") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} is not documented") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} is not documented") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} is not documented") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} is not documented") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} is not documented") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} is not documented") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} is not documented") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} is not documented") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} is not documented") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} is not documented") (($ (|FortranCode|)) "\\spad{coerce(fc)} is not documented"))) NIL NIL -(-367 -2958 UP) -((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) +(-395 -1333 UP) +((|constructor| (NIL "Full partial fraction expansion of rational functions")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + sum_{[j,{}Dj,{}Hj] in l} sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL -(-368 R) +(-396 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2951 . T)) +((-2537 . T)) NIL -(-369 S) -((|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) +(-397 S) +((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a**p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) NIL NIL -(-370) -((|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-398) +((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a**p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-371 S) -((|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) +(-399 S) +((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline 1: base of the exponent where the actual implemenations are usually binary or decimal)\\spad{\\br} 2: precision of the mantissa (arbitrary or fixed)\\spad{\\br} 3: rounding error for operations \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\indented{1}{base() returns the base of the} \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note that \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4150)) (|HasAttribute| |#1| (QUOTE -4158))) -(-372) -((|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2391 . T) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasAttribute| |#1| (QUOTE -4488)) (|HasAttribute| |#1| (QUOTE -4496))) +(-400) +((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline 1: base of the exponent where the actual implemenations are usually binary or decimal)\\spad{\\br} 2: precision of the mantissa (arbitrary or fixed)\\spad{\\br} 3: rounding error for operations \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\indented{1}{base() returns the base of the} \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note that \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) +((-2550 . T) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-373 R) -((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -278) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -256) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -256) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-1108))))) -(-374 R S) +(-401 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL NIL -(-375 S) -((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4154 -12 (|has| |#1| (-6 -4165)) (|has| |#1| (-419)) (|has| |#1| (-6 -4154))) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-750))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -256) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-276))) (|HasCategory| |#1| (QUOTE (-500))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751)))) (-12 (|HasAttribute| |#1| (QUOTE -4165)) (|HasAttribute| |#1| (QUOTE -4154)) (|HasCategory| |#1| (QUOTE (-419)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751))))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-750))) (|HasCategory| |#1| (QUOTE (-777)))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751))))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751))))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-751))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-376 A B) +(-402 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL NIL -(-377 S R UP) +(-403 S) +((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) +((-4492 -12 (|has| |#1| (-6 -4503)) (|has| |#1| (-447)) (|has| |#1| (-6 -4492))) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-807))) (|HasCategory| |#1| (QUOTE (-1128))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -276) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-542))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815)))) (-12 (|HasAttribute| |#1| (QUOTE -4503)) (|HasAttribute| |#1| (QUOTE -4492)) (|HasCategory| |#1| (QUOTE (-447)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815))))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-807))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815))))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-815))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-404 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL -(-378 R UP) +(-405 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4161 . T) (-4162 . T) (-4164 . T)) +((-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-379 A S) -((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) +(-406 A S) +((|constructor| (NIL "A is fully retractable to \\spad{B} means that A is retractable to \\spad{B} and if \\spad{B} is retractable to the integers or rational numbers then so is A. In particular,{} what we are asserting is that there are no integers (rationals) in A which don\\spad{'t} retract into \\spad{B}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501))))) -(-380 S) -((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) +((|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560))))) +(-407 S) +((|constructor| (NIL "A is fully retractable to \\spad{B} means that A is retractable to \\spad{B} and if \\spad{B} is retractable to the integers or rational numbers then so is A. In particular,{} what we are asserting is that there are no integers (rationals) in A which don\\spad{'t} retract into \\spad{B}."))) NIL NIL -(-381 R -2958 UP A) -((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) -((-4164 . T)) +(-408 R1 F1 U1 A1 R2 F2 U2 A2) +((|constructor| (NIL "Lifting of morphisms to fractional ideals.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL -(-382 R1 F1 U1 A1 R2 F2 U2 A2) -((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL +(-409 R -1333 UP A) +((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) +((-4502 . T)) NIL -(-383 R -2958 UP A |ibasis|) +(-410 R -1333 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -950) (|devaluate| |#2|)))) -(-384 AR R AS S) +((|HasCategory| |#4| (LIST (QUOTE -1029) (|devaluate| |#2|)))) +(-411 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-385 S R) -((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) +(-412 S R) +((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-331)))) -(-386 R) -((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4164 |has| |#1| (-508)) (-4162 . T) (-4161 . T)) +((|HasCategory| |#2| (QUOTE (-359)))) +(-413 R) +((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) +((-4502 |has| |#1| (-550)) (-4500 . T) (-4499 . T)) NIL -(-387 R) +(-414 R) +((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map(\\spad{fn},{}\\spad{u}) maps the function \\userfun{\\spad{fn}} across the factors of} \\indented{1}{\\spadvar{\\spad{u}} and creates a new factored object. Note: this clears} \\indented{1}{the information flags (sets them to \"nil\") because the effect of} \\indented{1}{\\userfun{\\spad{fn}} is clearly not known in general.} \\blankline \\spad{X} \\spad{m}(a:Factored Polynomial Integer):Factored Polynomial Integer \\spad{==} \\spad{a^2} \\spad{X} \\spad{f:=x*y^3}-3*x^2*y^2+3*x^3*y-\\spad{x^4} \\spad{X} map(\\spad{m},{}\\spad{f}) \\spad{X} g:=makeFR(\\spad{z},{}factorList \\spad{f}) \\spad{X} map(\\spad{m},{}\\spad{g})")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\indented{1}{unit(\\spad{u}) extracts the unit part of the factorization.} \\blankline \\spad{X} \\spad{f:=x*y^3}-3*x^2*y^2+3*x^3*y-\\spad{x^4} \\spad{X} unit \\spad{f} \\spad{X} g:=makeFR(\\spad{z},{}factorList \\spad{f}) \\spad{X} unit \\spad{g}")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\indented{1}{sqfrFactor(base,{}exponent) creates a factored object with} \\indented{1}{a single factor whose base is asserted to be square-free} \\indented{1}{(flag = \"sqfr\").} \\blankline \\spad{X} a:=sqfrFactor(3,{}5) \\spad{X} nthFlag(a,{}1)")) (|primeFactor| (($ |#1| (|Integer|)) "\\indented{1}{primeFactor(base,{}exponent) creates a factored object with} \\indented{1}{a single factor whose base is asserted to be prime} \\indented{1}{(flag = \"prime\").} \\blankline \\spad{X} a:=primeFactor(3,{}4) \\spad{X} nthFlag(a,{}1)")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\indented{1}{numberOfFactors(\\spad{u}) returns the number of factors in \\spadvar{\\spad{u}}.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} numberOfFactors a")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\indented{1}{nthFlag(\\spad{u},{}\\spad{n}) returns the information flag of the \\spad{n}th factor of} \\indented{1}{\\spadvar{\\spad{u}}.\\space{2}If \\spadvar{\\spad{n}} is not a valid index for a factor} \\indented{1}{(for example,{} less than 1 or too big),{} \"nil\" is returned.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} nthFlag(a,{}2)")) (|nthFactor| ((|#1| $ (|Integer|)) "\\indented{1}{nthFactor(\\spad{u},{}\\spad{n}) returns the base of the \\spad{n}th factor of} \\indented{1}{\\spadvar{\\spad{u}}.\\space{2}If \\spadvar{\\spad{n}} is not a valid index for a factor} \\indented{1}{(for example,{} less than 1 or too big),{} 1 is returned.\\space{2}If} \\indented{1}{\\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} nthFactor(a,{}2)")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\indented{1}{nthExponent(\\spad{u},{}\\spad{n}) returns the exponent of the \\spad{n}th factor of} \\indented{1}{\\spadvar{\\spad{u}}.\\space{2}If \\spadvar{\\spad{n}} is not a valid index for a factor} \\indented{1}{(for example,{} less than 1 or too big),{} 0 is returned.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} nthExponent(a,{}2)")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\indented{1}{irreducibleFactor(base,{}exponent) creates a factored object with} \\indented{1}{a single factor whose base is asserted to be irreducible} \\indented{1}{(flag = \"irred\").} \\blankline \\spad{X} a:=irreducibleFactor(3,{}1) \\spad{X} nthFlag(a,{}1)")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\indented{1}{factors(\\spad{u}) returns a list of the factors in a form suitable} \\indented{1}{for iteration. That is,{} it returns a list where each element} \\indented{1}{is a record containing a base and exponent.\\space{2}The original} \\indented{1}{object is the product of all the factors and the unit (which} \\indented{1}{can be extracted by \\axiom{unit(\\spad{u})}).} \\blankline \\spad{X} \\spad{f:=x*y^3}-3*x^2*y^2+3*x^3*y-\\spad{x^4} \\spad{X} factors \\spad{f} \\spad{X} g:=makeFR(\\spad{z},{}factorList \\spad{f}) \\spad{X} factors \\spad{g}")) (|nilFactor| (($ |#1| (|Integer|)) "\\indented{1}{nilFactor(base,{}exponent) creates a factored object with} \\indented{1}{a single factor with no information about the kind of} \\indented{1}{base (flag = \"nil\").} \\blankline \\spad{X} nilFactor(24,{}2) \\spad{X} nilFactor(\\spad{x}-\\spad{y},{}3)")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\indented{1}{factorList(\\spad{u}) returns the list of factors with flags (for} \\indented{1}{use by factoring code).} \\blankline \\spad{X} f:=nilFactor(\\spad{x}-\\spad{y},{}3) \\spad{X} factorList \\spad{f}")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\indented{1}{makeFR(unit,{}listOfFactors) creates a factored object (for} \\indented{1}{use by factoring code).} \\blankline \\spad{X} f:=nilFactor(\\spad{x}-\\spad{y},{}3) \\spad{X} g:=factorList \\spad{f} \\spad{X} makeFR(\\spad{z},{}\\spad{g})")) (|exponent| (((|Integer|) $) "\\indented{1}{exponent(\\spad{u}) returns the exponent of the first factor of} \\indented{1}{\\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.} \\blankline \\spad{X} f:=nilFactor(\\spad{y}-\\spad{x},{}3) \\spad{X} exponent(\\spad{f})")) (|expand| ((|#1| $) "\\indented{1}{expand(\\spad{f}) multiplies the unit and factors together,{} yielding an} \\indented{1}{\"unfactored\" object. Note: this is purposely not called} \\indented{1}{\\spadfun{coerce} which would cause the interpreter to do this} \\indented{1}{automatically.} \\blankline \\spad{X} f:=nilFactor(\\spad{y}-\\spad{x},{}3) \\spad{X} expand(\\spad{f})"))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -276) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-1191))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -276) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-1191))))) +(-415 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL NIL -(-388 S R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +(-416 R FE |x| |cen|) +((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-440))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490))))) -(-389 R) -((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4164 -1405 (|has| |#1| (-959)) (|has| |#1| (-440))) (-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) ((-4169 "*") |has| |#1| (-508)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-508)) (-4159 |has| |#1| (-508)) (-2951 . T)) NIL -(-390 R A S B) -((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) +(-417 R A S B) +((|constructor| (NIL "Lifting of maps to function spaces This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-391 R FE |x| |cen|) -((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) +(-418 R FE |Expon| UPS TRAN |x|) +((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) NIL NIL -(-392 R FE |Expon| UPS TRAN |x|) -((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) +(-419 S A R B) +((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note that third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-393 A S) -((|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) +(-420 A S) +((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note that \\axiom{cardinality(\\spad{u}) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-336)))) -(-394 S) -((|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4167 . T) (-4157 . T) (-4168 . T) (-2951 . T)) +((|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-364)))) +(-421 S) +((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note that \\axiom{cardinality(\\spad{u}) = \\#u}."))) +((-4505 . T) (-4495 . T) (-4506 . T) (-2537 . T)) NIL -(-395 S A R B) -((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) +(-422 R -1333) +((|constructor| (NIL "Top-level complex function integration \\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL -(-396 R -2958) -((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) +(-423 R E) +((|constructor| (NIL "This domain converts terms into Fourier series")) (|makeCos| (($ |#2| |#1|) "\\indented{1}{makeCos(\\spad{e},{}\\spad{r}) makes a sin expression with given} argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) +((-4492 -12 (|has| |#1| (-6 -4492)) (|has| |#2| (-6 -4492))) (-4499 . T) (-4500 . T) (-4502 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4492)) (|HasAttribute| |#2| (QUOTE -4492)))) +(-424 R -1333) +((|constructor| (NIL "Top-level real function integration \\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-397 R E) -((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4154 -12 (|has| |#1| (-6 -4154)) (|has| |#2| (-6 -4154))) (-4161 . T) (-4162 . T) (-4164 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4154)) (|HasAttribute| |#2| (QUOTE -4154)))) -(-398 R -2958) -((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) +(-425 S R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL +((|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) +(-426 R) +((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) +((-4502 -2318 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) ((-4507 "*") |has| |#1| (-550)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-550)) (-4497 |has| |#1| (-550)) (-2537 . T)) NIL -(-399 R -2958) -((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) +(-427 R -1333) +((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiAiryBi| ((|#2| |#2|) "\\spad{iiAiryBi(x)} should be local but conditional.")) (|iiAiryAi| ((|#2| |#2|) "\\spad{iiAiryAi(x)} should be local but conditional.")) (|iiBesselK| ((|#2| (|List| |#2|)) "\\spad{iiBesselK(x)} should be local but conditional.")) (|iiBesselI| ((|#2| (|List| |#2|)) "\\spad{iiBesselI(x)} should be local but conditional.")) (|iiBesselY| ((|#2| (|List| |#2|)) "\\spad{iiBesselY(x)} should be local but conditional.")) (|iiBesselJ| ((|#2| (|List| |#2|)) "\\spad{iiBesselJ(x)} should be local but conditional.")) (|iipolygamma| ((|#2| (|List| |#2|)) "\\spad{iipolygamma(x)} should be local but conditional.")) (|iidigamma| ((|#2| |#2|) "\\spad{iidigamma(x)} should be local but conditional.")) (|iiBeta| ((|#2| (|List| |#2|)) "iiGamma(\\spad{x}) should be local but conditional.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-400 R -2958) +(-428 R -1333) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-401 R -2958) -((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) +(-429 R -1333) +((|constructor| (NIL "Reduction from a function space to the rational numbers This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL -(-402) +(-430) ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-403 R -2958 UP) -((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) +(-431 R -1333 UP) +((|constructor| (NIL "This package is used internally by IR2F")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-47))))) -(-404) -((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) +((|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-53))))) +(-432) +((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL NIL -(-405) -((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) +(-433) +((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) NIL NIL -(-406 |f|) +(-434 |f|) ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-407) -((|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2951 . T)) +(-435) +((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) +((-2537 . T)) NIL -(-408) -((|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2951 . T)) +(-436) +((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) +((-2537 . T)) NIL -(-409 UP) -((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) +(-437 UP) +((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by completeHensel. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by ddFact for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by ddFact for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-410 R UP -2958) +(-438 R UP -1333) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL -(-411 R UP) -((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,{}f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,{}f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,{}c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,{}c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) +(-439 R UP) +((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored}")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,{}f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,{}f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,{}c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,{}c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) NIL NIL -(-412 R) +(-440 R) ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,{}r)} returns the binomial coefficient \\spad{C(n,{}r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) NIL -((|HasCategory| |#1| (QUOTE (-372)))) -(-413) +((|HasCategory| |#1| (QUOTE (-400)))) +(-441) ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(\\spad{zi})} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(\\spad{zi})} produces the complete factorization of the complex integer \\spad{zi}."))) NIL NIL -(-414 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) +(-442 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\" is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\indented{1}{euclideanGroebner(\\spad{lp},{} \"info\",{} \"redcrit\") computes a groebner basis} \\indented{1}{for a polynomial ideal generated by the list of polynomials \\spad{lp}.} \\indented{1}{If the second argument is \"info\",{}} \\indented{1}{a summary is given of the critical pairs.} \\indented{1}{If the third argument is \"redcrit\",{} critical pairs are printed.} \\blankline \\spad{X} a1:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (9*x**2 + 5*x - 3)+ \\spad{y*}(3*x**2 + 2*x + 1) \\spad{X} a2:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (6*x**3 - 2*x**2 - 3*x \\spad{+3}) + \\spad{y*}(2*x**3 - \\spad{x} - 1) \\spad{X} a3:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (3*x**3 + 2*x**2) + \\spad{y*}(\\spad{x**3} + \\spad{x**2}) \\spad{X} an:=[\\spad{a1},{}\\spad{a2},{}\\spad{a3}] \\spad{X} euclideanGroebner(an,{}\"info\",{}\"redcrit\")") (((|List| |#4|) (|List| |#4|) (|String|)) "\\indented{1}{euclideanGroebner(\\spad{lp},{} infoflag) computes a groebner basis} \\indented{1}{for a polynomial ideal over a euclidean domain} \\indented{1}{generated by the list of polynomials \\spad{lp}.} \\indented{1}{During computation,{} additional information is printed out} \\indented{1}{if infoflag is given as} \\indented{1}{either \"info\" (for summary information) or} \\indented{1}{\"redcrit\" (for reduced critical pairs)} \\blankline \\spad{X} a1:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (9*x**2 + 5*x - 3)+ \\spad{y*}(3*x**2 + 2*x + 1) \\spad{X} a2:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (6*x**3 - 2*x**2 - 3*x \\spad{+3}) + \\spad{y*}(2*x**3 - \\spad{x} - 1) \\spad{X} a3:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (3*x**3 + 2*x**2) + \\spad{y*}(\\spad{x**3} + \\spad{x**2}) \\spad{X} an:=[\\spad{a1},{}\\spad{a2},{}\\spad{a3}] \\spad{X} euclideanGroebner(an,{}\"redcrit\") \\spad{X} euclideanGroebner(an,{}\"info\")") (((|List| |#4|) (|List| |#4|)) "\\indented{1}{euclideanGroebner(\\spad{lp}) computes a groebner basis for a polynomial} \\indented{1}{ideal over a euclidean domain generated by the list of polys \\spad{lp}.} \\blankline \\spad{X} a1:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (9*x**2 + 5*x - 3)+ \\spad{y*}(3*x**2 + 2*x + 1) \\spad{X} a2:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (6*x**3 - 2*x**2 - 3*x \\spad{+3}) + \\spad{y*}(2*x**3 - \\spad{x} - 1) \\spad{X} a3:DMP([\\spad{y},{}\\spad{x}],{}INT)\\spad{:=} (3*x**3 + 2*x**2) + \\spad{y*}(\\spad{x**3} + \\spad{x**2}) \\spad{X} an:=[\\spad{a1},{}\\spad{a2},{}\\spad{a3}] \\spad{X} euclideanGroebner(an)")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL -((|HasCategory| |#1| (QUOTE (-331)))) -(-415 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL +(-443 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by \\spad{listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p}. If info is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\indented{1}{groebnerFactorize(listOfPolys) returns} \\indented{1}{a list of groebner bases. The union of their solutions} \\indented{1}{is the solution of the system of equations given by listOfPolys.} \\indented{1}{At each stage the polynomial \\spad{p} under consideration (either from} \\indented{1}{the given basis or obtained from a reduction of the next \\spad{S}-polynomial)} \\indented{1}{is factorized. For each irreducible factors of \\spad{p},{} a} \\indented{1}{new createGroebnerBasis is started} \\indented{1}{doing the usual updates with the factor} \\indented{1}{in place of \\spad{p}.} \\blankline \\spad{X} mfzn : SQMATRIX(6,{}\\spad{DMP}([\\spad{x},{}\\spad{y},{}\\spad{z}],{}Fraction INT)) \\spad{:=} \\spad{++X} [ [0,{}1,{}1,{}1,{}1,{}1],{} [1,{}0,{}1,{}8/3,{}\\spad{x},{}8/3],{} [1,{}1,{}0,{}1,{}8/3,{}\\spad{y}],{} \\spad{++X} [1,{}8/3,{}1,{}0,{}1,{}8/3],{} [1,{}\\spad{x},{}8/3,{}1,{}0,{}1],{} [1,{}8/3,{}\\spad{y},{}8/3,{}1,{}0] ] \\spad{X} eq \\spad{:=} determinant mfzn \\spad{X} groebnerFactorize \\spad{++X} [eq,{}eval(eq,{} [\\spad{x},{}\\spad{y},{}\\spad{z}],{}[\\spad{y},{}\\spad{z},{}\\spad{x}]),{} eval(eq,{}[\\spad{x},{}\\spad{y},{}\\spad{z}],{}[\\spad{z},{}\\spad{x},{}\\spad{y}])]") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by \\spad{listOfPolys} under the restriction that the polynomials of \\spad{nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p}. If argument info is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by \\spad{listOfPolys} under the restriction that the polynomials of nonZeroRestrictions don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument \\spad{info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL -(-416 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) NIL +(-444 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL -(-417 |Dom| |Expon| |VarSet| |Dpol|) -((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL +(-445 |Dom| |Expon| |VarSet| |Dpol|) +((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\indented{1}{groebner(\\spad{lp},{} \"info\",{} \"redcrit\") computes a groebner basis} \\indented{1}{for a polynomial ideal generated by the list of polynomials \\spad{lp},{}} \\indented{1}{displaying both a summary of the critical pairs considered (\"info\")} \\indented{1}{and the result of reducing each critical pair (\"redcrit\").} \\indented{1}{If the second or third arguments have any other string value,{}} \\indented{1}{the indicated information is suppressed.} \\blankline \\spad{X} s1:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[\\spad{s1},{}\\spad{s2},{}\\spad{s3},{}\\spad{s4},{}\\spad{s5},{}\\spad{s6},{}\\spad{s7}] \\spad{X} groebner(\\spad{sn7},{}\"info\",{}\"redcrit\")") (((|List| |#4|) (|List| |#4|) (|String|)) "\\indented{1}{groebner(\\spad{lp},{} infoflag) computes a groebner basis} \\indented{1}{for a polynomial ideal} \\indented{1}{generated by the list of polynomials \\spad{lp}.} \\indented{1}{Argument infoflag is used to get information on the computation.} \\indented{1}{If infoflag is \"info\",{} then summary information} \\indented{1}{is displayed for each \\spad{s}-polynomial generated.} \\indented{1}{If infoflag is \"redcrit\",{} the reduced critical pairs are displayed.} \\indented{1}{If infoflag is any other string,{}} \\indented{1}{no information is printed during computation.} \\blankline \\spad{X} s1:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[\\spad{s1},{}\\spad{s2},{}\\spad{s3},{}\\spad{s4},{}\\spad{s5},{}\\spad{s6},{}\\spad{s7}] \\spad{X} groebner(\\spad{sn7},{}\"info\") \\spad{X} groebner(\\spad{sn7},{}\"redcrit\")") (((|List| |#4|) (|List| |#4|)) "\\indented{1}{groebner(\\spad{lp}) computes a groebner basis for a polynomial ideal} \\indented{1}{generated by the list of polynomials \\spad{lp}.} \\blankline \\spad{X} s1:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([\\spad{w},{}\\spad{p},{}\\spad{z},{}\\spad{t},{}\\spad{s},{}\\spad{b}],{}FRAC(INT))\\spad{:=} \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[\\spad{s1},{}\\spad{s2},{}\\spad{s3},{}\\spad{s4},{}\\spad{s5},{}\\spad{s6},{}\\spad{s7}] \\spad{X} groebner(\\spad{sn7})"))) NIL -(-418 S) -((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) +((|HasCategory| |#1| (QUOTE (-359)))) +(-446 S) +((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the greatest common divisor (\\spad{gcd}) of univariate polynomials over the domain")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) NIL NIL -(-419) -((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-447) +((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the greatest common divisor (\\spad{gcd}) of univariate polynomials over the domain")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-420 R |n| |ls| |gamma|) +(-448 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4164 |has| (-375 (-866 |#1|)) (-508)) (-4162 . T) (-4161 . T)) -((|HasCategory| (-375 (-866 |#1|)) (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| (-375 (-866 |#1|)) (QUOTE (-508)))) -(-421 |vl| R E) -((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4169 "*") |has| |#2| (-156)) (-4160 |has| |#2| (-508)) (-4165 |has| |#2| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-508)))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-331))) (-1405 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#2| (QUOTE -4165)) (|HasCategory| |#2| (QUOTE (-419))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (|HasCategory| |#2| (QUOTE (-132))))) -(-422 R BP) -((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) +((-4502 |has| (-403 (-945 |#1|)) (-550)) (-4500 . T) (-4499 . T)) +((|HasCategory| (-403 (-945 |#1|)) (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-403 (-945 |#1|)) (QUOTE (-550)))) +(-449 |vl| R E) +((|constructor| (NIL "This type supports distributed multivariate polynomials whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) +(((-4507 "*") |has| |#2| (-170)) (-4498 |has| |#2| (-550)) (-4503 |has| |#2| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-450 R BP) +((|constructor| (NIL "The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note that this function is exported only because it\\spad{'s} conditional."))) NIL NIL -(-423 OV E S R P) -((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) +(-451 OV E S R P) +((|constructor| (NIL "This is the top level package for doing multivariate factorization over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-424 E OV R P) +(-452 E OV R P) ((|constructor| (NIL "This package provides operations for \\spad{GCD} computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{GCD} of \\spad{p} and \\spad{q}"))) NIL NIL -(-425 R) -((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) +(-453 R) +((|constructor| (NIL "This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) NIL NIL -(-426 R FE) +(-454 R FE) ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),{}n,{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(a(n),{}n,{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n=n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}."))) NIL NIL -(-427 RP TP) -((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,{}pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,{}lfact,{}prime,{}bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,{}lfacts,{}prime,{}bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) +(-455 RP TP) +((|constructor| (NIL "General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,{}pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,{}lfact,{}prime,{}bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,{}lfacts,{}prime,{}bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) +NIL +NIL +(-456 |vl| R IS E |ff| P) +((|constructor| (NIL "This package is undocumented")) (* (($ |#6| $) "\\spad{p*x} is not documented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} is not documented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} is not documented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} is not documented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} is not documented")) (|reductum| (($ $) "\\spad{reductum(x)} is not documented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} is not documented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} is not documented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} is not documented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} is not documented"))) +((-4500 . T) (-4499 . T)) +NIL +(-457) +((|constructor| (NIL "\\spad{GuessOptionFunctions0} provides operations that extract the values of options for \\spadtype{Guess}.")) (|debug| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{debug returns} whether we want additional output on the progress,{} default being \\spad{false}")) (|displayAsGF| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{displayAsGF specifies} whether the result is a generating function or a recurrence. This option should not be set by the user,{} but rather by the \\spad{HP}-specification,{} therefore,{} there is no default.")) (|indexName| (((|Symbol|) (|List| (|GuessOption|))) "\\spad{indexName returns} the name of the index variable used for the formulas,{} default being \\spad{n}")) (|variableName| (((|Symbol|) (|List| (|GuessOption|))) "\\spad{variableName returns} the name of the variable used in by the algebraic differential equation,{} default being \\spad{x}")) (|functionName| (((|Symbol|) (|List| (|GuessOption|))) "\\spad{functionName returns} the name of the function given by the algebraic differential equation,{} default being \\spad{f}")) (|homogeneous| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{homogeneous returns} whether we allow only homogeneous algebraic differential equations,{} default being \\spad{false}")) (|one| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{one returns} whether we need only one solution,{} default being \\spad{true}.")) (|safety| (((|NonNegativeInteger|) (|List| (|GuessOption|))) "\\spad{safety returns} the specified safety or 1 as default.")) (|allDegrees| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{allDegrees returns} whether all possibilities of the degree vector should be tried,{} the default being \\spad{false}.")) (|maxDegree| (((|Integer|) (|List| (|GuessOption|))) "\\spad{maxDegree returns} the specified maxDegree or \\spad{-1} as default.")) (|maxShift| (((|Integer|) (|List| (|GuessOption|))) "\\spad{maxShift returns} the specified maxShift or \\spad{-1} as default.")) (|maxDerivative| (((|Integer|) (|List| (|GuessOption|))) "\\spad{maxDerivative returns} the specified maxDerivative or \\spad{-1} as default.")) (|maxPower| (((|Integer|) (|List| (|GuessOption|))) "\\spad{maxPower returns} the specified maxPower or \\spad{-1} as default.")) (|maxLevel| (((|Integer|) (|List| (|GuessOption|))) "\\spad{maxLevel returns} the specified maxLevel or \\spad{-1} as default."))) +NIL +NIL +(-458) +((|constructor| (NIL "GuessOption is a domain whose elements are various options used by \\spadtype{Guess}.")) (|checkOptions| (((|Void|) (|List| $)) "\\spad{checkOptions checks} whether an option is given twice")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|displayAsGF| (($ (|Boolean|)) "\\spad{displayAsGF(d)} specifies whether the result is a generating function or a recurrence. This option should not be set by the user,{} but rather by the \\spad{HP}-specification.")) (|indexName| (($ (|Symbol|)) "\\spad{indexName(d)} specifies the index variable used for the formulas. This option is expressed in the form \\spad{indexName == d}.")) (|variableName| (($ (|Symbol|)) "\\spad{variableName(d)} specifies the variable used in by the algebraic differential equation. This option is expressed in the form \\spad{variableName == d}.")) (|functionName| (($ (|Symbol|)) "\\spad{functionName(d)} specifies the name of the function given by the algebraic differential equation or recurrence. This option is expressed in the form \\spad{functionName == d}.")) (|debug| (($ (|Boolean|)) "\\spad{debug(d)} specifies whether we want additional output on the progress. This option is expressed in the form \\spad{debug == d}.")) (|one| (($ (|Boolean|)) "\\spad{one(d)} specifies whether we are happy with one solution. This option is expressed in the form \\spad{one == d}.")) (|safety| (($ (|NonNegativeInteger|)) "\\spad{safety(d)} specifies the number of values reserved for testing any solutions found. This option is expressed in the form \\spad{safety == d}.")) (|allDegrees| (($ (|Boolean|)) "\\spad{allDegrees(d)} specifies whether all possibilities of the degree vector - taking into account maxDegree - should be tried. This is mainly interesting for rational interpolation. This option is expressed in the form \\spad{allDegrees == d}.")) (|maxDegree| (($ (|Integer|)) "\\spad{maxDegree(d)} specifies the maximum degree of the coefficient polynomials in an algebraic differential equation or a recursion with polynomial coefficients. For rational functions with an exponential term,{} \\spad{maxDegree} bounds the degree of the denominator polynomial. maxDegree(\\spad{-1}) specifies that the maximum degree can be arbitrary. This option is expressed in the form \\spad{maxDegree == d}.")) (|maxLevel| (($ (|Integer|)) "\\spad{maxLevel(d)} specifies the maximum number of recursion levels operators guessProduct and guessSum will be applied. maxLevel(\\spad{-1}) specifies that all levels are tried. This option is expressed in the form \\spad{maxLevel == d}.")) (|homogeneous| (($ (|Boolean|)) "\\spad{homogeneous(d)} specifies whether we allow only homogeneous algebraic differential equations. This option is expressed in the form \\spad{homogeneous == d}.")) (|maxPower| (($ (|Integer|)) "\\spad{maxPower(d)} specifies the maximum degree in an algebraic differential equation. For example,{} the degree of (\\spad{f}\\spad{''})\\spad{^3} \\spad{f'} is 4. maxPower(\\spad{-1}) specifies that the maximum exponent can be arbitrary. This option is expressed in the form \\spad{maxPower == d}.")) (|maxShift| (($ (|Integer|)) "\\spad{maxShift(d)} specifies the maximum shift in a recurrence equation. maxShift(\\spad{-1}) specifies that the maximum shift can be arbitrary. This option is expressed in the form \\spad{maxShift == d}.")) (|maxDerivative| (($ (|Integer|)) "\\spad{maxDerivative(d)} specifies the maximum derivative in an algebraic differential equation. maxDerivative(\\spad{-1}) specifies that the maximum derivative can be arbitrary. This option is expressed in the form \\spad{maxDerivative == d}."))) NIL NIL -(-428 |vl| R IS E |ff| P) -((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4162 . T) (-4161 . T)) +(-459 E V R P Q) +((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note that \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) NIL -(-429 E V R P Q) -((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) NIL +(-460 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +((|constructor| (NIL "A package that implements the Brill-Noether algorithm. Part of the PAFF package.")) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) "Returns the Zeta function of the curve in constant field extension. Calculated by using the \\spad{L}-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the \\spad{L}-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(\\spad{d},{} \\spad{n}) returns the number of places of degree \\spad{d} in the constant field extension of degree \\spad{n}")) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) "\\spad{numberRatPlacesExtDeg(n)} returns the number of rational places in the constant field extenstion of degree \\spad{n}")) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) "returns the number of places of the given degree")) (|placesOfDegree| (((|List| |#7|) (|PositiveInteger|)) "\\spad{placesOfDegree(d)} returns all places of degree \\spad{d} of the curve.")) (|classNumber| (((|Integer|)) "Returns the class number of the curve.")) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) "\\spad{LPolynomial(d)} returns the \\spad{L}-Polynomial of the curve in constant field extension of degree \\spad{d}.") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the \\spad{L}-Polynomial of the curve.")) (|rationalPlaces| (((|List| |#7|)) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| ((|#5| |#7|) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl}.")) (|adjunctionDivisor| ((|#8|) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial \\spad{crv}.")) (|intersectionDivisor| ((|#8| |#3|) "\\spad{intersectionDivisor(pol)} compute the intersection divisor (the Cartier divisor) of the form \\spad{pol} with the curve. If some intersection points lie in an extension of the ground field,{} an error message is issued specifying the extension degree needed to find all the intersection points. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| |#3|) |#7|) "\\spad{evalIfCan(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") |#3| |#3| |#7|) "\\spad{evalIfCan(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") |#3| |#7|) "\\spad{evalIfCan(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| |#3|) |#7|) "\\spad{eval(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl}.") ((|#1| |#3| |#3| |#7|) "\\spad{eval(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl}.") ((|#1| |#3| |#7|) "\\spad{eval(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl}.")) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|)) "\\spad{interpolateForms(d,{}n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d}.")) (|lBasis| (((|Record| (|:| |num| (|List| |#3|)) (|:| |den| |#3|)) |#8|) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| ((|#6| |#3| |#7|) "\\spad{parametrize(f,{}pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl}.")) (|singularPoints| (((|List| |#5|)) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|setSingularPoints| (((|List| |#5|) (|List| |#5|)) "\\spad{setSingularPoints(lpt)} sets the singular points to be used. Beware: no attempt is made to check if the points are singular or not,{} nor if all of the singular points are presents. Hence,{} results of some computation maybe \\spad{false}. It is intend to be use when one want to compute the singular points are computed by other means than to use the function singularPoints.")) (|desingTreeWoFullParam| (((|List| |#10|)) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|desingTree| (((|List| |#10|)) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| ((|#3|) "\\spad{theCurve returns} the specified polynomial for the package.")) (|printInfo| (((|Void|) (|List| (|Boolean|))) "\\spad{printInfo(lbool)} prints some information comming from various package and domain used by this package."))) NIL -(-430 R E |VarSet| P) +((|HasCategory| |#1| (QUOTE (-364)))) +(-461 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#4| (QUOTE (-1001))) (-12 (|HasCategory| |#4| (LIST (QUOTE -278) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508)))) -(-431 S R E) -((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#4| (QUOTE (-1082))) (-12 (|HasCategory| |#4| (LIST (QUOTE -298) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550)))) +(-462 S R E) +((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the product. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-432 R E) -((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) +(-463 R E) +((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the product. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL NIL -(-433) -((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,{}n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,{}n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(\\spad{vv}) if {\\em vv.2.1 = n}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect."))) +(-464) +((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector \\spad{ww} to start a loop using nextSubsetGray(\\spad{ww},{}\\spad{n})")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,{}n)} returns a vector \\spad{vv} whose components have the following meanings:\\spad{\\br} \\spad{vv}.1: a vector of length \\spad{n} whose entries are 0 or 1. This can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n}; \\spad{vv}.1 differs from \\spad{ww}.1 by exactly one entry;\\spad{\\br} \\spad{vv}.2.1 is the number of the entry of \\spad{vv}.1 which will be changed next time;\\spad{\\br} \\spad{vv}.2.1 = \\spad{n+1} means that \\spad{vv}.1 is the last subset; trying to compute nextSubsetGray(\\spad{vv}) if \\spad{vv}.2.1 = \\spad{n+1} will produce an error!\\spad{\\br} \\blankline The other components of \\spad{vv}.2 are needed to compute nextSubsetGray efficiently. Note that this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case \\spad{r1} = \\spad{r2} = ... = \\spad{rn} = 2; Note that nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} nextSubsetGray(\\spad{vv}) and \\spad{vv} \\spad{:=} nextSubsetGray(\\spad{vv}) will have the same effect."))) NIL NIL -(-434) +(-465) ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) NIL NIL -(-435) -((|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,{}lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(\\spad{gi})} returns the indicated graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}\\spad{pt}) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(\\spad{gi},{}pt,{}pal)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(\\spad{gi},{}pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{\\spad{gi}},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}pt,{}pal1,{}pal2,{}ps)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(\\spad{gi},{}pt)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}lp,{}pal1,{}pal2,{}p)} sets the components of the graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{\\spad{gi}} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(\\spad{gi},{}lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{\\spad{gi}}.") (((|List| (|Float|)) $) "\\spad{units(\\spad{gi})} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(\\spad{gi},{}lr)} modifies the list of ranges for the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{\\spad{gi}}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(\\spad{gi})} returns the list of ranges of the point components from the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(\\spad{gi})} returns the process ID of the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(\\spad{gi})} returns the list of lists of points which compose the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp,{}lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(\\spad{gi})} takes the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{\\spad{gi}} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) +(-466) +((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,{}lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(\\spad{gi})} returns the indicated graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}\\spad{pt}) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(\\spad{gi},{}pt,{}pal)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(\\spad{gi},{}pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{\\spad{gi}},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}pt,{}pal1,{}pal2,{}ps)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(\\spad{gi},{}pt)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}lp,{}pal1,{}pal2,{}p)} sets the components of the graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{\\spad{gi}} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(\\spad{gi},{}lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{\\spad{gi}}.") (((|List| (|Float|)) $) "\\spad{units(\\spad{gi})} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(\\spad{gi},{}lr)} modifies the list of ranges for the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{\\spad{gi}}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(\\spad{gi})} returns the list of ranges of the point components from the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(\\spad{gi})} returns the process ID of the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(\\spad{gi})} returns the list of lists of points which compose the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp,{}lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(\\spad{gi})} takes the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{\\spad{gi}} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) NIL NIL -(-436 S R E) -((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) +(-467 S R E) +((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with degree \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-437 R E) -((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) +(-468 R E) +((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with degree \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-438 |lv| -2958 R) -((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) +(-469 |lv| -1333 R) +((|constructor| (NIL "Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL -(-439 S) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +(-470 S) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftInverse(\"*\":(\\%,{}\\%)->\\%,{}inv)}\\tab{5}\\spad{ inv(x)*x = 1 }\\spad{\\br} \\tab{5}\\spad{rightInverse(\"*\":(\\%,{}\\%)->\\%,{}inv)}\\tab{4}\\spad{ x*inv(x) = 1 }")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) NIL NIL -(-440) -((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4164 . T)) +(-471) +((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftInverse(\"*\":(\\%,{}\\%)->\\%,{}inv)}\\tab{5}\\spad{ inv(x)*x = 1 }\\spad{\\br} \\tab{5}\\spad{rightInverse(\"*\":(\\%,{}\\%)->\\%,{}inv)}\\tab{4}\\spad{ x*inv(x) = 1 }")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) +((-4502 . T)) NIL -(-441 |Coef| |var| |cen|) +(-472 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|))))) (|HasCategory| (-375 (-501)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-442 |Key| |Entry| |Tbl| |dent|) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasCategory| (-403 (-560)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-473 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001))))) -(-443 R E V P) -((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#4| (QUOTE (-1001))) (-12 (|HasCategory| |#4| (LIST (QUOTE -278) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#3| (QUOTE (-336)))) -(-444) -((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-445 |Key| |Entry| |hashfn|) +((-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082))))) +(-474 R E V P) +((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#4| (QUOTE (-1082))) (-12 (|HasCategory| |#4| (LIST (QUOTE -298) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-364)))) +(-475) +((|constructor| (NIL "This package exports guessing of sequences of rational functions"))) +NIL +((|HasCategory| (-53) (LIST (QUOTE -1029) (QUOTE (-1153))))) +(-476 -1333) +((|constructor| (NIL "This package exports guessing of sequences of numbers in a finite field"))) +NIL +NIL +(-477 -1333) +((|constructor| (NIL "This package exports guessing of sequences of numbers in a finite field"))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-1153))))) +(-478) +((|constructor| (NIL "This package exports guessing of sequences of rational numbers"))) +NIL +((-12 (|HasCategory| (-403 (-560)) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-1153)))))) +(-479 -1333 S EXPRR R -3001 -2801) +((|constructor| (NIL "This package implements guessing of sequences. Packages for the most common cases are provided as \\spadtype{GuessInteger},{} \\spadtype{GuessPolynomial},{} etc.")) (|shiftHP| (((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the \\$\\spad{q}\\$-shift operator") (((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the shift operator")) (|diffHP| (((|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the \\$\\spad{q}\\$-dilation operator") (((|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|))) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the differential operator")) (|guessRat| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRat q} returns a guesser that tries to find a \\spad{q}-rational function whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec} with \\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessRat l} tries to find a rational function whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessRat(l,{} options)} tries to find a rational function whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.")) (|guessPRec| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessPRec q} returns a guesser that tries to find a linear \\spad{q}-recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(q)} with \\spad{maxPower == 1}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessPRec l} tries to find a linear recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxPower == 1)}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessPRec(l,{} options)} tries to find a linear recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} options)} with \\spad{maxPower == 1}.")) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRec q} returns a guesser that finds an ordinary \\spad{q}-difference equation whose first values are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessRec(l,{} options)} tries to find an ordinary difference equation whose first values are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessRec l} tries to find an ordinary difference equation whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessPade| (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessPade(l,{} options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} options)} with \\spad{maxDerivative == 0,{} maxPower == 1,{} allDegrees == true}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessPade(l,{} options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} maxDerivative == 0,{} maxPower == 1,{} allDegrees == true)}.")) (|guessHolo| (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessHolo(l,{} options)} tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} options)} with \\spad{maxPower == 1}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessHolo l} tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} maxPower == 1)}.")) (|guessAlg| (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessAlg(l,{} options)} tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}(\\spad{l},{} options) with \\spad{maxDerivative == 0}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessAlg l} tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}(\\spad{l},{} maxDerivative \\spad{==} 0).")) (|guessADE| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessADE q} returns a guesser that tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessADE(l,{} options)} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessADE l} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessHP| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Mapping| (|Record| (|:| |guessStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| |#1|)) (|UnivariateFormalPowerSeries| |#1|))) (|:| |degreeStream| (|Stream| (|NonNegativeInteger|))) (|:| |testStream| (|Mapping| (|Stream| (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|))) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| |exprStream| (|Mapping| (|Stream| |#3|) |#3| (|Symbol|))) (|:| A (|Mapping| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|) (|SparseUnivariatePolynomial| |#2|))) (|:| AF (|Mapping| (|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateFormalPowerSeries| (|SparseUnivariatePolynomial| |#1|)))) (|:| AX (|Mapping| |#3| (|NonNegativeInteger|) (|Symbol|) |#3|)) (|:| C (|Mapping| (|List| |#2|) (|NonNegativeInteger|)))) (|List| (|GuessOption|)))) "\\spad{guessHP f} constructs an operation that applies Hermite-Pade approximation to the series generated by the given function \\spad{f}.")) (|guessBinRat| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessBinRat q} returns a guesser that tries to find a function of the form \\spad{n+}->qbinomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{q^n}) is a \\spad{q}-rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessBinRat(l,{} options)} tries to find a function of the form \\spad{n+}->binomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessBinRat(l,{} options)} tries to find a function of the form \\spad{n+}->binomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.")) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessExpRat q} returns a guesser that tries to find a function of the form \\spad{n+}->(a+b \\spad{q^n})\\spad{^n} \\spad{r}(\\spad{q^n}),{} where \\spad{r}(\\spad{q^n}) is a \\spad{q}-rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guessExpRat(l,{} options)} tries to find a function of the form \\spad{n+}->(a+b \\spad{n})\\spad{^n} \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessExpRat l} tries to find a function of the form \\spad{n+}->(a+b \\spad{n})\\spad{^n} \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.")) (|guess| (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|))) "\\spad{guess(l,{} guessers,{} ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol \\spad{guessSum} and quotients if ops contains the symbol \\spad{guessProduct} to the list. The given options are used.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|)))) (|List| (|Symbol|))) "\\spad{guess(l,{} guessers,{} ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol guessSum and quotients if ops contains the symbol guessProduct to the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) "\\spad{guess(l,{} options)} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. The given options are used.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guess l} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used."))) +NIL +((-12 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153)))))) +(-480) +((|constructor| (NIL "This package exports guessing of sequences of rational functions"))) +NIL +((-12 (|HasCategory| (-403 (-945 (-560))) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-945 (-560)) (LIST (QUOTE -1029) (QUOTE (-1153)))))) +(-481 |q|) +((|constructor| (NIL "This package exports guessing of sequences of univariate rational functions")) (|shiftHP| (((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|)) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the \\$\\spad{q}\\$-shift operator") ((HPSPEC (|List| (|GuessOption|))) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the shift operator")) (|diffHP| (((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|)) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the \\$\\spad{q}\\$-dilation operator") ((HPSPEC (|List| (|GuessOption|))) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the differential operator")) (|guessRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRat q} returns a guesser that tries to find a \\spad{q}-rational function whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec} with \\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessRat l} tries to find a rational function whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessRat(l,{} options)} tries to find a rational function whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxShift == 0,{} maxPower == 1,{} allDegrees == true)}.")) (|guessPRec| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessPRec q} returns a guesser that tries to find a linear \\spad{q}-recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(q)} with \\spad{maxPower == 1}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessPRec l} tries to find a linear recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} maxPower == 1)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessPRec(l,{} options)} tries to find a linear recurrence with polynomial coefficients whose first values are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l,{} options)} with \\spad{maxPower == 1}.")) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRec q} returns a guesser that finds an ordinary \\spad{q}-difference equation whose first values are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessRec(l,{} options)} tries to find an ordinary difference equation whose first values are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessRec l} tries to find an ordinary difference equation whose first values are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessPade| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessPade(l,{} options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} options)} with \\spad{maxDerivative == 0,{} maxPower == 1,{} allDegrees == true}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessPade(l,{} options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} maxDerivative == 0,{} maxPower == 1,{} allDegrees == true)}.")) (|guessHolo| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessHolo(l,{} options)} tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} options)} with \\spad{maxPower == 1}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessHolo l} tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}\\spad{(l,{} maxPower == 1)}.")) (|guessAlg| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessAlg(l,{} options)} tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options. It is equivalent to \\spadfun{guessADE}(\\spad{l},{} options) with \\spad{maxDerivative == 0}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessAlg l} tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}(\\spad{l},{} maxDerivative \\spad{==} 0).")) (|guessADE| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessADE q} returns a guesser that tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessADE(l,{} options)} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessADE l} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l},{} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessHP| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Mapping| HPSPEC (|List| (|GuessOption|)))) "\\spad{guessHP f} constructs an operation that applies Hermite-Pade approximation to the series generated by the given function \\spad{f}.")) (|guessBinRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessBinRat q} returns a guesser that tries to find a function of the form \\spad{n+}->qbinomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{q^n}) is a \\spad{q}-rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessBinRat(l,{} options)} tries to find a function of the form \\spad{n+}->binomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessBinRat(l,{} options)} tries to find a function of the form \\spad{n+}->binomial(a+b \\spad{n},{} \\spad{n}) \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.")) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessExpRat q} returns a guesser that tries to find a function of the form \\spad{n+}->(a+b \\spad{q^n})\\spad{^n} \\spad{r}(\\spad{q^n}),{} where \\spad{r}(\\spad{q^n}) is a \\spad{q}-rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessExpRat(l,{} options)} tries to find a function of the form \\spad{n+}->(a+b \\spad{n})\\spad{^n} \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessExpRat l} tries to find a function of the form \\spad{n+}->(a+b \\spad{n})\\spad{^n} \\spad{r}(\\spad{n}),{} where \\spad{r}(\\spad{n}) is a rational function,{} that fits \\spad{l}.")) (|guess| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|))) "\\spad{guess(l,{} guessers,{} ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol \\spad{guessSum} and quotients if ops contains the symbol \\spad{guessProduct} to the list. The given options are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|))) "\\spad{guess(l,{} guessers,{} ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol guessSum and quotients if ops contains the symbol guessProduct to the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guess(l,{} options)} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. The given options are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guess l} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used."))) +NIL +NIL +(-482) +((|constructor| (NIL "Symbolic fractions in \\%\\spad{pi} with integer coefficients; The point for using \\spad{Pi} as the default domain for those fractions is that \\spad{Pi} is coercible to the float types,{} and not Expression.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-483 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001))))) -(-446) -((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) -NIL -NIL -(-447 |vl| R) -((|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4169 "*") |has| |#2| (-156)) (-4160 |has| |#2| (-508)) (-4165 |has| |#2| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . 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(|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-775)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-959)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))))) -(-449 S) -((|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-450 -2958 UP UPUP R) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082))))) +(-484) +((|constructor| (NIL "Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. 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T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-486 -2050 S) +((|constructor| (NIL "This type represents the finite direct or cartesian product of an underlying ordered component type. 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T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-488 -1333 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL -(-451 BP) -((|constructor| (NIL "This package provides the functions for the heuristic integer \\spad{gcd}. 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For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-560) (QUOTE (-896))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-560) (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-148))) (|HasCategory| (-560) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-560) (QUOTE (-1013))) (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1128))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-221))) (|HasCategory| (-560) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-560) (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -276) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-296))) (|HasCategory| (-560) (QUOTE (-542))) (|HasCategory| (-560) (QUOTE (-834))) (-2318 (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (QUOTE (-834)))) (|HasCategory| (-560) (LIST (QUOTE -622) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (|HasCategory| (-560) (QUOTE (-146))))) +(-491 A S) +((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4167)) (|HasAttribute| |#1| (QUOTE -4168)) (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) -(-454 S) -((|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2951 . T)) +((|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) +(-492 S) +((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) +((-2537 . T)) NIL -(-455 S) +(-493 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-456) +(-494) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-457 -2958 UP |AlExt| |AlPol|) -((|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) +(-495 -1333 UP |AlExt| |AlPol|) +((|constructor| (NIL "Factorisation in a simple algebraic extension Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL -(-458) +(-496) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| $ (QUOTE (-959))) (|HasCategory| $ (LIST (QUOTE -950) (QUOTE (-501))))) -(-459 S |mn|) -((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-460 R |mnRow| |mnCol|) -((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-461 K R UP) -((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) -NIL -NIL -(-462 R UP -2958) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1029) (QUOTE (-560))))) +(-497 S |mn|) +((|constructor| (NIL "This is the basic one dimensional array data type."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-498 R |mnRow| |mnCol|) +((|constructor| (NIL "This domain implements two dimensional arrays"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-499 K R UP) +((|constructor| (NIL "This package has no description")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) +NIL +NIL +(-500 R UP -1333) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-463 |mn|) -((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| (-107) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-107) (QUOTE (-777))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| (-107) (QUOTE (-1001))) (-12 (|HasCategory| (-107) (LIST (QUOTE -278) (QUOTE (-107)))) (|HasCategory| (-107) (QUOTE (-1001))))) -(-464 K R UP L) -((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) +(-501 |mn|) +((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical And of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical Or of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical Not of \\spad{n}."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| (-121) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-121) (QUOTE (-834))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| (-121) (QUOTE (-1082))) (-12 (|HasCategory| (-121) (LIST (QUOTE -298) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1082))))) +(-502 K R UP L) +((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for mapping functions on the coefficients of univariate and bivariate polynomials.")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL NIL -(-465) -((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{\\spad{s}} into an \\axiom{IndexCard}. Warning: if \\axiom{\\spad{s}} is not of the right format then an error will occur when using it.")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,{}s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) +(-503) +((|constructor| (NIL "This domain implements a container of information about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{\\spad{s}} into an \\axiom{IndexCard}. Warning: if \\axiom{\\spad{s}} is not of the right format then an error will occur")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,{}s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) NIL NIL -(-466 R Q A B) +(-504 R Q A B) ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-467 -2958 |Expon| |VarSet| |DPoly|) -((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) +(-505 K |symb| BLMET) +((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(\\spad{b}).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when \\spad{true},{} a coerce to OutputForm yields the full output of \\spad{tr},{} otherwise encode(\\spad{tr}) is output (see encode function). The default is \\spad{false}.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) +NIL +NIL +(-506 -1333 |Expon| |VarSet| |DPoly|) +((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by generalPosition from PolynomialIdeals and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -556) (QUOTE (-1070))))) -(-468 |vl| |nv|) -((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) +((|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-1153))))) +(-507 |vl| |nv|) +((|constructor| (NIL "This package provides functions for the primary decomposition of polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL NIL -(-469 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +(-508 A S) +((|constructor| (NIL "Indexed direct products of abelian groups over an abelian group \\spad{A} of generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL NIL -(-470 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) +(-509 A S) +((|constructor| (NIL "Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL NIL -(-471 A S) +(-510 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,{}s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL NIL -(-472 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) +(-511 A S) +((|constructor| (NIL "Indexed direct products of ordered abelian monoids \\spad{A} of generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL NIL -(-473 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) +(-512 A S) +((|constructor| (NIL "Indexed direct products of ordered abelian monoid sups \\spad{A},{} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL NIL -(-474 A S) -((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) +(-513 A S) +((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL NIL -(-475 S A B) +(-514 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-476 A B) +(-515 A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-477 S E |un|) -((|constructor| (NIL "Internal implementation of a free abelian monoid."))) +(-516 S E |un|) +((|constructor| (NIL "Internal implementation of a free abelian monoid on any set of generators"))) NIL -((|HasCategory| |#2| (QUOTE (-722)))) -(-478 S |mn|) -((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified \\spad{SMW} \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-479 |p| |n|) +((|HasCategory| |#2| (QUOTE (-779)))) +(-517 S |mn|) +((|constructor| (NIL "A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations\\spad{\\br} \\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}\\spad{\\br} \\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}\\spad{\\br} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\indented{1}{shrinkable(\\spad{b}) sets the shrinkable attribute of flexible arrays to \\spad{b}} \\indented{1}{and returns the previous value} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,{}20) \\spad{X} shrinkable(\\spad{false})\\$\\spad{T1}")) (|physicalLength!| (($ $ (|Integer|)) "\\indented{1}{physicalLength!(\\spad{x},{}\\spad{n}) changes the physical length of \\spad{x} to be \\spad{n} and} \\indented{1}{returns the new array.} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,{}20) \\spad{X} t2:=flexibleArray([\\spad{i} for \\spad{i} in 1..10])\\$\\spad{T1} \\spad{X} physicalLength!(\\spad{t2},{}15)")) (|physicalLength| (((|NonNegativeInteger|) $) "\\indented{1}{physicalLength(\\spad{x}) returns the number of elements \\spad{x} can} \\indented{1}{accomodate before growing} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,{}20) \\spad{X} t2:=flexibleArray([\\spad{i} for \\spad{i} in 1..10])\\$\\spad{T1} \\spad{X} physicalLength \\spad{t2}")) (|flexibleArray| (($ (|List| |#1|)) "\\indented{1}{flexibleArray(\\spad{l}) creates a flexible array from the list of elements \\spad{l}} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,{}20) \\spad{X} flexibleArray([\\spad{i} for \\spad{i} in 1..10])\\$\\spad{T1}"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-528 |#1|) (QUOTE (-134))) (|HasCategory| (-528 |#1|) (QUOTE (-336))) (|HasCategory| (-528 |#1|) (QUOTE (-132))) (-1405 (|HasCategory| (-528 |#1|) (QUOTE (-132))) (|HasCategory| (-528 |#1|) (QUOTE (-336))))) -(-480 R |mnRow| |mnCol| |Row| |Col|) -((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-481 S |mn|) -NIL -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-482 R |Row| |Col| M) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-573 |#1|) (QUOTE (-148))) (|HasCategory| (-573 |#1|) (QUOTE (-364))) (|HasCategory| (-573 |#1|) (QUOTE (-146))) (-2318 (|HasCategory| (-573 |#1|) (QUOTE (-146))) (|HasCategory| (-573 |#1|) (QUOTE (-364))))) +(-519 R |mnRow| |mnCol| |Row| |Col|) +((|constructor| (NIL "There is no description for this domain"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-520 S |mn|) +((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4168))) -(-483 R |Row| |Col| M QF |Row2| |Col2| M2) -((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) +((|HasAttribute| |#3| (QUOTE -4506))) +(-522 R |Row| |Col| M QF |Row2| |Col2| M2) +((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note that the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4168))) -(-484 R |mnRow| |mnCol|) +((|HasAttribute| |#7| (QUOTE -4506))) +(-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-276))) (|HasCategory| |#1| (QUOTE (-508))) (|HasAttribute| |#1| (QUOTE (-4169 "*"))) (|HasCategory| |#1| (QUOTE (-331)))) -(-485 GF) -((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4507 "*"))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359)))) +(-524 GF) +((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note that for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL NIL -(-486 R) +(-525 R) ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment()} then \\spad{f x} is \\spad{x+1}."))) NIL NIL -(-487 |Varset|) +(-526 |Varset|) ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-488 K -2958 |Par|) -((|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) +(-527 K -1333 |Par|) +((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL -(-489) -((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) +(-528 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) +((|constructor| (NIL "This category is part of the PAFF package")) (|excpDivV| ((|#8| $) "\\spad{excpDivV returns} the exceptional divisor of the infinitly close point.")) (|chartV| ((|#9| $) "chartV is the chart of the infinitly close point. The first integer correspond to variable defining the exceptional line,{} the last one the affine neighboorhood and the second one is the remaining integer. For example [1,{}2,{}3] means that \\spad{Z=1},{} \\spad{X=X} and Y=XY. [2,{}3,{}1] means that \\spad{X=1},{} \\spad{Y=Y} and Z=YZ.")) (|multV| (((|NonNegativeInteger|) $) "\\spad{multV returns} the multiplicity of the infinitly close point.")) (|localPointV| (((|AffinePlane| |#1|) $) "\\spad{localPointV returns} the coordinates of the local infinitly close point")) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $) "\\spad{curveV(p)} returns the defining polynomial of the strict transform on which lies the corresponding infinitly close point.")) (|pointV| ((|#5| $) "\\spad{pointV returns} the infinitly close point.")) (|create| (($ |#5| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) (|NonNegativeInteger|) |#9| (|NonNegativeInteger|) |#8| |#1| (|Symbol|)) "\\spad{create an} infinitly close point"))) NIL NIL -(-490) -((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) +(-529 K |symb| BLMET) +((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(\\spad{b}).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when \\spad{true},{} a coerce to OutputForm \\indented{1}{yields the full output of \\spad{tr},{} otherwise encode(\\spad{tr}) is output} (see encode function). The default is \\spad{false}.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) +NIL +NIL +(-530 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) +((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(\\spad{b}).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when \\spad{true},{} a coerce to OutputForm yields the full output of \\spad{tr},{} otherwise encode(\\spad{tr}) is output (see encode function). The default is \\spad{false}.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) +NIL NIL +(-531) +((|constructor| (NIL "Top-level infinity Default infinity signatures for the interpreter.")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL -(-491 R) +NIL +(-532 R) ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-492 |Coef| UTS) +(-533) +((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parse| (($ (|String|)) "parse is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\indented{1}{\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form} \\indented{1}{corresponding to\\space{2}\\spad{a1 op a2 op ... op an}.} \\blankline \\spad{X} a:=[1,{}2,{}3]::List(InputForm) \\spad{X} binary(_+::InputForm,{}a)")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) +NIL +NIL +(-534 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-493 K -2958 |Par|) -((|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) +(-535 K -1333 |Par|) +((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL -(-494 R BP |pMod| |nextMod|) -((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,{}p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,{}f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) +(-536 R BP |pMod| |nextMod|) +((|constructor| (NIL "This file contains the functions for modular \\spad{gcd} algorithm for univariate polynomials with coefficients in a non-trivial euclidean domain (\\spadignore{i.e.} not a field). The package parametrised by the coefficient domain,{} the polynomial domain,{} a prime,{} and a function for choosing the next prime")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,{}p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,{}f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) NIL NIL -(-495 OV E R P) -((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) +(-537 OV E R P) +((|constructor| (NIL "This is an inner package for factoring multivariate polynomials over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) NIL NIL -(-496 K UP |Coef| UTS) +(-538 K UP |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-497 |Coef| UTS) +(-539 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-498 R UP) +(-540 R UP) ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented"))) NIL NIL -(-499 S) +(-541 S) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) NIL NIL -(-500) +(-542) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4165 . T) (-4166 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-501) -((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4149 . T) (-4155 . T) (-4159 . T) (-4154 . T) (-4165 . T) (-4166 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4503 . T) (-4504 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-502 |Key| |Entry| |addDom|) +(-543 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001))))) -(-503 R -2958) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082))))) +(-544 R -1333) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-504 R0 -2958 UP UPUP R) +(-545 R0 -1333 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL -(-505) +(-546) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-506 R) -((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category is an implementation of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2391 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-547 R) +((|constructor| (NIL "This category implements of interval arithmetic and transcendental functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) +((-2550 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-548 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +((|constructor| (NIL "The following is part of the PAFF package")) (|placesOfDegree| (((|Void|) (|PositiveInteger|) |#3| (|List| |#5|)) "\\spad{placesOfDegree(d,{} f,{} pts)} compute the places of degree dividing \\spad{d} of the curve \\spad{f}. \\spad{pts} should be the singular points of the curve \\spad{f}. For \\spad{d} > 1 this only works if \\spad{K} has \\axiomType{PseudoAlgebraicClosureOfFiniteFieldCategory}.")) (|intersectionDivisor| ((|#8| |#3| |#3| (|List| |#10|) (|List| |#5|)) "\\spad{intersectionDivisor(f,{}pol,{}listOfTree)} returns the intersection divisor of \\spad{f} with a curve defined by \\spad{pol}. \\spad{listOfTree} must contain all the desingularisation trees of all singular points on the curve \\indented{1}{defined by \\spad{pol}.}"))) +NIL +NIL +(-549 S) +((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes\\spad{\\br} canonicalUnitNormal\\tab{5}the canonical field is the same for all associates\\spad{\\br} canonicalsClosed\\tab{5}the product of two canonicals is itself canonical")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL -(-507 S) -((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL +(-550) +((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes\\spad{\\br} canonicalUnitNormal\\tab{5}the canonical field is the same for all associates\\spad{\\br} canonicalsClosed\\tab{5}the product of two canonicals is itself canonical")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-508) -((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-551 R -1333) +((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elementary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL -(-509 R -2958) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL +(-552 K |symb| E OV R) +((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) NIL -(-510 I) -((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL +(-553 I) +((|constructor| (NIL "This Package contains basic methods for integer factorization. The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL -(-511) -((|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL +(-554 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR) +((|constructor| (NIL "The following is part of the PAFF package")) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|) |#3| (|List| |#3|)) "\\spad{interpolateForms(D,{}n,{}pol,{}base)} compute the basis of the sub-vector space \\spad{W} of \\spad{V} = ,{} such that for all \\spad{G} in \\spad{W},{} the divisor (\\spad{G}) \\spad{>=} \\spad{D}. All the elements in \\spad{base} must be homogeneous polynomial of degree \\spad{n}. Typicaly,{} \\spad{base} is the set of all monomial of degree \\spad{n:} in that case,{} interpolateForms(\\spad{D},{}\\spad{n},{}\\spad{pol},{}\\spad{base}) returns the basis of the vector space of all forms of degree \\spad{d} that interpolated \\spad{D}. The argument \\spad{pol} must be the same polynomial that defined the curve form which the divisor \\spad{D} is defined."))) NIL -(-512 R -2958 L) -((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -593) (|devaluate| |#2|)))) -(-513) -((|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ^= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(u1,{}m1,{}u2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = u1 mod m1} and \\spad{w = u2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) +(-555) +((|constructor| (NIL "There is no description for this domain")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} is not documented")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} is not documented")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} is not documented")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-514 -2958 UP UPUP R) -((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) +(-556 R -1333 L) +((|constructor| (NIL "Rationalization of several types of genus 0 integrands; This internal package rationalises integrands on curves of the form:\\spad{\\br} \\tab{5}\\spad{y\\^2 = a x\\^2 + b x + c}\\spad{\\br} \\tab{5}\\spad{y\\^2 = (a x + b) / (c x + d)}\\spad{\\br} \\tab{5}\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}\\spad{\\br} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL +((|HasCategory| |#3| (LIST (QUOTE -638) (|devaluate| |#2|)))) +(-557) +((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note that because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note that by convention,{} 0 is returned if \\spad{gcd(a,{}b) ^= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note that \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL -(-515 -2958 UP) +NIL +(-558 -1333 UP UPUP R) +((|constructor| (NIL "Algebraic Hermite reduction.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) +NIL +NIL +(-559 -1333 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL -(-516) -((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) +(-560) +((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) +((-4487 . T) (-4493 . T) (-4497 . T) (-4492 . T) (-4503 . T) (-4504 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-561) +((|constructor| (NIL "\\axiomType{AnnaNumericalIntegrationPackage} is a \\axiom{package} of functions for the \\axiom{category} \\axiomType{NumericalIntegrationCategory} with \\axiom{measure},{} and \\axiom{integrate}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-517 R -2958 L) -((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) +(-562 R -1333 L) +((|constructor| (NIL "Integration of pure algebraic functions; This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -593) (|devaluate| |#2|)))) -(-518 R -2958) +((|HasCategory| |#3| (LIST (QUOTE -638) (|devaluate| |#2|)))) +(-563 R -1333) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1034)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-568))))) -(-519 -2958 UP) -((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-612))))) +(-564 -1333 UP) +((|constructor| (NIL "Rational function integration This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL -(-520 S) -((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) +(-565 S) +((|constructor| (NIL "Provides integer testing and retraction functions.")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-521 -2958) +(-566 -1333) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL -(-522 R) -((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2391 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-567 R) +((|constructor| (NIL "This domain is an implementation of interval arithmetic and transcendental functions over intervals."))) +((-2550 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-523) +(-568) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-524 R -2958) -((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) +(-569 R -1333) +((|constructor| (NIL "Tools for the integrator")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-254))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-254)))) (|HasCategory| |#1| (QUOTE (-508)))) -(-525 -2958 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-274))) (|HasCategory| |#2| (QUOTE (-612)))) (-12 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-274)))) (|HasCategory| |#1| (QUOTE (-550)))) +(-570 -1333 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-526 R -2958) -((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) +(-571 R -1333) +((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form. Handles only rational \\spad{f(s)}."))) NIL NIL -(-527 |p| |unBalanced?|) +(-572 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-528 |p|) -((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-336)))) -(-529) +(-573 |p|) +((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-364)))) +(-574) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-530 -2958) -((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-1070))))) -(-531 E -2958) -((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) +(-575 R -1333) +((|constructor| (NIL "Conversion of integration results to top-level expressions This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-532 R -2958) -((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) +(-576 E -1333) +((|constructor| (NIL "Internally used by the integration packages")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented"))) NIL NIL -(-533 I) -((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) +(-577 -1333) +((|constructor| (NIL "The result of a transcendental integration. If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) +((-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-1153))))) +(-578 I) +((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\spad{n}th roots of integers efficiently.")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL NIL -(-534 GF) +(-579 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-535 R) -((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) +(-580 R) +((|constructor| (NIL "Conversion of integration results to top-level expressions. This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL -((|HasCategory| |#1| (QUOTE (-134)))) -(-536) -((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,{}2,{}...,{}n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,{}3,{}3,{}1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,{}listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,{}\\spad{pi})} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em \\spad{pi}} in the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) +((|HasCategory| |#1| (QUOTE (-148)))) +(-581) +((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {1,{}2,{}...,{}\\spad{n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} [3,{}3,{}3,{}1] labels an irreducible representation for \\spad{n} equals 10. Note that whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,{}listOfPerm)} is the list of the irreducible representations corresponding to \\spad{lambda} in Young\\spad{'s} natural form for the list of permutations given by \\spad{listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition \\spad{lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {1,{}2,{}...,{}\\spad{n}},{} namely (1 2) (2-cycle) and (1 2 ... \\spad{n}) (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,{}\\spad{pi})} is the irreducible representation corresponding to partition \\spad{lambda} in Young\\spad{'s} natural form of the permutation \\spad{pi} in the symmetric group,{} whose elements permute {1,{}2,{}...,{}\\spad{n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to \\spad{lambda}. Note that the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-537 R E V P TS) -((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,{}lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,{}univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) +(-582 R E V P TS) +((|constructor| (NIL "An internal package for computing the rational univariate representation of a zero-dimensional algebraic variety given by a square-free triangular set. The main operation is rur")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,{}lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,{}univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-538 |mn|) -((|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| (-131) (QUOTE (-1001))) (|HasCategory| (-131) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-131) (QUOTE (-777))) (-1405 (|HasCategory| (-131) (QUOTE (-777))) (|HasCategory| (-131) (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-777)))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))))) -(-539 E V R P) -((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) +(-583 |mn|) +((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| (-145) (QUOTE (-1082))) (|HasCategory| (-145) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-145) (QUOTE (-834))) (-2318 (|HasCategory| (-145) (QUOTE (-834))) (|HasCategory| (-145) (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-834)))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))))) +(-584 E V R P) +((|constructor| (NIL "Tools for the summation packages of polynomials")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL -(-540 |Coef|) -((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-501)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-501)) (|devaluate| |#1|))))) (|HasCategory| (-501) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-501))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070))))))) -(-541 |Coef|) +(-585 |Coef|) +((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain used for creating sparse Taylor and Laurent series.")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasCategory| (-560) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-359))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153))))))) +(-586 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4162 |has| |#1| (-508)) (-4161 |has| |#1| (-508)) ((-4169 "*") |has| |#1| (-508)) (-4160 |has| |#1| (-508)) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-508)))) -(-542 A B) +((-4500 |has| |#1| (-550)) (-4499 |has| |#1| (-550)) ((-4507 "*") |has| |#1| (-550)) (-4498 |has| |#1| (-550)) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-550)))) +(-587 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-543 A B C) +(-588 A B C) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-544 R -2958 FG) +(-589 R -1333 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL -(-545 S) -((|constructor| (NIL "\\indented{1}{This package implements 'infinite tuples' for the interpreter.} The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}s)} returns \\spad{[s,{}f(s),{}f(f(s)),{}...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) -NIL -NIL -(-546 R |mn|) +(-590 S) +((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}s)} returns \\spad{[s,{}f(s),{}f(f(s)),{}...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) NIL -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#1| (QUOTE (-959))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-959)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-547 S |Index| |Entry|) -((|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4168)) (|HasCategory| |#2| (QUOTE (-777))) (|HasAttribute| |#1| (QUOTE -4167)) (|HasCategory| |#3| (QUOTE (-1001)))) -(-548 |Index| |Entry|) -((|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2951 . T)) +(-591 R |mn|) +((|constructor| (NIL "This type represents vector like objects with varying lengths and a user-specified initial index."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-994))) (|HasCategory| |#1| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-592 S |Index| |Entry|) +((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note that in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note that in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order. to become indices:")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -(-549 R A) -((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4164 -1405 (-1280 (|has| |#2| (-335 |#1|)) (|has| |#1| (-508))) (-12 (|has| |#2| (-386 |#1|)) (|has| |#1| (-508)))) (-4162 . T) (-4161 . T)) -((|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|))) (-1405 (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))))) -(-550 |Entry|) -((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-1053) (QUOTE (-777))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (QUOTE (-1053))) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (QUOTE (-1001))))) -(-551 S |Key| |Entry|) -((|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) +((|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-834))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasCategory| |#3| (QUOTE (-1082)))) +(-593 |Index| |Entry|) +((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note that for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note that in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note that in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order. to become indices:")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) +((-2537 . T)) NIL +(-594 R A) +((|constructor| (NIL "AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2} (anticommutator). The usual notation \\spad{{a,{}b}_+} cannot be used due to restrictions in the current language. This domain only gives a Jordan algebra if the Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spadfun{jordanAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) +((-4502 -2318 (-2256 (|has| |#2| (-363 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-413 |#1|)) (|has| |#1| (-550)))) (-4500 . T) (-4499 . T)) +((|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))))) +(-595 |Entry|) +((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object. The KeyedAccessFile format is a directory containing a single file called ``index.kaf\\spad{''}. This file is a random access file. The first thing in the file is an integer which is the byte offset of an association list (the dictionary) at the end of the file. The association list is of the form ((key . byteoffset) (key . byteoffset)...) where the byte offset is the number of bytes from the beginning of the file. This offset contains an \\spad{s}-expression for the value of the key.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-1135) (QUOTE (-834))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (QUOTE (-1082))))) +(-596 S |Key| |Entry|) +((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL -(-552 |Key| |Entry|) -((|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4168 . T) (-2951 . T)) NIL -(-553 S) -((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) +(-597 |Key| |Entry|) +((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) +((-4506 . T) (-2537 . T)) NIL -((|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) -(-554 R S) +(-598 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-555 S) +(-599 S) +((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) +NIL +((|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) +(-600 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-556 S) +(-601 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-557 -2958 UP) +(-602 -1333 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL -(-558 A R S) -((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-775)))) -(-559 S R) +(-603 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-560 R) +(-604 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4164 . T)) +((-4502 . T)) NIL -(-561 R -2958) +(-605 A R S) +((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-832)))) +(-606 R -1333) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform."))) NIL NIL -(-562 R UP) -((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4162 . T) (-4161 . T) ((-4169 "*") . T) (-4160 . T) (-4164 . T)) -((|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501))))) -(-563 R E V P TS ST) -((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) +(-607 R UP) +((|constructor| (NIL "Univariate polynomials with negative and positive exponents.")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} is not documented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} is not documented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} is not documented")) (|trailingCoefficient| ((|#1| $) "trailingCoefficient is not documented")) (|leadingCoefficient| ((|#1| $) "leadingCoefficient is not documented")) (|reductum| (($ $) "\\spad{reductum(x)} is not documented")) (|order| (((|Integer|) $) "\\spad{order(x)} is not documented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} is not documented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} is not documented"))) +((-4500 . T) (-4499 . T) ((-4507 "*") . T) (-4498 . T) (-4502 . T)) +((|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560))))) +(-608 R E V P TS ST) +((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as zeroSetSplit(\\spad{lp},{}clos?) from RegularTriangularSetCategory.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL NIL -(-564 OV E Z P) +(-609 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"F\"}.")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,{}unilist,{}plead,{}vl,{}lvar,{}lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod,{} numFacts,{} evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-565 |VarSet| R |Order|) -((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4164 . T)) +(-610 |VarSet| R |Order|) +((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind.")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|listOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{listOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) +((-4502 . T)) NIL -(-566 R |ls|) -((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) +(-611 R |ls|) +((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are lexTriangular and squareFreeLexTriangular. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the lexTriangular method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the squareFreeLexTriangular operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets.")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the FGLM strategy is used,{} otherwise the Sugar strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the FGLM strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) NIL NIL -(-567 R -2958) -((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) +(-612) +((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-568) -((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) +(-613 R -1333) +((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-569 |lv| -2958) -((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) +(-614 |lv| -1333) +((|constructor| (NIL "Given a Groebner basis \\spad{B} with respect to the total degree ordering for a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL -(-570) -((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4168 . T)) -((|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 (-50))) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-1053) (QUOTE (-777))) (|HasCategory| (-50) (QUOTE (-1001))) (-12 (|HasCategory| (-50) (LIST (QUOTE -278) (QUOTE (-50)))) (|HasCategory| (-50) (QUOTE (-1001)))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 (-50))) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 (-50))) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (QUOTE (-1053))) (LIST (QUOTE |:|) (QUOTE -2922) (QUOTE (-50)))))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 (-50))) (QUOTE (-1001)))) (-1405 (|HasCategory| (-50) (QUOTE (-1001))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 (-50))) (QUOTE (-1001))))) -(-571 R A) -((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4164 -1405 (-1280 (|has| |#2| (-335 |#1|)) (|has| |#1| (-508))) (-12 (|has| |#2| (-386 |#1|)) (|has| |#1| (-508)))) (-4162 . T) (-4161 . T)) -((|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|))) (-1405 (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -335) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -386) (|devaluate| |#1|)))))) -(-572 S R) -((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) +(-615) +((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|close!| (($ $) "\\spad{close!(f)} returns the library \\spad{f} closed to input and output.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) +((-4506 . T)) +((|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 (-57))) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-1135) (QUOTE (-834))) (|HasCategory| (-57) (QUOTE (-1082))) (-12 (|HasCategory| (-57) (LIST (QUOTE -298) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1082)))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 (-57))) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 (-57))) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 (-57))) (QUOTE (-1082)))) (-2318 (|HasCategory| (-57) (QUOTE (-1082))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 (-57))) (QUOTE (-1082))))) +(-616 S R) +((|constructor| (NIL "The category of Lie Algebras. It is used by the domains of non-commutative algebra,{} LiePolynomial and XPBWPolynomial.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL -((|HasCategory| |#2| (QUOTE (-331)))) -(-573 R) -((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4162 . T) (-4161 . T)) +((|HasCategory| |#2| (QUOTE (-359)))) +(-617 R) +((|constructor| (NIL "The category of Lie Algebras. It is used by the domains of non-commutative algebra,{} LiePolynomial and XPBWPolynomial.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4500 . T) (-4499 . T)) NIL -(-574 R FE) +(-618 R A) +((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) +((-4502 -2318 (-2256 (|has| |#2| (-363 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-413 |#1|)) (|has| |#1| (-550)))) (-4500 . T) (-4499 . T)) +((|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -363) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -413) (|devaluate| |#1|)))))) +(-619 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL NIL -(-575 R) +(-620 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-576 S R) +(-621 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-331))) (-3031 (|HasCategory| |#1| (QUOTE (-331))))) -(-577 R) +((|HasCategory| |#1| (QUOTE (-359))) (-3186 (|HasCategory| |#1| (QUOTE (-359))))) +(-622 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4164 . T)) +((-4502 . T)) +NIL +(-623 A B) +((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note that when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL -(-578 S) -((|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-751))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-579 A B) -((|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL +(-624 A B) +((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}."))) NIL -(-580 A B) -((|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL +(-625 A B C) +((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL -(-581 A B C) -((|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) +NIL +(-626 S) +((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-627 K PCS) +((|constructor| (NIL "Part of the PAFF package")) (|finiteSeries2LinSys| (((|Matrix| |#1|) (|List| |#2|) (|Integer|)) "\\spad{finiteSeries2LinSys(ls,{}n)} returns a matrix which right kernel is the solution of the linear combinations of the series in \\spad{ls} which has order greater or equal to \\spad{n}. NOTE: All the series in \\spad{ls} must be finite and must have order at least 0: so one must first call on each of them the function filterUpTo(\\spad{s},{}\\spad{n}) and apply an appropriate shift (mult by a power of \\spad{t})."))) NIL NIL -(-582 S) -((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490))))) -(-583 R) -((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) +(-628 S) +((|constructor| (NIL "The \\spadtype{ListMultiDictionary} domain implements a dictionary with duplicates allowed. The representation is a list with duplicates represented explicitly. Hence most operations will be relatively inefficient when the number of entries in the dictionary becomes large. If the objects in the dictionary belong to an ordered set,{} the entries are maintained in ascending order.")) (|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) +(-629 R) +((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{ (a*b)*x = a*(b*x) }\\spad{\\br} \\tab{5}\\spad{ (a+b)*x = (a*x)+(b*x) }\\spad{\\br} \\tab{5}\\spad{ a*(x+y) = (a*x)+(a*y) }")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-584 S E |un|) +(-630 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,{}y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x,{} y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s,{} e,{} x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s,{} a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a,{} s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l,{} n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l,{} n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s,{} e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l,{} fop,{} fexp,{} unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a,{} b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a,{} n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-585 A S) -((|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) +(-631 A S) +((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note that \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note that \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note that \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note that \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note that for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note that in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note that for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note that \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note that for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note that for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4168))) -(-586 S) -((|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-2951 . T)) +((|HasAttribute| |#1| (QUOTE -4506))) +(-632 S) +((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note that \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note that \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note that \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note that \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note that for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note that in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note that for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note that \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note that for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note that for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) +((-2537 . T)) NIL -(-587 M R S) -((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-721)))) -(-588 R -2958 L) +(-633 K) +((|printInfo| (((|Boolean|)) "returns the value of the \\spad{printInfo} flag.") (((|Boolean|) (|Boolean|)) "\\spad{printInfo(b)} set a flag such that when \\spad{true} (\\spad{b} \\spad{<-} \\spad{true}) prints some information during some critical computation.")) (|coefOfFirstNonZeroTerm| ((|#1| $) "\\spad{coefOfFirstNonZeroTerm(s)} returns the first non zero coefficient of the series.")) (|filterUpTo| (($ $ (|Integer|)) "\\spad{filterUpTo(s,{}n)} returns the series consisting of the terms of \\spad{s} having degree strictly less than \\spad{n}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(s,{}n)} returns t**n * \\spad{s}")) (|series| (($ (|Integer|) |#1| $) "\\spad{series(e,{}c,{}s)} create the series c*t**e + \\spad{s}.")) (|removeZeroes| (($ $) "\\spad{removeZeroes(s)} removes the zero terms in \\spad{s}.") (($ (|Integer|) $) "\\spad{removeZeroes(n,{}s)} removes the zero terms in the first \\spad{n} terms of \\spad{s}.")) (|monomial2series| (($ (|List| $) (|List| (|NonNegativeInteger|)) (|Integer|)) "\\spad{monomial2series(ls,{}le,{}n)} returns t**n * reduce(\\spad{\"*\"},{}[\\spad{s} \\spad{**} \\spad{e} for \\spad{s} in \\spad{ls} for \\spad{e} in \\spad{le}])")) (|delay| (($ (|Mapping| $)) "\\spad{delay delayed} the computation of the next term of the series given by the input function.")) (|posExpnPart| (($ $) "\\spad{posExpnPart(s)} returns the series \\spad{s} less the terms with negative exponant.")) (|order| (((|Integer|) $) "\\spad{order(s)} returns the order of \\spad{s}."))) +(((-4507 "*") . T) (-4498 . T) (-4497 . T) (-4503 . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-634 R -1333 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-589 A -1331) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-331)))) -(-590 A) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-331)))) -(-591 A M) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-331)))) -(-592 S A) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -NIL -((|HasCategory| |#2| (QUOTE (-331)))) -(-593 A) -((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-594 -2958 UP) +(-635 A) +((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition:\\spad{\\br} \\spad{(L1 * L2).(f) = L1 L2 f}"))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-359)))) +(-636 A M) +((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition:\\spad{\\br} \\spad{(L1 * L2).(f) = L1 L2 f}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-359)))) +(-637 S A) +((|constructor| (NIL "LinearOrdinaryDifferentialOperatorCategory is the category of differential operators with coefficients in a ring A with a given derivation. \\blankline Multiplication of operators corresponds to functional composition:\\spad{\\br} (\\spad{L1} * \\spad{L2}).(\\spad{f}) = \\spad{L1} \\spad{L2} \\spad{f}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) +NIL +((|HasCategory| |#2| (QUOTE (-359)))) +(-638 A) +((|constructor| (NIL "LinearOrdinaryDifferentialOperatorCategory is the category of differential operators with coefficients in a ring A with a given derivation. \\blankline Multiplication of operators corresponds to functional composition:\\spad{\\br} (\\spad{L1} * \\spad{L2}).(\\spad{f}) = \\spad{L1} \\spad{L2} \\spad{f}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) +((-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-639 -1333 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-595 A L) +(-640 A -2533) +((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition:\\spad{\\br} \\spad{(L1 * L2).(f) = L1 L2 f}"))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-359)))) +(-641 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-596 S) +(-642 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-597) +(-643) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-598 R) -((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) +(-644 M R S) +((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) +((-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-778)))) +(-645 K) +((|constructor| (NIL "A package that exports several linear algebra operations over lines of matrices. Part of the PAFF package.")) (|reduceRowOnList| (((|List| (|List| |#1|)) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{reduceRowOnList(v,{}lvec)} applies a row reduction on each of the element of \\spad{lv} using \\spad{v} according to a pivot in \\spad{v} which is set to be the first non nul element in \\spad{v}.")) (|reduceLineOverLine| (((|List| |#1|) (|List| |#1|) (|List| |#1|) |#1|) "\\spad{reduceLineOverLine(v1,{}v2,{}a)} returns \\spad{v1}-\\spad{a*v1} where \\indented{1}{\\spad{v1} and \\spad{v2} are considered as vector space.}")) (|quotVecSpaceBasis| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{quotVecSpaceBasis(b1,{}b2)} returns a basis of \\spad{V1/V2} where \\spad{V1} and \\spad{V2} are vector space with basis \\spad{b1} and \\spad{b2} resp. and \\spad{V2} is suppose to be include in \\spad{V1}; Note that if it is not the case then it returs the basis of V1/W where \\spad{W} = intersection of \\spad{V1} and \\spad{V2}")) (|reduceRow| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "reduceRow: if the input is considered as a matrix,{} the output would be the row reduction matrix. It\\spad{'s} almost the rowEchelon form except that no permution of lines is performed."))) NIL NIL -(-599 |VarSet| R) -((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4162 . T) (-4161 . T)) -((|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-156)))) -(-600 A S) -((|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) +(-646 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) +((|constructor| (NIL "The following is part of the PAFF package")) (|localize| (((|Record| (|:| |fnc| |#3|) (|:| |crv| |#3|) (|:| |chart| (|List| (|Integer|)))) |#3| |#5| |#3| (|Integer|)) "\\spad{localize(f,{}pt,{}crv,{}n)} returns a record containing the polynomials \\spad{f} and \\spad{crv} translate to the origin with respect to \\spad{pt}. The last element of the records,{} consisting of three integers contains information about the local parameter that will be used (either \\spad{x} or \\spad{y}): the first integer correspond to the variable that will be used as a local parameter.")) (|pointDominateBy| ((|#5| |#7|) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl}.")) (|localParamOfSimplePt| (((|List| |#6|) |#5| |#3| (|Integer|)) "\\spad{localParamOfSimplePt(pt,{}pol,{}n)} computes the local parametrization of the simple point \\spad{pt} on the curve defined by \\spad{pol}. This local parametrization is done according to the standard open affine plane set by \\spad{n}")) (|pointToPlace| ((|#7| |#5| |#3|) "\\spad{pointToPlace(pt,{}pol)} takes for input a simple point \\spad{pt} on the curve defined by \\spad{pol} and set the local parametrization of the point.")) (|printInfo| (((|Boolean|)) "returns the value of the \\spad{printInfo} flag.") (((|Boolean|) (|Boolean|)) "\\spad{printInfo(b)} set a flag such that when \\spad{true} (\\spad{b} \\spad{<-} \\spad{true}) prints some information during some critical computation."))) NIL NIL -(-601 S) -((|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-647 R) +((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL -(-602 -2958 |Row| |Col| M) -((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL +(-648 |VarSet| R) +((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4500 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-170)))) +(-649 A S) +((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) +NIL +NIL +(-650 S) +((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-603 -2958) +(-651 -1333) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-604 R E OV P) -((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) +(-652 -1333 |Row| |Col| M) +((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) +NIL NIL +(-653 R E OV P) +((|constructor| (NIL "This package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL -(-605 |n| R) -((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4164 . T) (-4167 . T) (-4161 . T) (-4162 . T)) -((|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206))) (|HasAttribute| |#2| (QUOTE (-4169 "*"))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-508))) (-1405 (|HasAttribute| |#2| (QUOTE (-4169 "*"))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-206)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001))))) (|HasCategory| |#2| (QUOTE (-156)))) -(-606 |VarSet|) -((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL +(-654 |n| R) +((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by\\spad{\\br} \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{}\\spad{\\br} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) +((-4502 . T) (-4505 . T) (-4499 . T) (-4500 . T)) +((|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221))) (|HasAttribute| |#2| (QUOTE (-4507 "*"))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-550))) (-2318 (|HasAttribute| |#2| (QUOTE (-4507 "*"))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-221)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082))))) (|HasCategory| |#2| (QUOTE (-170)))) +(-655 |VarSet|) +((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule:\\spad{\\br} \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds.\\spad{\\br} Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic.")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if retractable?(\\spad{x}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if retractable?(\\spad{x}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL -(-607 A S) -((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) NIL +(-656 A S) +((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\indented{1}{complete(st) causes all entries of 'st' to be computed.} \\indented{1}{this function should only be called on streams which are} \\indented{1}{known to be finite.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} n:=filterUntil(i+-\\spad{>i>100},{}\\spad{m}) \\spad{X} numberOfComputedEntries \\spad{n} \\spad{X} complete \\spad{n} \\spad{X} numberOfComputedEntries \\spad{n}")) (|extend| (($ $ (|Integer|)) "\\indented{1}{extend(st,{}\\spad{n}) causes entries to be computed,{} if necessary,{}} \\indented{1}{so that 'st' will have at least \\spad{'n'} explicit entries or so} \\indented{1}{that all entries of 'st' will be computed if 'st' is finite} \\indented{1}{with length \\spad{<=} \\spad{n}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m} \\spad{X} extend(\\spad{m},{}20) \\spad{X} numberOfComputedEntries \\spad{m}")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\indented{1}{numberOfComputedEntries(st) returns the number of explicitly} \\indented{1}{computed entries of stream st which exist immediately prior to the} \\indented{1}{time this function is called.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m}")) (|rst| (($ $) "\\indented{1}{\\spad{rst}(\\spad{s}) returns a pointer to the next node of stream \\spad{s}.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} \\spad{rst} \\spad{m}")) (|frst| ((|#2| $) "\\indented{1}{frst(\\spad{s}) returns the first element of stream \\spad{s}.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} frst \\spad{m}")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note that a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\indented{1}{lazy?(\\spad{s}) returns \\spad{true} if the first node of the stream \\spad{s}} \\indented{1}{is a lazy evaluation mechanism which could produce an} \\indented{1}{additional entry to \\spad{s}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} lazy? \\spad{m}")) (|explicitlyEmpty?| (((|Boolean|) $) "\\indented{1}{explicitlyEmpty?(\\spad{s}) returns \\spad{true} if the stream is an} \\indented{1}{(explicitly) empty stream.} \\indented{1}{Note that this is a null test which will not cause lazy evaluation.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} explicitlyEmpty? \\spad{m}")) (|explicitEntries?| (((|Boolean|) $) "\\indented{1}{explicitEntries?(\\spad{s}) returns \\spad{true} if the stream \\spad{s} has} \\indented{1}{explicitly computed entries,{} and \\spad{false} otherwise.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} explicitEntries? \\spad{m}")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\indented{1}{select(\\spad{f},{}st) returns a stream consisting of those elements of stream} \\indented{1}{st satisfying the predicate \\spad{f}.} \\indented{1}{Note that \\spad{select(f,{}st) = [x for x in st | f(x)]}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} select(\\spad{x+}->prime? \\spad{x},{}\\spad{m})")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\indented{1}{remove(\\spad{f},{}st) returns a stream consisting of those elements of stream} \\indented{1}{st which do not satisfy the predicate \\spad{f}.} \\indented{1}{Note that \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{f}(i:PositiveInteger):Boolean \\spad{==} even? \\spad{i} \\spad{X} remove(\\spad{f},{}\\spad{m})"))) NIL -(-608 S) -((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2951 . T)) NIL -(-609 R) +(-657 S) +((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\indented{1}{complete(st) causes all entries of 'st' to be computed.} \\indented{1}{this function should only be called on streams which are} \\indented{1}{known to be finite.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} n:=filterUntil(i+-\\spad{>i>100},{}\\spad{m}) \\spad{X} numberOfComputedEntries \\spad{n} \\spad{X} complete \\spad{n} \\spad{X} numberOfComputedEntries \\spad{n}")) (|extend| (($ $ (|Integer|)) "\\indented{1}{extend(st,{}\\spad{n}) causes entries to be computed,{} if necessary,{}} \\indented{1}{so that 'st' will have at least \\spad{'n'} explicit entries or so} \\indented{1}{that all entries of 'st' will be computed if 'st' is finite} \\indented{1}{with length \\spad{<=} \\spad{n}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m} \\spad{X} extend(\\spad{m},{}20) \\spad{X} numberOfComputedEntries \\spad{m}")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\indented{1}{numberOfComputedEntries(st) returns the number of explicitly} \\indented{1}{computed entries of stream st which exist immediately prior to the} \\indented{1}{time this function is called.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m}")) (|rst| (($ $) "\\indented{1}{\\spad{rst}(\\spad{s}) returns a pointer to the next node of stream \\spad{s}.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} \\spad{rst} \\spad{m}")) (|frst| ((|#1| $) "\\indented{1}{frst(\\spad{s}) returns the first element of stream \\spad{s}.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} frst \\spad{m}")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note that a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\indented{1}{lazy?(\\spad{s}) returns \\spad{true} if the first node of the stream \\spad{s}} \\indented{1}{is a lazy evaluation mechanism which could produce an} \\indented{1}{additional entry to \\spad{s}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} lazy? \\spad{m}")) (|explicitlyEmpty?| (((|Boolean|) $) "\\indented{1}{explicitlyEmpty?(\\spad{s}) returns \\spad{true} if the stream is an} \\indented{1}{(explicitly) empty stream.} \\indented{1}{Note that this is a null test which will not cause lazy evaluation.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} explicitlyEmpty? \\spad{m}")) (|explicitEntries?| (((|Boolean|) $) "\\indented{1}{explicitEntries?(\\spad{s}) returns \\spad{true} if the stream \\spad{s} has} \\indented{1}{explicitly computed entries,{} and \\spad{false} otherwise.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} explicitEntries? \\spad{m}")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\indented{1}{select(\\spad{f},{}st) returns a stream consisting of those elements of stream} \\indented{1}{st satisfying the predicate \\spad{f}.} \\indented{1}{Note that \\spad{select(f,{}st) = [x for x in st | f(x)]}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 0..] \\spad{X} select(\\spad{x+}->prime? \\spad{x},{}\\spad{m})")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\indented{1}{remove(\\spad{f},{}st) returns a stream consisting of those elements of stream} \\indented{1}{st which do not satisfy the predicate \\spad{f}.} \\indented{1}{Note that \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{f}(i:PositiveInteger):Boolean \\spad{==} even? \\spad{i} \\spad{X} remove(\\spad{f},{}\\spad{m})"))) +((-2537 . T)) +NIL +(-658 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (QUOTE (-959))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-959)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-610 |VarSet|) -((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-659 |VarSet|) +((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if retractable?(\\spad{x}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if retractable?(\\spad{x}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if retractable?(\\spad{x}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if retractable?(\\spad{x}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\indented{1}{\\axiom{coerce(\\spad{x})} returns the element of} \\axiomType{OrderedFreeMonoid}(VarSet) \\indented{1}{corresponding to \\axiom{\\spad{x}} by removing parentheses.}")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL NIL -(-611 A) -((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}."))) +(-660 A) +((|constructor| (NIL "Various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-612 A C) -((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument."))) +(-661 A C) +((|constructor| (NIL "Various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument."))) NIL NIL -(-613 A B C) -((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}."))) +(-662 A B C) +((|constructor| (NIL "Various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}."))) NIL NIL -(-614 A) -((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) +(-663 A) +((|constructor| (NIL "Various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-615 A C) -((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) +(-664 A C) +((|constructor| (NIL "Various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-616 A B C) -((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) +(-665 A B C) +((|constructor| (NIL "Various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}"))) NIL NIL -(-617 S R |Row| |Col|) -((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) +(-666 A B) +((|constructor| (NIL "Functional Composition. Given functions \\spad{f} and \\spad{g},{} returns the applicable closure")) (/ (((|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|)) "\\indented{1}\\spad{(+) does functional addition} \\blankline \\spad{X} \\spad{p:=}(x:EXPR(INT)):EXPR(INT)+->3*x \\spad{X} \\spad{q:=}(x:EXPR(INT)):EXPR(INT)+-\\spad{>2*x+3} \\spad{X} (\\spad{p/q})(4) \\spad{X} (\\spad{p/q})(\\spad{x})")) (* (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}\\spad{(+) does functional addition} \\blankline \\spad{X} \\spad{f:=}(x:INT):INT +-> 3*x \\spad{X} \\spad{g:=}(x:INT):INT +-> 2*x+3 \\spad{X} (\\spad{f*g})(4)")) (- (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}\\spad{(+) does functional addition} \\blankline \\spad{X} \\spad{f:=}(x:INT):INT +-> 3*x \\spad{X} \\spad{g:=}(x:INT):INT +-> 2*x+3 \\spad{X} (\\spad{f}-\\spad{g})(4)")) (+ (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}\\spad{(+) does functional addition} \\blankline \\spad{X} \\spad{f:=}(x:INT):INT +-> 3*x \\spad{X} \\spad{g:=}(x:INT):INT +-> 2*x+3 \\spad{X} (\\spad{f+g})(4)"))) NIL -((|HasAttribute| |#2| (QUOTE (-4169 "*"))) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-508)))) -(-618 R |Row| |Col|) -((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4167 . T) (-4168 . T) (-2951 . T)) NIL -(-619 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-667 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-620 R |Row| |Col| M) +(-668 S R |Row| |Col|) +((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\indented{1}{\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}.} \\indented{1}{If the matrix is not invertible,{} \"failed\" is returned.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} inverse matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|pfaffian| ((|#2| $) "\\indented{1}{\\spad{pfaffian(m)} returns the Pfaffian of the matrix \\spad{m}.} \\indented{1}{Error if the matrix is not antisymmetric} \\blankline \\spad{X} pfaffian [[0,{}1,{}0,{}0],{}[\\spad{-1},{}0,{}0,{}0],{}[0,{}0,{}0,{}1],{}[0,{}0,{}\\spad{-1},{}0]]")) (|minordet| ((|#2| $) "\\indented{1}{\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using} \\indented{1}{minors. Error: if the matrix is not square.} \\blankline \\spad{X} minordet matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|determinant| ((|#2| $) "\\indented{1}{\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} determinant matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|nullSpace| (((|List| |#4|) $) "\\indented{1}{\\spad{nullSpace(m)} returns a basis for the null space of} \\indented{1}{the matrix \\spad{m}.} \\blankline \\spad{X} nullSpace matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|nullity| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is} \\indented{1}{the dimension of the null space of the matrix \\spad{m}.} \\blankline \\spad{X} nullity matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|rank| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{rank(m)} returns the rank of the matrix \\spad{m}.} \\blankline \\spad{X} rank matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|columnSpace| (((|List| |#4|) $) "\\indented{1}{\\spad{columnSpace(m)} returns a sublist of columns of the matrix \\spad{m}} \\indented{1}{forming a basis of its column space} \\blankline \\spad{X} columnSpace matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9],{}[1,{}1,{}1]]")) (|rowEchelon| (($ $) "\\indented{1}{\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.} \\blankline \\spad{X} rowEchelon matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (/ (($ $ |#2|) "\\indented{1}{\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.} \\blankline \\spad{X} m:=matrix [[2**i for \\spad{i} in 2..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m/4}")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\indented{1}{\\spad{exquo(m,{}r)} computes the exact quotient of the elements} \\indented{1}{of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.} \\blankline \\spad{X} m:=matrix [[2**i for \\spad{i} in 2..4] for \\spad{j} in 1..5] \\spad{X} exquo(\\spad{m},{}2)")) (** (($ $ (|Integer|)) "\\indented{1}{\\spad{m**n} computes an integral power of the matrix \\spad{m}.} \\indented{1}{Error: if matrix is not square or if the matrix} \\indented{1}{is square but not invertible.} \\blankline \\spad{X} (matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]) \\spad{**} 2") (($ $ (|NonNegativeInteger|)) "\\indented{1}{\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m**3}")) (* ((|#3| |#3| $) "\\indented{1}{\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} r:=transpose([1,{}2,{}3,{}4,{}5])@Matrix(INT) \\spad{X} \\spad{r*m}") ((|#4| $ |#4|) "\\indented{1}{\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} c:=coerce([1,{}2,{}3,{}4,{}5])@Matrix(INT) \\spad{X} \\spad{m*c}") (($ (|Integer|) $) "\\indented{1}{\\spad{n * x} is an integer multiple.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 3*m") (($ $ |#2|) "\\indented{1}{\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the} \\indented{1}{matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*1/3}") (($ |#2| $) "\\indented{1}{\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the} \\indented{1}{matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 1/3*m") (($ $ $) "\\indented{1}{\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*m}")) (- (($ $) "\\indented{1}{\\spad{-x} returns the negative of the matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{-m}") (($ $ $) "\\indented{1}{\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m}-\\spad{m}")) (+ (($ $ $) "\\indented{1}{\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m+m}")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\indented{1}{\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the} \\indented{1}{matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for} \\indented{1}{\\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setsubMatrix!(\\spad{m},{}2,{}2,{}matrix [[3,{}3],{}[3,{}3]])")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix} \\indented{1}{\\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2}} \\indented{1}{and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} subMatrix(\\spad{m},{}1,{}3,{}2,{}4)")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th} \\indented{1}{columns of \\spad{m}. This destructively alters the matrix.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} swapColumns!(\\spad{m},{}2,{}4)")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th} \\indented{1}{rows of \\spad{m}. This destructively alters the matrix.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} swapRows!(\\spad{m},{}2,{}4)")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\indented{1}{\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}.} \\indented{1}{If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]}} \\indented{1}{and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)}} \\indented{1}{is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setelt(\\spad{m},{}3,{}3,{}10)")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\indented{1}{\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting} \\indented{1}{of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}} \\indented{1}{If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList =} \\indented{1}{[j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of} \\indented{1}{\\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} elt(\\spad{m},{}3,{}3)")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\indented{1}{\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list} \\indented{1}{of lists.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} listOfLists \\spad{m}")) (|vertConcat| (($ $ $) "\\indented{1}{\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an} \\indented{1}{equal number of columns. The entries of \\spad{y} appear below} \\indented{1}{of the entries of \\spad{x}.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of columns.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} vertConcat(\\spad{m},{}\\spad{m})")) (|horizConcat| (($ $ $) "\\indented{1}{\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with} \\indented{1}{an equal number of rows. The entries of \\spad{y} appear to the right} \\indented{1}{of the entries of \\spad{x}.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of rows.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} horizConcat(\\spad{m},{}\\spad{m})")) (|squareTop| (($ $) "\\indented{1}{\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first} \\indented{1}{\\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if} \\indented{1}{\\spad{m < n}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..2] for \\spad{j} in 1..5] \\spad{X} squareTop \\spad{m}")) (|transpose| (($ $) "\\indented{1}{\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} transpose \\spad{m}") (($ |#3|) "\\indented{1}{\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.} \\blankline \\spad{X} transpose([1,{}2,{}3])@Matrix(INT)")) (|coerce| (($ |#4|) "\\indented{1}{\\spad{coerce(col)} converts the column col to a column matrix.} \\blankline \\spad{X} coerce([1,{}2,{}3])@Matrix(INT)")) (|diagonalMatrix| (($ (|List| $)) "\\indented{1}{\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix} \\indented{1}{\\spad{M} with block matrices \\spad{m1},{}...,{}\\spad{mk} down the diagonal,{}} \\indented{1}{with 0 block matrices elsewhere.} \\indented{1}{More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{}} \\indented{1}{then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix\\space{2}with entries} \\indented{1}{\\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if} \\indented{1}{\\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and} \\indented{1}{\\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{}} \\indented{1}{\\spad{m.i.j} = 0\\space{2}otherwise.} \\blankline \\spad{X} diagonalMatrix [matrix [[1,{}2],{}[3,{}4]],{} matrix [[4,{}5],{}[6,{}7]]]") (($ (|List| |#2|)) "\\indented{1}{\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements} \\indented{1}{of \\spad{l} on the diagonal.} \\blankline \\spad{X} diagonalMatrix [1,{}2,{}3]")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\indented{1}{\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the} \\indented{1}{diagonal and zeroes elsewhere.} \\blankline \\spad{X} z:Matrix(INT):=scalarMatrix(3,{}5)")) (|matrix| (($ (|List| (|List| |#2|))) "\\indented{1}{\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the} \\indented{1}{list of lists is viewed as a list of the rows of the matrix.} \\blankline \\spad{X} matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9],{}[1,{}1,{}1]]")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\indented{1}{\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.} \\blankline \\spad{X} z:Matrix(INT):=zero(3,{}3)")) (|antisymmetric?| (((|Boolean|) $) "\\indented{1}{\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j})} \\indented{1}{and \\spad{false} otherwise.} \\blankline \\spad{X} antisymmetric? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|symmetric?| (((|Boolean|) $) "\\indented{1}{\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false}} \\indented{1}{otherwise.} \\blankline \\spad{X} symmetric? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|diagonal?| (((|Boolean|) $) "\\indented{1}{\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and} \\indented{1}{\\spad{false} otherwise.} \\blankline \\spad{X} diagonal? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|square?| (((|Boolean|) $) "\\indented{1}{\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix} \\indented{1}{(if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.} \\blankline \\spad{X} square matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) +NIL +((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE (-4507 "*"))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-550)))) +(-669 R |Row| |Col|) +((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\indented{1}{\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}.} \\indented{1}{If the matrix is not invertible,{} \"failed\" is returned.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} inverse matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|pfaffian| ((|#1| $) "\\indented{1}{\\spad{pfaffian(m)} returns the Pfaffian of the matrix \\spad{m}.} \\indented{1}{Error if the matrix is not antisymmetric} \\blankline \\spad{X} pfaffian [[0,{}1,{}0,{}0],{}[\\spad{-1},{}0,{}0,{}0],{}[0,{}0,{}0,{}1],{}[0,{}0,{}\\spad{-1},{}0]]")) (|minordet| ((|#1| $) "\\indented{1}{\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using} \\indented{1}{minors. Error: if the matrix is not square.} \\blankline \\spad{X} minordet matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|determinant| ((|#1| $) "\\indented{1}{\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} determinant matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|nullSpace| (((|List| |#3|) $) "\\indented{1}{\\spad{nullSpace(m)} returns a basis for the null space of} \\indented{1}{the matrix \\spad{m}.} \\blankline \\spad{X} nullSpace matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|nullity| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is} \\indented{1}{the dimension of the null space of the matrix \\spad{m}.} \\blankline \\spad{X} nullity matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|rank| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{rank(m)} returns the rank of the matrix \\spad{m}.} \\blankline \\spad{X} rank matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9]]")) (|columnSpace| (((|List| |#3|) $) "\\indented{1}{\\spad{columnSpace(m)} returns a sublist of columns of the matrix \\spad{m}} \\indented{1}{forming a basis of its column space} \\blankline \\spad{X} columnSpace matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9],{}[1,{}1,{}1]]")) (|rowEchelon| (($ $) "\\indented{1}{\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.} \\blankline \\spad{X} rowEchelon matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (/ (($ $ |#1|) "\\indented{1}{\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.} \\blankline \\spad{X} m:=matrix [[2**i for \\spad{i} in 2..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m/4}")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\indented{1}{\\spad{exquo(m,{}r)} computes the exact quotient of the elements} \\indented{1}{of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.} \\blankline \\spad{X} m:=matrix [[2**i for \\spad{i} in 2..4] for \\spad{j} in 1..5] \\spad{X} exquo(\\spad{m},{}2)")) (** (($ $ (|Integer|)) "\\indented{1}{\\spad{m**n} computes an integral power of the matrix \\spad{m}.} \\indented{1}{Error: if matrix is not square or if the matrix} \\indented{1}{is square but not invertible.} \\blankline \\spad{X} (matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]) \\spad{**} 2") (($ $ (|NonNegativeInteger|)) "\\indented{1}{\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}.} \\indented{1}{Error: if the matrix is not square.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m**3}")) (* ((|#2| |#2| $) "\\indented{1}{\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} r:=transpose([1,{}2,{}3,{}4,{}5])@Matrix(INT) \\spad{X} \\spad{r*m}") ((|#3| $ |#3|) "\\indented{1}{\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} c:=coerce([1,{}2,{}3,{}4,{}5])@Matrix(INT) \\spad{X} \\spad{m*c}") (($ (|Integer|) $) "\\indented{1}{\\spad{n * x} is an integer multiple.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 3*m") (($ $ |#1|) "\\indented{1}{\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the} \\indented{1}{matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*1/3}") (($ |#1| $) "\\indented{1}{\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the} \\indented{1}{matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 1/3*m") (($ $ $) "\\indented{1}{\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*m}")) (- (($ $) "\\indented{1}{\\spad{-x} returns the negative of the matrix \\spad{x}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{-m}") (($ $ $) "\\indented{1}{\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m}-\\spad{m}")) (+ (($ $ $) "\\indented{1}{\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m+m}")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\indented{1}{\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the} \\indented{1}{matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for} \\indented{1}{\\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setsubMatrix!(\\spad{m},{}2,{}2,{}matrix [[3,{}3],{}[3,{}3]])")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix} \\indented{1}{\\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2}} \\indented{1}{and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} subMatrix(\\spad{m},{}1,{}3,{}2,{}4)")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th} \\indented{1}{columns of \\spad{m}. This destructively alters the matrix.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} swapColumns!(\\spad{m},{}2,{}4)")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th} \\indented{1}{rows of \\spad{m}. This destructively alters the matrix.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} swapRows!(\\spad{m},{}2,{}4)")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\indented{1}{\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}.} \\indented{1}{If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]}} \\indented{1}{and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)}} \\indented{1}{is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setelt(\\spad{m},{}3,{}3,{}10)")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\indented{1}{\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting} \\indented{1}{of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}} \\indented{1}{If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList =} \\indented{1}{[j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of} \\indented{1}{\\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} elt(\\spad{m},{}3,{}3)")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\indented{1}{\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list} \\indented{1}{of lists.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} listOfLists \\spad{m}")) (|vertConcat| (($ $ $) "\\indented{1}{\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an} \\indented{1}{equal number of columns. The entries of \\spad{y} appear below} \\indented{1}{of the entries of \\spad{x}.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of columns.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} vertConcat(\\spad{m},{}\\spad{m})")) (|horizConcat| (($ $ $) "\\indented{1}{\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with} \\indented{1}{an equal number of rows. The entries of \\spad{y} appear to the right} \\indented{1}{of the entries of \\spad{x}.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of rows.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} horizConcat(\\spad{m},{}\\spad{m})")) (|squareTop| (($ $) "\\indented{1}{\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first} \\indented{1}{\\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if} \\indented{1}{\\spad{m < n}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..2] for \\spad{j} in 1..5] \\spad{X} squareTop \\spad{m}")) (|transpose| (($ $) "\\indented{1}{\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} transpose \\spad{m}") (($ |#2|) "\\indented{1}{\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.} \\blankline \\spad{X} transpose([1,{}2,{}3])@Matrix(INT)")) (|coerce| (($ |#3|) "\\indented{1}{\\spad{coerce(col)} converts the column col to a column matrix.} \\blankline \\spad{X} coerce([1,{}2,{}3])@Matrix(INT)")) (|diagonalMatrix| (($ (|List| $)) "\\indented{1}{\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix} \\indented{1}{\\spad{M} with block matrices \\spad{m1},{}...,{}\\spad{mk} down the diagonal,{}} \\indented{1}{with 0 block matrices elsewhere.} \\indented{1}{More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{}} \\indented{1}{then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix\\space{2}with entries} \\indented{1}{\\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if} \\indented{1}{\\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and} \\indented{1}{\\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{}} \\indented{1}{\\spad{m.i.j} = 0\\space{2}otherwise.} \\blankline \\spad{X} diagonalMatrix [matrix [[1,{}2],{}[3,{}4]],{} matrix [[4,{}5],{}[6,{}7]]]") (($ (|List| |#1|)) "\\indented{1}{\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements} \\indented{1}{of \\spad{l} on the diagonal.} \\blankline \\spad{X} diagonalMatrix [1,{}2,{}3]")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\indented{1}{\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the} \\indented{1}{diagonal and zeroes elsewhere.} \\blankline \\spad{X} z:Matrix(INT):=scalarMatrix(3,{}5)")) (|matrix| (($ (|List| (|List| |#1|))) "\\indented{1}{\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the} \\indented{1}{list of lists is viewed as a list of the rows of the matrix.} \\blankline \\spad{X} matrix [[1,{}2,{}3],{}[4,{}5,{}6],{}[7,{}8,{}9],{}[1,{}1,{}1]]")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\indented{1}{\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.} \\blankline \\spad{X} z:Matrix(INT):=zero(3,{}3)")) (|antisymmetric?| (((|Boolean|) $) "\\indented{1}{\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j})} \\indented{1}{and \\spad{false} otherwise.} \\blankline \\spad{X} antisymmetric? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|symmetric?| (((|Boolean|) $) "\\indented{1}{\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false}} \\indented{1}{otherwise.} \\blankline \\spad{X} symmetric? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|diagonal?| (((|Boolean|) $) "\\indented{1}{\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and} \\indented{1}{diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and} \\indented{1}{\\spad{false} otherwise.} \\blankline \\spad{X} diagonal? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|square?| (((|Boolean|) $) "\\indented{1}{\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix} \\indented{1}{(if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.} \\blankline \\spad{X} square matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) +((-4505 . T) (-4506 . T) (-2537 . T)) +NIL +(-670 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-276))) (|HasCategory| |#1| (QUOTE (-508)))) -(-621 R) +((|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-550)))) +(-671 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-276))) (|HasCategory| |#1| (QUOTE (-508))) (|HasAttribute| |#1| (QUOTE (-4169 "*"))) (|HasCategory| |#1| (QUOTE (-331))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-331)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-622 R) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4507 "*"))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-672 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-623 S -2958 FLAF FLAS) -((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) +(-673 S -1333 FLAF FLAS) +((|constructor| (NIL "\\spadtype{MultiVariableCalculusFunctions} Package provides several functions for multivariable calculus. These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL -(-624 R Q) +(-674 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-625) +(-675) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4160 . T) (-4165 |has| (-630) (-331)) (-4159 |has| (-630) (-331)) (-1976 . T) (-4166 |has| (-630) (-6 -4166)) (-4163 |has| (-630) (-6 -4163)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-630) (QUOTE (-134))) (|HasCategory| (-630) (QUOTE (-132))) (|HasCategory| (-630) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-630) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-630) (QUOTE (-336))) (|HasCategory| (-630) (QUOTE (-331))) (|HasCategory| (-630) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-630) (QUOTE (-206))) (|HasCategory| (-630) (QUOTE (-318))) (-1405 (|HasCategory| (-630) (QUOTE (-331))) (|HasCategory| (-630) (QUOTE (-318)))) (|HasCategory| (-630) (LIST (QUOTE -256) (QUOTE (-630)) (QUOTE (-630)))) (|HasCategory| (-630) (LIST (QUOTE -278) (QUOTE (-630)))) (|HasCategory| (-630) (LIST (QUOTE -476) (QUOTE (-1070)) (QUOTE (-630)))) (|HasCategory| (-630) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-630) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-630) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-630) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-630) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-630) (QUOTE (-933))) (|HasCategory| (-630) (QUOTE (-1090))) (-12 (|HasCategory| (-630) (QUOTE (-916))) (|HasCategory| (-630) (QUOTE (-1090)))) (|HasCategory| (-630) (QUOTE (-500))) (|HasCategory| (-630) (QUOTE (-967))) (-12 (|HasCategory| (-630) (QUOTE (-967))) (|HasCategory| (-630) (QUOTE (-1090)))) (-1405 (|HasCategory| (-630) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-630) (QUOTE (-331)))) (|HasCategory| (-630) (QUOTE (-276))) (-1405 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-331))) (|HasCategory| (-630) (QUOTE (-318)))) (|HasCategory| (-630) (QUOTE (-830))) (-12 (|HasCategory| (-630) (QUOTE (-206))) (|HasCategory| (-630) (QUOTE (-331)))) (-12 (|HasCategory| (-630) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-630) (QUOTE (-331)))) (|HasCategory| (-630) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-630) (QUOTE (-777))) (|HasCategory| (-630) (QUOTE (-508))) (|HasAttribute| (-630) (QUOTE -4166)) (|HasAttribute| (-630) (QUOTE -4163)) (-12 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (|HasCategory| (-630) (QUOTE (-331))) (-12 (|HasCategory| (-630) (QUOTE (-318))) (|HasCategory| (-630) (QUOTE (-830))))) (-1405 (-12 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (-12 (|HasCategory| (-630) (QUOTE (-331))) (|HasCategory| (-630) (QUOTE (-830)))) (-12 (|HasCategory| (-630) (QUOTE (-318))) (|HasCategory| (-630) (QUOTE (-830))))) (-1405 (-12 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (|HasCategory| (-630) (QUOTE (-331)))) (-1405 (-12 (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (|HasCategory| (-630) (QUOTE (-508)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (|HasCategory| (-630) (QUOTE (-132)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-630) (QUOTE (-276))) (|HasCategory| (-630) (QUOTE (-830)))) (|HasCategory| (-630) (QUOTE (-318))))) -(-626 S) -((|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4168 . T) (-2951 . T)) +((-4498 . T) (-4503 |has| (-680) (-359)) (-4497 |has| (-680) (-359)) (-2556 . T) (-4504 |has| (-680) (-6 -4504)) (-4501 |has| (-680) (-6 -4501)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-680) (QUOTE (-148))) (|HasCategory| (-680) (QUOTE (-146))) (|HasCategory| (-680) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-680) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-680) (QUOTE (-364))) (|HasCategory| (-680) (QUOTE (-359))) (|HasCategory| (-680) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-680) (QUOTE (-221))) (|HasCategory| (-680) (QUOTE (-344))) (-2318 (|HasCategory| (-680) (QUOTE (-359))) (|HasCategory| (-680) (QUOTE (-344)))) (|HasCategory| (-680) (LIST (QUOTE -276) (QUOTE (-680)) (QUOTE (-680)))) (|HasCategory| (-680) (LIST (QUOTE -298) (QUOTE (-680)))) (|HasCategory| (-680) (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE (-680)))) (|HasCategory| (-680) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-680) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-680) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-680) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-680) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-680) (QUOTE (-1013))) (|HasCategory| (-680) (QUOTE (-1173))) (-12 (|HasCategory| (-680) (QUOTE (-994))) (|HasCategory| (-680) (QUOTE (-1173)))) (|HasCategory| (-680) (QUOTE (-542))) (|HasCategory| (-680) (QUOTE (-1048))) (-12 (|HasCategory| (-680) (QUOTE (-1048))) (|HasCategory| (-680) (QUOTE (-1173)))) (-2318 (|HasCategory| (-680) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-680) (QUOTE (-359)))) (|HasCategory| (-680) (QUOTE (-296))) (-2318 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-359))) (|HasCategory| (-680) (QUOTE (-344)))) (|HasCategory| (-680) (QUOTE (-896))) (-12 (|HasCategory| (-680) (QUOTE (-221))) (|HasCategory| (-680) (QUOTE (-359)))) (-12 (|HasCategory| (-680) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-680) (QUOTE (-359)))) (|HasCategory| (-680) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-680) (QUOTE (-834))) (|HasCategory| (-680) (QUOTE (-550))) (|HasAttribute| (-680) (QUOTE -4504)) (|HasAttribute| (-680) (QUOTE -4501)) (-12 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (|HasCategory| (-680) (QUOTE (-359))) (-12 (|HasCategory| (-680) (QUOTE (-344))) (|HasCategory| (-680) (QUOTE (-896))))) (-2318 (-12 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (-12 (|HasCategory| (-680) (QUOTE (-359))) (|HasCategory| (-680) (QUOTE (-896)))) (-12 (|HasCategory| (-680) (QUOTE (-344))) (|HasCategory| (-680) (QUOTE (-896))))) (-2318 (-12 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (|HasCategory| (-680) (QUOTE (-359)))) (-2318 (-12 (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (|HasCategory| (-680) (QUOTE (-550)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (|HasCategory| (-680) (QUOTE (-146)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-680) (QUOTE (-296))) (|HasCategory| (-680) (QUOTE (-896)))) (|HasCategory| (-680) (QUOTE (-344))))) +(-676 S) +((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) +((-4506 . T) (-2537 . T)) NIL -(-627 U) -((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) +(-677 U) +((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by ddFact to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-628) -((|constructor| (NIL "\\indented{1}{} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) +(-678) +((|constructor| (NIL "This package has no description")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-629 OV E -2958 PG) +(-679 OV E -1333 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL -(-630) -((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2391 . T) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-680) +((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} is not documented")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) +((-2550 . T) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-631 R) -((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) +(-681 R) +((|constructor| (NIL "Modular hermitian row reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) NIL NIL -(-632) +(-682) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4166 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4504 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-633 S D1 D2 I) -((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) +(-683 S D1 D2 I) +((|constructor| (NIL "Tools and transforms for making compiled functions from top-level expressions")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-634 S) +(-684 S) ((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s} viewed as an element of \\%."))) NIL NIL -(-635 S) -((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) +(-685 S) +((|constructor| (NIL "Tools for making compiled functions from top-level expressions MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-636 S) -((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}."))) +(-686 S) +((|constructor| (NIL "Tools for making interpreter functions from top-level expressions Transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-637 S T$) +(-687 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-638 S -3584 I) -((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) +(-688 S -2500 I) +((|constructor| (NIL "Tools for making compiled functions from top-level expressions Transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL -(-639 E OV R P) +(-689 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,{}lv,{}lu,{}lr,{}lp,{}lt,{}ln,{}t,{}r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,{}lv,{}lu,{}lr,{}lp,{}ln,{}r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,{}lv,{}lr,{}ln,{}lu,{}t,{}r)} \\undocumented"))) NIL NIL -(-640 R) -((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\^= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) +(-690 R) +((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\spad{sum(a(i)*G**i,{} i = 0..n)} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\^= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) 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(|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL -(-643 R |Rep|) -((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4163 |has| |#1| (-331)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . 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See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} is not documented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} is not documented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} is not documented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} is not documented"))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-645 R M) -((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) -(-646 R |Mod| -3220 -3216 |exactQuo|) -((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4164 . T)) +(-694 R |Rep|) +((|constructor| (NIL "This package has not been documented")) (|frobenius| (($ $) "\\spad{frobenius(x)} is not documented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} is not documented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} is not documented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} is not documented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} is not documented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} is not documented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} is not documented")) (|lift| ((|#2| $) "\\spad{lift(x)} is not documented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} is not documented")) (|modulus| ((|#2|) "\\spad{modulus()} is not documented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} is not documented"))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4501 |has| |#1| (-359)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1128))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-344))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-695 IS E |ff|) +((|constructor| (NIL "This package has no documentation")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} is not documented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} is not documented")) (|index| ((|#1| $) "\\spad{index(x)} is not documented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} is not documented"))) NIL -(-647 S R) -((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL +(-696 R M) +((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} is not documented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} is not documented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} is not documented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) +((-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) +(-697 R |Mod| -2512 -2492 |exactQuo|) +((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} is not documented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} is not documented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} is not documented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} is not documented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} is not documented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} is not documented"))) +((-4502 . T)) NIL -(-648 R) -((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4162 . T) (-4161 . T)) +(-698 S R) +((|constructor| (NIL "The category of modules over a commutative ring. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{1*x = x}\\spad{\\br} \\tab{5}\\spad{(a*b)*x = a*(b*x)}\\spad{\\br} \\tab{5}\\spad{(a+b)*x = (a*x)+(b*x)}\\spad{\\br} \\tab{5}\\spad{a*(x+y) = (a*x)+(a*y)}"))) NIL -(-649 -2958) -((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) -((-4164 . T)) NIL -(-650 S) +(-699 R) +((|constructor| (NIL "The category of modules over a commutative ring. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{1*x = x}\\spad{\\br} \\tab{5}\\spad{(a*b)*x = a*(b*x)}\\spad{\\br} \\tab{5}\\spad{(a+b)*x = (a*x)+(b*x)}\\spad{\\br} \\tab{5}\\spad{a*(x+y) = (a*x)+(a*y)}"))) +((-4500 . T) (-4499 . T)) +NIL +(-700 -1333) +((|constructor| (NIL "MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius) transformations over \\spad{F}. This a domain of 2-by-2 matrices acting on \\spad{P1}(\\spad{F}).")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see moebius from MoebiusTransform).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see moebius from MoebiusTransform).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see shift from MoebiusTransform).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see shift from MoebiusTransform).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) +((-4502 . T)) +NIL +(-701 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-651) +(-702) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-652 S) -((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) +(-703 S) +((|constructor| (NIL "MonadWithUnit is the class of multiplicative monads with unit,{} \\spadignore{i.e.} sets with a binary operation and a unit element. \\blankline Axioms\\spad{\\br} \\tab{5}leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1) \\spadignore{e.g.} 1*x=x\\spad{\\br} \\tab{5}rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1) \\spad{e}.\\spad{g} x*1=x \\blankline Common Additional Axioms\\spad{\\br} \\tab{5}unitsKnown - if \"recip\" says \"failed\",{} it PROVES input wasn\\spad{'t} a unit")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-653) -((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) +(-704) +((|constructor| (NIL "MonadWithUnit is the class of multiplicative monads with unit,{} \\spadignore{i.e.} sets with a binary operation and a unit element. \\blankline Axioms\\spad{\\br} \\tab{5}leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1) \\spadignore{e.g.} 1*x=x\\spad{\\br} \\tab{5}rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1) \\spad{e}.\\spad{g} x*1=x \\blankline Common Additional Axioms\\spad{\\br} \\tab{5}unitsKnown - if \"recip\" says \"failed\",{} it PROVES input wasn\\spad{'t} a unit")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-654 S R UP) +(-705 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-336)))) -(-655 R UP) +((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-364)))) +(-706 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4160 |has| |#1| (-331)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 |has| |#1| (-359)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-656 S) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) +(-707 S) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)}\\tab{5}\\spad{1*x=x}\\spad{\\br} \\tab{5}\\spad{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)}\\tab{4}\\spad{x*1=x} \\blankline Conditional attributes\\spad{\\br} \\tab{5}unitsKnown - \\spadfun{recip} only returns \"failed\" on non-units")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-657) -((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) +(-708) +((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)}\\tab{5}\\spad{1*x=x}\\spad{\\br} \\tab{5}\\spad{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)}\\tab{4}\\spad{x*1=x} \\blankline Conditional attributes\\spad{\\br} \\tab{5}unitsKnown - \\spadfun{recip} only returns \"failed\" on non-units")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-658 -2958 UP) +(-709 -1333 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL -(-659 |VarSet| E1 E2 R S PR PS) -((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented"))) +(-710 |VarSet| -3306 E2 R S PR PS) +((|constructor| (NIL "Utilities for MPolyCat")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-660 |Vars1| |Vars2| E1 E2 R PR1 PR2) -((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) +(-711 |Vars1| |Vars2| -3306 E2 R PR1 PR2) +((|constructor| (NIL "This package has no description")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-661 E OV R PPR) -((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) +(-712 E OV R PPR) +((|constructor| (NIL "This package exports a factor operation for multivariate polynomials with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-662 |vl| R) -((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4169 "*") |has| |#2| (-156)) (-4160 |has| |#2| (-508)) (-4165 |has| |#2| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-508)))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| (-787 |#1|) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-331))) (-1405 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#2| (QUOTE -4165)) (|HasCategory| |#2| (QUOTE (-419))) (-1405 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (|HasCategory| |#2| (QUOTE (-132))))) -(-663 E OV R PRF) -((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) +(-713 |vl| R) +((|constructor| (NIL "This type is the basic representation of sparse recursive multivariate polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) +(((-4507 "*") |has| |#2| (-170)) (-4498 |has| |#2| (-550)) (-4503 |has| |#2| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-844 |#1|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-714 E OV R PRF) +((|constructor| (NIL "This package exports a factor operation for multivariate polynomials with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-664 E OV R P) -((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) +(-715 E OV R P) +((|constructor| (NIL "MRationalFactorize contains the factor function for multivariate polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-665 R S M) +(-716 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-666 R M) -((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) (-4164 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#2| (QUOTE (-336)))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-777)))) -(-667 S) -((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4167 . T) (-4157 . T) (-4168 . T)) -((|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-668 S) +(-717 R M) +((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over \\spad{f}(a)\\spad{g}(\\spad{b}) such that ab = \\spad{c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) +((-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) (-4502 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#2| (QUOTE (-364)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-834)))) +(-718 S) +((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) +((-4495 . T) (-4506 . T) (-2537 . T)) NIL -((-4157 . T) (-4168 . T) (-2951 . T)) +(-719 S) +((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} without their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) +((-4505 . T) (-4495 . T) (-4506 . T)) +((|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-720) +((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} the \"what\" commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL -(-669) -((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL -NIL -(-670 S) +(-721 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,{}l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-671 |Coef| |Var|) +(-722 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4162 . T) (-4161 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-672 OV E R P) -((|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) +(-723 OV E R P) +((|constructor| (NIL "This is the top level package for doing multivariate factorization over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-673 E OV R P) -((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) +(-724 E OV R P) +((|constructor| (NIL "This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-674 S R) -((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) +(-725 |q| R) +((|constructor| (NIL "This domain has no description"))) +((-4503 |has| |#2| (-550)) (-4497 |has| |#2| (-550)) (-4502 -2318 (|has| |#2| (-471)) (|has| |#2| (-1039))) (-4500 |has| |#2| (-170)) (-4499 |has| |#2| (-170)) ((-4507 "*") |has| |#2| (-550)) (-4498 |has| |#2| (-550))) +((|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (-2318 (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1039)))) (-2318 (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1039)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-550)))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-550))))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1029) (QUOTE (-560))))) +(-726 |x| R) +((|constructor| (NIL "This domain has no description")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{x} : \\spad{p1} - \\spad{r} * x**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) +(((-4507 "*") |has| |#2| (-170)) (-4498 |has| |#2| (-550)) (-4501 |has| |#2| (-359)) (-4503 |has| |#2| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-1128))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| |#2| (QUOTE (-221))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-727 S R) +((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs).\\spad{\\br} \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) NIL NIL -(-675 R) -((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4162 . T) (-4161 . T)) +(-728 R) +((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs).\\spad{\\br} \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) +((-4500 . T) (-4499 . T)) NIL -(-676) -((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{\\spad{manpageXXc02}}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) +(-729) +((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) NIL NIL -(-677) -((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{\\spad{manpageXXc05}}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) +(-730) +((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.)")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) NIL NIL -(-678) -((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{\\spad{manpageXXc06}}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) +(-731) +((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) NIL NIL -(-679) -((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{\\spad{manpageXXd01}}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) +(-732) +((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) NIL NIL -(-680) -((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{\\spad{manpageXXd02}}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,{}mnp,{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{}liwork,{}np,{}x,{}y,{}deleps,{}ifail,{}fcn,{}g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains \\spad{Asp12} and \\spad{Asp33} are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) +(-733) +((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "d02raf(\\spad{n},{}\\spad{mnp},{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{} \\indented{7}{liwork,{}\\spad{np},{}\\spad{x},{}\\spad{y},{}deleps,{}ifail,{}\\spad{fcn},{}\\spad{g})} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "d02kef(xpoint,{}\\spad{m},{}\\spad{k},{}tol,{}maxfun,{}match,{}elam,{}delam,{} \\indented{7}{hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "d02kef(xpoint,{}\\spad{m},{}\\spad{k},{}tol,{}maxfun,{}match,{}elam,{}delam,{} \\indented{7}{hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains \\spad{Asp12} and \\spad{Asp33} are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) NIL NIL -(-681) -((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{\\spad{manpageXXd03}}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,{}xf,{}l,{}lbdcnd,{}bdxs,{}bdxf,{}ys,{}yf,{}m,{}mbdcnd,{}bdys,{}bdyf,{}zs,{}zf,{}n,{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}f,{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) +(-734) +((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "d03faf(\\spad{xs},{}\\spad{xf},{}\\spad{l},{}lbdcnd,{}bdxs,{}bdxf,{}\\spad{ys},{}\\spad{yf},{}\\spad{m},{}mbdcnd,{}bdys,{}bdyf,{}\\spad{zs},{} \\indented{7}{\\spad{zf},{}\\spad{n},{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}\\spad{f},{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) NIL NIL -(-682) -((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{\\spad{manpageXXe01}}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) +(-735) +((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) NIL NIL -(-683) -((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{\\spad{manpageXXe02}}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) +(-736) +((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{} ++ lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{} ++ lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) NIL NIL -(-684) -((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{\\spad{manpageXXe04}}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}bl,{}bu,{}liwork,{}lwork,{}sta,{}cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}clamda,{}r,{}x,{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}bl,{}bu,{}cvec,{}featol,{}hess,{}cold,{}lpp,{}orthog,{}liwork,{}lwork,{}x,{}istate,{}ifail,{}qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}a,{}bl,{}bu,{}cvec,{}linobj,{}liwork,{}lwork,{}x,{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) +(-737) +((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "e04ucf(\\spad{n},{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}\\spad{bl},{}bu,{}liwork,{}lwork,{}sta,{} \\indented{7}{cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}} \\indented{7}{minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}} \\indented{7}{clamda,{}\\spad{r},{}\\spad{x},{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "e04naf(itmax,{}msglvl,{}\\spad{n},{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}\\spad{bl},{} bu,{}cvec,{}featol,{}hess,{}cold,{}\\spad{lpp},{}orthog,{}liwork,{}lwork,{}\\spad{x},{}istate,{}ifail,{}qphess) is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "e04mbf(itmax,{}msglvl,{}\\spad{n},{}nclin,{}nctotl,{}nrowa,{}a,{}\\spad{bl},{}bu,{} \\indented{7}{cvec,{}linobj,{}liwork,{}lwork,{}\\spad{x},{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) NIL NIL -(-685) -((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{\\spad{manpageXXf01}}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,{}nz,{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{}eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) +(-738) +((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "f01bsf(\\spad{n},{}\\spad{nz},{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{} \\indented{7}{eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) NIL NIL -(-686) -((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{\\spad{manpageXXf02}}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) +(-739) +((|constructor| (NIL "This package uses the NAG Library to compute\\spad{\\br} \\tab{5}eigenvalues and eigenvectors of a matrix\\spad{\\br} \\tab{5} eigenvalues and eigenvectors of generalized matrix eigenvalue problems\\spad{\\br} \\tab{5}singular values and singular vectors of a matrix.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "f02fjf(\\spad{n},{}\\spad{k},{}tol,{}novecs,{}\\spad{nrx},{}lwork,{}lrwork,{} \\indented{7}{liwork,{}\\spad{m},{}noits,{}\\spad{x},{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "f02fjf(\\spad{n},{}\\spad{k},{}tol,{}novecs,{}\\spad{nrx},{}lwork,{}lrwork,{} \\indented{7}{liwork,{}\\spad{m},{}noits,{}\\spad{x},{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) NIL NIL -(-687) -((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{\\spad{manpageXXf04}}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,{}n,{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}b,{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,{}nz,{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{}inform,{}b,{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) +(-740) +((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\spad{\\br} \\tab{5}\\axiom{AX=B},{} where \\axiom{\\spad{B}}\\spad{\\br} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "f04qaf(\\spad{m},{}\\spad{n},{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{} \\indented{7}{lrwork,{}liwork,{}\\spad{b},{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{} ++ liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "f04maf(\\spad{n},{}\\spad{nz},{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{} \\indented{7}{inform,{}\\spad{b},{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) NIL NIL -(-688) -((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{\\spad{manpageXXf07}}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) +(-741) +((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) NIL NIL -(-689) -((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) +(-742) +((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) NIL NIL -(-690) +(-743) ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) NIL NIL -(-691 S) -((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) +(-744 S) +((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit.\\spad{\\br} Axioms\\spad{\\br} \\tab{5}\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}\\spad{\\br} \\tab{5}(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}\\spad{\\br} \\blankline Common Additional Axioms\\spad{\\br} \\tab{5}noZeroDivisors\\tab{5} ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-692) -((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) +(-745) +((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit.\\spad{\\br} Axioms\\spad{\\br} \\tab{5}\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}\\spad{\\br} \\tab{5}(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}\\spad{\\br} \\blankline Common Additional Axioms\\spad{\\br} \\tab{5}noZeroDivisors\\tab{5} ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-693 S) +(-746 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-694) +(-747) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-695 |Par|) -((|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) +(-748 |Par|) +((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-696 -2958) -((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) +(-749 -1333) +((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions for converting floating point numbers to continued fractions.")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-697 P -2958) -((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) +(-750 P -1333) +((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.\\spad{\\br} \\tab{5}[\\spad{q},{}\\spad{r}] = leftDivide(a,{}\\spad{b}) means a=b*q+r")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL -(-698 UP -2958) +(-751 -1333) +((|constructor| (NIL "This package exports Newton interpolation for the special case where the result is known to be in the original integral domain The packages defined in this file provide fast fraction free rational interpolation algorithms. (see \\spad{FAMR2},{} FFFG,{} FFFGF,{} NEWTON)")) (|newton| (((|SparseUnivariatePolynomial| |#1|) (|List| |#1|)) "\\spad{newton}(\\spad{l}) returns the interpolating polynomial for the values \\spad{l},{} where the \\spad{x}-coordinates are assumed to be [1,{}2,{}3,{}...,{}\\spad{n}] and the coefficients of the interpolating polynomial are known to be in the domain \\spad{F}. \\spad{I}.\\spad{e}.,{} it is a very streamlined version for a special case of interpolation."))) +NIL +NIL +(-752 UP -1333) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL -(-699) -((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) +(-753) +((|constructor| (NIL "\\axiomType{NumericalIntegrationProblem} is a \\axiom{domain} for the representation of Numerical Integration problems for use by ANNA. \\blankline The representation is a Union of two record types - one for integration of a function of one variable: \\blankline \\axiomType{Record}(var:\\axiomType{Symbol},{}\\spad{\\br} \\spad{fn:}\\axiomType{Expression DoubleFloat},{}\\spad{\\br} range:\\axiomType{Segment OrderedCompletion DoubleFloat},{}\\spad{\\br} abserr:\\axiomType{DoubleFloat},{}\\spad{\\br} relerr:\\axiomType{DoubleFloat},{}) \\blankline and one for multivariate integration: \\blankline \\axiomType{Record}(\\spad{fn:}\\axiomType{Expression DoubleFloat},{}\\spad{\\br} range:\\axiomType{List Segment OrderedCompletion DoubleFloat},{}\\spad{\\br} abserr:\\axiomType{DoubleFloat},{}\\spad{\\br} relerr:\\axiomType{DoubleFloat},{}). \\blankline")) (|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-700 R) +(-754 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-701) -((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-4169 "*") . T)) +(-755) +((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non-negative integers.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative,{} that is,{} \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) +(((-4507 "*") . T)) NIL -(-702 R -2958) +(-756 R -1333) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL -(-703) -((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) +(-757 S) +((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-704 S) -((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) +(-758) +((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-705 R |PolR| E |PolE|) -((|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) +(-759 R |PolR| E |PolE|) +((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-706 R E V P TS) -((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) +(-760 R E V P TS) +((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-707 -2958 |ExtF| |SUEx| |ExtP| |n|) -((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) +(-761 -1333 |ExtF| |SUEx| |ExtP| |n|) +((|constructor| (NIL "This package has no description")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL -(-708 BP E OV R P) +(-762 -1333) +((|constructor| (NIL "This is an implmenentation of the Nottingham Group"))) +((-4502 . T)) +NIL +(-763 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-709 |Par|) -((|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) +(-764 K |PolyRing| E -2050) +((|constructor| (NIL "The following is part of the PAFF package"))) +NIL NIL +(-765 |Par|) +((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) NIL -(-710 R |VarSet|) +NIL +(-766 K) +((|constructor| (NIL "This domain is part of the PAFF package"))) +(((-4507 "*") . T) (-4498 . T) (-4497 . T) (-4503 . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-1094))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-560)) (|:| |c| |#1|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| (-2 (|:| |k| (-560)) (|:| |c| |#1|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| |k| (-560)) (|:| |c| |#1|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE |k|) (QUOTE (-560))) (LIST (QUOTE |:|) (QUOTE |c|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-560)) (|:| |c| |#1|)) (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560)))))) +(-767 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . 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(|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-713 R) +(-769 R) +((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the fmecg from NewSparseUnivariatePolynomial operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * x**e * \\spad{p2}} where \\axiom{\\spad{x}} is \\axiom{monomial(1,{}1)}"))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4501 |has| |#1| (-359)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1128))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-770 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501)))))) -(-714 R E V P) -((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4168 . T) (-4167 . T) (-2951 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560)))))) +(-771 R E V P) +((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-715 S) +(-772 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-508))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-777)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-156)))) -(-716) +((|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-170)))) +(-773) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL NIL -(-717) -((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) +(-774) +((|constructor| (NIL "\\axiomType{NumericalIntegrationCategory} is the \\axiom{category} for describing the set of Numerical Integration \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{numericalIntegration}.")) (|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-718) -((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) +(-775) +((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables:\\spad{\\br} \\tab{5}dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\tab{5}\\spad{y} is an \\spad{n}-vector\\spad{\\br} All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments:\\spad{\\br} \\spad{n},{} the number of dependent variables;\\spad{\\br} \\spad{x1},{} the initial point;\\spad{\\br} \\spad{h},{} the step size;\\spad{\\br} \\spad{y},{} a vector of initial conditions of length \\spad{n}\\spad{\\br} which upon exit contains the solution at \\spad{x1 + h};\\spad{\\br} \\blankline \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline In order of increasing complexity:\\spad{\\br} \\tab{5}\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to\\spad{\\br} \\tab{5}\\spad{x1 + h} and return the values in \\spad{y}.\\spad{\\br} \\blankline \\tab{5}\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as\\spad{\\br} \\tab{5}\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch\\spad{\\br} \\tab{5}arrays \\spad{t1}-\\spad{t4} of size \\spad{n}.\\spad{\\br} \\blankline \\tab{5}Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)}\\spad{\\br} \\tab{5}uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta\\spad{\\br} \\tab{5}integrator to advance the solution vector to \\spad{x2} and return\\spad{\\br} \\tab{5}the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and\\spad{\\br} \\tab{5}\\spad{ns},{} the number of steps to take. \\blankline \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as\\spad{\\br} \\tab{5}\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}\\spad{\\br} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to\\spad{\\br} \\tab{5}\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}\\spad{\\br} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be\\spad{\\br} \\tab{5}\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(\\spad{-1/5})}\\spad{\\br} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. \\blankline Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as\\spad{\\br} \\tab{5}\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}\\spad{\\br} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. \\blankline The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use.")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation dy/dx = \\spad{f}(\\spad{y},{}\\spad{x}) of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation dy/dx = \\spad{f}(\\spad{y},{}\\spad{x}) of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation dy/dx = \\spad{f}(\\spad{y},{}\\spad{x}) of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation dy/dx = \\spad{f}(\\spad{y},{}\\spad{x}) of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation dy/dx = \\spad{f}(\\spad{y},{}\\spad{x}) of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-719) -((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) +(-776) +((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains value Float: estimate of the integral error Float: estimate of the error in the computation totalpts Integer: total number of function evaluations success Boolean: if the integral was computed within the user specified error criterion To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by \\spad{S}(\\spad{i}),{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either\\spad{\\br} \\tab{5}\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}\\spad{\\br} \\tab{5}or \\spad{ABS(S(i) - S(i-1)) < eps_a} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: closed: romberg,{} simpson,{} trapezoidal open: rombergo,{} simpsono,{} trapezoidalo adaptive closed: aromberg,{} asimpson,{} atrapezoidal \\blankline The \\spad{S}(\\spad{i}) for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\blankline The \\spad{S}(\\spad{i}) for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\blankline The \\spad{S}(\\spad{i}) for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}-th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the 2*(\\spad{i+1}) power only. \\blankline The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\blankline Each routine takes as arguments:\\spad{\\br} \\spad{f} integrand\\spad{\\br} a starting point\\spad{\\br} \\spad{b} ending point\\spad{\\br} eps_r relative error\\spad{\\br} eps_a absolute error\\spad{\\br} nmin refinement level when to start checking for convergence (> 1)\\spad{\\br} nmax maximum level of refinement\\spad{\\br} \\blankline The adaptive routines take as an additional parameter,{} nint,{} the number of independent intervals to apply a closed family integrator of the same name. \\blankline")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-720 |Curve|) -((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) +(-777 |Curve|) +((|constructor| (NIL "Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-721) +(-778) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) NIL NIL -(-722) +(-779) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-723) -((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) +(-780) +((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{sup(a,{}b)-a \\~~= \"failed\"}\\spad{\\br} \\tab{5}\\spad{sup(a,{}b)-b \\~~= \"failed\"}\\spad{\\br} \\tab{5}\\spad{x-a \\~~= \"failed\" and x-b \\~~= \"failed\" => x >= sup(a,{}b)}\\spad{\\br}")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-724) -((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) +(-781) +((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering.\\spad{\\br} \\blankline Axiom\\spad{\\br} \\tab{5} \\spad{x} < \\spad{y} \\spad{=>} \\spad{x+z} < \\spad{y+z}"))) NIL NIL -(-725 S R) -((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) +(-782) +((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL -((|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (QUOTE (-967))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-336)))) -(-726 R) -((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) NIL -(-727) -((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) +(-783 S R) +((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL +((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-364)))) +(-784 R) +((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) +((-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-728 R) -((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -256) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-967))) (|HasCategory| |#1| (QUOTE (-500))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| (-910 |#1|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-910 |#1|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (-1405 (|HasCategory| (-910 |#1|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (-1405 (|HasCategory| (-910 |#1|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))))) -(-729 -1405 R OS S) +(-785 -2318 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-730) -((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) +(-786 R) +((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is octon which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation \\spad{O} = \\spad{Q} + QE."))) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -276) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| (-991 |#1|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-991 |#1|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (-2318 (|HasCategory| (-991 |#1|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (-2318 (|HasCategory| (-991 |#1|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))))) +(-787) +((|constructor| (NIL "\\axiomType{OrdinaryDifferentialEquationsSolverCategory} is the \\axiom{category} for describing the set of ODE solver \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{ODEsolve}.")) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-731 R -2958 L) +(-788 R -1333 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-732 R -2958) +(-789 R -1333) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL -(-733) -((|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) +(-790) +((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-734 R -2958) +(-791 R -1333) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL -(-735) -((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) +(-792) +((|constructor| (NIL "\\axiomType{AnnaOrdinaryDifferentialEquationPackage} is a \\axiom{package} of functions for the \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} with \\axiom{measure},{} and \\axiom{solve}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{y}[1]..\\spad{y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{y}[1]..\\spad{y}[\\spad{n}] will be output for the values of \\spad{x} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{x},{}\\spad{y}[1],{}..,{}\\spad{y}[\\spad{n}]) evaluates to zero before \\spad{x} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{y}[1]..\\spad{y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{y}[1]..\\spad{y}[\\spad{n}] will be output for the values of \\spad{x} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{x},{}\\spad{y}[1],{}..,{}\\spad{y}[\\spad{n}]) evaluates to zero before \\spad{x} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{y}[1]..\\spad{y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{y}[1]..\\spad{y}[\\spad{n}] will be output for the values of \\spad{x} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{y}[1]..\\spad{y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{x},{}\\spad{y}[1],{}..,{}\\spad{y}[\\spad{n}]) evaluates to zero before \\spad{x} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{y}[1]..\\spad{y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}],{} together with a starting value for \\spad{x} and \\spad{y}[1]..\\spad{y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{x}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}],{} together with starting values for \\spad{x} and \\spad{y}[1]..\\spad{y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{x},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{y}[1]'..\\spad{y}[\\spad{n}]' defined in terms of \\spad{x},{}\\spad{y}[1]..\\spad{y}[\\spad{n}],{} together with starting values for \\spad{x} and \\spad{y}[1]..\\spad{y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{x},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-736 -2958 UP UPUP R) +(-793 -1333 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-737 -2958 UP L LQ) -((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) +(-794 -1333 UP L LQ) +((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear ordinary differential equations,{} in the transcendental case. The derivation to use is given by the parameter \\spad{L}.")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL -(-738) -((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) +(-795) +((|constructor| (NIL "\\axiomType{NumericalODEProblem} is a \\axiom{domain} for the representation of Numerical ODE problems for use by ANNA. \\blankline The representation is of type: \\blankline \\axiomType{Record}(xinit:\\axiomType{DoubleFloat},{}\\spad{\\br} xend:\\axiomType{DoubleFloat},{}\\spad{\\br} \\spad{fn:}\\axiomType{Vector Expression DoubleFloat},{}\\spad{\\br} yinit:\\axiomType{List DoubleFloat},{}intvals:\\axiomType{List DoubleFloat},{}\\spad{\\br} \\spad{g:}\\axiomType{Expression DoubleFloat},{}abserr:\\axiomType{DoubleFloat},{}\\spad{\\br} relerr:\\axiomType{DoubleFloat}) \\blankline")) (|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-739 -2958 UP L LQ) +(-796 -1333 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-740 -2958 UP) -((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) +(-797 -1333 UP) +((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear ordinary differential equations,{} in the rational case.")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-741 -2958 L UP A LO) +(-798 -1333 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-742 -2958 UP) -((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) +(-799 -1333 UP) +((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{}L1],{} [p2,{}L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-743 -2958 LO) +(-800 -1333 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-744 -2958 LODO) -((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) -NIL +(-801 -1333 LODO) +((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note that the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL -(-745 -2742 S |f|) -((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4161 |has| |#2| (-959)) (-4162 |has| |#2| (-959)) (-4164 |has| |#2| (-6 -4164)) ((-4169 "*") |has| |#2| (-156)) (-4167 . 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-298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-359)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-364)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-708)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-780)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))))) +(-803 R) +((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-805 (-1153)) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-805 (-1153)) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-805 (-1153)) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-805 (-1153)) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-805 (-1153)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-804 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4169 "*") |has| |#2| (-331)) (-4160 |has| |#2| (-331)) (-4165 |has| |#2| (-331)) (-4159 |has| |#2| (-331)) (-4164 . T) (-4162 . T) (-4161 . T)) -((|HasCategory| |#2| (QUOTE (-331)))) -(-748 S) -NIL -NIL +(((-4507 "*") |has| |#2| (-359)) (-4498 |has| |#2| (-359)) (-4503 |has| |#2| (-359)) (-4497 |has| |#2| (-359)) (-4502 . T) (-4500 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-359)))) +(-805 S) +((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) NIL -(-749 S) -((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l,{} r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,{}y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL +(-806 S) +((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\indented{1}{\\spad{varList(x)} returns the list of variables of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} varList \\spad{m1}")) (|length| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{length(x)} returns the length of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} length \\spad{m1}")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\indented{1}{\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns} \\indented{1}{\\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} factors \\spad{m1}")) (|nthFactor| ((|#1| $ (|Integer|)) "\\indented{1}{\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th}} \\indented{1}{monomial of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} nthFactor(\\spad{m1},{}2)")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\indented{1}{\\spad{nthExpon(x,{} n)} returns the exponent of the} \\indented{1}{\\spad{n-th} monomial of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} nthExpon(\\spad{m1},{}2)")) (|size| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{size(x)} returns the number of monomials in \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} size(\\spad{m1},{}2)")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\indented{1}{\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that} \\indented{1}{\\spad{x = l * m} and \\spad{y = m * r} hold and such that} \\indented{1}{\\spad{l} and \\spad{r} have no overlap,{}} \\indented{1}{that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(x*y)\\$OFMONOID(Symbol) \\spad{X} overlap(\\spad{m1},{}\\spad{m2})")) (|divide| (((|Union| (|Record| (|:| |lm| (|Union| $ "failed")) (|:| |rm| (|Union| $ "failed"))) "failed") $ $) "\\indented{1}{\\spad{divide(x,{}y)} returns the left and right exact quotients of} \\indented{1}{\\spad{x} by \\spad{y},{} that is \\spad{[l,{}r]} such that \\spad{x = l*y*r}.} \\indented{1}{\"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(x*y)\\$OFMONOID(Symbol) \\spad{X} divide(\\spad{m1},{}\\spad{m2})")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\indented{1}{\\spad{rquo(x,{} s)} returns the exact right quotient} \\indented{1}{of \\spad{x} by \\spad{s}.} \\blankline \\spad{X} m1:=(x*y)\\$OFMONOID(Symbol) \\spad{X} div(\\spad{m1},{}\\spad{y})") (((|Union| $ "failed") $ $) "\\indented{1}{\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x}} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{}} \\indented{1}{\"failed\" if \\spad{x} is not of the form \\spad{q * y}.} \\blankline \\spad{X} m1:=(\\spad{q*y^3})\\$OFMONOID(Symbol) \\spad{X} m2:=(\\spad{y^2})\\$OFMONOID(Symbol) \\spad{X} lquo(\\spad{m1},{}\\spad{m2})")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\indented{1}{\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x}} \\indented{1}{by \\spad{s}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} lquo(\\spad{m1},{}\\spad{x})") (((|Union| $ "failed") $ $) "\\indented{1}{\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x}} \\indented{2}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \\indented{1}{\"failed\" if \\spad{x} is not of the form \\spad{y * q}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(x*y)\\$OFMONOID(Symbol) \\spad{X} lquo(\\spad{m1},{}\\spad{m2})")) (|hcrf| (($ $ $) "\\indented{1}{\\spad{hcrf(x,{} y)} returns the highest common right} \\indented{1}{factor of \\spad{x} and \\spad{y},{}} \\indented{1}{that is the largest \\spad{d} such that \\spad{x = a d}} \\indented{1}{and \\spad{y = b d}.} \\blankline \\spad{X} m1:=(x*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(\\spad{y*z})\\$OFMONOID(Symbol) \\spad{X} hcrf(\\spad{m1},{}\\spad{m2})")) (|hclf| (($ $ $) "\\indented{1}{\\spad{hclf(x,{} y)} returns the highest common left factor} \\indented{1}{of \\spad{x} and \\spad{y},{}} \\indented{1}{that is the largest \\spad{d} such that \\spad{x = d a}} \\indented{1}{and \\spad{y = d b}.} \\blankline \\spad{X} m1:=(x*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(x*y)\\$OFMONOID(Symbol) \\spad{X} hclf(\\spad{m1},{}\\spad{m2})")) (|lexico| (((|Boolean|) $ $) "\\indented{1}{\\spad{lexico(x,{}y)} returns \\spad{true}} \\indented{1}{iff \\spad{x} is smaller than \\spad{y}} \\indented{1}{\\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} m2:=(x*y)\\$OFMONOID(Symbol) \\spad{X} lexico(\\spad{m1},{}\\spad{m2}) \\spad{X} lexico(\\spad{m2},{}\\spad{m1})")) (|mirror| (($ $) "\\indented{1}{\\spad{mirror(x)} returns the reversed word of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} mirror \\spad{m1}")) (|rest| (($ $) "\\indented{1}{\\spad{rest(x)} returns \\spad{x} except the first letter.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} rest \\spad{m1}")) (|first| ((|#1| $) "\\indented{1}{\\spad{first(x)} returns the first letter of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} first \\spad{m1}")) (** (($ |#1| (|NonNegativeInteger|)) "\\indented{1}{\\spad{s**n} returns the product of \\spad{s} by itself \\spad{n} times.} \\blankline \\spad{X} m1:=(\\spad{y**3})\\$OFMONOID(Symbol)")) (* (($ $ |#1|) "\\indented{1}{\\spad{x*s} returns the product of \\spad{x} by \\spad{s} on the right.} \\blankline \\spad{X} m1:=(\\spad{y**3})\\$OFMONOID(Symbol) \\spad{X} m1*x") (($ |#1| $) "\\indented{1}{\\spad{s*x} returns the product of \\spad{x} by \\spad{s} on the left.} \\blankline \\spad{X} m1:=(x*y*y*z)\\$OFMONOID(Symbol) \\spad{X} \\spad{x*m1}"))) NIL -(-750) -((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-751) -((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) NIL +(-807) +((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible"))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-752) +(-808) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL -(-753) +(-809) ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL -(-754) +(-810) ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL -(-755) -((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) +(-811) +((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL -(-756) -((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) +(-812) +((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-757 R) +(-813 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-758 P R) +(-814 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-206)))) -(-759) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-221)))) +(-815) +((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) +NIL +NIL +(-816) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL -(-760 S) -((|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4167 . T) (-4157 . T) (-4168 . T) (-2951 . T)) +(-817 S) +((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) +((-4505 . T) (-4495 . T) (-4506 . T) (-2537 . T)) NIL -(-761) -((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) +(-818) +((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\axiom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) NIL NIL -(-762 R) -((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4164 |has| |#1| (-775))) -((|HasCategory| |#1| (QUOTE (-775))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-500))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-775)))) (|HasCategory| |#1| (QUOTE (-21))) (-1405 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-775))))) -(-763 R S) -((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) +(-819 R S) +((|constructor| (NIL "Lifting of maps to one-point completions.")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-764 R) +(-820 R) +((|constructor| (NIL "Completion with infinity. Adjunction of a complex infinity to a set.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) +((-4502 |has| |#1| (-832))) +((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-542))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-21))) (-2318 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-832))))) +(-821 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) -(-765) +((-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) +(-822) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) NIL NIL -(-766) -((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) +(-823) +((|constructor| (NIL "\\axiomType{NumericalOptimizationCategory} is the \\axiom{category} for describing the set of Numerical Optimization \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{optimize}.")) (|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-767) -((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) +(-824) +((|constructor| (NIL "\\axiomType{AnnaNumericalOptimizationPackage} is a \\axiom{package} of functions for the \\axiomType{NumericalOptimizationCategory} with \\axiom{measure} and \\axiom{optimize}.")) (|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) NIL NIL -(-768) -((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) +(-825) +((|constructor| (NIL "\\axiomType{NumericalOptimizationProblem} is a \\axiom{domain} for the representation of Numerical Optimization problems for use by ANNA. \\blankline The representation is a Union of two record types - one for otimization of a single function of one or more variables: \\blankline \\axiomType{Record}(\\spad{\\br} \\spad{fn:}\\axiomType{Expression DoubleFloat},{}\\spad{\\br} init:\\axiomType{List DoubleFloat},{}\\spad{\\br} \\spad{lb:}\\axiomType{List OrderedCompletion DoubleFloat},{}\\spad{\\br} \\spad{cf:}\\axiomType{List Expression DoubleFloat},{}\\spad{\\br} ub:\\axiomType{List OrderedCompletion DoubleFloat}) \\blankline and one for least-squares problems \\spadignore{i.e.} optimization of a set of observations of a data set: \\blankline \\axiomType{Record}(lfn:\\axiomType{List Expression DoubleFloat},{}\\spad{\\br} init:\\axiomType{List DoubleFloat}).")) (|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-769 R) -((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4164 |has| |#1| (-775))) -((|HasCategory| |#1| (QUOTE (-775))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-500))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-775)))) (|HasCategory| |#1| (QUOTE (-21))) (-1405 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-775))))) -(-770 R S) -((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) +(-826 R S) +((|constructor| (NIL "Lifting of maps to ordered completions.")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-771) +(-827 R) +((|constructor| (NIL "Completion with + and - infinity. Adjunction of two real infinites quantities to a set.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) +((-4502 |has| |#1| (-832))) +((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-542))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-21))) (-2318 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-832))))) +(-828) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-772 -2742 S) -((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) +(-829 -2050 S) +((|constructor| (NIL "This package provides ordering functions on vectors which are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-773) -((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) +(-830) +((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{x < y => x*z < y*z}\\spad{\\br} \\tab{5}\\spad{x < y => z*x < z*y}"))) NIL NIL -(-774 S) -((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) +(-831 S) +((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline Axiom\\spad{\\br} \\tab{5}\\spad{0 ab< ac}")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-775) -((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4164 . T)) +(-832) +((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline Axiom\\spad{\\br} \\tab{5}\\spad{0 ab< ac}")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) +((-4502 . T)) NIL -(-776 S) +(-833 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a a= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-777) +(-834) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a a= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-778 S R) -((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) +(-835 S R) +((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and NonCommutativeOperatorDivision")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156)))) -(-779 R) -((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170)))) +(-836 R) +((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and NonCommutativeOperatorDivision")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) +((-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-780 R C) -((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) +(-837 R C) +((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and divisions of univariate skew polynomials.")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL -((|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) -(-781 R |sigma| -2808) +((|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) +(-838 R |sigma| -4349) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-331)))) -(-782 |x| R |sigma| -2808) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-359)))) +(-839 |x| R |sigma| -4349) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-331)))) -(-783 R) +((-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-359)))) +(-840 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501)))))) -(-784) -((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560)))))) +(-841) +((|constructor| (NIL "A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-785) -((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) +(-842) +((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (^= (($ $ $) "\\spad{f ^= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-786) -((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (^= (($ $ $) "\\spad{f ^= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) +(-843) +((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-787 |VariableList|) +(-844 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-788 R |vl| |wl| |wtlevel|) +(-845 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331)))) -(-789 R PS UP) -((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) +((-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359)))) +(-846) +((|constructor| (NIL "This category exports the function for the domain PseudoAlgebraicClosureOfAlgExtOfRationalNumber which implement dynamic extension using the simple notion of tower extensions. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-847 |downLevel|) +((|constructor| (NIL "This domain implement dynamic extension over the PseudoAlgebraicClosureOfRationalNumber. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-852) (QUOTE (-148))) (|HasCategory| (-852) (QUOTE (-146))) (|HasCategory| (-852) (QUOTE (-364))) (|HasCategory| (-403 (-560)) (QUOTE (-148))) (|HasCategory| (-403 (-560)) (QUOTE (-146))) (|HasCategory| (-403 (-560)) (QUOTE (-364))) (-2318 (|HasCategory| (-403 (-560)) (QUOTE (-146))) (|HasCategory| (-403 (-560)) (QUOTE (-364))) (|HasCategory| (-852) (QUOTE (-146))) (|HasCategory| (-852) (QUOTE (-364)))) (-2318 (|HasCategory| (-403 (-560)) (QUOTE (-364))) (|HasCategory| (-852) (QUOTE (-364))))) +(-848) +((|constructor| (NIL "This category exports the function for the domain PseudoAlgebraicClosureOfFiniteField which implement dynamic extension using the simple notion of tower extensions. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL +(-849 K) +((|constructor| (NIL "This domain implement dynamic extension using the simple notion of tower extensions. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-364)))) +(-850) +((|constructor| (NIL "This category exports the function for domains which implement dynamic extension using the simple notion of tower extensions. \\spad{++} A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions.")) (|previousTower| (($ $) "\\spad{previousTower(a)} returns the previous tower extension over which the element a is defined.")) (|extDegree| (((|PositiveInteger|) $) "\\spad{extDegree(a)} returns the extension degree of the extension tower over which the element is defined.")) (|maxTower| (($ (|List| $)) "\\spad{maxTower(l)} returns the tower in the list having the maximal extension degree over the ground field. It has no meaning if the towers are not related.")) (|distinguishedRootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) $) "\\spad{distinguishedRootsOf(p,{}a)} returns a (distinguised) root for each irreducible factor of the polynomial \\spad{p} (factored over the field defined by the element a)."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-790 R |x| |pt|) -((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) +(-851) +((|constructor| (NIL "This category exports the function for the domain PseudoAlgebraicClosureOfRationalNumber which implement dynamic extension using the simple notion of tower extensions. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL +(-852) +((|constructor| (NIL "This domain implements dynamic extension using the simple notion of tower extensions. A tower extension \\spad{T} of the ground field \\spad{K} is any sequence of field extension (\\spad{T} : \\spad{K_0},{} \\spad{K_1},{} ...,{} K_i...,{}\\spad{K_n}) where \\spad{K_0} = \\spad{K} and for \\spad{i} \\spad{=1},{}2,{}...,{}\\spad{n},{} K_i is an extension of \\spad{K_}{\\spad{i}-1} of degree > 1 and defined by an irreducible polynomial \\spad{p}(\\spad{Z}) in \\spad{K_}{\\spad{i}-1}. Two towers (T_1: \\spad{K_01},{} \\spad{K_11},{}...,{}\\spad{K_i1},{}...,{}\\spad{K_n1}) and (T_2: \\spad{K_02},{} \\spad{K_12},{}...,{}\\spad{K_i2},{}...,{}\\spad{K_n2}) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} \\spad{T_2}),{} that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1},{}2,{}...,{}\\spad{n1} (or \\spad{i=1},{}2,{}...,{}\\spad{n2}). Any algebraic operations defined for several elements are only defined if all of the concerned elements are comming from a set of related tour extensions."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-403 (-560)) (QUOTE (-148))) (|HasCategory| (-403 (-560)) (QUOTE (-146))) (|HasCategory| (-403 (-560)) (QUOTE (-364))) (-2318 (|HasCategory| (-403 (-560)) (QUOTE (-146))) (|HasCategory| (-403 (-560)) (QUOTE (-364))))) +(-853 R PS UP) +((|constructor| (NIL "This package computes reliable Pad&ea. approximants using a generalized Viskovatov continued fraction algorithm.")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) +NIL +NIL +(-854 R |x| |pt|) +((|constructor| (NIL "This package computes reliable Pad&ea. approximants using a generalized Viskovatov continued fraction algorithm.")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL -(-791 |p|) -((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) NIL -(-792 |p|) -((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-855 |p|) +((|constructor| (NIL "This is the category of stream-based representations of the \\spad{p}-adic integers.")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-793 |p|) +(-856 |p|) +((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-857 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-791 |#1|) (QUOTE (-830))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-791 |#1|) (QUOTE (-132))) (|HasCategory| (-791 |#1|) (QUOTE (-134))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-791 |#1|) (QUOTE (-933))) (|HasCategory| (-791 |#1|) (QUOTE (-750))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-791 |#1|) (QUOTE (-1046))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-791 |#1|) (QUOTE (-206))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -476) (QUOTE (-1070)) (LIST (QUOTE -791) (|devaluate| |#1|)))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -278) (LIST (QUOTE -791) (|devaluate| |#1|)))) (|HasCategory| (-791 |#1|) (LIST (QUOTE -256) (LIST (QUOTE -791) (|devaluate| |#1|)) (LIST (QUOTE -791) (|devaluate| |#1|)))) (|HasCategory| (-791 |#1|) (QUOTE (-276))) (|HasCategory| (-791 |#1|) (QUOTE (-500))) (|HasCategory| (-791 |#1|) (QUOTE (-777))) (-1405 (|HasCategory| (-791 |#1|) (QUOTE (-750))) (|HasCategory| (-791 |#1|) (QUOTE (-777)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-791 |#1|) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-791 |#1|) (QUOTE (-830)))) (|HasCategory| (-791 |#1|) (QUOTE (-132))))) -(-794 |p| PADIC) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-856 |#1|) (QUOTE (-896))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-856 |#1|) (QUOTE (-146))) (|HasCategory| (-856 |#1|) (QUOTE (-148))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-856 |#1|) (QUOTE (-1013))) (|HasCategory| (-856 |#1|) (QUOTE (-807))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-856 |#1|) (QUOTE (-1128))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-856 |#1|) (QUOTE (-221))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -515) (QUOTE (-1153)) (LIST (QUOTE -856) (|devaluate| |#1|)))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -856) (|devaluate| |#1|)))) (|HasCategory| (-856 |#1|) (LIST (QUOTE -276) (LIST (QUOTE -856) (|devaluate| |#1|)) (LIST (QUOTE -856) (|devaluate| |#1|)))) (|HasCategory| (-856 |#1|) (QUOTE (-296))) (|HasCategory| (-856 |#1|) (QUOTE (-542))) (|HasCategory| (-856 |#1|) (QUOTE (-834))) (-2318 (|HasCategory| (-856 |#1|) (QUOTE (-807))) (|HasCategory| (-856 |#1|) (QUOTE (-834)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-856 |#1|) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-856 |#1|) (QUOTE (-896)))) (|HasCategory| (-856 |#1|) (QUOTE (-146))))) +(-858 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-750))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-206))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -256) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (QUOTE (-777))) (-1405 (|HasCategory| |#2| (QUOTE (-750))) (|HasCategory| |#2| (QUOTE (-777)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-830)))) (|HasCategory| |#2| (QUOTE (-132))))) -(-795) -((|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-807))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1128))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-221))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -276) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-834))) (-2318 (|HasCategory| |#2| (QUOTE (-807))) (|HasCategory| |#2| (QUOTE (-834)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-859 K |symb| BLMET) +((|constructor| (NIL "A package that implements the Brill-Noether algorithm. Part of the PAFF package")) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) "Returns the Zeta function of the curve in constant field extension. Calculated by using the \\spad{L}-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the \\spad{L}-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(\\spad{d},{} \\spad{n}) returns the number of places of degree \\spad{d} in the constant field extension of degree \\spad{n}")) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) "\\spad{numberRatPlacesExtDeg(n)} returns the number of rational places in the constant field extenstion of degree \\spad{n}")) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) "returns the number of places of the given degree")) (|placesOfDegree| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|PositiveInteger|)) "\\spad{placesOfDegree(d)} returns all places of degree \\spad{d} of the curve.")) (|classNumber| (((|Integer|)) "Returns the class number of the curve.")) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) "\\spad{LPolynomial(d)} returns the \\spad{L}-Polynomial of the curve in constant field extension of degree \\spad{d}.") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the \\spad{L}-Polynomial of the curve.")) (|adjunctionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial defined by setCurve.")) (|intersectionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{intersectionDivisor(pol)} compute the intersection divisor of the form \\spad{pol} with the curve. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl}.") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl}.") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl}.")) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|)) "\\spad{interpolateForms(d,{}n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d}.")) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| (((|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{parametrize(f,{}pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl}.")) (|singularPoints| (((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|desingTree| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{theCurve returns} the specified polynomial for the package.")) (|rationalPlaces| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl}."))) +NIL +((|HasCategory| (-849 |#1|) (QUOTE (-364)))) +(-860 K |symb| BLMET) +((|constructor| (NIL "A package that implements the Brill-Noether algorithm. Part of the PAFF package")) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) "Returns the Zeta function of the curve in constant field extension. Calculated by using the \\spad{L}-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the \\spad{L}-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(\\spad{d},{} \\spad{n}) returns the number of places of degree \\spad{d} in the constant field extension of degree \\spad{n}")) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) "\\spad{numberRatPlacesExtDeg(n)} returns the number of rational places in the constant field extenstion of degree \\spad{n}")) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) "returns the number of places of the given degree")) (|placesOfDegree| (((|List| (|Places| |#1|)) (|PositiveInteger|)) "\\spad{placesOfDegree(d)} returns all places of degree \\spad{d} of the curve.")) (|classNumber| (((|Integer|)) "Returns the class number of the curve.")) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) "\\spad{LPolynomial(d)} returns the \\spad{L}-Polynomial of the curve in constant field extension of degree \\spad{d}.") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the \\spad{L}-Polynomial of the curve.")) (|adjunctionDivisor| (((|Divisor| (|Places| |#1|))) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial set with the function setCurve.")) (|intersectionDivisor| (((|Divisor| (|Places| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{intersectionDivisor(pol)} compute the intersection divisor (the Cartier divisor) of the form \\spad{pol} with the curve. If some intersection points lie in an extension of the ground field,{} an error message is issued specifying the extension degree needed to find all the intersection points. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) "\\spad{evalIfCan(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{evalIfCan(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{evalIfCan(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) "\\spad{eval(u,{}pl)} evaluate the function \\spad{u} at the place \\spad{pl}.") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{eval(f,{}g,{}pl)} evaluate the function \\spad{f/g} at the place \\spad{pl}.") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{eval(f,{}pl)} evaluate \\spad{f} at the place \\spad{pl}.")) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|)) "\\spad{interpolateForms(d,{}n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d}.")) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|))) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| (((|NeitherSparseOrDensePowerSeries| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{parametrize(f,{}pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl}.")) (|singularPoints| (((|List| (|ProjectivePlane| |#1|))) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|desingTree| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{theCurve returns} the specified polynomial for the package.")) (|rationalPlaces| (((|List| (|Places| |#1|))) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| (((|ProjectivePlane| |#1|) (|Places| |#1|)) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl}."))) NIL +((|HasCategory| |#1| (QUOTE (-364)))) +(-861) +((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL -(-796) +NIL +(-862) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-797 CF1 CF2) -((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) +(-863 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) +((|constructor| (NIL "The following is part of the PAFF package")) (|parametrize| ((|#6| |#3| |#7| (|Integer|)) "\\spad{parametrize(f,{}pl,{}n)} returns t**n * parametrize(\\spad{f},{}\\spad{p}).") ((|#6| |#3| |#3| |#7|) "\\spad{parametrize(f,{}g,{}pl)} returns the local parametrization of the rational function \\spad{f/g} at the place \\spad{pl}. Note that local parametrization of the place must have first been compute and set. For simple point on a curve,{} this done with \\spad{pointToPlace}. The local parametrization places corresponding to a leaf in a desingularization tree are compute at the moment of their \"creation\". (See package \\spad{DesingTreePackage}.") ((|#6| |#3| |#7|) "\\spad{parametrize(f,{}pl)} returns the local parametrization of the polynomial function \\spad{f} at the place \\spad{pl}. Note that local parametrization of the place must have first been compute and set. For simple point on a curve,{} this done with \\spad{pointToPlace}. The local parametrization places corresponding to a leaf in a desingularization tree are compute at the moment of their \"creation\". (See package \\spad{DesingTreePackage}."))) +NIL +NIL +(-864 CF1 CF2) +((|constructor| (NIL "This package has no description")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-798 |ComponentFunction|) +(-865 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-799 CF1 CF2) -((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) +(-866 CF1 CF2) +((|constructor| (NIL "This package has no description")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-800 |ComponentFunction|) +(-867 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-801 CF1 CF2) -((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) +(-868 CF1 CF2) +((|constructor| (NIL "This package has no description")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-802 |ComponentFunction|) +(-869 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-803) +(-870) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL -(-804 R) +(-871 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-805 R S L) +(-872 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-806 S) +(-873 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-807 |Base| |Subject| |Pat|) +(-874 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070)))) (-12 (-3031 (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070))))) (-3031 (|HasCategory| |#2| (QUOTE (-959))))) (-12 (|HasCategory| |#2| (QUOTE (-959))) (-3031 (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070))))))) -(-808 R S) -((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) +((|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153)))) (-12 (-3186 (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153))))) (-3186 (|HasCategory| |#2| (QUOTE (-1039))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-3186 (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153))))))) +(-875 R A B) +((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-809 R A B) -((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) +(-876 R S) +((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-810 R) -((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) +(-877 R -2500) +((|constructor| (NIL "Utilities for handling patterns")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL -(-811 R -3584) -((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) +(-878 R S) +((|constructor| (NIL "Lifts maps to patterns")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-812 R S) -((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) +(-879 R) +((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-813 |VarSet|) -((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) +(-880 |VarSet|) +((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|listOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{listOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-814 UP R) -((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) +(-881 UP R) +((|constructor| (NIL "Polynomial composition and decomposition functions\\spad{\\br} If \\spad{f} = \\spad{g} \\spad{o} \\spad{h} then g=leftFactor(\\spad{f},{}\\spad{h}) and h=rightFactor(\\spad{f},{}\\spad{g})")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) NIL NIL -(-815) -((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) +(-882) +((|constructor| (NIL "\\axiomType{PartialDifferentialEquationsSolverCategory} is the \\axiom{category} for describing the set of PDE solver \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{PDEsolve}.")) (|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-816 UP -2958) -((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) +(-883 UP -1333) +((|constructor| (NIL "Polynomial composition and decomposition functions\\spad{\\br} If \\spad{f} = \\spad{g} \\spad{o} \\spad{h} then g=leftFactor(\\spad{f},{}\\spad{h}) and h=rightFactor(\\spad{f},{}\\spad{g})")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL -(-817) -((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) +(-884) +((|constructor| (NIL "AnnaPartialDifferentialEquationPackage is an uncompleted package for the interface to NAG PDE routines. It has been realised that a new approach to solving PDEs will need to be created.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-818) -((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) +(-885) +((|constructor| (NIL "\\axiomType{NumericalPDEProblem} is a \\axiom{domain} for the representation of Numerical PDE problems for use by ANNA. \\blankline The representation is of type: \\blankline \\axiomType{Record}(pde:\\axiomType{List Expression DoubleFloat},{} \\spad{\\br} constraints:\\axiomType{List PDEC},{} \\spad{\\br} \\spad{f:}\\axiomType{List List Expression DoubleFloat},{}\\spad{\\br} \\spad{st:}\\axiomType{String},{}\\spad{\\br} tol:\\axiomType{DoubleFloat}) \\blankline where \\axiomType{PDEC} is of type: \\blankline \\axiomType{Record}(start:\\axiomType{DoubleFloat},{} \\spad{\\br} finish:\\axiomType{DoubleFloat},{}\\spad{\\br} grid:\\axiomType{NonNegativeInteger},{}\\spad{\\br} boundaryType:\\axiomType{Integer},{}\\spad{\\br} dStart:\\axiomType{Matrix DoubleFloat},{} \\spad{\\br} dFinish:\\axiomType{Matrix DoubleFloat})")) (|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-819 A S) -((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) +(-886 A S) +((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{differentiate(x+y,{}e)=differentiate(x,{}e)+differentiate(y,{}e)}\\spad{\\br} \\tab{5}\\spad{differentiate(x*y,{}e)=x*differentiate(y,{}e)+differentiate(x,{}e)*y}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-820 S) -((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4164 . T)) +(-887 S) +((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{differentiate(x+y,{}e)=differentiate(x,{}e)+differentiate(y,{}e)}\\spad{\\br} \\tab{5}\\spad{differentiate(x*y,{}e)=x*differentiate(y,{}e)+differentiate(x,{}e)*y}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) +((-4502 . T)) NIL -(-821 S) -((|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) +(-888 S) +((|constructor| (NIL "This domain has no description")) (|coerce| (((|Tree| |#1|) $) "\\indented{1}{coerce(\\spad{x}) is not documented} \\blankline \\spad{X} t1:=ptree([1,{}2,{}3]) \\spad{X} t2:=ptree(\\spad{t1},{}ptree([1,{}2,{}3])) \\spad{X} t2::Tree List PositiveInteger")) (|ptree| (($ $ $) "\\indented{1}{ptree(\\spad{x},{}\\spad{y}) is not documented} \\blankline \\spad{X} t1:=ptree([1,{}2,{}3]) \\spad{X} ptree(\\spad{t1},{}ptree([1,{}2,{}3]))") (($ |#1|) "\\indented{1}{ptree(\\spad{s}) is a leaf? pendant tree} \\blankline \\spad{X} t1:=ptree([1,{}2,{}3])"))) NIL -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-822 S) -((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}."))) -((-4164 . T)) -((|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-777))))) -(-823 |n| R) -((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ^= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-889 |n| R) +((|constructor| (NIL "Permanent implements the functions permanent,{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The permanent is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the determinant. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note that permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\spad{\\br} if 2 has an inverse in \\spad{R} we can use the algorithm of [Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{} some modifications are necessary:\\spad{\\br} if \\spad{n} > 6 and \\spad{R} is an integral domain with characteristic different from 2 (the algorithm works if and only 2 is not a zero-divisor of \\spad{R} and characteristic()\\$\\spad{R} \\spad{^=} 2,{} but how to check that for any given \\spad{R} ?),{} the local function \\spad{permanent2} is called;\\spad{\\br} else,{} the local function \\spad{permanent3} is called (works for all commutative rings \\spad{R})."))) NIL NIL -(-824 S) -((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4164 . T)) +(-890 S) +((|constructor| (NIL "PermutationCategory provides a categorial environment for subgroups of bijections of a set (\\spadignore{i.e.} permutations)")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note that this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of el under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to el.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of el under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of el under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles \\spad{lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps \\spad{ls}.\\spad{i} to \\spad{ls}.\\spad{i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle \\spad{ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps \\spad{ls}.\\spad{i} to \\spad{ls}.\\spad{i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) +((-4502 . T)) NIL -(-825 S) -((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) +(-891 S) +((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group \\spad{gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group \\spad{gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: initializeGroupForWordProblem(\\spad{gp},{}0,{}1). Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if \\spad{gp1} is a subgroup of \\spad{gp2}. Note: because of a bug in the parser you have to call this function explicitly by \\spad{gp1} \\spad{<=}\\$(PERMGRP \\spad{S}) \\spad{gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if \\spad{gp1} is a proper subgroup of \\spad{gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group \\spad{gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group \\spad{gp},{} represented by the indices of the list,{} given by generators.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group \\spad{gp},{} represented by the indices of the list,{} given by strongGenerators.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation \\spad{pp} is in the group \\spad{gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group \\spad{gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list \\spad{ls} under the group \\spad{gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set \\spad{els} under the group \\spad{gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element \\spad{el} under the group \\spad{gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to \\spad{el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group \\spad{gp} in the original generators of \\spad{gp},{} represented by their indices in the list,{} given by generators.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group \\spad{gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group \\spad{gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group \\spad{gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group \\spad{gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group \\spad{gp}. Note: random(\\spad{gp})=random(\\spad{gp},{}20).") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group \\spad{gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group \\spad{gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group \\spad{gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group \\spad{gp}."))) NIL NIL -(-826 |p|) -((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-336)))) -(-827 R E |VarSet| S) -((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) +(-892 S) +((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections on a set \\spad{S},{} which move only a finite number of points. A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular multiplication is defined as composition of maps:\\spad{\\br} \\spad{pi1} * \\spad{pi2} = \\spad{pi1} \\spad{o} \\spad{pi2}.\\spad{\\br} The internal representation of permuatations are two lists of equal length representing preimages and images.")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list \\spad{ls} to a permutation whose image is given by \\spad{ls} and the preimage is fixed to be [1,{}...,{}\\spad{n}]. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\indented{1}{fixedPoints(\\spad{p}) returns the points fixed by the permutation \\spad{p}.} \\spad{X} \\spad{p} \\spad{:=} coercePreimagesImages([[0,{}1,{}2,{}3],{}[3,{}0,{}2,{}1]])\\$PERM ZMOD 4 \\spad{X} fixedPoints \\spad{p}")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations \\spad{lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} sign(\\spad{p}) is \\spad{-1}.")) (|even?| (((|Boolean|) $) "\\indented{1}{even?(\\spad{p}) returns \\spad{true} if and only if \\spad{p} is an even permutation,{}} \\indented{1}{\\spadignore{i.e.} sign(\\spad{p}) is 1.} \\blankline \\spad{X} \\spad{p} \\spad{:=} coercePreimagesImages([[1,{}2,{}3],{}[1,{}2,{}3]]) \\spad{X} even? \\spad{p}")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\indented{1}{movedPoints(\\spad{p}) returns the set of points moved by the permutation \\spad{p}.} \\blankline \\spad{X} \\spad{p} \\spad{:=} coercePreimagesImages([[1,{}2,{}3],{}[1,{}2,{}3]]) \\spad{X} movedPoints \\spad{p}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs \\spad{lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle \\spad{ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps \\spad{ls}.\\spad{i} to \\spad{ls}.\\spad{i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles \\spad{lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps \\spad{ls}.\\spad{i} to \\spad{ls}.\\spad{i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\indented{1}{coercePreimagesImages(\\spad{lls}) coerces the representation \\spad{lls}} \\indented{1}{of a permutation as a list of preimages and images to a permutation.} \\indented{1}{We assume that both preimage and image do not contain repetitions.} \\blankline \\spad{X} \\spad{p} \\spad{:=} coercePreimagesImages([[1,{}2,{}3],{}[1,{}2,{}3]]) \\spad{X} \\spad{q} \\spad{:=} coercePreimagesImages([[0,{}1,{}2,{}3],{}[3,{}0,{}2,{}1]])\\$PERM ZMOD 4")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation rep of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps (rep.preimage).\\spad{k} to (rep.image).\\spad{k} for all indices \\spad{k}. Elements of \\spad{S} not in (rep.preimage).\\spad{k} are fixed points,{} and these are the only fixed points of the permutation."))) +((-4502 . T)) +((|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-834))))) +(-893 R E |VarSet| S) +((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of solveLinearPolynomialEquationByRecursion its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-828 R S) -((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) +(-894 R S) +((|constructor| (NIL "PolynomialFactorizationByRecursionUnivariate \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-829 S) +(-895 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL -((|HasCategory| |#1| (QUOTE (-132)))) -(-830) +((|HasCategory| |#1| (QUOTE (-146)))) +(-896) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-831 R0 -2958 UP UPUP R) +(-897 |p|) +((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-364)))) +(-898 R0 -1333 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-832 UP UPUP R) +(-899 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-833 UP UPUP) -((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) +(-900 R |PolyRing| E -2050) +((|constructor| (NIL "The following is part of the PAFF package")) (|degreeOfMinimalForm| (((|NonNegativeInteger|) |#2|) "\\spad{degreeOfMinimalForm does} what it says")) (|listAllMono| (((|List| |#2|) (|NonNegativeInteger|)) "\\spad{listAllMono(l)} returns all the monomials of degree \\spad{l}")) (|listAllMonoExp| (((|List| |#3|) (|Integer|)) "\\spad{listAllMonoExp(l)} returns all the exponents of degree \\spad{l}")) (|homogenize| ((|#2| |#2| (|Integer|)) "\\spad{homogenize(pol,{}n)} returns the homogenized polynomial of \\spad{pol} with respect to the \\spad{n}-th variable.")) (|constant| ((|#1| |#2|) "\\spad{constant(pol)} returns the constant term of the polynomial.")) (|degOneCoef| ((|#1| |#2| (|PositiveInteger|)) "\\spad{degOneCoef(pol,{}n)} returns the coefficient in front of the monomial specified by the positive integer.")) (|translate| ((|#2| |#2| (|List| |#1|)) "\\spad{translate(pol,{}[a,{}b,{}c])} apply to \\spad{pol} the linear change of coordinates,{} \\spad{x}->x+a,{} \\spad{y}->y+b,{} \\spad{z}->z+c") ((|#2| |#2| (|List| |#1|) (|Integer|)) "\\spad{translate(pol,{}[a,{}b,{}c],{}3)} apply to \\spad{pol} the linear change of coordinates,{} \\spad{x}->x+a,{} \\spad{y}->y+b,{} \\spad{z}-\\spad{>1}.")) (|replaceVarByOne| ((|#2| |#2| (|Integer|)) "\\spad{replaceVarByOne(pol,{}a)} evaluate to one the variable in \\spad{pol} specified by the integer a.")) (|replaceVarByZero| ((|#2| |#2| (|Integer|)) "\\spad{replaceVarByZero(pol,{}a)} evaluate to zero the variable in \\spad{pol} specified by the integer a.")) (|firstExponent| ((|#3| |#2|) "\\spad{firstExponent(pol)} returns the exponent of the first term in the representation of \\spad{pol}. Not to be confused with the leadingExponent \\indented{1}{which is the highest exponent according to the order} over the monomial.")) (|minimalForm| ((|#2| |#2|) "\\spad{minimalForm(pol)} returns the minimal forms of the polynomial \\spad{pol}."))) NIL NIL -(-834 R) -((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-901 UP UPUP) +((|constructor| (NIL "Utilities for PFOQ and PFO")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL -(-835 R) -((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL +(-902 R) +((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function padicFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function partialFraction takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\indented{1}{wholePart(\\spad{p}) extracts the whole part of the partial fraction} \\indented{1}{\\spad{p}.} \\blankline \\spad{X} a:=(74/13)::PFR(INT) \\spad{X} wholePart(a)")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\indented{1}{partialFraction(numer,{}denom) is the main function for} \\indented{1}{constructing partial fractions. The second argument is the} \\indented{1}{denominator and should be factored.} \\blankline \\spad{X} partialFraction(1,{}factorial 10)")) (|padicFraction| (($ $) "\\indented{1}{padicFraction(\\spad{q}) expands the fraction \\spad{p}-adically in the primes} \\indented{1}{\\spad{p} in the denominator of \\spad{q}. For example,{}} \\indented{1}{\\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}.} \\indented{1}{Use compactFraction from PartialFraction to} \\indented{1}{return to compact form.} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} padicFraction(a)")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\indented{1}{numberOfFractionalTerms(\\spad{p}) computes the number of fractional} \\indented{1}{terms in \\spad{p}. This returns 0 if there is no fractional} \\indented{1}{part.} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} b:=padicFraction(a) \\spad{X} numberOfFractionalTerms(\\spad{b})")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\indented{1}{nthFractionalTerm(\\spad{p},{}\\spad{n}) extracts the \\spad{n}th fractional term from} \\indented{1}{the partial fraction \\spad{p}.\\space{2}This returns 0 if the index} \\indented{1}{\\spad{n} is out of range.} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} b:=padicFraction(a) \\spad{X} nthFractionalTerm(\\spad{b},{}3)")) (|firstNumer| ((|#1| $) "\\indented{1}{firstNumer(\\spad{p}) extracts the numerator of the first fractional} \\indented{1}{term. This returns 0 if there is no fractional part (use} \\indented{1}{wholePart from PartialFraction to get the whole part).} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} firstNumer(a)")) (|firstDenom| (((|Factored| |#1|) $) "\\indented{1}{firstDenom(\\spad{p}) extracts the denominator of the first fractional} \\indented{1}{term. This returns 1 if there is no fractional part (use} \\indented{1}{wholePart from PartialFraction to get the whole part).} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} firstDenom(a)")) (|compactFraction| (($ $) "\\indented{1}{compactFraction(\\spad{p}) normalizes the partial fraction \\spad{p}} \\indented{1}{to the compact representation. In this form,{} the partial} \\indented{1}{fraction has only one fractional term per prime in the} \\indented{1}{denominator.} \\blankline \\spad{X} a:=partialFraction(1,{}factorial 10) \\spad{X} b:=padicFraction(a) \\spad{X} compactFraction(\\spad{b})")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\indented{1}{coerce(\\spad{f}) takes a fraction with numerator and denominator in} \\indented{1}{factored form and creates a partial fraction.\\space{2}It is} \\indented{1}{necessary for the parts to be factored because it is not} \\indented{1}{known in general how to factor elements of \\spad{R} and} \\indented{1}{this is needed to decompose into partial fractions.} \\blankline \\spad{X} (13/74)::PFR(INT)") (((|Fraction| |#1|) $) "\\indented{1}{coerce(\\spad{p}) sums up the components of the partial fraction and} \\indented{1}{returns a single fraction.} \\blankline \\spad{X} a:=(13/74)::PFR(INT) \\spad{X} a::FRAC(INT)"))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-836 E OV R P) -((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) +(-903 R) +((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{partialFraction(\\spad{rf},{} var) returns the partial fraction decomposition} \\indented{1}{of the rational function \\spad{rf} with respect to the variable var.} \\blankline \\spad{X} a:=x+1/(\\spad{y+1}) \\spad{X} partialFraction(a,{}\\spad{y})\\$PFRPAC(INT)"))) NIL NIL -(-837) -((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) +(-904 E OV R P) +((|constructor| (NIL "This package computes multivariate polynomial \\spad{gcd}\\spad{'s} using a hensel lifting strategy. The contraint on the coefficient domain is imposed by the lifting strategy. It is assumed that the coefficient domain has the property that almost all specializations preserve the degree of the \\spad{gcd}.")) (|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-838 -2958) -((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) +(-905) +((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition \\spad{lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups \\spad{Sn1},{}...,{}\\spad{Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=} 8. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer ij where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list \\spad{li}. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list \\spad{li}. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list \\spad{li}. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list \\spad{li}. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list \\spad{li}. Note that duplicates in the list will be removed Error: if \\spad{li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list \\spad{li}. Note that duplicates in the list will be removed. error,{} if \\spad{li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of \\spad{i1},{}...,{}ik. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers \\spad{i1},{}...,{}ik. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order \\spad{ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list \\spad{li},{} generators are in general the \\spad{n}-2-cycle (\\spad{li}.3,{}...,{}\\spad{li}.\\spad{n}) and the 3-cycle (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3),{} if \\spad{n} is odd and product of the 2-cycle (\\spad{li}.1,{}\\spad{li}.2) with \\spad{n}-2-cycle (\\spad{li}.3,{}...,{}\\spad{li}.\\spad{n}) and the 3-cycle (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3),{} if \\spad{n} is even. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group An acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the \\spad{n}-2-cycle (3,{}...,{}\\spad{n}) and the 3-cycle (1,{}2,{}3) if \\spad{n} is odd and the product of the 2-cycle (1,{}2) with \\spad{n}-2-cycle (3,{}...,{}\\spad{n}) and the 3-cycle (1,{}2,{}3) if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list \\spad{li},{} generators are the cycle given by \\spad{li} and the 2-cycle (\\spad{li}.1,{}\\spad{li}.2). Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group \\spad{Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the \\spad{n}-cycle (1,{}...,{}\\spad{n}) and the 2-cycle (1,{}2)."))) NIL NIL -(-839) -((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4169 "*") . T)) +(-906 -1333) +((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} This package is an interface package to the groebner basis package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL -(-840 R) -((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL +(-907 R) +((|constructor| (NIL "Provides a coercion from the symbolic fractions in \\%\\spad{pi} with integer coefficients to any Expression type.")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL -(-841) +NIL +(-908) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-909) +((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for positive integers.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) +(((-4507 "*") . T)) +NIL +(-910 -1333 P) +((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL -(-842 |xx| -2958) +NIL +(-911 |xx| -1333) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL -(-843 -2958 P) -((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) +(-912 K PCS) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates if the places correspnd to a simple point")) (|setFoundPlacesToEmpty| (((|List| $)) "\\spad{setFoundPlacesToEmpty()} does what it says. (this should not be used)\\spad{!!!}")) (|foundPlaces| (((|List| $)) "\\spad{foundPlaces()} returns the list of all \"created\" places up to now.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(pl)} test if the place \\spad{pl} correspond to a leaf of a desingularisation tree.")) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) "\\spad{setDegree!(pl,{}ls)} set the degree.")) (|setParam!| (((|Void|) $ (|List| |#2|)) "\\spad{setParam!(pl,{}ls)} set the local parametrization of \\spad{pl} to \\spad{ls}.")) (|localParam| (((|List| |#2|) $) "\\spad{localParam(pl)} returns the local parametrization associated to the place \\spad{pl}."))) +NIL +NIL +(-913 K) +((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-844 R |Var| |Expon| GR) -((|constructor| (NIL "Author: William Sit,{} spring 89")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) +(-914 K) +((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-845) -((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) +(-915 K PCS) +((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-846 S) +(-916 R |Var| |Expon| GR) +((|constructor| (NIL "This package completely solves a parametric linear system of equations by decomposing the set of all parametric values for which the linear system is consistent into a union of quasi-algebraic sets (which need not be irredundant,{} but most of the time is). Each quasi-algebraic set is described by a list of polynomials that vanish on the set,{} and a list of polynomials that vanish at no point of the set. For each quasi-algebraic set,{} the solution of the linear system is given,{} as a particular solution and a basis of the homogeneous system. \\blankline The parametric linear system should be given in matrix form,{} with a coefficient matrix and a right hand side vector. The entries of the coefficient matrix and right hand side vector should be polynomials in the parametric variables,{} over a Euclidean domain of characteristic zero. \\blankline If the system is homogeneous,{} the right hand side need not be given. The right hand side can also be replaced by an indeterminate vector,{} in which case,{} the conditions required for consistency will also be given. \\blankline The package has other facilities for saving results to external files,{} as well as solving the system for a specified minimum rank. Altogether there are 12 mode maps for psolve,{} as explained below.")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) +NIL +NIL +(-917 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-847) -((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) +(-918) +((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} is not documented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} is not documented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} is not documented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} is not documented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-848) +(-919) +((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} is not documented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} is not documented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} is not documented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t)*cos(t)},{} \\spad{y = f(t)*sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t)*cos(t)},{} \\spad{y = f(t)*sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\indented{1}{plot(\\spad{f},{}a..\\spad{b}) plots the function \\spad{f(x)}} \\indented{1}{on the interval \\spad{[a,{}b]}.} \\blankline \\spad{X} fp:=(t:DFLOAT):DFLOAT +-> sin(\\spad{t}) \\spad{X} plot(\\spad{fp},{}\\spad{-1}.0..1.0)\\$PLOT"))) +NIL +NIL +(-920) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-849) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) +(-921 K |PolyRing| E -2050 |ProjPt|) +((|constructor| (NIL "The following is part of the PAFF package")) (|multiplicity| (((|NonNegativeInteger|) |#2| |#5| (|Integer|)) "\\spad{multiplicity returns} the multiplicity of the polynomial at given point.") (((|NonNegativeInteger|) |#2| |#5|) "\\spad{multiplicity returns} the multiplicity of the polynomial at given point.")) (|minimalForm| ((|#2| |#2| |#5| (|Integer|)) "\\spad{minimalForm returns} the minimal form after translation to the origin.") ((|#2| |#2| |#5|) "\\spad{minimalForm returns} the minimal form after translation to the origin.")) (|translateToOrigin| ((|#2| |#2| |#5|) "\\spad{translateToOrigin translate} the polynomial from the given point to the origin") ((|#2| |#2| |#5| (|Integer|)) "\\spad{translateToOrigin translate} the polynomial from the given point to the origin")) (|eval| ((|#1| |#2| |#5|) "\\spad{eval returns} the value at given point.")) (|pointInIdeal?| (((|Boolean|) (|List| |#2|) |#5|) "\\spad{pointInIdeal? test} if the given point is in the algebraic set defined by the given list of polynomials."))) +NIL NIL +(-922 R -1333) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching.")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL -(-850 R -2958) -((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL +(-923) +((|constructor| (NIL "Attaching assertions to symbols for pattern matching.")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL -(-851 S A B) -((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL +(-924 S A B) +((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note that this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL -(-852 S R -2958) +NIL +(-925 S R -1333) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-853 I) +(-926 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-854 S E) +(-927 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-855 S R L) +(-928 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-856 S E V R P) +(-929 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -806) (|devaluate| |#1|)))) -(-857 -3584) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) +((|HasCategory| |#3| (LIST (QUOTE -873) (|devaluate| |#1|)))) +(-930 R -1333 -2500) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching.")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-858 R -2958 -3584) -((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) +(-931 -2500) +((|constructor| (NIL "Attaching predicates to symbols for pattern matching.")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-859 S R Q) +(-932 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-860 S) +(-933 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-861 S R P) +(-934 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-862) -((|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}."))) -NIL +(-935) +((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note that Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note that Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note that Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note that fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note that Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note that \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note that Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note that Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}."))) NIL -(-863 R) NIL -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#1| (QUOTE (-959))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-959)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-864 |lv| R) +(-936 R) +((|constructor| (NIL "This domain implements points in coordinate space"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-994))) (|HasCategory| |#1| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-937 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-865 |TheField| |ThePols|) +(-938 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-775)))) -(-866 R) -((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| (-1070) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| (-1070) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| (-1070) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| (-1070) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| (-1070) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#1| (QUOTE -4165)) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-867 R S) -((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) +((|HasCategory| |#1| (QUOTE (-832)))) +(-939 R S) +((|constructor| (NIL "This package takes a mapping between coefficient rings,{} and lifts it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-868 |x| R) +(-940 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-869 S R E |VarSet|) -((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) +(-941 S R E |VarSet|) +((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note that \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-830))) (|HasAttribute| |#2| (QUOTE -4165)) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#4| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#4| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#4| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-777)))) -(-870 R E |VarSet|) -((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#4| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#4| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#4| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-834)))) +(-942 R E |VarSet|) +((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note that \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-871 E V R P -2958) -((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) +(-943 E V R P -1333) +((|constructor| (NIL "Manipulations on polynomial quotients This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-872 E |Vars| R P S) +(-944 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-873 E V R P -2958) -((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) +(-945 R) +((|constructor| (NIL "This type is the basic representation of sparse recursive multivariate polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1153) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1153) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1153) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1153) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1153) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-946 E V R P -1333) +((|constructor| (NIL "Computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL -((|HasCategory| |#3| (QUOTE (-419)))) -(-874) +((|HasCategory| |#3| (QUOTE (-447)))) +(-947) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-875 R E) -((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-419))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-123)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#1| (QUOTE -4165))) -(-876 R L) +(-948 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-877 S) -((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-878 A B) -((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) +(-949 A B) +((|constructor| (NIL "This package provides tools for operating on primitive arrays with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\indented{1}{map(\\spad{f},{}a) applies function \\spad{f} to each member of primitive array} \\indented{1}{\\spad{a} resulting in a new primitive array over a} \\indented{1}{possibly different underlying domain.} \\blankline \\spad{X} \\spad{T1:=PrimitiveArrayFunctions2}(Integer,{}Integer) \\spad{X} map(\\spad{x+}-\\spad{>x+2},{}[\\spad{i} for \\spad{i} in 1..10])\\$\\spad{T1}")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\indented{1}{reduce(\\spad{f},{}a,{}\\spad{r}) applies function \\spad{f} to each} \\indented{1}{successive element of the} \\indented{1}{primitive array \\spad{a} and an accumulant initialized to \\spad{r}.} \\indented{1}{For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)}} \\indented{1}{does \\spad{3+(2+(1+0))}. Note that third argument \\spad{r}} \\indented{1}{may be regarded as the identity element for the function \\spad{f}.} \\blankline \\spad{X} \\spad{T1:=PrimitiveArrayFunctions2}(Integer,{}Integer) \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} reduce(adder,{}[\\spad{i} for \\spad{i} in 1..10],{}0)\\$\\spad{T1}")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\indented{1}{scan(\\spad{f},{}a,{}\\spad{r}) successively applies} \\indented{1}{\\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays} \\indented{1}{\\spad{x} of primitive array \\spad{a}.} \\indented{1}{More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then} \\indented{1}{\\spad{scan(f,{}a,{}r)} returns} \\indented{1}{\\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.} \\blankline \\spad{X} \\spad{T1:=PrimitiveArrayFunctions2}(Integer,{}Integer) \\spad{X} adder(a:Integer,{}b:Integer):Integer \\spad{==} a+b \\spad{X} scan(adder,{}[\\spad{i} for \\spad{i} in 1..10],{}0)\\$\\spad{T1}"))) NIL NIL -(-879) +(-950 S) +((|constructor| (NIL "This provides a fast array type with no bound checking on elt\\spad{'s}. Minimum index is 0 in this type,{} cannot be changed"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-951) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-880 -2958) +(-952 -1333) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL -(-881 I) +(-953 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-882) +(-954) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-883 A B) -((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) -((-4164 -12 (|has| |#2| (-440)) (|has| |#1| (-440)))) -((-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#2| (QUOTE (-440)))) (-12 (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#2| (QUOTE (-336)))) (-12 (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#2| (QUOTE (-657)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#2| (QUOTE (-440)))) (-12 (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#2| (QUOTE (-657))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-440))) (|HasCategory| |#2| (QUOTE (-440)))) (-12 (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#2| (QUOTE (-657)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-777)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-777)))))) -(-884 S) -((|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-955 K |symb| |PolyRing| E |ProjPt|) +((|constructor| (NIL "The following is part of the PAFF package")) (|rationalPoints| (((|List| |#5|) |#3| (|PositiveInteger|)) "\\axiom{rationalPoints(\\spad{f},{}\\spad{d})} returns all points on the curve \\axiom{\\spad{f}} in the extension of the ground field of degree \\axiom{\\spad{d}}. For \\axiom{\\spad{d} > 1} this only works if \\axiom{\\spad{K}} is a \\axiomType{LocallyAlgebraicallyClosedField}")) (|algebraicSet| (((|List| |#5|) (|List| |#3|)) "\\spad{algebraicSet returns} the algebraic set if finite (dimension 0).")) (|singularPoints| (((|List| |#5|) |#3|) "\\spad{singularPoints retourne} les points singulier")) (|singularPointsWithRestriction| (((|List| |#5|) |#3| (|List| |#3|)) "return the singular points that anhilate"))) +NIL +NIL +(-956 R E) +((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{x} : \\spad{p1} - \\spad{r} * x**e * \\spad{p2}"))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-447))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-137)))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503))) +(-957 A B) +((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} is not documented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} is not documented")) (|makeprod| (($ |#1| |#2|) "\\indented{1}{makeprod(a,{}\\spad{b}) computes the product of two functions} \\blankline \\spad{X} \\spad{f:=}(x:INT):INT +-> 3*x \\spad{X} \\spad{g:=}(x:INT):INT +-> \\spad{x^3} \\spad{X} \\spad{h}(x:INT):Product(INT,{}INT) \\spad{==} makeprod(\\spad{f} \\spad{x},{} \\spad{g} \\spad{x}) \\spad{X} \\spad{h}(3)"))) +((-4502 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) +((-12 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#2| (QUOTE (-780)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#2| (QUOTE (-364)))) (-12 (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#2| (QUOTE (-708)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#2| (QUOTE (-708))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#2| (QUOTE (-780))))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#2| (QUOTE (-780))))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#2| (QUOTE (-708)))) (-12 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#2| (QUOTE (-780))))) (-12 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-834)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-780))) (|HasCategory| |#2| (QUOTE (-780)))) (-12 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-834)))))) +(-958 K) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) +NIL NIL -(-885 R |polR|) -((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) +(-959 K) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL -((|HasCategory| |#1| (QUOTE (-419)))) -(-886) -((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) NIL +(-960 -2050 K) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL -(-887 S |Coef| |Expon| |Var|) -((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) NIL +(-961 S) +((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-888 |Coef| |Expon| |Var|) -((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) +(-962 R |polR|) +((|constructor| (NIL "This package contains some functions: discriminant,{} resultant,{} subResultantGcd,{} chainSubResultants,{} degreeSubResultant,{} lastSubResultant,{} resultantEuclidean,{} subResultantGcdEuclidean,{} \\spad{semiSubResultantGcdEuclidean1},{} \\spad{semiSubResultantGcdEuclidean2}\\spad{\\br} These procedures come from improvements of the subresultants algorithm.")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning. \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL -(-889) +((|HasCategory| |#1| (QUOTE (-447)))) +(-963 K) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space.")) (|pointValue| (((|List| |#1|) $) "\\spad{pointValue returns} the coordinates of the point or of the point of origin that represent an infinitly close point")) (|setelt| ((|#1| $ (|Integer|) |#1|) "\\spad{setelt sets} the value of a specified coordinates")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates")) (|list| (((|List| |#1|) $) "\\spad{list returns} the list of the coordinates")) (|lastNonNull| (((|Integer|) $) "\\spad{lastNonNull returns} the integer corresponding to the last non null coordinates.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(p)} test if the point is rational according to the characteristic of the ground field.") (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{rational?(p,{}n)} test if the point is rational according to \\spad{n}.")) (|removeConjugate| (((|List| $) (|List| $)) "\\spad{removeConjugate(lp)} returns removeConjugate(\\spad{lp},{}\\spad{n}) where \\spad{n} is the characteristic of the ground field.") (((|List| $) (|List| $) (|NonNegativeInteger|)) "\\spad{removeConjugate(lp,{}n)} returns a list of points such that no points in the list is the conjugate (according to \\spad{n}) of another point.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns conjugate(\\spad{p},{}\\spad{n}) where \\spad{n} is the characteristic of the ground field.") (($ $ (|NonNegativeInteger|)) "\\spad{conjugate(p,{}n)} returns p**n,{} that is all the coordinates of \\spad{p} to the power of \\spad{n}")) (|orbit| (((|List| $) $ (|NonNegativeInteger|)) "\\spad{orbit(p,{}n)} returns the orbit of the point \\spad{p} according to \\spad{n},{} that is orbit(\\spad{p},{}\\spad{n}) = \\spad{\\{} \\spad{p},{} p**n,{} \\spad{p**}(\\spad{n**2}),{} \\spad{p**}(\\spad{n**3}),{} ..... \\spad{\\}}") (((|List| $) $) "\\spad{orbit(p)} returns the orbit of the point \\spad{p} according to the characteristic of \\spad{K},{} that is,{} for \\spad{q=} char \\spad{K},{} orbit(\\spad{p}) = \\spad{\\{} \\spad{p},{} p**q,{} \\spad{p**}(\\spad{q**2}),{} \\spad{p**}(\\spad{q**3}),{} ..... \\spad{\\}}")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce a} list of \\spad{K} to a projective point.") (((|List| |#1|) $) "\\spad{coerce a} a projective point list of \\spad{K}")) (|projectivePoint| (($ (|List| |#1|)) "\\spad{projectivePoint creates} a projective point from a list")) (|homogenize| (($ $) "\\spad{homogenize(pt)} the point according to the coordinate which is the last non null.") (($ $ (|Integer|)) "\\spad{homogenize the} point according to the coordinate specified by the integer"))) +NIL +NIL +(-964) +((|constructor| (NIL "Domain for partitions of positive integers Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition"))) +NIL +NIL +(-965 S |Coef| |Expon| |Var|) +((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note that this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) +NIL +NIL +(-966 |Coef| |Expon| |Var|) +((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note that this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-967) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-890 S R E |VarSet| P) -((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) +(-968 S R E |VarSet| P) +((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains \\indented{1}{some non null element lying in the base ring \\axiom{\\spad{R}}.}")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-508)))) -(-891 R E |VarSet| P) -((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4167 . T) (-2951 . T)) +((|HasCategory| |#2| (QUOTE (-550)))) +(-969 R E |VarSet| P) +((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains \\indented{1}{some non null element lying in the base ring \\axiom{\\spad{R}}.}")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) +((-4505 . T) (-2537 . T)) NIL -(-892 R E V P) +(-970 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-276)))) (|HasCategory| |#1| (QUOTE (-419)))) -(-893 K) +((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-447)))) +(-971 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-894 |VarSet| E RC P) +(-972 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-895 R) -((|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-973 R) +((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-896 R1 R2) -((|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) +(-974 R1 R2) +((|constructor| (NIL "This package has no description")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) NIL NIL -(-897 R) -((|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) +(-975 R) +((|constructor| (NIL "This package has no description")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-898 K) +(-976 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-899 R E OV PPR) -((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) +(-977 R E OV PPR) +((|constructor| (NIL "This package has no description")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-900 K R UP -2958) +(-978 K R UP -1333) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-901 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) -NIL -((-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-276))))) -(-902 |vl| |nv|) +(-979 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-903 R E V P TS) -((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) +(-980 R |Var| |Expon| |Dpoly|) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +NIL +((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-296))))) +(-981 R E V P TS) +((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets.")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff internalSubQuasiComponent? returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. infRittWu? from RecursivePolynomialCategory.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} supDimElseRittWu?")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-904) +(-982) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation."))) NIL NIL -(-905 A S) -((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) +(-983 A B R S) +((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL -((|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-750))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-1046)))) -(-906 S) -((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-2951 . T) (-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) NIL -(-907 A B R S) -((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) +(-984 A S) +((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-807))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1128)))) +(-985 S) +((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) +((-2537 . T) (-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-908 |n| K) +(-986 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-909 S) -((|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-987 S) +((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note that \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note that rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-910 R) -((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((-4160 |has| |#1| (-260)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-260))) (-1405 (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-331)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -476) (QUOTE (-1070)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -256) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-967))) (|HasCategory| |#1| (QUOTE (-500))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-331))))) -(-911 S R) -((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) +(-988 S R) +((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note that if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (QUOTE (-967))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-260)))) -(-912 R) -((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4160 |has| |#1| (-260)) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-280)))) +(-989 R) +((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note that if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) +((-4498 |has| |#1| (-280)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-913 QR R QS S) -((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) +(-990 QR R QS S) +((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\indented{1}{map(\\spad{f},{}\\spad{u}) maps \\spad{f} onto the component parts of the quaternion \\spad{u}.} \\indented{1}{to convert an expression in Quaterion(\\spad{R}) to Quaternion(\\spad{S})} \\blankline \\spad{X} \\spad{f}(a:FRAC(INT)):COMPLEX(FRAC(INT)) \\spad{==} a::COMPLEX(FRAC(INT)) \\spad{X} q:=quatern(2/11,{}\\spad{-8},{}3/4,{}1) \\spad{X} map(\\spad{f},{}\\spad{q})"))) NIL NIL -(-914 S) -((|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-915 S) -((** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) +(-991 R) +((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a commutative ring. The main constructor function is \\spadfun{quatern} which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part and the \\spad{k} imaginary part."))) +((-4498 |has| |#1| (-280)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-280))) (-2318 (|HasCategory| |#1| (QUOTE (-280))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -515) (QUOTE (-1153)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -276) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-542))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359))))) +(-992 S) +((|constructor| (NIL "Linked List implementation of a Queue")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} member?(3,{}a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} count(4,{}a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} count(\\spad{x+}->(\\spad{x>2}),{}a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} any?(\\spad{x+}->(\\spad{x=4}),{}a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} every?(\\spad{x+}->(\\spad{x=4}),{}a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} b:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} map!(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} map(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} eq?(a,{}\\spad{b})")) (|copy| (($ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()\\$Queue(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()\\$(Queue INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,{}2,{}3,{}4,{}5])\\$Queue(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} size?(a,{}5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} more?(a,{}9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} less?(a,{}9)")) (|length| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} length a")) (|rotate!| (($ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} rotate! a")) (|back| ((|#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} back a")) (|front| ((|#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} front a")) (|inspect| ((|#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} insert! (8,{}a) \\spad{X} a")) (|enqueue!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} enqueue! (9,{}a) \\spad{X} a")) (|extract!| ((|#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} extract! a \\spad{X} a")) (|dequeue!| ((|#1| $) "\\blankline \\spad{X} a:Queue INT:= queue [1,{}2,{}3,{}4,{}5] \\spad{X} dequeue! a \\spad{X} a")) (|queue| (($ (|List| |#1|)) "\\indented{1}{queue([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) creates a queue with first (top)} \\indented{1}{element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}.} \\blankline \\spad{E} e:Queue INT:= queue [1,{}2,{}3,{}4,{}5]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-993 S) +((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-916) -((** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) +(-994) +((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-917 -2958 UP UPUP |radicnd| |n|) +(-995 -1333 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4160 |has| (-375 |#2|) (-331)) (-4165 |has| (-375 |#2|) (-331)) (-4159 |has| (-375 |#2|) (-331)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-375 |#2|) (QUOTE (-132))) (|HasCategory| (-375 |#2|) (QUOTE (-134))) (|HasCategory| (-375 |#2|) (QUOTE (-318))) (|HasCategory| (-375 |#2|) (QUOTE (-331))) (-1405 (|HasCategory| (-375 |#2|) (QUOTE (-331))) (|HasCategory| (-375 |#2|) (QUOTE (-318)))) (|HasCategory| (-375 |#2|) (QUOTE (-336))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-336))) (-1405 (|HasCategory| (-375 |#2|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-1405 (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-12 (|HasCategory| (-375 |#2|) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-375 |#2|) (QUOTE (-318))))) (-12 (|HasCategory| (-375 |#2|) (QUOTE (-206))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (-1405 (-12 (|HasCategory| (-375 |#2|) (QUOTE (-206))) (|HasCategory| (-375 |#2|) (QUOTE (-331)))) (|HasCategory| (-375 |#2|) (QUOTE (-318))))) -(-918 |bb|) -((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-501) (QUOTE (-830))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-1070)))) (|HasCategory| (-501) (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-134))) (|HasCategory| (-501) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-501) (QUOTE (-933))) (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-1046))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| (-501) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| (-501) (QUOTE (-206))) (|HasCategory| (-501) (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| (-501) (LIST (QUOTE -476) (QUOTE (-1070)) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -278) (QUOTE (-501)))) (|HasCategory| (-501) (LIST (QUOTE -256) (QUOTE (-501)) (QUOTE (-501)))) (|HasCategory| (-501) (QUOTE (-276))) (|HasCategory| (-501) (QUOTE (-500))) (|HasCategory| (-501) (QUOTE (-777))) (-1405 (|HasCategory| (-501) (QUOTE (-750))) (|HasCategory| (-501) (QUOTE (-777)))) (|HasCategory| (-501) (LIST (QUOTE -577) (QUOTE (-501)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-501) (QUOTE (-830)))) (|HasCategory| (-501) (QUOTE (-132))))) -(-919) +((-4498 |has| (-403 |#2|) (-359)) (-4503 |has| (-403 |#2|) (-359)) (-4497 |has| (-403 |#2|) (-359)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-403 |#2|) (QUOTE (-146))) (|HasCategory| (-403 |#2|) (QUOTE (-148))) (|HasCategory| (-403 |#2|) (QUOTE (-344))) (|HasCategory| (-403 |#2|) (QUOTE (-359))) (-2318 (|HasCategory| (-403 |#2|) (QUOTE (-359))) (|HasCategory| (-403 |#2|) (QUOTE (-344)))) (|HasCategory| (-403 |#2|) (QUOTE (-364))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-364))) (-2318 (|HasCategory| (-403 |#2|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-2318 (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-12 (|HasCategory| (-403 |#2|) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-403 |#2|) (QUOTE (-344))))) (-12 (|HasCategory| (-403 |#2|) (QUOTE (-221))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (-2318 (-12 (|HasCategory| (-403 |#2|) (QUOTE (-221))) (|HasCategory| (-403 |#2|) (QUOTE (-359)))) (|HasCategory| (-403 |#2|) (QUOTE (-344))))) +(-996 |bb|) +((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. \\spadignore{e.g.} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-560) (QUOTE (-896))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-1153)))) (|HasCategory| (-560) (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-148))) (|HasCategory| (-560) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-560) (QUOTE (-1013))) (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1128))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| (-560) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-221))) (|HasCategory| (-560) (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| (-560) (LIST (QUOTE -515) (QUOTE (-1153)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -276) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-296))) (|HasCategory| (-560) (QUOTE (-542))) (|HasCategory| (-560) (QUOTE (-834))) (-2318 (|HasCategory| (-560) (QUOTE (-807))) (|HasCategory| (-560) (QUOTE (-834)))) (|HasCategory| (-560) (LIST (QUOTE -622) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-560) (QUOTE (-896)))) (|HasCategory| (-560) (QUOTE (-146))))) +(-997) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-920) -((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) +(-998) +((|constructor| (NIL "Random number generators. All random numbers used in the system should originate from the same generator. This package is intended to be the source.")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-921 RP) -((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) +(-999 RP) +((|constructor| (NIL "Factorization of extended polynomials with rational coefficients. This package implements factorization of extended polynomials whose coefficients are rational numbers. It does this by taking the \\spad{lcm} of the coefficients of the polynomial and creating a polynomial with integer coefficients. The algorithm in \\spadtype{GaloisGroupFactorizer} is then used to factor the integer polynomial. The result is normalized with respect to the original \\spad{lcm} of the denominators.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-922 S) -((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) +(-1000 S) +((|constructor| (NIL "Rational number testing and retraction functions.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-923 A S) -((|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) +(-1001 A S) +((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a node consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4168)) (|HasCategory| |#2| (QUOTE (-1001)))) -(-924 S) -((|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-2951 . T)) +((|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-1082)))) +(-1002 S) +((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a node consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) +((-2537 . T)) NIL -(-925 S) +(-1003 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-926) +(-1004) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4160 . T) (-4165 . T) (-4159 . T) (-4162 . T) (-4161 . T) ((-4169 "*") . T) (-4164 . T)) +((-4498 . T) (-4503 . T) (-4497 . T) (-4500 . T) (-4499 . T) ((-4507 "*") . T) (-4502 . T)) NIL -(-927 R -2958) -((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) +(-1005 R -1333) +((|constructor| (NIL "Risch differential equation,{} elementary case.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-928 R -2958) -((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) +(-1006 R -1333) +((|constructor| (NIL "Risch differential equation,{} elementary case.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-929 -2958 UP) -((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) +(-1007 -1333 UP) +((|constructor| (NIL "Risch differential equation,{} transcendental case.")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-930 -2958 UP) -((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) +(-1008 -1333 UP) +((|constructor| (NIL "Risch differential equation system,{} transcendental case.")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL -(-931 S) +(-1009 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-932 F1 UP UPUP R F2) -((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented"))) +(-1010 F1 UP UPUP R F2) +((|constructor| (NIL "Finds the order of a divisor over a finite field")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented"))) NIL NIL -(-933) +(-1011 |Pol|) +((|constructor| (NIL "This package provides functions for finding the real zeros of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL +(-1012 |Pol|) +((|constructor| (NIL "This package provides functions for finding the real zeros of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL -(-934 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL +(-1013) +((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL -(-935 |Pol|) -((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL +(-1014) +((|constructor| (NIL "This package provides numerical solutions of systems of polynomial equations for use in ACPLOT")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\indented{1}{realSolve(\\spad{lp},{}\\spad{lv},{}eps) = compute the list of the real} \\indented{1}{solutions of the list \\spad{lp} of polynomials with integer} \\indented{1}{coefficients with respect to the variables in \\spad{lv},{}} \\indented{1}{with precision eps.} \\blankline \\spad{X} \\spad{p1} \\spad{:=} x**2*y*z + \\spad{y*z} \\spad{X} \\spad{p2} \\spad{:=} x**2*y**2*z + \\spad{x} + \\spad{z} \\spad{X} \\spad{p3} \\spad{:=} \\spad{x**2*y**2*z**2} + \\spad{z} + 1 \\spad{X} \\spad{lp} \\spad{:=} [\\spad{p1},{} \\spad{p2},{} \\spad{p3}] \\spad{X} realSolve(\\spad{lp},{}[\\spad{x},{}\\spad{y},{}\\spad{z}],{}0.01)")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\indented{1}{solve(\\spad{p},{}eps) finds the real zeroes of a univariate} \\indented{1}{integer polynomial \\spad{p} with precision eps.} \\blankline \\spad{X} \\spad{p} \\spad{:=} 4*x^3 - 3*x^2 + 2*x - 4 \\spad{X} solve(\\spad{p},{}0.01)\\$REALSOLV") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\indented{1}{solve(\\spad{p},{}eps) finds the real zeroes of a} \\indented{1}{univariate rational polynomial \\spad{p} with precision eps.} \\blankline \\spad{X} \\spad{p} \\spad{:=} 4*x^3 - 3*x^2 + 2*x - 4 \\spad{X} solve(p::POLY(FRAC(INT)),{}0.01)\\$REALSOLV"))) NIL -(-936) -((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL -NIL -(-937 |TheField|) +(-1015 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-4160 . T) (-4165 . T) (-4159 . T) (-4162 . T) (-4161 . T) ((-4169 "*") . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-375 (-501)) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-375 (-501)) (LIST (QUOTE -950) (QUOTE (-501)))) (-1405 (|HasCategory| (-375 (-501)) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))))) -(-938 -2958 L) +((-4498 . T) (-4503 . T) (-4497 . T) (-4500 . T) (-4499 . T) ((-4507 "*") . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-403 (-560)) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-403 (-560)) (LIST (QUOTE -1029) (QUOTE (-560)))) (-2318 (|HasCategory| (-403 (-560)) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))))) +(-1016 R -1333) +((|constructor| (NIL "This package provides an operator for the \\spad{n}-th term of a recurrence and an operator for the coefficient of \\spad{x^n} in a function specified by a functional equation.")) (|getOp| (((|BasicOperator|) |#2|) "\\spad{getOp f},{} if \\spad{f} represents the coefficient of a recurrence or ADE,{} returns the operator representing the solution")) (|getEq| ((|#2| |#2|) "\\spad{getEq f} returns the defining equation,{} if \\spad{f} represents the coefficient of an ADE or a recurrence.")) (|evalADE| ((|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|)) "\\spad{evalADE(f,{} dummy,{} x,{} n,{} eq,{} values)} creates an expression that stands for the coefficient of \\spad{x^n} in the Taylor expansion of \\spad{f}(\\spad{x}),{} where \\spad{f}(\\spad{x}) is given by the functional equation \\spad{eq}. However,{} for technical reasons the variable \\spad{x} has to be replaced by a \\spad{dummy} variable \\spad{dummy} in \\spad{eq}. The argument values specifies the first few Taylor coefficients.")) (|evalRec| ((|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|)) "\\spad{evalRec(u,{} dummy,{} n,{} n0,{} eq,{} values)} creates an expression that stands for \\spad{u}(\\spad{n0}),{} where \\spad{u}(\\spad{n}) is given by the equation \\spad{eq}. However,{} for technical reasons the variable \\spad{n} has to be replaced by a \\spad{dummy} variable \\spad{dummy} in \\spad{eq}. The argument values specifies the initial values of the recurrence \\spad{u}(0),{} \\spad{u}(1),{}... For the moment we don\\spad{'t} allow recursions that contain \\spad{u} inside of another operator."))) +NIL +((|HasCategory| |#1| (QUOTE (-1039)))) +(-1017 -1333 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-939 S) -((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) +(-1018 S) +((|constructor| (NIL "\\spadtype{Reference} is for making a changeable instance of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1001)))) -(-940 R E V P) -((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#4| (QUOTE (-1001))) (-12 (|HasCategory| |#4| (LIST (QUOTE -278) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#3| (QUOTE (-336)))) -(-941) -((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) +((|HasCategory| |#1| (QUOTE (-1082)))) +(-1019 R E V P) +((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation zeroSetSplit is an implementation of a new algorithm for solving polynomial systems by means of regular chains.")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as zeroSetSplit from RegularTriangularSetCategory. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#4| (QUOTE (-1082))) (-12 (|HasCategory| |#4| (LIST (QUOTE -298) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-364)))) +(-1020 R) +((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note that instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices [(deltai,{}\\spad{pi1}(\\spad{i})),{}...,{}(deltai,{}pik(\\spad{i}))] if the permutations \\spad{pi1},{}...,{}pik are in list notation and are permuting {1,{}2,{}...,{}\\spad{n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices [(deltai,{}\\spad{pi1}(\\spad{i})),{}...,{}(deltai,{}pik(\\spad{i}))] (Kronecker delta) for the permutations \\spad{pi1},{}...,{}pik of {1,{}2,{}...,{}\\spad{n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix (deltai,{}\\spad{pi}(\\spad{i})) (Kronecker delta) if the permutation \\spad{pi} is in list notation and permutes {1,{}2,{}...,{}\\spad{n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix (deltai,{}\\spad{pi}(\\spad{i})) (Kronecker delta) for a permutation \\spad{pi} of {1,{}2,{}...,{}\\spad{n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix \\spad{ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note that if the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix a with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices \\spad{ai} and \\spad{bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note that if each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices a and \\spad{b}. Note that if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list \\spad{la} the irreducible,{} polynomial representation of the general linear group \\spad{GLm} which corresponds to the partition (\\spad{n},{}0,{}...,{}0) of \\spad{n}. Error: if the matrices in \\spad{la} are not square matrices. Note that this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group \\spad{Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix a the irreducible,{} polynomial representation of the general linear group \\spad{GLm} which corresponds to the partition (\\spad{n},{}0,{}...,{}0) of \\spad{n}. Error: if a is not a square matrix. Note that this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group \\spad{Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate \\spad{x}[\\spad{i},{}\\spad{j}] (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list \\spad{la} the irreducible,{} polynomial representation of the general linear group \\spad{GLm} which corresponds to the partition (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0) of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note that this corresponds to the symmetrization of the representation with the sign representation of the symmetric group \\spad{Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix a the irreducible,{} polynomial representation of the general linear group \\spad{GLm},{} where \\spad{m} is the number of rows of a,{} which corresponds to the partition (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0) of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note that this corresponds to the symmetrization of the representation with the sign representation of the symmetric group \\spad{Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL +((|HasAttribute| |#1| (QUOTE (-4507 "*")))) +(-1021 R) +((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note that most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the \\spad{n}-th one-dimensional subspace of the vector space generated by the elements of \\spad{basis},{} all from R**n. The coefficients of the representative are of shape (0,{}...,{}0,{}1,{}*,{}...,{}*),{} * in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are (q**n-1)/(\\spad{q}-1) of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that \\spad{+/}[q**i for \\spad{i} in 0..\\spad{i}-1] \\spad{<=} \\spad{n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls meatAxe(\\spad{aG},{}\\spad{true},{}numberOfTries,{}7). Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls meatAxe(\\spad{aG},{}\\spad{false},{}6,{}7),{} only using Parker\\spad{'s} fingerprints,{} if randomElemnts is \\spad{false}. If it is \\spad{true},{} it calls meatAxe(\\spad{aG},{}\\spad{true},{}25,{}7),{} only using random elements. Note that the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls meatAxe(\\spad{aG},{}\\spad{false},{}25,{}7) returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. \\spad{V} \\spad{R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. \\spad{V} \\spad{R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most \\spad{numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most maxTests elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If \\spad{randomElements} is \\spad{false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of R**n to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. \\spad{V} \\spad{R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by vector is a proper submodule of \\spad{V} \\spad{R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note that a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls isAbsolutelyIrreducible?(\\spad{aG},{}25). Note that the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of meatAxe would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls areEquivalent?(\\spad{aG0},{}\\spad{aG1},{}\\spad{true},{}25). Note that the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls areEquivalent?(\\spad{aG0},{}\\spad{aG1},{}\\spad{true},{}25). Note that the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries \\spad{numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use standardBasisOfCyclicSubmodule to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from aGi. The way to choose the singular matrices is as in meatAxe. If the two representations are equivalent,{} this routine returns the transformation matrix \\spad{TM} with \\spad{aG0}.\\spad{i} * \\spad{TM} = \\spad{TM} * \\spad{aG1}.\\spad{i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note that the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. \\spad{V} \\spad{R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of Av achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note that in contrast to cyclicSubmodule,{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. \\spad{V} \\spad{R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of Av as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note that in contrast to the description in \"The Meat-Axe\" and to standardBasisOfCyclicSubmodule the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by \\spad{aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis \\spad{lv} assumed to be in echelon form of a subspace of R**n (\\spad{n} the length of all the vectors in \\spad{lv} with unit vectors to a basis of R**n. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note that the rows of the result correspond to the vectors of the basis."))) NIL -(-942 R) -((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) +((|HasCategory| |#1| (QUOTE (-359))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-364)))) (|HasCategory| |#1| (QUOTE (-296)))) +(-1022 S) +((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL -((|HasAttribute| |#1| (QUOTE (-4169 "*")))) -(-943 R) -((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL -((|HasCategory| |#1| (QUOTE (-331))) (-12 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-336)))) (|HasCategory| |#1| (QUOTE (-276)))) -(-944 S) -((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) +(-1023) +((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-945 S) +(-1024 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-946 S) +(-1025 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-947 -2958 |Expon| |VarSet| |FPol| |LFPol|) +(-1026 -1333 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) -(((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-948) +(-1027) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2922) (QUOTE (-50)))))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001)))) (|HasCategory| (-1070) (QUOTE (-777))) (|HasCategory| (-50) (QUOTE (-1001))) (-1405 (|HasCategory| (-50) (QUOTE (-1001))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001)))) (-12 (|HasCategory| (-50) (LIST (QUOTE -278) (QUOTE (-50)))) (|HasCategory| (-50) (QUOTE (-1001))))) -(-949 A S) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (QUOTE (-1153))) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082)))) (|HasCategory| (-1153) (QUOTE (-834))) (|HasCategory| (-57) (QUOTE (-1082))) (-2318 (|HasCategory| (-57) (QUOTE (-1082))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -298) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1082))))) +(-1028 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL NIL -(-950 S) +(-1029 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL NIL -(-951 Q R) +(-1030 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-952 R) -((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) -NIL -NIL -(-953) +(-1031) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-954 UP) -((|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) +(-1032 UP) +((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-955 R) +(-1033 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-956 R |ls|) -((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| (-710 |#1| (-787 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-710 |#1| (-787 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-710 |#1| (-787 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -710) (|devaluate| |#1|) (LIST (QUOTE -787) (|devaluate| |#2|))))) (|HasCategory| (-710 |#1| (-787 |#2|)) (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| (-787 |#2|) (QUOTE (-336)))) -(-957) -((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) +(-1034 R) +((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) +NIL +NIL +(-1035 K) +((|constructor| (NIL "This pacackage finds all the roots of a polynomial. If the constant field is not large enough then it returns the list of found zeros and the degree of the extension need to find the other roots missing. If the return degree is 1 then all the roots have been found. If 0 is return for the extension degree then there are an infinite number of zeros,{} that is you ask for the zeroes of 0. In the case of infinite field a list of all found zeros is kept and for each other call of a function that finds zeroes,{} a check is made on that list; this is to keep a kind of \"canonical\" representation of the elements.")) (|setFoundZeroes| (((|List| |#1|) (|List| |#1|)) "\\spad{setFoundZeroes sets} the list of foundZeroes to the given one.")) (|foundZeroes| (((|List| |#1|)) "\\spad{foundZeroes returns} the list of already found zeros by the functions distinguishedRootsOf and distinguishedCommonRootsOf.")) (|distinguishedCommonRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|List| (|SparseUnivariatePolynomial| |#1|)) |#1|) "\\spad{distinguishedCommonRootsOf returns} the common zeros of a list of polynomial. It returns a record as in distinguishedRootsOf. If 0 is returned as extension degree then there are an infinite number of common zeros (in this case,{} the polynomial 0 was given in the list of input polynomials).")) (|distinguishedRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|SparseUnivariatePolynomial| |#1|) |#1|) "\\spad{distinguishedRootsOf returns} a record consisting of a list of zeros of the input polynomial followed by the smallest extension degree needed to find all the zeros. If \\spad{K} has \\spad{PseudoAlgebraicClosureOfFiniteFieldCategory} or \\spad{PseudoAlgebraicClosureOfRationalNumberCategory} then a root is created for each irreducible factor,{} and only these roots are returns and not their conjugate."))) +NIL NIL +(-1036 R |ls|) +((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See zeroSetSplit from RegularTriangularSet."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| (-767 |#1| (-844 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-767 |#1| (-844 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-767 |#1| (-844 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -767) (|devaluate| |#1|) (LIST (QUOTE -844) (|devaluate| |#2|))))) (|HasCategory| (-767 |#1| (-844 |#2|)) (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| (-844 |#2|) (QUOTE (-364)))) +(-1037) +((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} as \\indented{4}{\\spad{l} + \\spad{u0} + \\spad{w*u1} + \\spad{w**2*u2} +...+ \\spad{w**}(\\spad{n}-1)*u-1 + w**n*m} where \\indented{4}{\\spad{s} = a..\\spad{b}} \\indented{4}{\\spad{l} = min(a,{}\\spad{b})} \\indented{4}{\\spad{m} = abs(\\spad{b}-a) + 1} \\indented{4}{w**n < \\spad{m} < \\spad{w**}(\\spad{n+1})} \\indented{4}{\\spad{u0},{}...,{}un-1\\space{2}are uniform on\\space{2}0..\\spad{w}-1} \\indented{4}{\\spad{m}\\space{12}is\\space{2}uniform on\\space{2}0..(\\spad{m} quo w**n)\\spad{-1}}"))) NIL -(-958 S) -((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL +(-1038 S) +((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note that \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL -(-959) -((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4164 . T)) NIL -(-960 S |m| |n| R |Row| |Col|) -((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) +(-1039) +((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note that \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) +((-4502 . T)) NIL -((|HasCategory| |#4| (QUOTE (-276))) (|HasCategory| |#4| (QUOTE (-331))) (|HasCategory| |#4| (QUOTE (-508))) (|HasCategory| |#4| (QUOTE (-156)))) -(-961 |m| |n| R |Row| |Col|) -((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4167 . T) (-2951 . T) (-4162 . T) (-4161 . T)) +(-1040 |xx| -1333) +((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL -(-962 |m| |n| R) +NIL +(-1041 S |m| |n| R |Row| |Col|) +((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note that there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) +NIL +((|HasCategory| |#4| (QUOTE (-296))) (|HasCategory| |#4| (QUOTE (-359))) (|HasCategory| |#4| (QUOTE (-550))) (|HasCategory| |#4| (QUOTE (-170)))) +(-1042 |m| |n| R |Row| |Col|) +((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note that there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) +((-4505 . T) (-2537 . T) (-4500 . T) (-4499 . T)) +NIL +(-1043 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4167 . T) (-4162 . T) (-4161 . T)) -((|HasCategory| |#3| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#3| (QUOTE (-331))) (|HasCategory| |#3| (QUOTE (-1001))) (|HasCategory| |#3| (QUOTE (-276))) (|HasCategory| |#3| (QUOTE (-508))) (|HasCategory| |#3| (QUOTE (-156))) (-1405 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-331)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -278) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#3| (LIST (QUOTE -278) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-156)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -278) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-331)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -278) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1001)))))) -(-963 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4505 . T) (-4500 . T) (-4499 . T)) +((|HasCategory| |#3| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (QUOTE (-1082))) (|HasCategory| |#3| (QUOTE (-296))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-170))) (-2318 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-359)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-170)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-359)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))))) +(-1044 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-964 R) -((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) +(-1045 R) +((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplication by elements of the \\spad{rng}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{ x*(a*b) = (x*a)*b }\\spad{\\br} \\tab{5}\\spad{ x*(a+b) = (x*a)+(x*b) }\\spad{\\br} \\tab{5}\\spad{ (x+y)*x = (x*a)+(y*a) }")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL NIL -(-965) -((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) +(-1046) +((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{ x*(y+z) = x*y + x*z}\\spad{\\br} \\tab{5}\\spad{ (x+y)*z = x*z + y*z } \\blankline Conditional attributes\\spad{\\br} \\tab{5}noZeroDivisors\\tab{5}\\spad{ ab = 0 => a=0 or b=0}"))) NIL NIL -(-966 S) -((|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) +(-1047 S) +((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-967) -((|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-1048) +((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-968 |TheField| |ThePolDom|) +(-1049 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-969) -((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4155 . T) (-4159 . T) (-4154 . T) (-4165 . T) (-4166 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-1050) +((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting integers to roman numerals.")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) +((-4493 . T) (-4497 . T) (-4492 . T) (-4503 . T) (-4504 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-970) -((|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2922) (QUOTE (-50)))))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001)))) (|HasCategory| (-1070) (QUOTE (-777))) (|HasCategory| (-50) (QUOTE (-1001))) (-1405 (|HasCategory| (-50) (QUOTE (-1001))) (|HasCategory| (-2 (|:| -3626 (-1070)) (|:| -2922 (-50))) (QUOTE (-1001)))) (-12 (|HasCategory| (-50) (LIST (QUOTE -278) (QUOTE (-50)))) (|HasCategory| (-50) (QUOTE (-1001))))) -(-971 S R E V) -((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) +(-1051) +((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (QUOTE (-1153))) (LIST (QUOTE |:|) (QUOTE -2371) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082)))) (|HasCategory| (-1153) (QUOTE (-834))) (|HasCategory| (-57) (QUOTE (-1082))) (-2318 (|HasCategory| (-57) (QUOTE (-1082))) (|HasCategory| (-2 (|:| -3655 (-1153)) (|:| -2371 (-57))) (QUOTE (-1082)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -298) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1082))))) +(-1052 S R E V) +((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\spad{next_sousResultant2} from PseudoRemainderSequence from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial \\indented{1}{in its main variable.}")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-500))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-1070))))) -(-972 R E V) -((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -43) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -985) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-1153))))) +(-1053 R E V) +((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\spad{next_sousResultant2} from PseudoRemainderSequence from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial \\indented{1}{in its main variable.}")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-973 S |TheField| |ThePols|) -((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common access functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) +(-1054 S |TheField| |ThePols|) +((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-974 |TheField| |ThePols|) -((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common access functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) +(-1055 |TheField| |ThePols|) +((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-975 R E V P TS) -((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) +(-1056 R E V P TS) +((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented."))) NIL NIL -(-976 S R E V P) -((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) +(-1057 S R E V P) +((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the RegularTriangularSet constructor for more explanations about decompositions by means of regular triangular sets.")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same main variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is select from TriangularSetCategory(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is collectUnder from TriangularSetCategory(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-977 R E V P) -((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-1058 R E V P) +((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the RegularTriangularSet constructor for more explanations about decompositions by means of regular triangular sets.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same main variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is select from TriangularSetCategory(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is collectUnder from TriangularSetCategory(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-978 R E V P TS) -((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) +(-1059 R E V P TS) +((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as squareFreePart from RegularTriangularSetCategory.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as invertibleSet from RegularTriangularSetCategory.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as invertible? from RegularTriangularSetCategory.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as invertible? from RegularTriangularSetCategory.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as lastSubResultant from RegularTriangularSetCategory.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-979 |Base| R -2958) -((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) +(-1060 |f|) +((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-980 |f|) -((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) +(-1061 |Base| R -1333) +((|constructor| (NIL "Rules for the pattern matcher")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-981 |Base| R -2958) -((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) +(-1062 |Base| R -1333) +((|constructor| (NIL "Sets of rules for the pattern matcher. A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL -(-982 R |ls|) -((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) +(-1063 R |ls|) +((|constructor| (NIL "A package for computing the rational univariate representation of a zero-dimensional algebraic variety given by a regular triangular set. This package is essentially an interface for the \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-983 R UP M) -((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((-4160 |has| |#1| (-331)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-331)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-331)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-318))))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-331)))) (-12 (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (QUOTE (-331)))) (-1405 (-12 (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (QUOTE (-331)))) (|HasCategory| |#1| (QUOTE (-318))))) -(-984 UP SAE UPA) -((|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) +(-1064 UP SAE UPA) +((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-985 UP SAE UPA) -((|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) +(-1065 R UP M) +((|constructor| (NIL "Algebraic extension of a ring by a single polynomial. Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) +((-4498 |has| |#1| (-359)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-359)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-344))))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (QUOTE (-359)))) (-2318 (-12 (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-344))))) +(-1066 UP SAE UPA) +((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-986) +(-1067) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-987 S) -((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) +(-1068 S) +((|constructor| (NIL "A sorted cache of a cachable set \\spad{S} is a dynamic structure that keeps the elements of \\spad{S} sorted and assigns an integer to each element of \\spad{S} once it is in the cache. This way,{} equality and ordering on \\spad{S} are tested directly on the integers associated with the elements of \\spad{S},{} once they have been entered in the cache.")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-988 R) +(-1069 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-989 R) -NIL -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| (-990 (-1070)) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| (-990 (-1070)) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| (-990 (-1070)) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| (-990 (-1070)) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| (-990 (-1070)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-206))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#1| (QUOTE -4165)) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-990 S) +(-1070 R) +((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1071 (-1153)) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1071 (-1153)) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1071 (-1153)) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1071 (-1153)) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1071 (-1153)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-221))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1071 S) +((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL +(-1072 R S) +((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -(-991 S) -((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) +((|HasCategory| |#1| (QUOTE (-832)))) +(-1073 R S) +((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL -((|HasCategory| |#1| (QUOTE (-775))) (|HasCategory| |#1| (QUOTE (-1001)))) -(-992 R S) -((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-775)))) -(-993 S) +(-1074 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1001)))) -(-994 R S) -((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) -NIL +((|HasCategory| |#1| (QUOTE (-1082)))) +(-1075 S) +((|constructor| (NIL "This category provides operations on ranges,{} or segments as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note that \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note that \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note that \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note that \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note that \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) +((-2537 . T)) NIL -(-995 S) -((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2951 . T)) +(-1076 S) +((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -(-996 S L) +((|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-1082)))) +(-1077 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2951 . T)) +((-2537 . T)) NIL -(-997 S) -((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4167 . T) (-4157 . T) (-4168 . T)) -((|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-336))) (|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (QUOTE (-777))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-336)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-998 A S) -((|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) +(-1078 A S) +((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note that equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note that \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = \\indented{1}{union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note that \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note that equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note that equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-999 S) -((|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4157 . T) (-2951 . T)) +(-1079 S) +((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note that equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note that \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = \\indented{1}{union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note that \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note that equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note that equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) +((-4495 . T) (-2537 . T)) NIL -(-1000 S) -((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) +(-1080) +((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL NIL -(-1001) -((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) +(-1081 S) +((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes\\spad{\\br} \\tab{5}canonical\\tab{5}data structure equality is the same as \\spadop{=}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1002 |m| |n|) +(-1082) +((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes\\spad{\\br} \\tab{5}canonical\\tab{5}data structure equality is the same as \\spadop{=}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) +NIL +NIL +(-1083 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1003) -((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) +(-1084 S) +((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of\\spad{\\br} \\tab{5}\\spad{s = t} is \\spad{O(min(n,{}m))}\\spad{\\br} \\tab{5}\\spad{s < t} is \\spad{O(max(n,{}m))}\\spad{\\br} \\tab{5}\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{}\\spad{\\br} \\tab{10 \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}\\spad{\\br} \\tab{5}\\spad{member(x,{}t)} is \\spad{O(n log n)}\\spad{\\br} \\tab{5}\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}"))) +((-4505 . T) (-4495 . T) (-4506 . T)) +((|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-364))) (|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-834))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-364)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-1085 |Str| |Sym| |Int| |Flt| |Expr|) +((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns \\spad{a1}.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns an \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1004 |Str| |Sym| |Int| |Flt| |Expr|) -((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns \\spad{a1}.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) +(-1086) +((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1005 |Str| |Sym| |Int| |Flt| |Expr|) +(-1087 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1006 R FS) +(-1088 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1007 R E V P TS) -((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) +(-1089 R E V P TS) +((|constructor| (NIL "A internal package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets.")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff internalSubQuasiComponent?(\\spad{ts},{}us) from QuasiComponentPackage returns \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. infRittWu? from RecursivePolynomialCategory.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} supDimElseRittWu from QuasiComponentPackage.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1008 R E V P TS) -((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) +(-1090 R E V P TS) +((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}."))) NIL NIL -(-1009 R E V P) -((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-1091 R E V P) +((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and differentiate(\\spad{p},{}mvar(\\spad{p})) \\spad{w}.\\spad{r}.\\spad{t}. collectUnder(\\spad{ts},{}mvar(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-1010) -((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) +(-1092) +((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the \\spad{k}-th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using subSet: [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]. Note that counting of subtrees is done by numberOfImproperPartitionsInternal.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the \\spad{k}-th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]. Error: if \\spad{k} is negative or too big. Note that counting of subtrees is done by numberOfImproperPartitions")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the \\spad{k}-th \\spad{m}-subset of the set 0,{}1,{}...,{}(\\spad{n}-1) in the lexicographic order considered as a decreasing map from 0,{}...,{}(\\spad{m}-1) into 0,{}...,{}(\\spad{n}-1). See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not (0 \\spad{<=} \\spad{m} \\spad{<=} \\spad{n} and 0 < = \\spad{k} < (\\spad{n} choose \\spad{m})).")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: numberOfImproperPartitions (3,{}3) is 10,{} since [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0] are the possibilities. Note that this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of \\spad{number} which follows \\spad{part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of \\spad{gamma}. the first partition is achieved by part=[]. Also,{} [] indicates that \\spad{part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of \\spad{number} which follows \\spad{part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of \\spad{gamma}. The first partition is achieved by part=[]. Also,{} [] indicates that \\spad{part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition \\spad{lambda} succeeding the lattice permutation \\spad{lattP} in lexicographical order as long as \\spad{constructNotFirst} is \\spad{true}. If \\spad{constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result nil indicates that \\spad{lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums \\spad{alpha} and row sums \\spad{beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by C=new(1,{}1,{}0). Also,{} new(1,{}1,{}0) indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation \\spad{gitter} and for an improper partition \\spad{lambda} the corresponding standard tableau of shape \\spad{lambda}. Notes: see listYoungTableaus. The entries are from 0,{}...,{}\\spad{n}-1.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where \\spad{lambda} is a proper partition generates the list of all standard tableaus of shape \\spad{lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of \\spad{lambda}. Notes: the functions nextLatticePermutation and makeYoungTableau are used. The entries are from 0,{}...,{}\\spad{n}-1.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums \\spad{alpha},{} column sums \\spad{beta} to the set of Salpha - Sbeta double cosets of the symmetric group \\spad{Sn}. (Salpha is the Young subgroup corresponding to the improper partition \\spad{alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest \\spad{pi} in the corresponding double coset. Note that the resulting permutation \\spad{pi} of {1,{}2,{}...,{}\\spad{n}} is given in list form. Notes: the inverse of this map is coleman. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums \\spad{alpha},{} column sums \\spad{beta} to the set of Salpha - Sbeta double cosets of the symmetric group \\spad{Sn}. (Salpha is the Young subgroup corresponding to the improper partition \\spad{alpha}). For a representing element \\spad{pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to \\spad{alpha},{} \\spad{beta},{} \\spad{pi}. Note that The permutation \\spad{pi} of {1,{}2,{}...,{}\\spad{n}} has to be given in list form. Note that the inverse of this map is inverseColeman (if \\spad{pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1011 S) -((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) +(-1093 S) +((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{associative(\"*\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ (x*y)*z = x*(y*z)} \\blankline Conditional attributes\\spad{\\br} \\tab{5}\\spad{commutative(\"*\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ x*y = y*x }")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1012) -((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) +(-1094) +((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{associative(\"*\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ (x*y)*z = x*(y*z)} \\blankline Conditional attributes\\spad{\\br} \\tab{5}\\spad{commutative(\"*\":(\\%,{}\\%)->\\%)}\\tab{5}\\spad{ x*y = y*x }")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 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(|HasCategory| |#3| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1082))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-1153))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-25)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-137)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-170)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-221)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-359)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-364)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-708)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-780)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-832)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -298) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1082)))))) +(-1096 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and \\spad{c_}{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and \\spad{c_}{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL -((|HasCategory| |#1| (QUOTE (-419)))) -(-1015 R -2958) +((|HasCategory| |#1| (QUOTE (-447)))) +(-1097 R -1333) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1016 R) +(-1098 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1017) -((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) +(-1099) +((|constructor| (NIL "Package to allow simplify to be called on AlgebraicNumbers by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1018) -((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4155 . T) (-4159 . T) (-4154 . T) (-4165 . T) (-4166 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(-1100) +((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical or of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical and of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical not of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical xor of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical or of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical and of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical not of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical not of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) +((-4493 . T) (-4497 . T) (-4492 . T) (-4503 . T) (-4504 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1019 S) -((|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4167 . T) (-4168 . T) (-2951 . T)) +(-1101 S) +((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\indented{1}{depth(\\spad{s}) returns the number of elements of stack \\spad{s}.} \\indented{1}{Note that \\axiom{depth(\\spad{s}) = \\spad{#s}}.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} depth a")) (|top| ((|#1| $) "\\indented{1}{top(\\spad{s}) returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged.} \\indented{1}{Note that Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} top a")) (|pop!| ((|#1| $) "\\indented{1}{pop!(\\spad{s}) returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}.} \\indented{1}{Note that Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}.} \\indented{1}{Error: if \\spad{s} is empty.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} pop! a \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\indented{1}{push!(\\spad{x},{}\\spad{s}) pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s}} \\indented{1}{so as to have a new first (top) element \\spad{x}.} \\indented{1}{Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} push! a \\spad{X} a"))) +((-4505 . T) (-4506 . T) (-2537 . T)) NIL -(-1020 S |ndim| R |Row| |Col|) +(-1102 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-331))) (|HasAttribute| |#3| (QUOTE (-4169 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) -(-1021 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-359))) (|HasAttribute| |#3| (QUOTE (-4507 "*"))) (|HasCategory| |#3| (QUOTE (-170)))) +(-1103 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-2951 . T) (-4167 . T) (-4161 . T) (-4162 . T) (-4164 . T)) +((-2537 . T) (-4505 . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1022 R |Row| |Col| M) +(-1104 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1023 R |VarSet|) -((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasAttribute| |#1| (QUOTE -4165)) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-1024 |Coef| |Var| SMP) -((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-508))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-331)))) -(-1025 R E V P) -((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-1105 R |VarSet|) +((|constructor| (NIL "This type is the basic representation of sparse recursive multivariate polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-896))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasAttribute| |#1| (QUOTE -4503)) (|HasCategory| |#1| (QUOTE (-447))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (|HasCategory| |#1| (QUOTE (-447))) (|HasCategory| |#1| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-896)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1106 |Coef| |Var| SMP) +((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\indented{1}{\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}.} \\blankline \\spad{X} xts:=x::TaylorSeries Fraction Integer \\spad{X} t1:=sin(\\spad{xts}) \\spad{X} coefficient(\\spad{t1},{}3)"))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-550))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-359)))) +(-1107 R E V P) +((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-1026 UP -2958) +(-1108 UP -1333) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL -(-1027 R) -((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) +(-1109 R) +((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{contractSolve(\\spad{rf},{}\\spad{x}) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{}} \\indented{1}{where \\spad{rf} is a rational function. The result contains\\space{2}new} \\indented{1}{symbols for common subexpressions in order to reduce the} \\indented{1}{size of the output.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} contractSolve(\\spad{b},{}\\spad{x})") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\indented{1}{contractSolve(eq,{}\\spad{x}) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation of rational functions eq} \\indented{1}{with respect to the symbol \\spad{x}.\\space{2}The result contains new} \\indented{1}{symbols for common subexpressions in order to reduce the} \\indented{1}{size of the output.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} contractSolve(\\spad{b=0},{}\\spad{x})")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\indented{1}{radicalRoots(\\spad{lrf},{}lvar) finds the roots expressed in terms of} \\indented{1}{radicals of the list of rational functions \\spad{lrf}} \\indented{1}{with respect to the list of symbols lvar.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer))\\spad{:=}(\\spad{y^2+4})/(\\spad{y+1}) \\spad{X} radicalRoots([\\spad{b},{}\\spad{c}],{}[\\spad{x},{}\\spad{y}])") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{radicalRoots(\\spad{rf},{}\\spad{x}) finds the roots expressed in terms of radicals} \\indented{1}{of the rational function \\spad{rf} with respect to the symbol \\spad{x}.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} radicalRoots(\\spad{b},{}\\spad{x})")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\indented{1}{radicalSolve(leq) finds the solutions expressed in terms of} \\indented{1}{radicals of the system of equations of rational functions leq} \\indented{1}{with respect to the unique symbol \\spad{x} appearing in leq.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer))\\spad{:=}(\\spad{y^2+4})/(\\spad{y+1}) \\spad{X} radicalSolve([\\spad{b=0},{}\\spad{c=0}])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\indented{1}{radicalSolve(leq,{}lvar) finds the solutions expressed in terms of} \\indented{1}{radicals of the system of equations of rational functions leq} \\indented{1}{with respect to the list of symbols lvar.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer))\\spad{:=}(\\spad{y^2+4})/(\\spad{y+1}) \\spad{X} radicalSolve([\\spad{b=0},{}\\spad{c=0}],{}[\\spad{x},{}\\spad{y}])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\indented{1}{radicalSolve(\\spad{lrf}) finds the solutions expressed in terms of} \\indented{1}{radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a} \\indented{1}{system of univariate rational functions.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer))\\spad{:=}(\\spad{y^2+4})/(\\spad{y+1}) \\spad{X} radicalSolve([\\spad{b},{}\\spad{c}])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\indented{1}{radicalSolve(\\spad{lrf},{}lvar) finds the solutions expressed in terms of} \\indented{1}{radicals of the system of equations \\spad{lrf} = 0 with} \\indented{1}{respect to the list of symbols lvar,{}} \\indented{1}{where \\spad{lrf} is a list of rational functions.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer))\\spad{:=}(\\spad{y^2+4})/(\\spad{y+1}) \\spad{X} radicalSolve([\\spad{b},{}\\spad{c}],{}[\\spad{x},{}\\spad{y}])") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\indented{1}{radicalSolve(eq) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation of rational functions eq} \\indented{1}{with respect to the unique symbol \\spad{x} appearing in eq.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(\\spad{b=0})") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\indented{1}{radicalSolve(eq,{}\\spad{x}) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation of rational functions eq} \\indented{1}{with respect to the symbol \\spad{x}.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(\\spad{b=0},{}\\spad{x})") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\indented{1}{radicalSolve(\\spad{rf}) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a} \\indented{1}{univariate rational function.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(\\spad{b})") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{radicalSolve(\\spad{rf},{}\\spad{x}) finds the solutions expressed in terms of} \\indented{1}{radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{}} \\indented{1}{where \\spad{rf} is a rational function.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer))\\spad{:=}(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(\\spad{b},{}\\spad{x})"))) NIL NIL -(-1028 R) -((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) +(-1110 R) +((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} are given and \\spad{func1} = \\spad{func3}(\\spad{func2}) . If there is no solution then function \\spad{func1} will be returned. An example would be \\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and \\spad{func2:=2*X ::EXPR INT} convert them via univariate to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X} of type FRAC SUP EXPR INT")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1029 R) -((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) +(-1111 R) +((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2} by using the function normalize and then to \\spad{-2 tan(x)**2 + tan(x) -2} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\spad{sqrt(sin(x))+1} .")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\indented{1}{solve(expr,{}\\spad{x}) finds the solutions of the equation expr = 0} \\indented{1}{with respect to the symbol \\spad{x} where expr is a function} \\indented{1}{of type Expression(\\spad{R}).} \\blankline \\spad{X} solve(1/2*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l,{}phi) \\spad{X} definingPolynomial \\%\\spad{phi0} \\spad{X} definingPolynomial \\%\\spad{phi1}") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1030 S A) +(-1112 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-777)))) -(-1031 R) -NIL +((|HasCategory| |#1| (QUOTE (-834)))) +(-1113 R) +((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1032 R) -((|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) +(-1114 R) +((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "mesh(\\spad{s},{}[ [[\\spad{r10}]...,{}[\\spad{r1m}]],{}[[\\spad{r20}]...,{}[\\spad{r2m}]],{}...,{}[[\\spad{rn0}]...,{}[\\spad{rnm}]] ],{} \\indented{5}{\\spad{close1},{} \\spad{close2})} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "mesh(\\spad{s},{}[ [[\\spad{r10}]...,{}[\\spad{r1m}]],{}[[\\spad{r20}]...,{}[\\spad{r2m}]],{}...,{}[[\\spad{rn0}]...,{}[\\spad{rnm}]] ],{} \\indented{7}{[props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1033) -((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) +(-1115) +((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and Script Formula Formatter output from programs.")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1034) +(-1116) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1035 V C) +(-1117 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1036 V C) +(-1118 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-1035 |#1| |#2|) (QUOTE (-1001))) (-12 (|HasCategory| (-1035 |#1| |#2|) (LIST (QUOTE -278) (LIST (QUOTE -1035) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1035 |#1| |#2|) (QUOTE (-1001))))) -(-1037 |ndim| R) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-1117 |#1| |#2|) (QUOTE (-1082))) (-12 (|HasCategory| (-1117 |#1| |#2|) (LIST (QUOTE -298) (LIST (QUOTE -1117) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1117 |#1| |#2|) (QUOTE (-1082))))) +(-1119 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) -((-4164 . T) (-4156 |has| |#2| (-6 (-4169 "*"))) (-4167 . T) (-4161 . T) (-4162 . T)) -((|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206))) (|HasAttribute| |#2| (QUOTE (-4169 "*"))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#2| (QUOTE (-276))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-331))) (-1405 (|HasAttribute| |#2| (QUOTE (-4169 "*"))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasCategory| |#2| (QUOTE (-206)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -577) (QUOTE (-501))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-206)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001))))) (|HasCategory| |#2| (QUOTE (-156)))) -(-1038 S) -((|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) +((-4502 . T) (-4494 |has| |#2| (-6 (-4507 "*"))) (-4505 . T) (-4499 . T) (-4500 . T)) +((|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221))) (|HasAttribute| |#2| (QUOTE (-4507 "*"))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-359))) (-2318 (|HasAttribute| |#2| (QUOTE (-4507 "*"))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasCategory| |#2| (QUOTE (-221)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-221)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082))))) (|HasCategory| |#2| (QUOTE (-170)))) +(-1120 S) +((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note that \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note that \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} \\indented{1}{reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])}} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note that \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} \\indented{2}{reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.}")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1039) -((|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +(-1121) +((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note that \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note that \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} \\indented{1}{reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])}} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note that \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} \\indented{2}{reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.}")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-1040 R E V P TS) -((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) +(-1122 R E V P TS) +((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented."))) NIL NIL -(-1041 R E V P) -((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#4| (QUOTE (-1001))) (-12 (|HasCategory| |#4| (LIST (QUOTE -278) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#3| (QUOTE (-336)))) -(-1042 S) -((|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-1043 A S) -((|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) +(-1123 R E V P) +((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation zeroSetSplit is an implementation of a new algorithm for solving polynomial systems by means of regular chains.")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as zeroSetSplit from RegularTriangularSetCategory from \\spadtype{RegularTriangularSetCategory} Moreover,{} if clos? then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#4| (QUOTE (-1082))) (-12 (|HasCategory| |#4| (LIST (QUOTE -298) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-364)))) +(-1124 S) +((|constructor| (NIL "Linked List implementation of a Stack")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} member?(3,{}a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} count(4,{}a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} count(\\spad{x+}->(\\spad{x>2}),{}a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} any?(\\spad{x+}->(\\spad{x=4}),{}a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} every?(\\spad{x+}->(\\spad{x=4}),{}a)")) (~= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} (a~=b)")) (= (((|Boolean|) $ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} b:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} (a=b)@Boolean")) (|coerce| (((|OutputForm|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} coerce a")) (|hash| (((|SingleInteger|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} hash a")) (|latex| (((|String|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} latex a")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} map!(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} map(\\spad{x+}-\\spad{>x+10},{}a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} eq?(a,{}\\spad{b})")) (|copy| (($ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} copy a")) (|sample| (($) "\\blankline \\spad{X} sample()\\$Stack(INT)")) (|empty| (($) "\\blankline \\spad{X} b:=empty()\\$(Stack INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} empty? a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,{}2,{}3,{}4,{}5])\\$Stack(INT)")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} size?(a,{}5)")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} more?(a,{}9)")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} less?(a,{}9)")) (|depth| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} depth a")) (|top| ((|#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} top a")) (|inspect| ((|#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} inspect a")) (|insert!| (($ |#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} insert!(8,{}a) \\spad{X} a")) (|push!| ((|#1| |#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} push!(9,{}a) \\spad{X} a")) (|extract!| ((|#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} extract! a \\spad{X} a")) (|pop!| ((|#1| $) "\\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} pop! a \\spad{X} a")) (|stack| (($ (|List| |#1|)) "\\indented{1}{stack([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) creates a stack with first (top)} \\indented{1}{element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5]"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-1125 A S) +((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note that for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note that for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1044 S) -((|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) -((-2951 . T)) +(-1126 S) +((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note that for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note that for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) +((-2537 . T)) NIL -(-1045 |Key| |Ent| |dent|) +(-1127 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4168 . T)) -((|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-1001))) (-12 (|HasCategory| |#2| (LIST (QUOTE -278) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1001)))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001)))) (-1405 (|HasCategory| (-2 (|:| -3626 |#1|) (|:| -2922 |#2|)) (QUOTE (-1001))) (|HasCategory| |#2| (QUOTE (-1001))))) -(-1046) -((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) +((-4506 . T)) +((|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#2| (QUOTE (-1082))) (-12 (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1082)))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082)))) (-2318 (|HasCategory| (-2 (|:| -3655 |#1|) (|:| -2371 |#2|)) (QUOTE (-1082))) (|HasCategory| |#2| (QUOTE (-1082))))) +(-1128) +((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes\\spad{\\br} \\tab{5}infinite\\tab{5}repeated nextItem\\spad{'s} are never \"failed\".")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1047 |Coef|) +(-1129 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1048 S) -((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4168 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-501) (QUOTE (-777)))) -(-1049 S) -((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) -NIL +(-1130 S) +((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\indented{1}{concat(\\spad{u}) returns the left-to-right concatentation of the} \\indented{1}{streams in \\spad{u}. Note that \\spad{concat(u) = reduce(concat,{}u)}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 10..] \\spad{X} \\spad{n:=}[\\spad{j} for \\spad{j} in 1.. | prime? \\spad{j}] \\spad{X} \\spad{p:=}[\\spad{m},{}\\spad{n}]::Stream(Stream(PositiveInteger)) \\spad{X} concat(\\spad{p})"))) NIL -(-1050 A B) -((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL +(-1131 A B) +((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\indented{1}{reduce(\\spad{b},{}\\spad{f},{}\\spad{u}),{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{}} \\indented{1}{returns the value \\spad{r(n)} computed as follows:} \\indented{1}{\\spad{r0 = f(x0,{}b),{}} \\indented{1}{\\spad{r1} = \\spad{f}(\\spad{x1},{}\\spad{r0}),{}...,{}} \\indented{1}{\\spad{r}(\\spad{n}) = \\spad{f}(\\spad{xn},{}\\spad{r}(\\spad{n}-1))}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..300]::Stream(Integer) \\spad{X} \\spad{f}(i:Integer,{}j:Integer):Integer==i+j \\spad{X} reduce(1,{}\\spad{f},{}\\spad{m})")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\indented{1}{scan(\\spad{b},{}\\spad{h},{}[\\spad{x0},{}\\spad{x1},{}\\spad{x2},{}...]) returns \\spad{[y0,{}y1,{}y2,{}...]},{} where} \\indented{1}{\\spad{y0 = h(x0,{}b)},{}} \\indented{1}{\\spad{y1 = h(x1,{}y0)},{}\\spad{...}} \\indented{1}{\\spad{yn = h(xn,{}y(n-1))}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..]::Stream(Integer) \\spad{X} \\spad{f}(i:Integer,{}j:Integer):Integer==i+j \\spad{X} scan(1,{}\\spad{f},{}\\spad{m})")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\indented{1}{map(\\spad{f},{}\\spad{s}) returns a stream whose elements are the function \\spad{f} applied} \\indented{1}{to the corresponding elements of \\spad{s}.} \\indented{1}{Note that \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{f}(i:PositiveInteger)\\spad{:PositiveInteger==i**2} \\spad{X} map(\\spad{f},{}\\spad{m})"))) NIL -(-1051 A B C) -((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL +(-1132 A B C) +((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\indented{1}{map(\\spad{f},{}\\spad{st1},{}\\spad{st2}) returns the stream whose elements are the} \\indented{1}{function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}.} \\indented{1}{\\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}.} \\blankline \\spad{S} \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..]::Stream(Integer) \\spad{X} \\spad{n:=}[\\spad{i} for \\spad{i} in 1..]::Stream(Integer) \\spad{X} \\spad{f}(i:Integer,{}j:Integer):Integer \\spad{==} i+j \\spad{X} map(\\spad{f},{}\\spad{m},{}\\spad{n})"))) NIL -(-1052) -((|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4168 . T) (-4167 . T) (-2951 . T)) NIL -(-1053) +(-1133 S) +((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\indented{1}{filterUntil(\\spad{p},{}\\spad{s}) returns \\spad{[x0,{}x1,{}...,{}x(n)]} where} \\indented{1}{\\spad{s = [x0,{}x1,{}x2,{}..]} and} \\indented{1}{\\spad{n} is the smallest index such that \\spad{p(xn) = true}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{f}(x:PositiveInteger):Boolean \\spad{==} \\spad{x} < 5 \\spad{X} filterUntil(\\spad{f},{}\\spad{m})")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\indented{1}{filterWhile(\\spad{p},{}\\spad{s}) returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where} \\indented{1}{\\spad{s = [x0,{}x1,{}x2,{}..]} and} \\indented{1}{\\spad{n} is the smallest index such that \\spad{p(xn) = false}.} \\blankline \\spad{X} \\spad{m:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{f}(x:PositiveInteger):Boolean \\spad{==} \\spad{x} < 5 \\spad{X} filterWhile(\\spad{f},{}\\spad{m})")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\indented{1}{generate(\\spad{f},{}\\spad{x}) creates an infinite stream whose first element is} \\indented{1}{\\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous} \\indented{1}{element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.} \\blankline \\spad{X} \\spad{f}(x:Integer):Integer \\spad{==} \\spad{x+10} \\spad{X} generate(\\spad{f},{}10)") (($ (|Mapping| |#1|)) "\\indented{1}{generate(\\spad{f}) creates an infinite stream all of whose elements are} \\indented{1}{equal to \\spad{f()}.} \\indented{1}{Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.} \\blankline \\spad{X} \\spad{f}():Integer \\spad{==} 1 \\spad{X} generate(\\spad{f})")) (|setrest!| (($ $ (|Integer|) $) "\\indented{1}{setrest!(\\spad{x},{}\\spad{n},{}\\spad{y}) sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand} \\indented{1}{cycles if necessary.} \\blankline \\spad{X} \\spad{p:=}[\\spad{i} for \\spad{i} in 1..] \\spad{X} \\spad{q:=}[\\spad{i} for \\spad{i} in 9..] \\spad{X} setrest!(\\spad{p},{}4,{}\\spad{q}) \\spad{X} \\spad{p}")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\indented{1}{showAllElements(\\spad{s}) creates an output form which displays all} \\indented{1}{computed elements.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3,{}4,{}5,{}6,{}7,{}8,{}9,{}10,{}11,{}12] \\spad{X} n:=m::Stream(PositiveInteger) \\spad{X} showAllElements \\spad{n}")) (|output| (((|Void|) (|Integer|) $) "\\indented{1}{output(\\spad{n},{}st) computes and displays the first \\spad{n} entries} \\indented{1}{of st.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3] \\spad{X} n:=repeating(\\spad{m}) \\spad{X} output(5,{}\\spad{n})")) (|cons| (($ |#1| $) "\\indented{1}{cons(a,{}\\spad{s}) returns a stream whose \\spad{first} is \\spad{a}} \\indented{1}{and whose \\spad{rest} is \\spad{s}.} \\indented{1}{Note: \\spad{cons(a,{}s) = concat(a,{}s)}.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3] \\spad{X} n:=repeating(\\spad{m}) \\spad{X} cons(4,{}\\spad{n})")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\indented{1}{findCycle(\\spad{n},{}st) determines if st is periodic within \\spad{n}.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3] \\spad{X} n:=repeating(\\spad{m}) \\spad{X} findCycle(3,{}\\spad{n}) \\spad{X} findCycle(2,{}\\spad{n})")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\indented{1}{repeating?(\\spad{l},{}\\spad{s}) returns \\spad{true} if a stream \\spad{s} is periodic} \\indented{1}{with period \\spad{l},{} and \\spad{false} otherwise.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3] \\spad{X} n:=repeating(\\spad{m}) \\spad{X} repeating?(\\spad{m},{}\\spad{n})")) (|repeating| (($ (|List| |#1|)) "\\indented{1}{repeating(\\spad{l}) is a repeating stream whose period is the list \\spad{l}.} \\blankline \\spad{X} m:=repeating([\\spad{-1},{}0,{}1,{}2,{}3])")) (|coerce| (($ (|List| |#1|)) "\\indented{1}{coerce(\\spad{l}) converts a list \\spad{l} to a stream.} \\blankline \\spad{X} \\spad{m:=}[1,{}2,{}3,{}4,{}5,{}6,{}7,{}8,{}9,{}10,{}11,{}12] \\spad{X} coerce(\\spad{m})@Stream(Integer) \\spad{X} m::Stream(Integer)")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) +((-4506 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-560) (QUOTE (-834)))) +(-1134) +((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -((-4168 . T) (-4167 . T)) -((|HasCategory| (-131) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-131) (QUOTE (-777))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| (-131) (QUOTE (-1001))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-777)))) (-12 (|HasCategory| (-131) (LIST (QUOTE -278) (QUOTE (-131)))) (|HasCategory| (-131) (QUOTE (-1001)))))) -(-1054 |Entry|) +(-1135) +((|constructor| (NIL "This is the domain of character strings. Strings are 1 based."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| (-145) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-145) (QUOTE (-834))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| (-145) (QUOTE (-1082))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-834)))) (-12 (|HasCategory| (-145) (LIST (QUOTE -298) (QUOTE (-145)))) (|HasCategory| (-145) (QUOTE (-1082)))))) +(-1136 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4167 . T) (-4168 . T)) -((|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (QUOTE (-1001))) (-12 (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (LIST (QUOTE -278) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3626) (QUOTE (-1053))) (LIST (QUOTE |:|) (QUOTE -2922) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (QUOTE (-1001)))) (|HasCategory| (-1053) (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001))) (-1405 (|HasCategory| (-2 (|:| -3626 (-1053)) (|:| -2922 |#1|)) (QUOTE (-1001))) (|HasCategory| |#1| (QUOTE (-1001)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-1055 A) -((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b = sum(i+j=k,{}a)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) +((-4505 . T) (-4506 . T)) +((|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (QUOTE (-1082))) (-12 (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (LIST (QUOTE -298) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3655) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -2371) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (QUOTE (-1082)))) (|HasCategory| (-1135) (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082))) (-2318 (|HasCategory| (-2 (|:| -3655 (-1135)) (|:| -2371 |#1|)) (QUOTE (-1082))) (|HasCategory| |#1| (QUOTE (-1082)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-1137 A) +((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y'=sum(i=0 to infinity,{}j=0 to infinity,{}b*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b = sum(i+j=k,{}a)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501)))))) -(-1056 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +((|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560)))))) +(-1138 |Coef|) +((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1057 |Coef|) -((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) +(-1139 |Coef|) +((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1058 R UP) -((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}."))) +(-1140 R UP) +((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one.")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}."))) NIL -((|HasCategory| |#1| (QUOTE (-276)))) -(-1059 |n| R) -((|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,{}s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,{}n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) +((|HasCategory| |#1| (QUOTE (-296)))) +(-1141 |n| R) +((|constructor| (NIL "This domain is not documented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,{}s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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sums of top-level expressions")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1063 R) -((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) +(-1145 R) +((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\indented{1}{sum(\\spad{f}(\\spad{n}),{} \\spad{n} = a..\\spad{b}) returns \\spad{f(a) + f(a+1) + ... f(b)}.} \\blankline \\spad{X} sum(i::Fraction(Polynomial(Integer)),{}\\spad{i=1}..\\spad{n})") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\indented{1}{sum(\\spad{f}(\\spad{n}),{} \\spad{n} = a..\\spad{b}) returns \\spad{f(a) + f(a+1) + ... f(b)}.} \\blankline \\spad{X} sum(\\spad{i},{}\\spad{i=1}..\\spad{n})") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{sum(a(\\spad{n}),{} \\spad{n}) returns \\spad{A} which} \\indented{1}{is the indefinite sum of \\spad{a} with respect to} \\indented{1}{upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.} \\blankline \\spad{X} sum(i::Fraction(Polynomial(Integer)),{}i::Symbol)") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\indented{1}{sum(a(\\spad{n}),{} \\spad{n}) returns \\spad{A} which} \\indented{1}{is the indefinite sum of \\spad{a} with respect to} \\indented{1}{upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.} \\blankline \\spad{X} sum(i::Polynomial(Integer),{}variable(\\spad{i=1}..\\spad{n}))"))) NIL NIL -(-1064 R) -((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4163 |has| |#1| (-331)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (-12 (|HasCategory| (-986) (LIST (QUOTE -806) (QUOTE (-346)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-346))))) (-12 (|HasCategory| (-986) (LIST (QUOTE -806) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -806) (QUOTE (-501))))) (-12 (|HasCategory| (-986) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-346)))))) (-12 (|HasCategory| (-986) (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (QUOTE (-501)))))) (-12 (|HasCategory| (-986) (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490))))) (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -577) (QUOTE (-501)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (-1405 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasCategory| |#1| (QUOTE (-206))) (|HasAttribute| |#1| (QUOTE -4165)) (|HasCategory| |#1| (QUOTE (-419))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-419))) (|HasCategory| |#1| (QUOTE (-830)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (-1405 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-830)))) (|HasCategory| |#1| (QUOTE (-132))))) -(-1065 R S) +(-1146 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1066 E OV R P) -((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) -NIL -NIL -(-1067 |Coef| |var| |cen|) -((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|))))) (|HasCategory| (-375 (-501)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-1068 |Coef| |var| |cen|) -((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-701)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-701)) (|devaluate| |#1|))))) (|HasCategory| (-701) (QUOTE (-1012))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-701))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-701))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-1069) -((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1083) +(-1166) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1084) -((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) +(-1167 S) +((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1085 S) -((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) +(-1168) +((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1086) +(-1169) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1087 R) +(-1170 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1088) -((|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) +(-1171) +((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1089 S) +(-1172 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1090) +(-1173) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1091 S) -((|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001))))) -(-1092 S) +(-1174 S) +((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a node consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\indented{1}{cyclicParents(\\spad{t}) returns a list of cycles that are parents of \\spad{t}.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} cyclicParents \\spad{t1}")) (|cyclicEqual?| (((|Boolean|) $ $) "\\indented{1}{cyclicEqual?(\\spad{t1},{} \\spad{t2}) tests of two cyclic trees have} \\indented{1}{the same structure.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} t2:=tree [1,{}2,{}3,{}4] \\spad{X} cyclicEqual?(\\spad{t1},{}\\spad{t2})")) (|cyclicEntries| (((|List| $) $) "\\indented{1}{cyclicEntries(\\spad{t}) returns a list of top-level cycles in tree \\spad{t}.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} cyclicEntries \\spad{t1}")) (|cyclicCopy| (($ $) "\\indented{1}{cyclicCopy(\\spad{l}) makes a copy of a (possibly) cyclic tree \\spad{l}.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} cyclicCopy \\spad{t1}")) (|cyclic?| (((|Boolean|) $) "\\indented{1}{cyclic?(\\spad{t}) tests if \\spad{t} is a cyclic tree.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} cyclic? \\spad{t1}")) (|tree| (($ |#1|) "\\indented{1}{tree(\\spad{nd}) creates a tree with value \\spad{nd},{} and no children} \\blankline \\spad{X} tree 6") (($ (|List| |#1|)) "\\indented{1}{tree(\\spad{ls}) creates a tree from a list of elements of \\spad{s}.} \\blankline \\spad{X} tree [1,{}2,{}3,{}4]") (($ |#1| (|List| $)) "\\indented{1}{tree(\\spad{nd},{}\\spad{ls}) creates a tree with value \\spad{nd},{} and children \\spad{ls}.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} tree(5,{}[\\spad{t1}])"))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082))))) +(-1175 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1093) +(-1176) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1094 R -2958) +(-1177 R -1333) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-1095 R |Row| |Col| M) +(-1178 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1096 R -2958) +(-1179 R -1333) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -556) (LIST (QUOTE -810) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -806) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -556) (LIST (QUOTE -810) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -806) (|devaluate| |#1|))))) -(-1097 |Coef|) -((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-508))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-331)))) -(-1098 S R E V P) -((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -601) (LIST (QUOTE -879) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -873) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -873) (|devaluate| |#1|))))) +(-1180 S R E V P) +((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}.")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category. If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}}. \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}.in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in \\axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL -((|HasCategory| |#4| (QUOTE (-336)))) -(-1099 R E V P) -((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +((|HasCategory| |#4| (QUOTE (-364)))) +(-1181 R E V P) +((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}.")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category. If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}}. \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}.in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in \\axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-1100 |Curve|) -((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) +(-1182 |Coef|) +((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-550))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-359)))) +(-1183 |Curve|) +((|constructor| (NIL "Package for constructing tubes around 3-dimensional parametric curves. Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1101) -((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) +(-1184) +((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form \\spad{[[cos(n-1) a,{}sin(n-1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note that \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note that \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1102 S) -((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) +(-1185 S) +((|constructor| (NIL "This domain is used to interface with the interpreter\\spad{'s} notion of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\indented{1}{length(\\spad{x}) returns the number of elements in tuple \\spad{x}} \\blankline \\spad{X} t1:PrimitiveArray(Integer)\\spad{:=} [\\spad{i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(\\spad{t1})\\$Tuple(Integer) \\spad{X} length(\\spad{t2})")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\indented{1}{select(\\spad{x},{}\\spad{n}) returns the \\spad{n}-th element of tuple \\spad{x}.} \\indented{1}{tuples are 0-based} \\blankline \\spad{X} t1:PrimitiveArray(Integer)\\spad{:=} [\\spad{i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(\\spad{t1})\\$Tuple(Integer) \\spad{X} select(\\spad{t2},{}3)")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\indented{1}{coerce(a) makes a tuple from primitive array a} \\blankline \\spad{X} t1:PrimitiveArray(Integer)\\spad{:=} [\\spad{i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(\\spad{t1})\\$Tuple(Integer)"))) NIL -((|HasCategory| |#1| (QUOTE (-1001)))) -(-1103 -2958) +((|HasCategory| |#1| (QUOTE (-1082)))) +(-1186 -1333) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL -(-1104) +(-1187) ((|constructor| (NIL "The fundamental Type."))) -((-2951 . T)) +((-2537 . T)) NIL -(-1105 S) -((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) +(-1188 S) +((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares a and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if a and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by setOrder is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) 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The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) 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(|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1112 S |Coef| UTS) -((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) +(-1196 S |Coef| UTS) +((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note that \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL -((|HasCategory| |#2| (QUOTE (-331)))) -(-1113 |Coef| UTS) -((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-2951 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (QUOTE (-359)))) +(-1197 |Coef| UTS) +((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. 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factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1116 S) -((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) 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(|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1120 R Q UP) +(-1204 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1121 R UP) +(-1205 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1122 R UP) +(-1206 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1123 R U) +(-1207 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1124 S R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(-1208 |x| R) +((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented. Note that if the coefficient ring is a field,{} then this domain forms a euclidean domain.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{x} : \\spad{p1} - \\spad{r} * x**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) +(((-4507 "*") |has| |#2| (-170)) (-4498 |has| |#2| (-550)) (-4501 |has| |#2| (-359)) (-4503 |has| |#2| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-896))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-375)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-375))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -873) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-560))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-375)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -601) (LIST (QUOTE -879) (QUOTE (-560)))))) (-12 (|HasCategory| (-1067) (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#2| (LIST (QUOTE -601) (QUOTE (-533))))) (|HasCategory| |#2| (QUOTE (-834))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-1128))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (-2318 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| |#2| (QUOTE (-221))) (|HasAttribute| |#2| (QUOTE -4503)) (|HasCategory| |#2| (QUOTE (-447))) (-2318 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-896)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (-2318 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-896)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-1209 R PR S PS) +((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note that since the map is not applied to zero elements,{} it may map zero to zero."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-331))) (|HasCategory| |#2| (QUOTE (-419))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1046)))) -(-1125 R) -((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4163 |has| |#1| (-331)) (-4165 |has| |#1| (-6 -4165)) (-4162 . T) (-4161 . T) (-4164 . T)) NIL -(-1126 R PR S PS) -((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) +(-1210 S R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note that converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL +((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-447))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1128)))) +(-1211 R) +((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note that converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4501 |has| |#1| (-359)) (-4503 |has| |#1| (-6 -4503)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-1127 S |Coef| |Expon|) -((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) +(-1212 S |Coef| |Expon|) +((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note that this category exports a substitution function if it is possible to multiply exponents. Also note that this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1012))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3691) (LIST (|devaluate| |#2|) (QUOTE (-1070)))))) -(-1128 |Coef| |Expon|) -((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) +((|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2801) (LIST (|devaluate| |#2|) (QUOTE (-1153)))))) +(-1213 |Coef| |Expon|) +((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note that this category exports a substitution function if it is possible to multiply exponents. Also note that this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1129 RC P) +(-1214 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1130 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|))))) (|HasCategory| (-375 (-501)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-1131 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1215 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1132 |Coef|) +(-1216 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1133 S |Coef| ULS) +(-1217 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1134 |Coef| ULS) +(-1218 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) NIL -(-1135 |Coef| ULS) +(-1219 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4165 |has| |#1| (-331)) (-4159 |has| |#1| (-331)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501))) (|devaluate| |#1|))))) (|HasCategory| (-375 (-501)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (-1405 (|HasCategory| |#1| (QUOTE (-331))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-1136 R FE |var| |cen|) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasCategory| (-403 (-560)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-1220 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Puiseux series in one variable \\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4503 |has| |#1| (-359)) (-4497 |has| |#1| (-359)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasCategory| (-403 (-560)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (-2318 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-1221 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) -(((-4169 "*") |has| (-1130 |#2| |#3| |#4|) (-156)) (-4160 |has| (-1130 |#2| |#3| |#4|) (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| (-1130 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1130 |#2| |#3| |#4|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-1130 |#2| |#3| |#4|) (LIST (QUOTE -950) (QUOTE (-501)))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-331))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-419))) (-1405 (|HasCategory| (-1130 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| (-1130 |#2| |#3| |#4|) (LIST (QUOTE -950) (LIST (QUOTE -375) (QUOTE (-501)))))) (|HasCategory| (-1130 |#2| |#3| |#4|) (QUOTE (-508)))) -(-1137 A S) -((|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) +(((-4507 "*") |has| (-1220 |#2| |#3| |#4|) (-170)) (-4498 |has| (-1220 |#2| |#3| |#4|) (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1029) (QUOTE (-560)))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-359))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-447))) (-2318 (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (LIST (QUOTE -1029) (LIST (QUOTE -403) (QUOTE (-560)))))) (|HasCategory| (-1220 |#2| |#3| |#4|) (QUOTE (-550)))) +(-1222 A S) +((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note that afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note that \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note that \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note that \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note that \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note that if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note that \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note that for lists,{} \\axiom{last(\\spad{u})=u . (maxIndex \\spad{u})=u . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note that \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note that if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4168))) -(-1138 S) -((|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2951 . T)) +((|HasAttribute| |#1| (QUOTE -4506))) +(-1223 S) +((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note that afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note that \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note that \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note that \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note that \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note that if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note that \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note that for lists,{} \\axiom{last(\\spad{u})=u . (maxIndex \\spad{u})=u . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note that \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note that if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) +((-2537 . T)) NIL -(-1139 |Coef| |var| |cen|) -((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-156))) (-1405 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-508)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-701)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -820) (QUOTE (-1070)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-701)) (|devaluate| |#1|))))) (|HasCategory| (-701) (QUOTE (-1012))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-701))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-701))))) (|HasSignature| |#1| (LIST (QUOTE -3691) (LIST (|devaluate| |#1|) (QUOTE (-1070)))))) (|HasCategory| |#1| (QUOTE (-331))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#1| (QUOTE (-879))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasSignature| |#1| (LIST (QUOTE -3188) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1070))))) (|HasSignature| |#1| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#1|))))))) -(-1140 |Coef1| |Coef2| UTS1 UTS2) -((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) +(-1224 |Coef1| |Coef2| UTS1 UTS2) +((|constructor| (NIL "Mapping package for univariate Taylor series. This package allows one to apply a function to the coefficients of a univariate Taylor series.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1141 S |Coef|) +(-1225 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-501)))) (|HasCategory| |#2| (QUOTE (-879))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasSignature| |#2| (LIST (QUOTE -3800) (LIST (LIST (QUOTE -578) (QUOTE (-1070))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3188) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1070))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasCategory| |#2| (QUOTE (-331)))) -(-1142 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-951))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasSignature| |#2| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2376) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1153))))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-359)))) +(-1226 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4169 "*") |has| |#1| (-156)) (-4160 |has| |#1| (-508)) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-1227 |Coef| |var| |cen|) +((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-755)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-755)) (|devaluate| |#1|))))) (|HasCategory| (-755) (QUOTE (-1094))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-755))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-755))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-1228 |Coef| UTS) +((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}. This package provides Taylor series solutions to regular linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y=f(y,{}y',{}..,{}y)} such that \\spad{y(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL -(-1143 |Coef| UTS) -((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y=f(y,{}y',{}..,{}y)} such that \\spad{y(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL +(-1229 -1333 UP L UTS) +((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series ODE solver when presented with linear ODEs.")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL -(-1144 -2958 UP L UTS) -((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) +((|HasCategory| |#1| (QUOTE (-550)))) +(-1230 -1333 UTSF UTSSUPF) +((|constructor| (NIL "This package has no description"))) NIL -((|HasCategory| |#1| (QUOTE (-508)))) -(-1145 |sym|) +NIL +(-1231 |Coef| |var|) +((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n)))=exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) +(((-4507 "*") |has| |#1| (-170)) (-4498 |has| |#1| (-550)) (-4499 . T) (-4500 . T) (-4502 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-170))) (-2318 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-755)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-1153)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-755)) (|devaluate| |#1|))))) (|HasCategory| (-755) (QUOTE (-1094))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-755))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-755))))) (|HasSignature| |#1| (LIST (QUOTE -2801) (LIST (|devaluate| |#1|) (QUOTE (-1153)))))) (|HasCategory| |#1| (QUOTE (-359))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-951))) (|HasCategory| |#1| (QUOTE (-1173)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -2376) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1153))))) (|HasSignature| |#1| (LIST (QUOTE -1654) (LIST (LIST (QUOTE -626) (QUOTE (-1153))) (|devaluate| |#1|))))))) +(-1232 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1146 S R) -((|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) +(-1233 S R) +((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-657))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1147 R) -((|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4168 . T) (-4167 . T) (-2951 . T)) +((|HasCategory| |#2| (QUOTE (-994))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-708))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1234 R) +((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) +((-4506 . T) (-4505 . T) (-2537 . T)) NIL -(-1148 R) -((|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#1| (QUOTE (-1001))) (|HasCategory| |#1| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#1| (QUOTE (-777))) (-1405 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1001)))) (|HasCategory| (-501) (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-657))) (|HasCategory| |#1| (QUOTE (-959))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-959)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))) (-1405 (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-777)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -278) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1001)))))) -(-1149 A B) -((|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) +(-1235 A B) +((|constructor| (NIL "This package provides operations which all take as arguments vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1150) -((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) +(-1236 R) +((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-1082))) (|HasCategory| |#1| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#1| (QUOTE (-834))) (-2318 (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1082)))) (|HasCategory| (-560) (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-708))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-994))) (|HasCategory| |#1| (QUOTE (-1039)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))) (-2318 (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1082)))))) +(-1237) +((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1151) -((|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) +(-1238) +((|constructor| (NIL "ThreeDimensionalViewport creates viewports to display graphs")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{x},{}\\spad{y} and \\spad{z} scales,{} and the \\spad{x} and \\spad{y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1152) -((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) +(-1239) +((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewalone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewalone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1153) -((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) +(-1240) +((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1154) +(-1241) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1155 A S) +(-1242 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1156 S) +(-1243 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4162 . T) (-4161 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1157 R) +(-1244 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1158 K R UP -2958) +(-1245 K R UP -1333) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-1159 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1246 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) -((-4162 |has| |#1| (-156)) (-4161 |has| |#1| (-156)) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331)))) -(-1160 R E V P) -((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4168 . T) (-4167 . T)) -((|HasCategory| |#4| (LIST (QUOTE -556) (QUOTE (-490)))) (|HasCategory| |#4| (QUOTE (-1001))) (-12 (|HasCategory| |#4| (LIST (QUOTE -278) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1001)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#3| (QUOTE (-336)))) -(-1161 R) -((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) -((-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-1162 |vl| R) -((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4164 . T) (-4160 |has| |#2| (-6 -4160)) (-4162 . T) (-4161 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4160))) -(-1163 R |VarSet| XPOLY) -((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) -NIL -NIL -(-1164 S -2958) -((|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -NIL -((|HasCategory| |#2| (QUOTE (-336))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134)))) -(-1165 -2958) -((|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4159 . T) (-4165 . T) (-4160 . T) ((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) -NIL -(-1166 |vl| R) -((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4160 |has| |#2| (-6 -4160)) (-4162 . T) (-4161 . T) (-4164 . T)) -NIL -(-1167 |VarSet| R) -((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4160 |has| |#2| (-6 -4160)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -648) (LIST (QUOTE -375) (QUOTE (-501))))) (|HasAttribute| |#2| (QUOTE -4160))) -(-1168 R) -((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4160 |has| |#1| (-6 -4160)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4160))) -(-1169 |vl| R) +((-4500 |has| |#1| (-170)) (-4499 |has| |#1| (-170)) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359)))) +(-1247 R E V P) +((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The construct operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) +((-4506 . T) (-4505 . T)) +((|HasCategory| |#4| (LIST (QUOTE -601) (QUOTE (-533)))) (|HasCategory| |#4| (QUOTE (-1082))) (-12 (|HasCategory| |#4| (LIST (QUOTE -298) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1082)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-364)))) +(-1248 R) +((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as XPolynomialRing and XFreeAlgebra")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) +((-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-1249 |vl| R) +((|constructor| (NIL "This type supports distributed multivariate polynomials whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) +((-4502 . T) (-4498 |has| |#2| (-6 -4498)) (-4500 . T) (-4499 . T)) +((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4498))) +(-1250 R |VarSet| XPOLY) +((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables.")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) +NIL +NIL +(-1251 |vl| R) +((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) +((-4498 |has| |#2| (-6 -4498)) (-4500 . T) (-4499 . T) (-4502 . T)) +NIL +(-1252 S -1333) +((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) +NIL +((|HasCategory| |#2| (QUOTE (-364))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) +(-1253 -1333) +((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) +((-4497 . T) (-4503 . T) (-4498 . T) ((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) +NIL +(-1254 |VarSet| R) +((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations.")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) +((-4498 |has| |#2| (-6 -4498)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -699) (LIST (QUOTE -403) (QUOTE (-560))))) (|HasAttribute| |#2| (QUOTE -4498))) +(-1255 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4160 |has| |#2| (-6 -4160)) (-4162 . T) (-4161 . T) (-4164 . T)) +((-4498 |has| |#2| (-6 -4498)) (-4500 . T) (-4499 . T) (-4502 . T)) NIL -(-1170 R E) +(-1256 R) +((|constructor| (NIL "This type supports multivariate polynomials whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) +((-4498 |has| |#1| (-6 -4498)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4498))) +(-1257 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4164 . T) (-4165 |has| |#1| (-6 -4165)) (-4160 |has| |#1| (-6 -4160)) (-4162 . T) (-4161 . T)) -((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-331))) (|HasAttribute| |#1| (QUOTE -4164)) (|HasAttribute| |#1| (QUOTE -4165)) (|HasAttribute| |#1| (QUOTE -4160))) -(-1171 |VarSet| R) -((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4160 |has| |#2| (-6 -4160)) (-4162 . T) (-4161 . T) (-4164 . T)) -((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4160))) -(-1172 A) +((-4502 . T) (-4503 |has| |#1| (-6 -4503)) (-4498 |has| |#1| (-6 -4498)) (-4500 . T) (-4499 . T)) +((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-359))) (|HasAttribute| |#1| (QUOTE -4502)) (|HasAttribute| |#1| (QUOTE -4503)) (|HasAttribute| |#1| (QUOTE -4498))) +(-1258 |VarSet| R) +((|constructor| (NIL "This type supports multivariate polynomials whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) +((-4498 |has| |#2| (-6 -4498)) (-4500 . T) (-4499 . T) (-4502 . T)) +((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4498))) +(-1259 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1173 R |ls| |ls2|) -((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) +(-1260 R |ls| |ls2|) +((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING. The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations univariateSolve,{} realSolve and positiveSolve admit an optional argument.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING. \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the zeroSetSplit from \\spadtype{RegularChain}. WARNING. For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the zeroSetSplit from \\spadtype{RegularChain}. WARNING. For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING. For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See rur from RationalUnivariateRepresentationPackage(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the zeroSetSplit from RegularChain") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See rur from RationalUnivariateRepresentationPackage(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See zeroSetSplit from RegularTriangularSetCategory(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the zeroSetSplit from RegularChain"))) NIL NIL -(-1174 R) +(-1261 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1175 |p|) +(-1262 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4169 "*") . T) (-4161 . T) (-4162 . T) (-4164 . T)) +(((-4507 "*") . T) (-4499 . T) (-4500 . T) (-4502 . T)) NIL NIL NIL @@ -4652,4 +5000,4 @@ NIL NIL NIL NIL -((-1180 NIL 2135105 2135110 2135115 2135120) (-3 NIL 2135085 2135090 2135095 2135100) (-2 NIL 2135065 2135070 2135075 2135080) (-1 NIL 2135045 2135050 2135055 2135060) (0 NIL 2135025 2135030 2135035 2135040) (-1175 "ZMOD.spad" 2134834 2134847 2134963 2135020) (-1174 "ZLINDEP.spad" 2133878 2133889 2134824 2134829) (-1173 "ZDSOLVE.spad" 2123727 2123749 2133868 2133873) (-1172 "YSTREAM.spad" 2123220 2123231 2123717 2123722) (-1171 "XRPOLY.spad" 2122440 2122460 2123076 2123145) (-1170 "XPR.spad" 2120169 2120182 2122158 2122257) (-1169 "XPOLYC.spad" 2119486 2119502 2120095 2120164) (-1168 "XPOLY.spad" 2119041 2119052 2119342 2119411) (-1167 "XPBWPOLY.spad" 2117478 2117498 2118821 2118890) (-1166 "XFALG.spad" 2114502 2114518 2117404 2117473) (-1165 "XF.spad" 2113070 2113085 2114404 2114497) (-1164 "XF.spad" 2111618 2111635 2112954 2112959) (-1163 "XEXPPKG.spad" 2110869 2110895 2111608 2111613) (-1162 "XDPOLY.spad" 2110483 2110499 2110725 2110794) (-1161 "XALG.spad" 2110081 2110092 2110439 2110478) (-1160 "WUTSET.spad" 2105968 2105985 2109783 2109810) (-1159 "WP.spad" 2104982 2105026 2105826 2105893) (-1158 "WFFINTBS.spad" 2102545 2102567 2104972 2104977) (-1157 "WEIER.spad" 2100751 2100762 2102535 2102540) (-1156 "VSPACE.spad" 2100424 2100435 2100719 2100746) (-1155 "VSPACE.spad" 2100117 2100130 2100414 2100419) (-1154 "VOID.spad" 2099707 2099716 2100107 2100112) (-1153 "VIEWDEF.spad" 2094904 2094913 2099697 2099702) (-1152 "VIEW3D.spad" 2078739 2078748 2094894 2094899) (-1151 "VIEW2D.spad" 2066560 2066569 2078729 2078734) (-1150 "VIEW.spad" 2064182 2064191 2066550 2066555) (-1149 "VECTOR2.spad" 2063137 2063150 2064172 2064177) (-1148 "VECTOR.spad" 2062182 2062193 2062288 2062315) (-1147 "VECTCAT.spad" 2060509 2060520 2062138 2062177) (-1146 "VECTCAT.spad" 2058657 2058670 2060288 2060293) (-1145 "VARIABLE.spad" 2058437 2058452 2058647 2058652) (-1144 "UTSODETL.spad" 2057730 2057754 2058393 2058398) (-1143 "UTSODE.spad" 2055918 2055938 2057720 2057725) (-1142 "UTSCAT.spad" 2053369 2053385 2055816 2055913) (-1141 "UTSCAT.spad" 2050464 2050482 2052913 2052918) (-1140 "UTS2.spad" 2050057 2050092 2050454 2050459) (-1139 "UTS.spad" 2044846 2044874 2048524 2048621) (-1138 "URAGG.spad" 2040016 2040027 2044826 2044841) (-1137 "URAGG.spad" 2035160 2035173 2039972 2039977) (-1136 "UPXSSING.spad" 2032806 2032832 2034244 2034377) (-1135 "UPXSCONS.spad" 2030563 2030583 2030938 2031087) (-1134 "UPXSCCA.spad" 2029021 2029041 2030409 2030558) (-1133 "UPXSCCA.spad" 2027621 2027643 2029011 2029016) (-1132 "UPXSCAT.spad" 2026202 2026218 2027467 2027616) (-1131 "UPXS2.spad" 2025743 2025796 2026192 2026197) (-1130 "UPXS.spad" 2022770 2022798 2023875 2024024) (-1129 "UPSQFREE.spad" 2021182 2021196 2022760 2022765) (-1128 "UPSCAT.spad" 2018775 2018799 2021080 2021177) (-1127 "UPSCAT.spad" 2016074 2016100 2018381 2018386) (-1126 "UPOLYC2.spad" 2015543 2015562 2016064 2016069) (-1125 "UPOLYC.spad" 2010521 2010532 2015385 2015538) (-1124 "UPOLYC.spad" 2005391 2005404 2010257 2010262) (-1123 "UPMP.spad" 2004281 2004294 2005381 2005386) (-1122 "UPDIVP.spad" 2003844 2003858 2004271 2004276) (-1121 "UPDECOMP.spad" 2002081 2002095 2003834 2003839) (-1120 "UPCDEN.spad" 2001288 2001304 2002071 2002076) (-1119 "UP2.spad" 2000650 2000671 2001278 2001283) (-1118 "UP.spad" 1997700 1997715 1998208 1998361) (-1117 "UNISEG2.spad" 1997193 1997206 1997656 1997661) (-1116 "UNISEG.spad" 1996546 1996557 1997112 1997117) (-1115 "UNIFACT.spad" 1995647 1995659 1996536 1996541) (-1114 "ULSCONS.spad" 1989690 1989710 1990062 1990211) (-1113 "ULSCCAT.spad" 1987287 1987307 1989510 1989685) (-1112 "ULSCCAT.spad" 1985018 1985040 1987243 1987248) (-1111 "ULSCAT.spad" 1983234 1983250 1984864 1985013) (-1110 "ULS2.spad" 1982746 1982799 1983224 1983229) (-1109 "ULS.spad" 1973305 1973333 1974398 1974827) (-1108 "UFD.spad" 1972370 1972379 1973231 1973300) (-1107 "UFD.spad" 1971497 1971508 1972360 1972365) (-1106 "UDVO.spad" 1970344 1970353 1971487 1971492) (-1105 "UDPO.spad" 1967771 1967782 1970300 1970305) (-1104 "TYPE.spad" 1967693 1967702 1967751 1967766) (-1103 "TWOFACT.spad" 1966343 1966358 1967683 1967688) (-1102 "TUPLE.spad" 1965785 1965796 1966298 1966303) (-1101 "TUBETOOL.spad" 1962622 1962631 1965775 1965780) (-1100 "TUBE.spad" 1961263 1961280 1962612 1962617) (-1099 "TSETCAT.spad" 1948378 1948395 1961219 1961258) (-1098 "TSETCAT.spad" 1935491 1935510 1948334 1948339) (-1097 "TS.spad" 1934080 1934096 1935056 1935153) (-1096 "TRMANIP.spad" 1928446 1928463 1933786 1933791) (-1095 "TRIMAT.spad" 1927405 1927430 1928436 1928441) (-1094 "TRIGMNIP.spad" 1925922 1925939 1927395 1927400) (-1093 "TRIGCAT.spad" 1925434 1925443 1925912 1925917) (-1092 "TRIGCAT.spad" 1924944 1924955 1925424 1925429) (-1091 "TREE.spad" 1923920 1923931 1924774 1924801) (-1090 "TRANFUN.spad" 1923751 1923760 1923910 1923915) (-1089 "TRANFUN.spad" 1923580 1923591 1923741 1923746) (-1088 "TOPSP.spad" 1923346 1923355 1923570 1923575) (-1087 "TOOLSIGN.spad" 1923009 1923020 1923336 1923341) (-1086 "TEXTFILE.spad" 1921566 1921575 1922999 1923004) (-1085 "TEX1.spad" 1921122 1921133 1921556 1921561) (-1084 "TEX.spad" 1918139 1918148 1921112 1921117) (-1083 "TEMUTL.spad" 1917694 1917703 1918129 1918134) (-1082 "TBCMPPK.spad" 1915787 1915810 1917684 1917689) (-1081 "TBAGG.spad" 1914950 1914973 1915755 1915782) (-1080 "TBAGG.spad" 1914133 1914158 1914940 1914945) (-1079 "TANEXP.spad" 1913509 1913520 1914123 1914128) (-1078 "TABLEAU.spad" 1912990 1913001 1913499 1913504) (-1077 "TABLE.spad" 1911963 1911986 1912233 1912260) (-1076 "TABLBUMP.spad" 1908714 1908725 1911953 1911958) (-1075 "SYSSOLP.spad" 1906187 1906198 1908704 1908709) (-1074 "SYMTAB.spad" 1904243 1904252 1906177 1906182) (-1073 "SYMS.spad" 1900228 1900237 1904233 1904238) (-1072 "SYMPOLY.spad" 1899238 1899249 1899320 1899447) (-1071 "SYMFUNC.spad" 1898713 1898724 1899228 1899233) (-1070 "SYMBOL.spad" 1896041 1896050 1898703 1898708) (-1069 "SWITCH.spad" 1892798 1892807 1896031 1896036) (-1068 "SUTS.spad" 1889697 1889725 1891265 1891362) (-1067 "SUPXS.spad" 1886711 1886739 1887829 1887978) (-1066 "SUPFRACF.spad" 1885816 1885834 1886701 1886706) (-1065 "SUP2.spad" 1885206 1885219 1885806 1885811) (-1064 "SUP.spad" 1881983 1881994 1882764 1882917) (-1063 "SUMRF.spad" 1880949 1880960 1881973 1881978) (-1062 "SUMFS.spad" 1880574 1880591 1880939 1880944) (-1061 "SULS.spad" 1871120 1871148 1872226 1872655) (-1060 "SUCH.spad" 1870800 1870815 1871110 1871115) (-1059 "SUBSPACE.spad" 1862858 1862873 1870790 1870795) (-1058 "SUBRESP.spad" 1862018 1862032 1862814 1862819) (-1057 "STTFNC.spad" 1858486 1858502 1862008 1862013) (-1056 "STTF.spad" 1854585 1854601 1858476 1858481) (-1055 "STTAYLOR.spad" 1846983 1846994 1854466 1854471) (-1054 "STRTBL.spad" 1846062 1846079 1846211 1846238) (-1053 "STRING.spad" 1845529 1845538 1845543 1845570) (-1052 "STRICAT.spad" 1845364 1845373 1845485 1845524) (-1051 "STREAM3.spad" 1844909 1844924 1845354 1845359) (-1050 "STREAM2.spad" 1843977 1843990 1844899 1844904) (-1049 "STREAM1.spad" 1843681 1843692 1843967 1843972) (-1048 "STREAM.spad" 1840672 1840683 1843429 1843444) (-1047 "STINPROD.spad" 1839578 1839594 1840662 1840667) (-1046 "STEP.spad" 1838779 1838788 1839568 1839573) (-1045 "STBL.spad" 1837867 1837895 1838034 1838049) (-1044 "STAGG.spad" 1837322 1837333 1837847 1837862) (-1043 "STAGG.spad" 1836785 1836798 1837312 1837317) (-1042 "STACK.spad" 1836421 1836432 1836615 1836642) (-1041 "SREGSET.spad" 1834181 1834198 1836123 1836150) (-1040 "SRDCMPK.spad" 1832726 1832746 1834171 1834176) (-1039 "SRAGG.spad" 1827932 1827941 1832682 1832721) (-1038 "SRAGG.spad" 1823170 1823181 1827922 1827927) (-1037 "SQMATRIX.spad" 1820852 1820870 1821760 1821847) (-1036 "SPLTREE.spad" 1815719 1815732 1820603 1820630) (-1035 "SPLNODE.spad" 1812259 1812272 1815709 1815714) (-1034 "SPFCAT.spad" 1811036 1811045 1812249 1812254) (-1033 "SPECOUT.spad" 1809586 1809595 1811026 1811031) (-1032 "SPACEC.spad" 1793761 1793772 1809576 1809581) (-1031 "SPACE3.spad" 1793735 1793746 1793751 1793756) (-1030 "SORTPAK.spad" 1793280 1793293 1793691 1793696) (-1029 "SOLVETRA.spad" 1791037 1791048 1793270 1793275) (-1028 "SOLVESER.spad" 1789485 1789496 1791027 1791032) (-1027 "SOLVERAD.spad" 1785495 1785506 1789475 1789480) (-1026 "SOLVEFOR.spad" 1783915 1783933 1785485 1785490) (-1025 "SNTSCAT.spad" 1783503 1783520 1783871 1783910) (-1024 "SMTS.spad" 1781763 1781789 1783068 1783165) (-1023 "SMP.spad" 1779205 1779225 1779595 1779722) (-1022 "SMITH.spad" 1778048 1778073 1779195 1779200) (-1021 "SMATCAT.spad" 1776146 1776176 1777980 1778043) (-1020 "SMATCAT.spad" 1774188 1774220 1776024 1776029) (-1019 "SKAGG.spad" 1773236 1773247 1774144 1774183) (-1018 "SINT.spad" 1771544 1771553 1773102 1773231) (-1017 "SIMPAN.spad" 1771272 1771281 1771534 1771539) (-1016 "SIGNRF.spad" 1770380 1770391 1771262 1771267) (-1015 "SIGNEF.spad" 1769649 1769666 1770370 1770375) (-1014 "SHP.spad" 1767519 1767534 1769605 1769610) (-1013 "SHDP.spad" 1759617 1759644 1760134 1760263) (-1012 "SGROUP.spad" 1759083 1759092 1759607 1759612) (-1011 "SGROUP.spad" 1758547 1758558 1759073 1759078) (-1010 "SGCF.spad" 1751428 1751437 1758537 1758542) (-1009 "SFRTCAT.spad" 1750344 1750361 1751384 1751423) (-1008 "SFRGCD.spad" 1749399 1749419 1750334 1750339) (-1007 "SFQCMPK.spad" 1744020 1744040 1749389 1749394) (-1006 "SFORT.spad" 1743455 1743469 1744010 1744015) (-1005 "SEXOF.spad" 1743298 1743338 1743445 1743450) (-1004 "SEXCAT.spad" 1740386 1740426 1743288 1743293) (-1003 "SEX.spad" 1740278 1740287 1740376 1740381) (-1002 "SETMN.spad" 1738696 1738713 1740268 1740273) (-1001 "SETCAT.spad" 1738181 1738190 1738686 1738691) (-1000 "SETCAT.spad" 1737664 1737675 1738171 1738176) (-999 "SETAGG.spad" 1734531 1734541 1737632 1737659) (-998 "SETAGG.spad" 1731418 1731430 1734521 1734526) (-997 "SET.spad" 1729775 1729785 1730895 1730934) (-996 "SEGXCAT.spad" 1728888 1728900 1729755 1729770) (-995 "SEGCAT.spad" 1727708 1727718 1728868 1728883) (-994 "SEGBIND2.spad" 1727405 1727417 1727698 1727703) (-993 "SEGBIND.spad" 1726478 1726488 1727360 1727365) (-992 "SEG2.spad" 1725904 1725916 1726434 1726439) (-991 "SEG.spad" 1725718 1725728 1725823 1725828) (-990 "SDVAR.spad" 1725693 1725703 1725708 1725713) (-989 "SDPOL.spad" 1723367 1723377 1723382 1723509) (-988 "SCPKG.spad" 1721447 1721457 1723357 1723362) (-987 "SCACHE.spad" 1720130 1720140 1721437 1721442) (-986 "SAOS.spad" 1720003 1720011 1720120 1720125) (-985 "SAERFFC.spad" 1719869 1719888 1719993 1719998) (-984 "SAEFACT.spad" 1719735 1719754 1719859 1719864) (-983 "SAE.spad" 1717914 1717929 1718524 1718659) (-982 "RURPK.spad" 1715556 1715571 1717904 1717909) (-981 "RULESET.spad" 1714998 1715021 1715546 1715551) (-980 "RULECOLD.spad" 1714851 1714863 1714988 1714993) (-979 "RULE.spad" 1713056 1713079 1714841 1714846) (-978 "RSETGCD.spad" 1709427 1709446 1713046 1713051) (-977 "RSETCAT.spad" 1699200 1699216 1709383 1709422) (-976 "RSETCAT.spad" 1689005 1689023 1699190 1699195) (-975 "RSDCMPK.spad" 1687458 1687477 1688995 1689000) (-974 "RRCC.spad" 1685842 1685871 1687448 1687453) (-973 "RRCC.spad" 1684224 1684255 1685832 1685837) (-972 "RPOLCAT.spad" 1663545 1663559 1684092 1684219) (-971 "RPOLCAT.spad" 1642581 1642597 1663130 1663135) (-970 "ROUTINE.spad" 1639165 1639173 1641810 1641837) (-969 "ROMAN.spad" 1638398 1638406 1639031 1639160) (-968 "ROIRC.spad" 1637479 1637510 1638388 1638393) (-967 "RNS.spad" 1636697 1636705 1637381 1637474) (-966 "RNS.spad" 1636001 1636011 1636687 1636692) (-965 "RNG.spad" 1635737 1635745 1635991 1635996) (-964 "RMODULE.spad" 1635376 1635386 1635727 1635732) (-963 "RMCAT2.spad" 1634785 1634841 1635366 1635371) (-962 "RMATRIX.spad" 1633521 1633539 1634008 1634047) (-961 "RMATCAT.spad" 1629043 1629073 1633465 1633516) (-960 "RMATCAT.spad" 1624467 1624499 1628891 1628896) (-959 "RING.spad" 1623825 1623833 1624447 1624462) (-958 "RING.spad" 1623191 1623201 1623815 1623820) (-957 "RIDIST.spad" 1622576 1622584 1623181 1623186) (-956 "RGCHAIN.spad" 1621231 1621246 1622136 1622163) (-955 "RFFACTOR.spad" 1620694 1620704 1621221 1621226) (-954 "RFFACT.spad" 1620568 1620579 1620684 1620689) (-953 "RFDIST.spad" 1619557 1619565 1620558 1620563) (-952 "RF.spad" 1617172 1617182 1619547 1619552) (-951 "RETSOL.spad" 1616590 1616602 1617162 1617167) (-950 "RETRACT.spad" 1615940 1615950 1616580 1616585) (-949 "RETRACT.spad" 1615288 1615300 1615930 1615935) (-948 "RESULT.spad" 1613931 1613939 1614517 1614544) (-947 "RESRING.spad" 1613279 1613325 1613869 1613926) (-946 "RESLATC.spad" 1612604 1612614 1613269 1613274) (-945 "REPSQ.spad" 1612334 1612344 1612594 1612599) (-944 "REPDB.spad" 1612040 1612050 1612324 1612329) (-943 "REP2.spad" 1601605 1601615 1611882 1611887) (-942 "REP1.spad" 1595588 1595598 1601555 1601560) (-941 "REP.spad" 1593141 1593149 1595578 1595583) (-940 "REGSET.spad" 1590995 1591011 1592843 1592870) (-939 "REF.spad" 1590325 1590335 1590950 1590955) (-938 "REDORDER.spad" 1589502 1589518 1590315 1590320) (-937 "RECLOS.spad" 1588292 1588311 1588995 1589088) (-936 "REALSOLV.spad" 1587425 1587433 1588282 1588287) (-935 "REAL0Q.spad" 1584708 1584722 1587415 1587420) (-934 "REAL0.spad" 1581537 1581551 1584698 1584703) (-933 "REAL.spad" 1581514 1581522 1581527 1581532) (-932 "RDIV.spad" 1581166 1581190 1581504 1581509) (-931 "RDIST.spad" 1580730 1580740 1581156 1581161) (-930 "RDETRS.spad" 1579527 1579544 1580720 1580725) (-929 "RDETR.spad" 1577635 1577652 1579517 1579522) (-928 "RDEEFS.spad" 1576709 1576725 1577625 1577630) (-927 "RDEEF.spad" 1575706 1575722 1576699 1576704) (-926 "RCFIELD.spad" 1572890 1572898 1575608 1575701) (-925 "RCFIELD.spad" 1570160 1570170 1572880 1572885) (-924 "RCAGG.spad" 1568529 1568539 1570140 1570155) (-923 "RCAGG.spad" 1566835 1566847 1568448 1568453) (-922 "RATRET.spad" 1566196 1566206 1566825 1566830) (-921 "RATFACT.spad" 1565889 1565900 1566186 1566191) (-920 "RANDSRC.spad" 1565209 1565217 1565879 1565884) (-919 "RADUTIL.spad" 1564964 1564972 1565199 1565204) (-918 "RADIX.spad" 1561757 1561770 1563434 1563527) (-917 "RADFF.spad" 1560174 1560210 1560292 1560448) (-916 "RADCAT.spad" 1559857 1559865 1560164 1560169) (-915 "RADCAT.spad" 1559538 1559548 1559847 1559852) (-914 "QUEUE.spad" 1559166 1559176 1559368 1559395) (-913 "QUATCT2.spad" 1558785 1558803 1559156 1559161) (-912 "QUATCAT.spad" 1556950 1556960 1558715 1558780) (-911 "QUATCAT.spad" 1554867 1554879 1556634 1556639) (-910 "QUAT.spad" 1553453 1553463 1553795 1553860) (-909 "QUAGG.spad" 1552367 1552377 1553409 1553448) (-908 "QFORM.spad" 1551830 1551844 1552357 1552362) (-907 "QFCAT2.spad" 1551521 1551537 1551820 1551825) (-906 "QFCAT.spad" 1550212 1550222 1551411 1551516) (-905 "QFCAT.spad" 1548509 1548521 1549710 1549715) (-904 "QEQUAT.spad" 1548066 1548074 1548499 1548504) (-903 "QCMPACK.spad" 1542797 1542816 1548056 1548061) (-902 "QALGSET2.spad" 1540793 1540811 1542787 1542792) (-901 "QALGSET.spad" 1536868 1536900 1540707 1540712) 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952542 953265 953270) (-597 "LOGIC.spad" 952134 952142 952522 952527) (-596 "LOGIC.spad" 951734 951744 952124 952129) (-595 "LODOOPS.spad" 950652 950664 951724 951729) (-594 "LODOF.spad" 949696 949713 950609 950614) (-593 "LODOCAT.spad" 948354 948364 949652 949691) (-592 "LODOCAT.spad" 947010 947022 948310 948315) (-591 "LODO2.spad" 946285 946297 946692 946731) (-590 "LODO1.spad" 945687 945697 945967 946006) (-589 "LODO.spad" 945073 945089 945369 945408) (-588 "LODEEF.spad" 943845 943863 945063 945068) (-587 "LO.spad" 943246 943260 943779 943806) (-586 "LNAGG.spad" 939678 939688 943226 943241) (-585 "LNAGG.spad" 936084 936096 939634 939639) (-584 "LMOPS.spad" 932820 932837 936074 936079) (-583 "LMODULE.spad" 932462 932472 932810 932815) (-582 "LMDICT.spad" 931968 931978 932236 932263) (-581 "LIST3.spad" 931427 931441 931958 931963) (-580 "LIST2MAP.spad" 928743 928755 931417 931422) (-579 "LIST2.spad" 927549 927561 928733 928738) (-578 "LIST.spad" 925797 925807 926919 926946) (-577 "LINEXP.spad" 925229 925239 925777 925792) (-576 "LINDEP.spad" 924006 924018 925141 925146) (-575 "LIMITRF.spad" 921920 921930 923996 924001) (-574 "LIMITPS.spad" 920803 920816 921910 921915) (-573 "LIECAT.spad" 920279 920289 920729 920798) (-572 "LIECAT.spad" 919783 919795 920235 920240) (-571 "LIE.spad" 917797 917809 919073 919218) (-570 "LIB.spad" 916427 916435 917038 917053) (-569 "LGROBP.spad" 913780 913799 916417 916422) (-568 "LFCAT.spad" 912799 912807 913770 913775) (-567 "LF.spad" 911718 911734 912789 912794) (-566 "LEXTRIPK.spad" 907221 907236 911708 911713) (-565 "LEXP.spad" 905224 905251 907201 907216) (-564 "LEADCDET.spad" 903608 903625 905214 905219) (-563 "LAZM3PK.spad" 902312 902334 903598 903603) (-562 "LAUPOL.spad" 901003 901016 901907 901976) (-561 "LAPLACE.spad" 900576 900592 900993 900998) (-560 "LALG.spad" 900352 900362 900556 900571) (-559 "LALG.spad" 900136 900148 900342 900347) (-558 "LA.spad" 899576 899590 900058 900097) (-557 "KOVACIC.spad" 898289 898306 899566 899571) (-556 "KONVERT.spad" 898011 898021 898279 898284) (-555 "KOERCE.spad" 897748 897758 898001 898006) (-554 "KERNEL2.spad" 897451 897463 897738 897743) (-553 "KERNEL.spad" 895986 895996 897235 897240) (-552 "KDAGG.spad" 895203 895225 895954 895981) (-551 "KDAGG.spad" 894440 894464 895193 895198) (-550 "KAFILE.spad" 893552 893568 893787 893814) (-549 "JORDAN.spad" 891379 891391 892842 892987) (-548 "IXAGG.spad" 889768 889792 891359 891374) (-547 "IXAGG.spad" 888022 888048 889615 889620) (-546 "IVECTOR.spad" 887153 887168 887173 887200) (-545 "ITUPLE.spad" 886298 886308 887143 887148) (-544 "ITRIGMNP.spad" 885109 885128 886288 886293) (-543 "ITFUN3.spad" 884603 884617 885099 885104) (-542 "ITFUN2.spad" 884333 884345 884593 884598) (-541 "ITAYLOR.spad" 882125 882140 884169 884294) (-540 "ISUPS.spad" 874536 874551 881099 881196) (-539 "ISUMP.spad" 874033 874049 874526 874531) (-538 "ISTRING.spad" 873328 873341 873429 873456) (-537 "IRURPK.spad" 872041 872060 873318 873323) (-536 "IRSN.spad" 870001 870009 872031 872036) (-535 "IRRF2F.spad" 868476 868486 869957 869962) (-534 "IRREDFFX.spad" 868077 868088 868466 868471) (-533 "IROOT.spad" 866408 866418 868067 868072) (-532 "IR2F.spad" 865608 865624 866398 866403) (-531 "IR2.spad" 864628 864644 865598 865603) (-530 "IR.spad" 862418 862432 864484 864511) (-529 "IPRNTPK.spad" 862178 862186 862408 862413) (-528 "IPF.spad" 861743 861755 861983 862076) (-527 "IPADIC.spad" 861504 861530 861669 861738) (-526 "INVLAPLA.spad" 861149 861165 861494 861499) (-525 "INTTR.spad" 854395 854412 861139 861144) (-524 "INTTOOLS.spad" 852107 852123 853970 853975) (-523 "INTSLPE.spad" 851413 851421 852097 852102) (-522 "INTRVL.spad" 850979 850989 851327 851408) (-521 "INTRF.spad" 849343 849357 850969 850974) (-520 "INTRET.spad" 848775 848785 849333 849338) (-519 "INTRAT.spad" 847450 847467 848765 848770) (-518 "INTPM.spad" 845813 845829 847093 847098) (-517 "INTPAF.spad" 843581 843599 845745 845750) (-516 "INTPACK.spad" 833891 833899 843571 843576) (-515 "INTHERTR.spad" 833157 833174 833881 833886) (-514 "INTHERAL.spad" 832823 832847 833147 833152) (-513 "INTHEORY.spad" 829334 829342 832813 832818) (-512 "INTG0.spad" 822797 822815 829266 829271) (-511 "INTFTBL.spad" 816862 816870 822787 822792) (-510 "INTFACT.spad" 815921 815931 816852 816857) (-509 "INTEF.spad" 814236 814252 815911 815916) (-508 "INTDOM.spad" 812851 812859 814162 814231) (-507 "INTDOM.spad" 811528 811538 812841 812846) (-506 "INTCAT.spad" 809771 809781 811442 811523) (-505 "INTBIT.spad" 809274 809282 809761 809766) (-504 "INTALG.spad" 808456 808483 809264 809269) (-503 "INTAF.spad" 807948 807964 808446 808451) (-502 "INTABL.spad" 807028 807059 807191 807218) (-501 "INT.spad" 806389 806397 806882 807023) (-500 "INS.spad" 803785 803793 806291 806384) (-499 "INS.spad" 801267 801277 803775 803780) (-498 "INPSIGN.spad" 800701 800714 801257 801262) (-497 "INPRODPF.spad" 799767 799786 800691 800696) (-496 "INPRODFF.spad" 798825 798849 799757 799762) (-495 "INNMFACT.spad" 798084 798101 798815 798820) (-494 "INMODGCD.spad" 797568 797598 798074 798079) (-493 "INFSP.spad" 796470 796492 797558 797563) (-492 "INFPROD0.spad" 795520 795539 796460 796465) (-491 "INFORM1.spad" 795145 795155 795510 795515) (-490 "INFORM.spad" 792413 792421 795135 795140) (-489 "INFINITY.spad" 791965 791973 792403 792408) (-488 "INEP.spad" 790685 790707 791955 791960) (-487 "INDE.spad" 790591 790608 790675 790680) (-486 "INCRMAPS.spad" 790012 790022 790581 790586) (-485 "INBFF.spad" 785782 785793 790002 790007) (-484 "IMATRIX.spad" 784950 784976 785462 785489) (-483 "IMATQF.spad" 784044 784088 784906 784911) (-482 "IMATLIN.spad" 782649 782673 784000 784005) (-481 "ILIST.spad" 782035 782050 782055 782082) (-480 "IIARRAY2.spad" 781646 781684 781865 781892) (-479 "IFF.spad" 781056 781072 781327 781420) (-478 "IFARRAY.spad" 778750 778765 780462 780489) (-477 "IFAMON.spad" 778612 778629 778706 778711) (-476 "IEVALAB.spad" 778001 778013 778602 778607) (-475 "IEVALAB.spad" 777388 777402 777991 777996) (-474 "IDPOAMS.spad" 777144 777156 777378 777383) (-473 "IDPOAM.spad" 776864 776876 777134 777139) (-472 "IDPO.spad" 776662 776674 776854 776859) (-471 "IDPC.spad" 775596 775608 776652 776657) (-470 "IDPAM.spad" 775341 775353 775586 775591) (-469 "IDPAG.spad" 775088 775100 775331 775336) (-468 "IDECOMP.spad" 772325 772343 775078 775083) (-467 "IDEAL.spad" 767248 767287 772260 772265) (-466 "ICDEN.spad" 766399 766415 767238 767243) (-465 "ICARD.spad" 765588 765596 766389 766394) (-464 "IBPTOOLS.spad" 764181 764198 765578 765583) (-463 "IBITS.spad" 763438 763451 763875 763902) (-462 "IBATOOL.spad" 760313 760332 763428 763433) (-461 "IBACHIN.spad" 758800 758815 760303 760308) (-460 "IARRAY2.spad" 758011 758037 758630 758657) (-459 "IARRAY1.spad" 757271 757286 757417 757444) (-458 "IAN.spad" 755486 755494 757089 757182) (-457 "IALGFACT.spad" 755245 755278 755476 755481) (-456 "HYPCAT.spad" 754669 754677 755235 755240) (-455 "HYPCAT.spad" 754091 754101 754659 754664) (-454 "HOAGG.spad" 751782 751792 754071 754086) (-453 "HOAGG.spad" 749314 749326 751605 751610) (-452 "HEXADEC.spad" 747186 747194 747784 747877) (-451 "HEUGCD.spad" 746201 746212 747176 747181) (-450 "HELLFDIV.spad" 745791 745815 746191 746196) (-449 "HEAP.spad" 745491 745501 745621 745648) (-448 "HDP.spad" 737729 737745 738106 738235) (-447 "HDMP.spad" 735327 735342 735526 735653) (-446 "HB.spad" 733564 733572 735317 735322) (-445 "HASHTBL.spad" 732596 732627 732807 732834) (-444 "HACKPI.spad" 732079 732087 732498 732591) (-443 "GTSET.spad" 731074 731090 731781 731808) (-442 "GSTBL.spad" 730155 730190 730329 730344) (-441 "GSERIES.spad" 727322 727349 728287 728436) (-440 "GROUP.spad" 726496 726504 727302 727317) (-439 "GROUP.spad" 725678 725688 726486 726491) (-438 "GROEBSOL.spad" 724166 724187 725668 725673) (-437 "GRMOD.spad" 722737 722749 724156 724161) (-436 "GRMOD.spad" 721306 721320 722727 722732) (-435 "GRIMAGE.spad" 714040 714048 721296 721301) (-434 "GRDEF.spad" 712419 712427 714030 714035) (-433 "GRAY.spad" 710882 710890 712409 712414) (-432 "GRALG.spad" 709929 709941 710872 710877) (-431 "GRALG.spad" 708974 708988 709919 709924) (-430 "GPOLSET.spad" 708484 708507 708712 708739) (-429 "GOSPER.spad" 707749 707767 708474 708479) (-428 "GMODPOL.spad" 706887 706914 707717 707744) (-427 "GHENSEL.spad" 705956 705970 706877 706882) (-426 "GENUPS.spad" 702057 702070 705946 705951) (-425 "GENUFACT.spad" 701634 701644 702047 702052) (-424 "GENPGCD.spad" 701218 701235 701624 701629) (-423 "GENMFACT.spad" 700670 700689 701208 701213) (-422 "GENEEZ.spad" 698609 698622 700660 700665) (-421 "GDMP.spad" 695630 695647 696406 696533) (-420 "GCNAALG.spad" 689525 689552 695424 695491) (-419 "GCDDOM.spad" 688697 688705 689451 689520) (-418 "GCDDOM.spad" 687931 687941 688687 688692) (-417 "GBINTERN.spad" 683951 683989 687921 687926) (-416 "GBF.spad" 679708 679746 683941 683946) (-415 "GBEUCLID.spad" 677582 677620 679698 679703) (-414 "GB.spad" 675100 675138 677538 677543) (-413 "GAUSSFAC.spad" 674397 674405 675090 675095) (-412 "GALUTIL.spad" 672719 672729 674353 674358) (-411 "GALPOLYU.spad" 671165 671178 672709 672714) (-410 "GALFACTU.spad" 669330 669349 671155 671160) (-409 "GALFACT.spad" 659463 659474 669320 669325) (-408 "FVFUN.spad" 656645 656653 659443 659458) (-407 "FVC.spad" 655924 655932 656625 656640) (-406 "FUNCTION.spad" 655773 655785 655914 655919) (-405 "FTEM.spad" 654936 654944 655763 655768) (-404 "FT.spad" 653148 653156 654926 654931) (-403 "FSUPFACT.spad" 652049 652068 653085 653090) (-402 "FST.spad" 650135 650143 652039 652044) (-401 "FSRED.spad" 649613 649629 650125 650130) (-400 "FSPRMELT.spad" 648421 648437 649570 649575) (-399 "FSPECF.spad" 646498 646514 648411 648416) (-398 "FSINT.spad" 646156 646172 646488 646493) (-397 "FSERIES.spad" 645343 645355 645976 646075) (-396 "FSCINT.spad" 644656 644672 645333 645338) (-395 "FSAGG2.spad" 643347 643363 644646 644651) (-394 "FSAGG.spad" 642673 642683 643291 643342) (-393 "FSAGG.spad" 641973 641985 642593 642598) (-392 "FS2UPS.spad" 636362 636396 641963 641968) (-391 "FS2EXPXP.spad" 635485 635508 636352 636357) (-390 "FS2.spad" 635130 635146 635475 635480) (-389 "FS.spad" 629165 629175 634894 635125) (-388 "FS.spad" 622991 623003 628722 628727) (-387 "FRUTIL.spad" 621933 621943 622981 622986) (-386 "FRNAALG.spad" 617020 617030 621875 621928) (-385 "FRNAALG.spad" 612119 612131 616976 616981) (-384 "FRNAAF2.spad" 611565 611583 612109 612114) (-383 "FRMOD.spad" 610960 610990 611497 611502) (-382 "FRIDEAL2.spad" 610562 610594 610950 610955) (-381 "FRIDEAL.spad" 609757 609778 610542 610557) (-380 "FRETRCT.spad" 609268 609278 609747 609752) (-379 "FRETRCT.spad" 608647 608659 609128 609133) (-378 "FRAMALG.spad" 606975 606988 608603 608642) (-377 "FRAMALG.spad" 605335 605350 606965 606970) (-376 "FRAC2.spad" 604938 604950 605325 605330) (-375 "FRAC.spad" 602041 602051 602444 602617) (-374 "FR2.spad" 601375 601387 602031 602036) (-373 "FR.spad" 595072 595082 600402 600471) (-372 "FPS.spad" 592925 592933 594962 595067) (-371 "FPS.spad" 590806 590816 592845 592850) (-370 "FPC.spad" 590108 590116 590708 590801) (-369 "FPC.spad" 589496 589506 590098 590103) (-368 "FPATMAB.spad" 589248 589258 589476 589491) (-367 "FPARFRAC.spad" 587713 587730 589238 589243) (-366 "FORTRAN.spad" 586213 586262 587703 587708) (-365 "FORTFN.spad" 583527 583535 586193 586208) (-364 "FORTCAT.spad" 583360 583368 583507 583522) (-363 "FORT.spad" 582289 582297 583350 583355) (-362 "FORMULA1.spad" 581768 581778 582279 582284) (-361 "FORMULA.spad" 579106 579114 581758 581763) (-360 "FORDER.spad" 578797 578821 579096 579101) (-359 "FOP.spad" 577998 578006 578787 578792) (-358 "FNLA.spad" 577422 577444 577966 577993) (-357 "FNCAT.spad" 575750 575758 577412 577417) (-356 "FNAME.spad" 575642 575650 575740 575745) (-355 "FMTC.spad" 575555 575563 575568 575637) (-354 "FMONOID.spad" 572610 572620 575511 575516) (-353 "FMFUN.spad" 569792 569800 572590 572605) (-352 "FMCAT.spad" 567446 567464 569760 569787) (-351 "FMC.spad" 566725 566733 567426 567441) (-350 "FM1.spad" 566082 566094 566659 566686) (-349 "FM.spad" 565777 565789 566016 566043) (-348 "FLOATRP.spad" 563836 563850 565767 565772) (-347 "FLOATCP.spad" 561630 561644 563826 563831) (-346 "FLOAT.spad" 554794 554802 561496 561625) (-345 "FLINEXP.spad" 554506 554516 554774 554789) (-344 "FLINEXP.spad" 554172 554184 554442 554447) (-343 "FLASORT.spad" 553492 553504 554162 554167) (-342 "FLALG.spad" 551138 551157 553418 553487) (-341 "FLAGG2.spad" 549811 549827 551128 551133) (-340 "FLAGG.spad" 547081 547091 549779 549806) (-339 "FLAGG.spad" 544264 544276 546964 546969) (-338 "FINRALG.spad" 542293 542306 544220 544259) (-337 "FINRALG.spad" 540248 540263 542177 542182) (-336 "FINITE.spad" 539400 539408 540238 540243) (-335 "FINAALG.spad" 528381 528391 539342 539395) (-334 "FINAALG.spad" 517374 517386 528337 528342) (-333 "FILECAT.spad" 515892 515909 517364 517369) (-332 "FILE.spad" 515475 515485 515882 515887) (-331 "FIELD.spad" 514881 514889 515377 515470) (-330 "FIELD.spad" 514373 514383 514871 514876) (-329 "FGROUP.spad" 512982 512992 514353 514368) (-328 "FGLMICPK.spad" 511769 511784 512972 512977) (-327 "FFX.spad" 511144 511159 511485 511578) (-326 "FFSLPE.spad" 510751 510772 511134 511139) (-325 "FFPOLY2.spad" 509803 509820 510741 510746) (-324 "FFPOLY.spad" 501055 501066 509793 509798) (-323 "FFP.spad" 500452 500472 500771 500864) (-322 "FFNBX.spad" 498964 498984 500168 500261) (-321 "FFNBP.spad" 497477 497494 498680 498773) (-320 "FFNB.spad" 495942 495963 497158 497251) (-319 "FFINTBAS.spad" 493356 493375 495932 495937) (-318 "FFIELDC.spad" 491008 491016 493258 493351) (-317 "FFIELDC.spad" 488746 488756 490998 491003) (-316 "FFHOM.spad" 487494 487511 488736 488741) (-315 "FFF.spad" 484929 484940 487484 487489) (-314 "FFCGX.spad" 483776 483796 484645 484738) (-313 "FFCGP.spad" 482665 482685 483492 483585) (-312 "FFCG.spad" 481457 481478 482346 482439) (-311 "FFCAT2.spad" 481202 481242 481447 481452) (-310 "FFCAT.spad" 474095 474117 481041 481197) (-309 "FFCAT.spad" 467067 467091 474015 474020) (-308 "FF.spad" 466515 466531 466748 466841) (-307 "FEXPR.spad" 458220 458266 466275 466314) (-306 "FEVALAB.spad" 457926 457936 458210 458215) (-305 "FEVALAB.spad" 457417 457429 457703 457708) (-304 "FDIVCAT.spad" 455459 455483 457407 457412) (-303 "FDIVCAT.spad" 453499 453525 455449 455454) (-302 "FDIV2.spad" 453153 453193 453489 453494) (-301 "FDIV.spad" 452595 452619 453143 453148) (-300 "FCPAK1.spad" 451116 451124 452585 452590) (-299 "FCOMP.spad" 450495 450505 451106 451111) (-298 "FC.spad" 440320 440328 450485 450490) (-297 "FAXF.spad" 434811 434825 440222 440315) (-296 "FAXF.spad" 429354 429370 434767 434772) (-295 "FARRAY.spad" 428745 428755 428760 428787) (-294 "FAMR.spad" 426865 426877 428643 428740) (-293 "FAMR.spad" 424969 424983 426749 426754) (-292 "FAMONOID.spad" 424619 424629 424923 424928) (-291 "FAMONC.spad" 422825 422837 424609 424614) (-290 "FAGROUP.spad" 422431 422441 422721 422748) (-289 "FACUTIL.spad" 420627 420644 422421 422426) (-288 "FACTFUNC.spad" 419803 419813 420617 420622) (-287 "EXPUPXS.spad" 416636 416659 417935 418084) (-286 "EXPRTUBE.spad" 413864 413872 416626 416631) (-285 "EXPRODE.spad" 410736 410752 413854 413859) (-284 "EXPR2UPS.spad" 406828 406841 410726 410731) (-283 "EXPR2.spad" 406531 406543 406818 406823) (-282 "EXPR.spad" 401833 401843 402547 402950) (-281 "EXPEXPAN.spad" 398774 398799 399408 399501) (-280 "EXIT.spad" 398445 398453 398764 398769) (-279 "EVALCYC.spad" 397903 397917 398435 398440) (-278 "EVALAB.spad" 397467 397477 397893 397898) (-277 "EVALAB.spad" 397029 397041 397457 397462) (-276 "EUCDOM.spad" 394571 394579 396955 397024) (-275 "EUCDOM.spad" 392175 392185 394561 394566) (-274 "ESTOOLS2.spad" 391937 391951 392165 392170) (-273 "ESTOOLS1.spad" 391791 391802 391927 391932) (-272 "ESTOOLS.spad" 383778 383786 391781 391786) (-271 "ESCONT1.spad" 383626 383638 383768 383773) (-270 "ESCONT.spad" 380563 380571 383616 383621) (-269 "ES2.spad" 380058 380074 380553 380558) (-268 "ES1.spad" 379624 379640 380048 380053) (-267 "ES.spad" 372171 372179 379614 379619) (-266 "ES.spad" 364626 364636 372071 372076) (-265 "ERROR.spad" 361947 361955 364616 364621) (-264 "EQTBL.spad" 360981 361003 361190 361217) (-263 "EQ2.spad" 360697 360709 360971 360976) (-262 "EQ.spad" 355565 355575 358380 358489) (-261 "EP.spad" 351879 351889 355555 355560) (-260 "ENTIRER.spad" 351547 351555 351823 351874) (-259 "EMR.spad" 350748 350789 351473 351542) (-258 "ELTAGG.spad" 349369 349388 350738 350743) (-257 "ELTAGG.spad" 347954 347975 349325 349330) (-256 "ELTAB.spad" 347735 347753 347944 347949) (-255 "ELFUTS.spad" 347114 347133 347725 347730) (-254 "ELEMFUN.spad" 346803 346811 347104 347109) (-253 "ELEMFUN.spad" 346490 346500 346793 346798) (-252 "ELAGG.spad" 344846 344856 346458 346485) (-251 "ELAGG.spad" 343151 343163 344765 344770) (-250 "EFUPXS.spad" 339927 339957 343107 343112) (-249 "EFULS.spad" 336763 336786 339883 339888) (-248 "EFSTRUC.spad" 334718 334734 336753 336758) (-247 "EF.spad" 329484 329500 334708 334713) (-246 "EAB.spad" 327760 327768 329474 329479) (-245 "E04UCFA.spad" 327737 327745 327750 327755) (-244 "E04NAFA.spad" 327714 327722 327727 327732) (-243 "E04MBFA.spad" 327691 327699 327704 327709) (-242 "E04JAFA.spad" 327668 327676 327681 327686) (-241 "E04GCFA.spad" 327645 327653 327658 327663) (-240 "E04FDFA.spad" 327622 327630 327635 327640) (-239 "E04DGFA.spad" 327599 327607 327612 327617) (-238 "E04AGNT.spad" 323441 323449 327589 327594) (-237 "DVARCAT.spad" 322505 322515 323431 323436) (-236 "DVARCAT.spad" 321567 321579 322495 322500) (-235 "DSMP.spad" 319287 319301 319306 319433) (-234 "DROPT1.spad" 319004 319014 319277 319282) (-233 "DROPT0.spad" 313885 313893 318994 318999) (-232 "DROPT.spad" 307942 307950 313875 313880) (-231 "DRAWPT.spad" 306097 306105 307932 307937) (-230 "DRAWHACK.spad" 305405 305415 306087 306092) (-229 "DRAWCX.spad" 302847 302855 305395 305400) (-228 "DRAWCURV.spad" 302384 302399 302837 302842) (-227 "DRAWCFUN.spad" 291556 291564 302374 302379) (-226 "DRAW.spad" 284156 284169 291546 291551) (-225 "DQAGG.spad" 282509 282519 284112 284151) (-224 "DPOLCAT.spad" 279189 279205 282377 282504) (-223 "DPOLCAT.spad" 275955 275973 279145 279150) (-222 "DPMO.spad" 269998 270014 270136 270432) (-221 "DPMM.spad" 264054 264072 264179 264475) (-220 "DMP.spad" 261652 261667 261851 261978) (-219 "DLP.spad" 261137 261147 261642 261647) (-218 "DLIST.spad" 259772 259782 260543 260570) (-217 "DLAGG.spad" 258397 258407 259752 259767) (-216 "DIVRING.spad" 257844 257852 258341 258392) (-215 "DIVRING.spad" 257335 257345 257834 257839) (-214 "DISPLAY.spad" 255515 255523 257325 257330) (-213 "DIRPROD2.spad" 254664 254682 255505 255510) (-212 "DIRPROD.spad" 247258 247274 247279 247408) (-211 "DIRPCAT.spad" 246365 246381 247112 247253) (-210 "DIRPCAT.spad" 245212 245230 245961 245966) (-209 "DIOSP.spad" 244037 244045 245202 245207) (-208 "DIOPS.spad" 243158 243168 244005 244032) (-207 "DIOPS.spad" 242265 242277 243114 243119) (-206 "DIFRING.spad" 241557 241565 242245 242260) (-205 "DIFRING.spad" 240857 240867 241547 241552) (-204 "DIFEXT.spad" 240016 240026 240837 240852) (-203 "DIFEXT.spad" 239092 239104 239915 239920) (-202 "DIAGG.spad" 239045 239055 239060 239087) (-201 "DIAGG.spad" 239018 239030 239035 239040) (-200 "DFSFUN.spad" 232426 232434 239008 239013) (-199 "DFLOAT.spad" 231028 231036 232316 232421) (-198 "DFINTTLS.spad" 229237 229253 231018 231023) (-197 "DERHAM.spad" 227147 227179 229217 229232) (-196 "DEQUEUE.spad" 226752 226762 226977 227004) (-195 "DEGRED.spad" 226367 226381 226742 226747) (-194 "DEFINTRF.spad" 223892 223902 226357 226362) (-193 "DEFINTEF.spad" 222388 222404 223882 223887) (-192 "DECIMAL.spad" 220272 220280 220858 220951) (-191 "DDFACT.spad" 218071 218088 220262 220267) (-190 "DBLRESP.spad" 217669 217693 218061 218066) (-189 "DBASE.spad" 216241 216251 217659 217664) (-188 "D03FAFA.spad" 216218 216226 216231 216236) (-187 "D03EEFA.spad" 216195 216203 216208 216213) (-186 "D03AGNT.spad" 215275 215283 216185 216190) (-185 "D02EJFA.spad" 215252 215260 215265 215270) (-184 "D02CJFA.spad" 215229 215237 215242 215247) (-183 "D02BHFA.spad" 215206 215214 215219 215224) (-182 "D02BBFA.spad" 215183 215191 215196 215201) (-181 "D02AGNT.spad" 210129 210137 215173 215178) (-180 "D01WGTS.spad" 208775 208783 210119 210124) (-179 "D01TRNS.spad" 208752 208760 208765 208770) (-178 "D01GBFA.spad" 208729 208737 208742 208747) (-177 "D01FCFA.spad" 208706 208714 208719 208724) (-176 "D01ASFA.spad" 208683 208691 208696 208701) (-175 "D01AQFA.spad" 208660 208668 208673 208678) (-174 "D01APFA.spad" 208637 208645 208650 208655) (-173 "D01ANFA.spad" 208614 208622 208627 208632) (-172 "D01AMFA.spad" 208591 208599 208604 208609) (-171 "D01ALFA.spad" 208568 208576 208581 208586) (-170 "D01AKFA.spad" 208545 208553 208558 208563) (-169 "D01AJFA.spad" 208522 208530 208535 208540) (-168 "D01AGNT.spad" 204991 204999 208512 208517) (-167 "CYCLOTOM.spad" 204497 204505 204981 204986) (-166 "CYCLES.spad" 201329 201337 204487 204492) (-165 "CVMP.spad" 200746 200756 201319 201324) (-164 "CTRIGMNP.spad" 199236 199252 200736 200741) (-163 "CSTTOOLS.spad" 198479 198492 199226 199231) (-162 "CRFP.spad" 192183 192196 198469 198474) (-161 "CRAPACK.spad" 191226 191236 192173 192178) (-160 "CPMATCH.spad" 190820 190835 191151 191156) (-159 "CPIMA.spad" 190525 190544 190810 190815) (-158 "COORDSYS.spad" 185418 185428 190515 190520) (-157 "CONTFRAC.spad" 181030 181040 185320 185413) (-156 "COMRING.spad" 180704 180712 180968 181025) (-155 "COMPPROP.spad" 180302 180310 180694 180699) (-154 "COMPLPAT.spad" 180158 180173 180292 180297) (-153 "COMPLEX2.spad" 179985 179997 180148 180153) (-152 "COMPLEX.spad" 174247 174257 174262 174523) (-151 "COMPFACT.spad" 174099 174113 174237 174242) (-150 "COMPCAT.spad" 172260 172270 173821 174094) (-149 "COMPCAT.spad" 170128 170140 171691 171696) (-148 "COMMUPC.spad" 169874 169892 170118 170123) (-147 "COMMONOP.spad" 169407 169415 169864 169869) (-146 "COMM.spad" 169216 169224 169397 169402) (-145 "COMBOPC.spad" 168121 168129 169206 169211) (-144 "COMBINAT.spad" 166866 166876 168111 168116) (-143 "COMBF.spad" 164234 164250 166856 166861) (-142 "COLOR.spad" 163200 163208 164224 164229) (-141 "CMPLXRT.spad" 162909 162926 163190 163195) (-140 "CLIP.spad" 159001 159009 162899 162904) (-139 "CLIF.spad" 157640 157656 158957 158996) (-138 "CLAGG.spad" 154574 154584 157620 157635) (-137 "CLAGG.spad" 151389 151401 154437 154442) (-136 "CINTSLPE.spad" 150857 150870 151379 151384) (-135 "CHVAR.spad" 148935 148957 150847 150852) (-134 "CHARZ.spad" 148850 148858 148915 148930) (-133 "CHARPOL.spad" 148358 148368 148840 148845) (-132 "CHARNZ.spad" 148111 148119 148338 148353) (-131 "CHAR.spad" 146077 146085 148101 148106) (-130 "CFCAT.spad" 145393 145401 146067 146072) (-129 "CDEN.spad" 144551 144565 145383 145388) (-128 "CCLASS.spad" 142866 142874 144020 144059) (-127 "CARTEN2.spad" 142252 142279 142856 142861) (-126 "CARTEN.spad" 137355 137379 142242 142247) (-125 "CARD.spad" 134644 134652 137329 137350) (-124 "CACHSET.spad" 134266 134274 134634 134639) (-123 "CABMON.spad" 133819 133827 134256 134261) (-122 "BTREE.spad" 133361 133371 133649 133676) (-121 "BTOURN.spad" 132902 132912 133191 133218) (-120 "BTCAT.spad" 132514 132524 132858 132897) (-119 "BTCAT.spad" 132158 132170 132504 132509) (-118 "BTAGG.spad" 131290 131298 132114 132153) (-117 "BTAGG.spad" 130454 130464 131280 131285) (-116 "BSTREE.spad" 129713 129723 130284 130311) (-115 "BRILL.spad" 127908 127919 129703 129708) (-114 "BRAGG.spad" 126979 126989 127888 127903) (-113 "BRAGG.spad" 126024 126036 126935 126940) (-112 "BPADICRT.spad" 124008 124020 124263 124356) (-111 "BPADIC.spad" 123672 123684 123934 124003) (-110 "BOUNDZRO.spad" 123328 123345 123662 123667) (-109 "BOP1.spad" 120706 120716 123284 123289) (-108 "BOP.spad" 116122 116130 120696 120701) (-107 "BOOLEAN.spad" 114980 114988 116112 116117) (-106 "BMODULE.spad" 114692 114704 114948 114975) (-105 "BITS.spad" 114169 114177 114386 114413) (-104 "BINFILE.spad" 113512 113520 114159 114164) (-103 "BINARY.spad" 111405 111413 111982 112075) (-102 "BGAGG.spad" 110835 110845 111373 111400) (-101 "BGAGG.spad" 110285 110297 110825 110830) (-100 "BFUNCT.spad" 109849 109857 110265 110280) (-99 "BEZOUT.spad" 108984 109010 109799 109804) (-98 "BBTREE.spad" 106397 106406 108814 108841) (-97 "BASTYPE.spad" 106070 106077 106387 106392) (-96 "BASTYPE.spad" 105741 105750 106060 106065) (-95 "BALFACT.spad" 105181 105193 105731 105736) (-94 "AUTOMOR.spad" 104628 104637 105161 105176) (-93 "ATTREG.spad" 101348 101355 104380 104623) (-92 "ATTRBUT.spad" 98431 98438 101328 101343) (-91 "ATRIG.spad" 97901 97908 98421 98426) (-90 "ATRIG.spad" 97369 97378 97891 97896) (-89 "ASTACK.spad" 96990 96999 97199 97226) (-88 "ASSOCEQ.spad" 95790 95801 96946 96951) (-87 "ASP9.spad" 94871 94884 95780 95785) (-86 "ASP80.spad" 94193 94206 94861 94866) (-85 "ASP8.spad" 93236 93249 94183 94188) (-84 "ASP78.spad" 92687 92700 93226 93231) (-83 "ASP77.spad" 92056 92069 92677 92682) (-82 "ASP74.spad" 91148 91161 92046 92051) (-81 "ASP73.spad" 90419 90432 91138 91143) (-80 "ASP7.spad" 89579 89592 90409 90414) (-79 "ASP6.spad" 88211 88224 89569 89574) (-78 "ASP55.spad" 86720 86733 88201 88206) (-77 "ASP50.spad" 84537 84550 86710 86715) (-76 "ASP49.spad" 83536 83549 84527 84532) (-75 "ASP42.spad" 81943 81982 83526 83531) (-74 "ASP41.spad" 80522 80561 81933 81938) (-73 "ASP4.spad" 79817 79830 80512 80517) (-72 "ASP35.spad" 78805 78818 79807 79812) (-71 "ASP34.spad" 78106 78119 78795 78800) (-70 "ASP33.spad" 77666 77679 78096 78101) (-69 "ASP31.spad" 76806 76819 77656 77661) (-68 "ASP30.spad" 75698 75711 76796 76801) (-67 "ASP29.spad" 75164 75177 75688 75693) (-66 "ASP28.spad" 66437 66450 75154 75159) (-65 "ASP27.spad" 65334 65347 66427 66432) (-64 "ASP24.spad" 64421 64434 65324 65329) (-63 "ASP20.spad" 63637 63650 64411 64416) (-62 "ASP19.spad" 58323 58336 63627 63632) (-61 "ASP12.spad" 57737 57750 58313 58318) (-60 "ASP10.spad" 57008 57021 57727 57732) (-59 "ASP1.spad" 56389 56402 56998 57003) (-58 "ARRAY2.spad" 55972 55981 56219 56246) (-57 "ARRAY12.spad" 54641 54652 55962 55967) (-56 "ARRAY1.spad" 53776 53785 54047 54074) (-55 "ARR2CAT.spad" 49426 49447 53732 53771) (-54 "ARR2CAT.spad" 45108 45131 49416 49421) (-53 "APPRULE.spad" 44352 44374 45098 45103) (-52 "APPLYORE.spad" 43967 43980 44342 44347) (-51 "ANY1.spad" 43038 43047 43957 43962) (-50 "ANY.spad" 41380 41387 43028 43033) (-49 "ANTISYM.spad" 39819 39835 41360 41375) (-48 "ANON.spad" 39732 39739 39809 39814) (-47 "AN.spad" 38035 38042 39550 39643) (-46 "AMR.spad" 36214 36225 37933 38030) (-45 "AMR.spad" 34230 34243 35951 35956) (-44 "ALIST.spad" 32598 32619 32624 32651) (-43 "ALGSC.spad" 31721 31747 32470 32523) (-42 "ALGPKG.spad" 27430 27441 31677 31682) (-41 "ALGMFACT.spad" 26848 26862 27420 27425) (-40 "ALGMANIP.spad" 24269 24284 26646 26651) (-39 "ALGFF.spad" 22587 22614 22804 22960) (-38 "ALGFACT.spad" 21814 21824 22577 22582) (-37 "ALGEBRA.spad" 21545 21554 21770 21809) (-36 "ALGEBRA.spad" 21308 21319 21535 21540) (-35 "ALAGG.spad" 20992 21013 21264 21303) (-34 "AHYP.spad" 20373 20380 20982 20987) (-33 "AGG.spad" 18672 18679 20353 20368) (-32 "AGG.spad" 16945 16954 18628 18633) (-31 "AF.spad" 15371 15386 16881 16886) (-30 "ACPLOT.spad" 13942 13949 15361 15366) (-29 "ACFS.spad" 11681 11690 13832 13937) (-28 "ACFS.spad" 9518 9529 11671 11676) (-27 "ACF.spad" 6120 6127 9420 9513) (-26 "ACF.spad" 2808 2817 6110 6115) (-25 "ABELSG.spad" 2349 2356 2798 2803) (-24 "ABELSG.spad" 1888 1897 2339 2344) (-23 "ABELMON.spad" 1431 1438 1878 1883) (-22 "ABELMON.spad" 972 981 1421 1426) (-21 "ABELGRP.spad" 544 551 962 967) (-20 "ABELGRP.spad" 114 123 534 539) (-19 "A1AGG.spad" 56 65 70 109) (-18 "A1AGG.spad" 30 41 46 51)) \ No newline at end of file +((-1267 NIL 2456407 2456412 2456417 2456422) (-3 NIL 2456387 2456392 2456397 2456402) (-2 NIL 2456367 2456372 2456377 2456382) (-1 NIL 2456347 2456352 2456357 2456362) (0 NIL 2456327 2456332 2456337 2456342) (-1262 "bookvol10.3.pamphlet" 2456136 2456149 2456265 2456322) (-1261 "bookvol10.4.pamphlet" 2455180 2455191 2456126 2456131) (-1260 "bookvol10.4.pamphlet" 2445420 2445442 2455170 2455175) (-1259 "bookvol10.4.pamphlet" 2444913 2444924 2445410 2445415) (-1258 "bookvol10.3.pamphlet" 2444148 2444168 2444769 2444838) (-1257 "bookvol10.3.pamphlet" 2441877 2441890 2443866 2443965) (-1256 "bookvol10.3.pamphlet" 2441447 2441458 2441733 2441802) (-1255 "bookvol10.2.pamphlet" 2440764 2440780 2441373 2441442) (-1254 "bookvol10.3.pamphlet" 2439261 2439281 2440544 2440613) (-1253 "bookvol10.2.pamphlet" 2437721 2437736 2439163 2439256) (-1252 NIL 2436161 2436178 2437605 2437610) (-1251 "bookvol10.2.pamphlet" 2433186 2433202 2436087 2436156) (-1250 "bookvol10.4.pamphlet" 2432497 2432523 2433176 2433181) (-1249 "bookvol10.3.pamphlet" 2432126 2432142 2432353 2432422) (-1248 "bookvol10.2.pamphlet" 2431825 2431836 2432082 2432121) (-1247 "bookvol10.3.pamphlet" 2428099 2428116 2431527 2431554) (-1246 "bookvol10.3.pamphlet" 2427113 2427157 2427957 2428024) (-1245 "bookvol10.4.pamphlet" 2424676 2424698 2427103 2427108) (-1244 "bookvol10.4.pamphlet" 2422882 2422893 2424666 2424671) (-1243 "bookvol10.2.pamphlet" 2422555 2422566 2422850 2422877) (-1242 NIL 2422248 2422261 2422545 2422550) (-1241 "bookvol10.3.pamphlet" 2421838 2421847 2422238 2422243) (-1240 "bookvol10.4.pamphlet" 2419460 2419469 2421828 2421833) (-1239 "bookvol10.4.pamphlet" 2414657 2414666 2419450 2419455) (-1238 "bookvol10.3.pamphlet" 2398411 2398420 2414647 2414652) (-1237 "bookvol10.3.pamphlet" 2386148 2386157 2398401 2398406) (-1236 "bookvol10.3.pamphlet" 2385046 2385057 2385297 2385324) (-1235 "bookvol10.4.pamphlet" 2383688 2383701 2385036 2385041) (-1234 "bookvol10.2.pamphlet" 2381576 2381587 2383644 2383683) (-1233 NIL 2379284 2379297 2381354 2381359) (-1232 "bookvol10.3.pamphlet" 2379064 2379079 2379274 2379279) (-1231 "bookvol10.3.pamphlet" 2374248 2374270 2377531 2377628) (-1230 "bookvol10.4.pamphlet" 2374151 2374179 2374238 2374243) (-1229 "bookvol10.4.pamphlet" 2373459 2373483 2374107 2374112) (-1228 "bookvol10.4.pamphlet" 2371611 2371631 2373449 2373454) (-1227 "bookvol10.3.pamphlet" 2366400 2366428 2370078 2370175) (-1226 "bookvol10.2.pamphlet" 2363851 2363867 2366298 2366395) (-1225 NIL 2360946 2360964 2363395 2363400) (-1224 "bookvol10.4.pamphlet" 2360569 2360604 2360936 2360941) (-1223 "bookvol10.2.pamphlet" 2355167 2355178 2360549 2360564) (-1222 NIL 2349739 2349752 2355123 2355128) (-1221 "bookvol10.3.pamphlet" 2347382 2347408 2348820 2348953) (-1220 "bookvol10.3.pamphlet" 2344517 2344545 2345514 2345663) (-1219 "bookvol10.3.pamphlet" 2342274 2342294 2342649 2342798) (-1218 "bookvol10.2.pamphlet" 2340732 2340752 2342120 2342269) (-1217 NIL 2339332 2339354 2340722 2340727) (-1216 "bookvol10.2.pamphlet" 2337913 2337929 2339178 2339327) (-1215 "bookvol10.4.pamphlet" 2337454 2337507 2337903 2337908) (-1214 "bookvol10.4.pamphlet" 2335866 2335880 2337444 2337449) (-1213 "bookvol10.2.pamphlet" 2333446 2333470 2335764 2335861) (-1212 NIL 2330732 2330758 2333052 2333057) (-1211 "bookvol10.2.pamphlet" 2325706 2325717 2330574 2330727) (-1210 NIL 2320572 2320585 2325442 2325447) (-1209 "bookvol10.4.pamphlet" 2320037 2320056 2320562 2320567) (-1208 "bookvol10.3.pamphlet" 2316988 2317003 2317587 2317740) (-1207 "bookvol10.4.pamphlet" 2315878 2315891 2316978 2316983) (-1206 "bookvol10.4.pamphlet" 2315441 2315455 2315868 2315873) (-1205 "bookvol10.4.pamphlet" 2313678 2313692 2315431 2315436) (-1204 "bookvol10.4.pamphlet" 2312885 2312901 2313668 2313673) (-1203 "bookvol10.4.pamphlet" 2312247 2312268 2312875 2312880) (-1202 "bookvol10.3.pamphlet" 2311600 2311611 2312166 2312171) (-1201 "bookvol10.4.pamphlet" 2311093 2311106 2311556 2311561) (-1200 "bookvol10.4.pamphlet" 2310194 2310206 2311083 2311088) (-1199 "bookvol10.3.pamphlet" 2300854 2300882 2301839 2302268) (-1198 "bookvol10.3.pamphlet" 2294891 2294911 2295263 2295412) (-1197 "bookvol10.2.pamphlet" 2292484 2292504 2294711 2294886) (-1196 NIL 2290211 2290233 2292440 2292445) (-1195 "bookvol10.2.pamphlet" 2288427 2288443 2290057 2290206) (-1194 "bookvol10.4.pamphlet" 2287969 2288022 2288417 2288422) (-1193 "bookvol10.3.pamphlet" 2286362 2286378 2286436 2286533) (-1192 "bookvol10.4.pamphlet" 2286277 2286293 2286352 2286357) (-1191 "bookvol10.2.pamphlet" 2285342 2285351 2286203 2286272) (-1190 NIL 2284469 2284480 2285332 2285337) (-1189 "bookvol10.4.pamphlet" 2283316 2283325 2284459 2284464) (-1188 "bookvol10.4.pamphlet" 2280802 2280813 2283272 2283277) (-1187 "bookvol10.2.pamphlet" 2280724 2280733 2280782 2280797) (-1186 "bookvol10.4.pamphlet" 2279374 2279389 2280714 2280719) (-1185 "bookvol10.3.pamphlet" 2278277 2278288 2279329 2279334) (-1184 "bookvol10.4.pamphlet" 2275111 2275120 2278267 2278272) (-1183 "bookvol10.3.pamphlet" 2273767 2273784 2275101 2275106) (-1182 "bookvol10.3.pamphlet" 2272356 2272372 2273332 2273429) (-1181 "bookvol10.2.pamphlet" 2259666 2259683 2272312 2272351) (-1180 NIL 2246974 2246993 2259622 2259627) (-1179 "bookvol10.4.pamphlet" 2241340 2241357 2246680 2246685) (-1178 "bookvol10.4.pamphlet" 2240299 2240324 2241330 2241335) (-1177 "bookvol10.4.pamphlet" 2238816 2238833 2240289 2240294) (-1176 "bookvol10.2.pamphlet" 2238328 2238337 2238806 2238811) (-1175 NIL 2237838 2237849 2238318 2238323) (-1174 "bookvol10.3.pamphlet" 2235887 2235898 2237668 2237695) (-1173 "bookvol10.2.pamphlet" 2235718 2235727 2235877 2235882) (-1172 NIL 2235547 2235558 2235708 2235713) (-1171 "bookvol10.4.pamphlet" 2235221 2235230 2235537 2235542) (-1170 "bookvol10.4.pamphlet" 2234884 2234895 2235211 2235216) (-1169 "bookvol10.3.pamphlet" 2233441 2233450 2234874 2234879) (-1168 "bookvol10.3.pamphlet" 2230458 2230467 2233431 2233436) (-1167 "bookvol10.4.pamphlet" 2230014 2230025 2230448 2230453) (-1166 "bookvol10.4.pamphlet" 2229569 2229578 2230004 2230009) (-1165 "bookvol10.4.pamphlet" 2227662 2227685 2229559 2229564) (-1164 "bookvol10.2.pamphlet" 2226509 2226532 2227630 2227657) (-1163 NIL 2225376 2225401 2226499 2226504) (-1162 "bookvol10.4.pamphlet" 2224752 2224763 2225366 2225371) (-1161 "bookvol10.3.pamphlet" 2223725 2223748 2223995 2224022) (-1160 "bookvol10.3.pamphlet" 2223221 2223232 2223715 2223720) (-1159 "bookvol10.4.pamphlet" 2220073 2220084 2223211 2223216) (-1158 "bookvol10.4.pamphlet" 2216666 2216677 2220063 2220068) (-1157 "bookvol10.3.pamphlet" 2214719 2214728 2216656 2216661) (-1156 "bookvol10.3.pamphlet" 2210704 2210713 2214709 2214714) (-1155 "bookvol10.3.pamphlet" 2209711 2209722 2209793 2209920) (-1154 "bookvol10.4.pamphlet" 2209186 2209197 2209701 2209706) (-1153 "bookvol10.3.pamphlet" 2206514 2206523 2209176 2209181) (-1152 "bookvol10.3.pamphlet" 2203270 2203279 2206504 2206509) (-1151 "bookvol10.3.pamphlet" 2200277 2200305 2201737 2201834) (-1150 "bookvol10.3.pamphlet" 2197399 2197427 2198409 2198558) (-1149 "bookvol10.3.pamphlet" 2194082 2194093 2194949 2195102) (-1148 "bookvol10.4.pamphlet" 2193202 2193220 2194072 2194077) (-1147 "bookvol10.3.pamphlet" 2190646 2190657 2190715 2190868) (-1146 "bookvol10.4.pamphlet" 2190036 2190049 2190636 2190641) (-1145 "bookvol10.4.pamphlet" 2188514 2188525 2190026 2190031) (-1144 "bookvol10.4.pamphlet" 2188140 2188157 2188504 2188509) (-1143 "bookvol10.3.pamphlet" 2178787 2178815 2179785 2180214) (-1142 "bookvol10.3.pamphlet" 2178467 2178482 2178777 2178782) (-1141 "bookvol10.3.pamphlet" 2170438 2170453 2178457 2178462) (-1140 "bookvol10.4.pamphlet" 2169610 2169624 2170394 2170399) (-1139 "bookvol10.4.pamphlet" 2165709 2165725 2169600 2169605) (-1138 "bookvol10.4.pamphlet" 2162177 2162193 2165699 2165704) (-1137 "bookvol10.4.pamphlet" 2154577 2154588 2162058 2162063) (-1136 "bookvol10.3.pamphlet" 2153656 2153673 2153805 2153832) (-1135 "bookvol10.3.pamphlet" 2153039 2153048 2153137 2153164) (-1134 "bookvol10.2.pamphlet" 2152815 2152824 2152995 2153034) (-1133 "bookvol10.3.pamphlet" 2147763 2147774 2152563 2152578) (-1132 "bookvol10.4.pamphlet" 2146974 2146989 2147753 2147758) (-1131 "bookvol10.4.pamphlet" 2145183 2145196 2146964 2146969) (-1130 "bookvol10.4.pamphlet" 2144607 2144618 2145173 2145178) (-1129 "bookvol10.4.pamphlet" 2143513 2143529 2144597 2144602) (-1128 "bookvol10.2.pamphlet" 2142719 2142728 2143503 2143508) (-1127 "bookvol10.3.pamphlet" 2141807 2141835 2141974 2141989) (-1126 "bookvol10.2.pamphlet" 2140864 2140875 2141787 2141802) (-1125 NIL 2139929 2139942 2140854 2140859) (-1124 "bookvol10.3.pamphlet" 2135554 2135565 2139759 2139786) (-1123 "bookvol10.3.pamphlet" 2133597 2133614 2135256 2135283) (-1122 "bookvol10.4.pamphlet" 2132324 2132344 2133587 2133592) (-1121 "bookvol10.2.pamphlet" 2127367 2127376 2132280 2132319) (-1120 NIL 2122442 2122453 2127357 2127362) (-1119 "bookvol10.3.pamphlet" 2120122 2120140 2121030 2121117) (-1118 "bookvol10.3.pamphlet" 2114989 2115002 2119873 2119900) (-1117 "bookvol10.3.pamphlet" 2111529 2111542 2114979 2114984) (-1116 "bookvol10.2.pamphlet" 2110306 2110315 2111519 2111524) (-1115 "bookvol10.4.pamphlet" 2108871 2108880 2110296 2110301) (-1114 "bookvol10.2.pamphlet" 2092698 2092709 2108861 2108866) (-1113 "bookvol10.3.pamphlet" 2092474 2092485 2092688 2092693) (-1112 "bookvol10.4.pamphlet" 2092019 2092032 2092430 2092435) (-1111 "bookvol10.4.pamphlet" 2089612 2089623 2092009 2092014) (-1110 "bookvol10.4.pamphlet" 2088177 2088188 2089602 2089607) (-1109 "bookvol10.4.pamphlet" 2081604 2081615 2088167 2088172) (-1108 "bookvol10.4.pamphlet" 2080024 2080042 2081594 2081599) (-1107 "bookvol10.2.pamphlet" 2079791 2079808 2079980 2080019) (-1106 "bookvol10.3.pamphlet" 2077907 2077933 2079356 2079453) (-1105 "bookvol10.3.pamphlet" 2075361 2075381 2075736 2075863) (-1104 "bookvol10.4.pamphlet" 2074204 2074229 2075351 2075356) (-1103 "bookvol10.2.pamphlet" 2072302 2072332 2074136 2074199) (-1102 NIL 2070344 2070376 2072180 2072185) (-1101 "bookvol10.2.pamphlet" 2068782 2068793 2070300 2070339) (-1100 "bookvol10.3.pamphlet" 2067147 2067156 2068648 2068777) (-1099 "bookvol10.4.pamphlet" 2066890 2066899 2067137 2067142) (-1098 "bookvol10.4.pamphlet" 2065998 2066009 2066880 2066885) (-1097 "bookvol10.4.pamphlet" 2065267 2065284 2065988 2065993) (-1096 "bookvol10.4.pamphlet" 2063137 2063152 2065223 2065228) (-1095 "bookvol10.3.pamphlet" 2054850 2054877 2055352 2055483) (-1094 "bookvol10.2.pamphlet" 2054085 2054094 2054840 2054845) (-1093 NIL 2053318 2053329 2054075 2054080) (-1092 "bookvol10.4.pamphlet" 2046344 2046353 2053308 2053313) (-1091 "bookvol10.2.pamphlet" 2045823 2045840 2046300 2046339) (-1090 "bookvol10.4.pamphlet" 2045522 2045542 2045813 2045818) (-1089 "bookvol10.4.pamphlet" 2040847 2040867 2045512 2045517) (-1088 "bookvol10.3.pamphlet" 2040282 2040296 2040837 2040842) (-1087 "bookvol10.3.pamphlet" 2040125 2040165 2040272 2040277) (-1086 "bookvol10.3.pamphlet" 2040017 2040026 2040115 2040120) (-1085 "bookvol10.2.pamphlet" 2037106 2037146 2040007 2040012) (-1084 "bookvol10.3.pamphlet" 2035416 2035427 2036583 2036622) (-1083 "bookvol10.3.pamphlet" 2033834 2033851 2035406 2035411) (-1082 "bookvol10.2.pamphlet" 2033316 2033325 2033824 2033829) (-1081 NIL 2032796 2032807 2033306 2033311) (-1080 "bookvol10.2.pamphlet" 2032685 2032694 2032786 2032791) (-1079 "bookvol10.2.pamphlet" 2029173 2029184 2032653 2032680) (-1078 NIL 2025681 2025694 2029163 2029168) (-1077 "bookvol10.2.pamphlet" 2024793 2024806 2025661 2025676) (-1076 "bookvol10.3.pamphlet" 2024606 2024617 2024712 2024717) (-1075 "bookvol10.2.pamphlet" 2023412 2023423 2024586 2024601) (-1074 "bookvol10.3.pamphlet" 2022484 2022495 2023367 2023372) (-1073 "bookvol10.4.pamphlet" 2022180 2022193 2022474 2022479) (-1072 "bookvol10.4.pamphlet" 2021605 2021618 2022136 2022141) (-1071 "bookvol10.3.pamphlet" 2020881 2020892 2021595 2021600) (-1070 "bookvol10.3.pamphlet" 2018283 2018294 2018562 2018689) (-1069 "bookvol10.4.pamphlet" 2016362 2016373 2018273 2018278) (-1068 "bookvol10.4.pamphlet" 2015243 2015254 2016352 2016357) (-1067 "bookvol10.3.pamphlet" 2015115 2015124 2015233 2015238) (-1066 "bookvol10.4.pamphlet" 2014828 2014848 2015105 2015110) (-1065 "bookvol10.3.pamphlet" 2012949 2012965 2013614 2013749) (-1064 "bookvol10.4.pamphlet" 2012650 2012670 2012939 2012944) (-1063 "bookvol10.4.pamphlet" 2010336 2010352 2012640 2012645) (-1062 "bookvol10.3.pamphlet" 2009738 2009762 2010326 2010331) (-1061 "bookvol10.3.pamphlet" 2008082 2008106 2009728 2009733) (-1060 "bookvol10.3.pamphlet" 2007934 2007947 2008072 2008077) (-1059 "bookvol10.4.pamphlet" 2005002 2005022 2007924 2007929) (-1058 "bookvol10.2.pamphlet" 1995462 1995479 2004958 2004997) (-1057 NIL 1985954 1985973 1995452 1995457) (-1056 "bookvol10.4.pamphlet" 1984588 1984608 1985944 1985949) (-1055 "bookvol10.2.pamphlet" 1982972 1983002 1984578 1984583) (-1054 NIL 1981354 1981386 1982962 1982967) (-1053 "bookvol10.2.pamphlet" 1960670 1960685 1981222 1981349) (-1052 NIL 1939700 1939717 1960254 1960259) (-1051 "bookvol10.3.pamphlet" 1936145 1936154 1938929 1938956) (-1050 "bookvol10.3.pamphlet" 1935392 1935401 1936011 1936140) (-1049 NIL 1934472 1934504 1935382 1935387) (-1048 "bookvol10.2.pamphlet" 1933375 1933384 1934374 1934467) (-1047 NIL 1932364 1932375 1933365 1933370) (-1046 "bookvol10.2.pamphlet" 1931886 1931895 1932354 1932359) (-1045 "bookvol10.2.pamphlet" 1931363 1931374 1931876 1931881) (-1044 "bookvol10.4.pamphlet" 1930771 1930828 1931353 1931358) (-1043 "bookvol10.3.pamphlet" 1929506 1929525 1929994 1930033) (-1042 "bookvol10.2.pamphlet" 1925023 1925054 1929450 1929501) (-1041 NIL 1920442 1920475 1924871 1924876) (-1040 "bookvol10.4.pamphlet" 1920330 1920350 1920432 1920437) (-1039 "bookvol10.2.pamphlet" 1919683 1919692 1920310 1920325) (-1038 NIL 1919044 1919055 1919673 1919678) (-1037 "bookvol10.4.pamphlet" 1917938 1917947 1919034 1919039) (-1036 "bookvol10.3.pamphlet" 1916603 1916619 1917498 1917525) (-1035 "bookvol10.4.pamphlet" 1914645 1914656 1916593 1916598) (-1034 "bookvol10.4.pamphlet" 1912259 1912270 1914635 1914640) (-1033 "bookvol10.4.pamphlet" 1911721 1911732 1912249 1912254) (-1032 "bookvol10.4.pamphlet" 1911456 1911468 1911711 1911716) (-1031 "bookvol10.4.pamphlet" 1910444 1910453 1911446 1911451) (-1030 "bookvol10.4.pamphlet" 1909861 1909874 1910434 1910439) (-1029 "bookvol10.2.pamphlet" 1909210 1909221 1909851 1909856) (-1028 NIL 1908557 1908570 1909200 1909205) (-1027 "bookvol10.3.pamphlet" 1907199 1907208 1907786 1907813) (-1026 "bookvol10.3.pamphlet" 1906546 1906593 1907137 1907194) (-1025 "bookvol10.4.pamphlet" 1905870 1905881 1906536 1906541) (-1024 "bookvol10.4.pamphlet" 1905599 1905610 1905860 1905865) (-1023 "bookvol10.4.pamphlet" 1903151 1903160 1905589 1905594) (-1022 "bookvol10.4.pamphlet" 1902856 1902867 1903141 1903146) (-1021 "bookvol10.4.pamphlet" 1892298 1892309 1902698 1902703) (-1020 "bookvol10.4.pamphlet" 1886274 1886285 1892248 1892253) (-1019 "bookvol10.3.pamphlet" 1884365 1884382 1885976 1886003) (-1018 "bookvol10.3.pamphlet" 1883709 1883720 1884320 1884325) (-1017 "bookvol10.4.pamphlet" 1882885 1882902 1883699 1883704) (-1016 "bookvol10.4.pamphlet" 1881182 1881199 1882840 1882845) (-1015 "bookvol10.3.pamphlet" 1879965 1879985 1880669 1880762) (-1014 "bookvol10.4.pamphlet" 1878420 1878429 1879955 1879960) (-1013 "bookvol10.2.pamphlet" 1878292 1878301 1878410 1878415) (-1012 "bookvol10.4.pamphlet" 1875589 1875604 1878282 1878287) (-1011 "bookvol10.4.pamphlet" 1872432 1872447 1875579 1875584) (-1010 "bookvol10.4.pamphlet" 1872177 1872202 1872422 1872427) (-1009 "bookvol10.4.pamphlet" 1871740 1871751 1872167 1872172) (-1008 "bookvol10.4.pamphlet" 1870640 1870658 1871730 1871735) (-1007 "bookvol10.4.pamphlet" 1868845 1868863 1870630 1870635) (-1006 "bookvol10.4.pamphlet" 1868070 1868087 1868835 1868840) (-1005 "bookvol10.4.pamphlet" 1867220 1867237 1868060 1868065) (-1004 "bookvol10.2.pamphlet" 1864403 1864412 1867122 1867215) (-1003 NIL 1861672 1861683 1864393 1864398) (-1002 "bookvol10.2.pamphlet" 1859581 1859592 1861652 1861667) (-1001 NIL 1857427 1857440 1859500 1859505) (-1000 "bookvol10.4.pamphlet" 1856844 1856855 1857417 1857422) (-999 "bookvol10.4.pamphlet" 1856029 1856040 1856834 1856839) (-998 "bookvol10.4.pamphlet" 1855387 1855395 1856019 1856024) (-997 "bookvol10.4.pamphlet" 1855142 1855150 1855377 1855382) (-996 "bookvol10.3.pamphlet" 1851928 1851941 1853609 1853702) (-995 "bookvol10.3.pamphlet" 1850342 1850378 1850460 1850616) (-994 "bookvol10.2.pamphlet" 1849936 1849944 1850332 1850337) (-993 NIL 1849528 1849538 1849926 1849931) (-992 "bookvol10.3.pamphlet" 1844918 1844928 1849358 1849385) (-991 "bookvol10.3.pamphlet" 1843545 1843555 1843842 1843907) (-990 "bookvol10.4.pamphlet" 1842868 1842886 1843535 1843540) (-989 "bookvol10.2.pamphlet" 1841029 1841039 1842798 1842863) (-988 NIL 1838941 1838953 1840712 1840717) (-987 "bookvol10.2.pamphlet" 1837747 1837757 1838897 1838936) (-986 "bookvol10.3.pamphlet" 1837210 1837224 1837737 1837742) (-985 "bookvol10.2.pamphlet" 1835901 1835911 1837100 1837205) (-984 NIL 1834195 1834207 1835396 1835401) (-983 "bookvol10.4.pamphlet" 1833886 1833902 1834185 1834190) (-982 "bookvol10.3.pamphlet" 1833443 1833451 1833876 1833881) (-981 "bookvol10.4.pamphlet" 1828845 1828864 1833433 1833438) (-980 "bookvol10.3.pamphlet" 1824920 1824952 1828759 1828764) (-979 "bookvol10.4.pamphlet" 1822916 1822934 1824910 1824915) (-978 "bookvol10.4.pamphlet" 1820226 1820247 1822906 1822911) (-977 "bookvol10.4.pamphlet" 1819553 1819572 1820216 1820221) (-976 "bookvol10.2.pamphlet" 1815679 1815689 1819543 1819548) (-975 "bookvol10.4.pamphlet" 1812763 1812773 1815669 1815674) (-974 "bookvol10.4.pamphlet" 1812580 1812594 1812753 1812758) (-973 "bookvol10.2.pamphlet" 1811662 1811672 1812536 1812575) (-972 "bookvol10.4.pamphlet" 1810969 1810993 1811652 1811657) (-971 "bookvol10.4.pamphlet" 1809827 1809837 1810959 1810964) (-970 "bookvol10.4.pamphlet" 1795228 1795244 1809705 1809710) (-969 "bookvol10.2.pamphlet" 1789121 1789144 1795196 1795223) (-968 NIL 1783000 1783025 1789077 1789082) (-967 "bookvol10.2.pamphlet" 1781983 1781991 1782990 1782995) (-966 "bookvol10.2.pamphlet" 1780746 1780775 1781881 1781978) (-965 NIL 1779599 1779630 1780736 1780741) (-964 "bookvol10.3.pamphlet" 1778414 1778422 1779589 1779594) (-963 "bookvol10.2.pamphlet" 1775747 1775757 1778404 1778409) (-962 "bookvol10.4.pamphlet" 1765892 1765909 1775703 1775708) (-961 "bookvol10.2.pamphlet" 1765311 1765321 1765848 1765887) (-960 "bookvol10.3.pamphlet" 1765193 1765209 1765301 1765306) (-959 "bookvol10.3.pamphlet" 1765081 1765091 1765183 1765188) (-958 "bookvol10.3.pamphlet" 1764969 1764979 1765071 1765076) (-957 "bookvol10.3.pamphlet" 1762370 1762382 1762935 1762990) (-956 "bookvol10.3.pamphlet" 1760756 1760768 1761461 1761588) (-955 "bookvol10.4.pamphlet" 1759960 1759999 1760746 1760751) (-954 "bookvol10.4.pamphlet" 1759712 1759720 1759950 1759955) (-953 "bookvol10.4.pamphlet" 1757955 1757965 1759702 1759707) (-952 "bookvol10.4.pamphlet" 1755928 1755942 1757945 1757950) (-951 "bookvol10.2.pamphlet" 1755551 1755559 1755918 1755923) (-950 "bookvol10.3.pamphlet" 1754794 1754804 1754957 1754984) (-949 "bookvol10.4.pamphlet" 1752686 1752698 1754784 1754789) (-948 "bookvol10.4.pamphlet" 1752058 1752070 1752676 1752681) (-947 "bookvol10.2.pamphlet" 1751195 1751203 1752048 1752053) (-946 "bookvol10.4.pamphlet" 1749967 1749989 1751151 1751156) (-945 "bookvol10.3.pamphlet" 1747279 1747289 1747781 1747908) (-944 "bookvol10.4.pamphlet" 1746540 1746563 1747269 1747274) (-943 "bookvol10.4.pamphlet" 1744604 1744626 1746530 1746535) (-942 "bookvol10.2.pamphlet" 1738006 1738027 1744472 1744599) (-941 NIL 1730710 1730733 1737178 1737183) (-940 "bookvol10.4.pamphlet" 1730158 1730172 1730700 1730705) (-939 "bookvol10.4.pamphlet" 1729768 1729780 1730148 1730153) (-938 "bookvol10.4.pamphlet" 1728709 1728738 1729724 1729729) (-937 "bookvol10.4.pamphlet" 1727457 1727472 1728699 1728704) (-936 "bookvol10.3.pamphlet" 1726519 1726529 1726606 1726633) (-935 "bookvol10.4.pamphlet" 1723159 1723167 1726509 1726514) (-934 "bookvol10.4.pamphlet" 1721916 1721930 1723149 1723154) (-933 "bookvol10.4.pamphlet" 1721461 1721471 1721906 1721911) (-932 "bookvol10.4.pamphlet" 1721048 1721062 1721451 1721456) (-931 "bookvol10.4.pamphlet" 1720574 1720588 1721038 1721043) (-930 "bookvol10.4.pamphlet" 1720075 1720097 1720564 1720569) (-929 "bookvol10.4.pamphlet" 1719145 1719163 1720007 1720012) (-928 "bookvol10.4.pamphlet" 1718726 1718740 1719135 1719140) (-927 "bookvol10.4.pamphlet" 1718293 1718305 1718716 1718721) (-926 "bookvol10.4.pamphlet" 1717869 1717879 1718283 1718288) (-925 "bookvol10.4.pamphlet" 1717442 1717460 1717859 1717864) (-924 "bookvol10.4.pamphlet" 1716724 1716738 1717432 1717437) (-923 "bookvol10.4.pamphlet" 1715793 1715801 1716714 1716719) (-922 "bookvol10.4.pamphlet" 1714819 1714835 1715783 1715788) (-921 "bookvol10.4.pamphlet" 1713717 1713755 1714809 1714814) (-920 "bookvol10.4.pamphlet" 1713497 1713505 1713707 1713712) (-919 "bookvol10.3.pamphlet" 1708169 1708177 1713487 1713492) (-918 "bookvol10.3.pamphlet" 1704571 1704579 1708159 1708164) (-917 "bookvol10.4.pamphlet" 1703704 1703714 1704561 1704566) (-916 "bookvol10.4.pamphlet" 1689661 1689688 1703694 1703699) (-915 "bookvol10.3.pamphlet" 1689568 1689582 1689651 1689656) (-914 "bookvol10.3.pamphlet" 1689479 1689489 1689558 1689563) (-913 "bookvol10.3.pamphlet" 1689390 1689400 1689469 1689474) (-912 "bookvol10.2.pamphlet" 1688418 1688432 1689380 1689385) (-911 "bookvol10.4.pamphlet" 1688034 1688053 1688408 1688413) (-910 "bookvol10.4.pamphlet" 1687816 1687832 1688024 1688029) (-909 "bookvol10.3.pamphlet" 1687438 1687446 1687790 1687811) (-908 "bookvol10.2.pamphlet" 1686394 1686402 1687364 1687433) (-907 "bookvol10.4.pamphlet" 1686123 1686133 1686384 1686389) (-906 "bookvol10.4.pamphlet" 1684735 1684749 1686113 1686118) (-905 "bookvol10.4.pamphlet" 1676101 1676109 1684725 1684730) (-904 "bookvol10.4.pamphlet" 1674651 1674668 1676091 1676096) (-903 "bookvol10.4.pamphlet" 1673666 1673676 1674641 1674646) (-902 "bookvol10.3.pamphlet" 1669034 1669044 1673568 1673661) (-901 "bookvol10.4.pamphlet" 1668389 1668405 1669024 1669029) (-900 "bookvol10.4.pamphlet" 1666424 1666453 1668379 1668384) (-899 "bookvol10.4.pamphlet" 1665794 1665812 1666414 1666419) (-898 "bookvol10.4.pamphlet" 1665213 1665240 1665784 1665789) (-897 "bookvol10.3.pamphlet" 1664880 1664892 1665018 1665111) (-896 "bookvol10.2.pamphlet" 1662546 1662554 1664806 1664875) (-895 NIL 1660240 1660250 1662502 1662507) (-894 "bookvol10.4.pamphlet" 1658125 1658137 1660230 1660235) (-893 "bookvol10.4.pamphlet" 1655725 1655748 1658115 1658120) (-892 "bookvol10.3.pamphlet" 1650711 1650721 1655555 1655570) (-891 "bookvol10.3.pamphlet" 1645401 1645411 1650701 1650706) (-890 "bookvol10.2.pamphlet" 1643954 1643964 1645381 1645396) (-889 "bookvol10.4.pamphlet" 1642617 1642631 1643944 1643949) (-888 "bookvol10.3.pamphlet" 1641887 1641897 1642469 1642474) (-887 "bookvol10.2.pamphlet" 1640181 1640191 1641867 1641882) (-886 NIL 1638483 1638495 1640171 1640176) (-885 "bookvol10.3.pamphlet" 1636588 1636596 1638473 1638478) (-884 "bookvol10.4.pamphlet" 1630380 1630388 1636578 1636583) (-883 "bookvol10.4.pamphlet" 1629680 1629697 1630370 1630375) (-882 "bookvol10.2.pamphlet" 1627824 1627832 1629670 1629675) (-881 "bookvol10.4.pamphlet" 1627513 1627526 1627814 1627819) (-880 "bookvol10.3.pamphlet" 1626155 1626172 1627503 1627508) (-879 "bookvol10.3.pamphlet" 1620586 1620596 1626145 1626150) (-878 "bookvol10.4.pamphlet" 1620323 1620335 1620576 1620581) (-877 "bookvol10.4.pamphlet" 1618613 1618629 1620313 1620318) (-876 "bookvol10.3.pamphlet" 1616152 1616164 1618603 1618608) (-875 "bookvol10.4.pamphlet" 1615806 1615820 1616142 1616147) (-874 "bookvol10.4.pamphlet" 1613963 1613994 1615514 1615519) (-873 "bookvol10.2.pamphlet" 1613388 1613398 1613953 1613958) (-872 "bookvol10.3.pamphlet" 1612472 1612486 1613378 1613383) (-871 "bookvol10.2.pamphlet" 1612236 1612246 1612462 1612467) (-870 "bookvol10.4.pamphlet" 1609598 1609606 1612226 1612231) (-869 "bookvol10.3.pamphlet" 1609026 1609054 1609588 1609593) (-868 "bookvol10.4.pamphlet" 1608817 1608833 1609016 1609021) (-867 "bookvol10.3.pamphlet" 1608245 1608273 1608807 1608812) (-866 "bookvol10.4.pamphlet" 1608030 1608046 1608235 1608240) (-865 "bookvol10.3.pamphlet" 1607488 1607516 1608020 1608025) (-864 "bookvol10.4.pamphlet" 1607273 1607289 1607478 1607483) (-863 "bookvol10.4.pamphlet" 1606064 1606113 1607263 1607268) (-862 "bookvol10.4.pamphlet" 1605476 1605484 1606054 1606059) (-861 "bookvol10.3.pamphlet" 1604446 1604454 1605466 1605471) (-860 "bookvol10.4.pamphlet" 1598829 1598852 1604402 1604407) (-859 "bookvol10.4.pamphlet" 1592648 1592671 1598778 1598783) (-858 "bookvol10.3.pamphlet" 1589978 1589996 1591153 1591246) (-857 "bookvol10.3.pamphlet" 1587993 1588005 1588214 1588307) (-856 "bookvol10.3.pamphlet" 1587688 1587700 1587919 1587988) (-855 "bookvol10.2.pamphlet" 1586244 1586256 1587614 1587683) (-854 "bookvol10.4.pamphlet" 1585173 1585192 1586234 1586239) (-853 "bookvol10.4.pamphlet" 1584154 1584170 1585163 1585168) (-852 "bookvol10.3.pamphlet" 1582755 1582763 1583825 1583918) (-851 "bookvol10.2.pamphlet" 1581505 1581513 1582657 1582750) (-850 "bookvol10.2.pamphlet" 1579568 1579576 1581407 1581500) (-849 "bookvol10.3.pamphlet" 1578293 1578303 1579364 1579457) (-848 "bookvol10.2.pamphlet" 1577046 1577054 1578195 1578288) (-847 "bookvol10.3.pamphlet" 1575351 1575371 1576436 1576529) (-846 "bookvol10.2.pamphlet" 1574093 1574101 1575253 1575346) (-845 "bookvol10.3.pamphlet" 1573077 1573107 1573951 1574018) (-844 "bookvol10.3.pamphlet" 1572858 1572881 1573067 1573072) (-843 "bookvol10.4.pamphlet" 1571942 1571950 1572848 1572853) (-842 "bookvol10.3.pamphlet" 1561356 1561364 1571932 1571937) (-841 "bookvol10.3.pamphlet" 1560945 1560953 1561346 1561351) (-840 "bookvol10.4.pamphlet" 1559406 1559416 1560862 1560867) (-839 "bookvol10.3.pamphlet" 1558764 1558792 1559086 1559125) (-838 "bookvol10.3.pamphlet" 1558063 1558087 1558444 1558483) (-837 "bookvol10.4.pamphlet" 1555897 1555909 1557983 1557988) (-836 "bookvol10.2.pamphlet" 1550043 1550053 1555853 1555892) (-835 NIL 1544079 1544091 1549891 1549896) (-834 "bookvol10.2.pamphlet" 1543245 1543253 1544069 1544074) (-833 NIL 1542409 1542419 1543235 1543240) (-832 "bookvol10.2.pamphlet" 1541743 1541751 1542389 1542404) (-831 NIL 1541085 1541095 1541733 1541738) (-830 "bookvol10.2.pamphlet" 1540839 1540847 1541075 1541080) (-829 "bookvol10.4.pamphlet" 1539980 1539996 1540829 1540834) (-828 "bookvol10.2.pamphlet" 1539914 1539922 1539970 1539975) (-827 "bookvol10.3.pamphlet" 1538400 1538410 1539461 1539490) (-826 "bookvol10.4.pamphlet" 1537740 1537752 1538390 1538395) (-825 "bookvol10.3.pamphlet" 1535424 1535432 1537730 1537735) (-824 "bookvol10.4.pamphlet" 1527608 1527616 1535414 1535419) (-823 "bookvol10.2.pamphlet" 1525074 1525082 1527598 1527603) (-822 "bookvol10.4.pamphlet" 1524623 1524631 1525064 1525069) (-821 "bookvol10.3.pamphlet" 1524365 1524375 1524445 1524512) (-820 "bookvol10.3.pamphlet" 1523139 1523149 1523912 1523941) (-819 "bookvol10.4.pamphlet" 1522612 1522624 1523129 1523134) (-818 "bookvol10.4.pamphlet" 1521614 1521622 1522602 1522607) (-817 "bookvol10.2.pamphlet" 1521390 1521400 1521558 1521609) (-816 "bookvol10.4.pamphlet" 1520002 1520010 1521380 1521385) (-815 "bookvol10.2.pamphlet" 1518967 1518975 1519992 1519997) (-814 "bookvol10.3.pamphlet" 1518392 1518404 1518853 1518892) (-813 "bookvol10.4.pamphlet" 1518226 1518236 1518382 1518387) (-812 "bookvol10.3.pamphlet" 1517769 1517777 1518216 1518221) (-811 "bookvol10.3.pamphlet" 1516803 1516811 1517759 1517764) (-810 "bookvol10.3.pamphlet" 1516147 1516155 1516793 1516798) (-809 "bookvol10.3.pamphlet" 1510436 1510444 1516137 1516142) (-808 "bookvol10.3.pamphlet" 1509845 1509853 1510426 1510431) (-807 "bookvol10.2.pamphlet" 1509620 1509628 1509771 1509840) (-806 "bookvol10.3.pamphlet" 1502991 1503001 1509610 1509615) (-805 "bookvol10.3.pamphlet" 1502252 1502262 1502981 1502986) (-804 "bookvol10.3.pamphlet" 1501700 1501726 1502064 1502213) (-803 "bookvol10.3.pamphlet" 1499058 1499068 1499386 1499513) (-802 "bookvol10.3.pamphlet" 1490915 1490935 1491273 1491404) (-801 "bookvol10.4.pamphlet" 1489494 1489513 1490905 1490910) (-800 "bookvol10.4.pamphlet" 1487144 1487161 1489484 1489489) (-799 "bookvol10.4.pamphlet" 1483087 1483104 1487101 1487106) (-798 "bookvol10.4.pamphlet" 1482474 1482498 1483077 1483082) (-797 "bookvol10.4.pamphlet" 1480040 1480057 1482464 1482469) (-796 "bookvol10.4.pamphlet" 1476931 1476953 1480030 1480035) (-795 "bookvol10.3.pamphlet" 1475517 1475525 1476921 1476926) (-794 "bookvol10.4.pamphlet" 1472821 1472843 1475507 1475512) (-793 "bookvol10.4.pamphlet" 1472197 1472221 1472811 1472816) (-792 "bookvol10.4.pamphlet" 1458559 1458567 1472187 1472192) (-791 "bookvol10.4.pamphlet" 1457990 1458006 1458549 1458554) (-790 "bookvol10.3.pamphlet" 1455385 1455393 1457980 1457985) (-789 "bookvol10.4.pamphlet" 1450752 1450768 1455375 1455380) (-788 "bookvol10.4.pamphlet" 1450271 1450289 1450742 1450747) (-787 "bookvol10.2.pamphlet" 1448656 1448664 1450261 1450266) (-786 "bookvol10.3.pamphlet" 1446792 1446802 1447510 1447549) (-785 "bookvol10.4.pamphlet" 1446428 1446449 1446782 1446787) (-784 "bookvol10.2.pamphlet" 1444202 1444212 1446384 1446423) (-783 NIL 1441701 1441713 1443885 1443890) (-782 "bookvol10.2.pamphlet" 1441549 1441557 1441691 1441696) (-781 "bookvol10.2.pamphlet" 1441297 1441305 1441539 1441544) (-780 "bookvol10.2.pamphlet" 1440589 1440597 1441287 1441292) (-779 "bookvol10.2.pamphlet" 1440450 1440458 1440579 1440584) (-778 "bookvol10.2.pamphlet" 1440312 1440320 1440440 1440445) (-777 "bookvol10.4.pamphlet" 1440035 1440051 1440302 1440307) (-776 "bookvol10.4.pamphlet" 1428352 1428360 1440025 1440030) (-775 "bookvol10.4.pamphlet" 1419111 1419119 1428342 1428347) (-774 "bookvol10.2.pamphlet" 1416450 1416458 1419101 1419106) (-773 "bookvol10.4.pamphlet" 1415290 1415298 1416440 1416445) (-772 "bookvol10.4.pamphlet" 1407362 1407372 1415095 1415100) (-771 "bookvol10.2.pamphlet" 1406659 1406675 1407318 1407357) (-770 "bookvol10.4.pamphlet" 1406204 1406214 1406576 1406581) (-769 "bookvol10.3.pamphlet" 1399193 1399203 1403754 1403907) (-768 "bookvol10.4.pamphlet" 1398585 1398597 1399183 1399188) (-767 "bookvol10.3.pamphlet" 1394780 1394799 1395088 1395215) (-766 "bookvol10.3.pamphlet" 1393304 1393314 1393381 1393474) (-765 "bookvol10.4.pamphlet" 1391676 1391690 1393294 1393299) (-764 "bookvol10.4.pamphlet" 1391568 1391597 1391666 1391671) (-763 "bookvol10.4.pamphlet" 1390814 1390834 1391558 1391563) (-762 "bookvol10.3.pamphlet" 1390702 1390716 1390794 1390809) (-761 "bookvol10.4.pamphlet" 1390296 1390335 1390692 1390697) (-760 "bookvol10.4.pamphlet" 1388830 1388849 1390286 1390291) (-759 "bookvol10.4.pamphlet" 1388518 1388544 1388820 1388825) (-758 "bookvol10.3.pamphlet" 1388259 1388267 1388508 1388513) (-757 "bookvol10.4.pamphlet" 1387935 1387945 1388249 1388254) (-756 "bookvol10.4.pamphlet" 1387404 1387420 1387925 1387930) (-755 "bookvol10.3.pamphlet" 1386294 1386302 1387378 1387399) (-754 "bookvol10.4.pamphlet" 1384916 1384926 1386284 1386289) (-753 "bookvol10.3.pamphlet" 1382514 1382522 1384906 1384911) (-752 "bookvol10.4.pamphlet" 1379974 1379991 1382504 1382509) (-751 "bookvol10.4.pamphlet" 1379227 1379241 1379964 1379969) (-750 "bookvol10.4.pamphlet" 1377339 1377355 1379217 1379222) (-749 "bookvol10.4.pamphlet" 1376996 1377010 1377329 1377334) (-748 "bookvol10.4.pamphlet" 1375156 1375170 1376986 1376991) (-747 "bookvol10.2.pamphlet" 1374752 1374760 1375146 1375151) (-746 NIL 1374346 1374356 1374742 1374747) (-745 "bookvol10.2.pamphlet" 1373632 1373640 1374336 1374341) (-744 NIL 1372916 1372926 1373622 1373627) (-743 "bookvol10.4.pamphlet" 1371989 1371997 1372906 1372911) (-742 "bookvol10.4.pamphlet" 1361555 1361563 1371979 1371984) (-741 "bookvol10.4.pamphlet" 1359991 1359999 1361545 1361550) (-740 "bookvol10.4.pamphlet" 1354165 1354173 1359981 1359986) (-739 "bookvol10.4.pamphlet" 1347909 1347917 1354155 1354160) (-738 "bookvol10.4.pamphlet" 1343531 1343539 1347899 1347904) (-737 "bookvol10.4.pamphlet" 1336905 1336913 1343521 1343526) (-736 "bookvol10.4.pamphlet" 1327300 1327308 1336895 1336900) (-735 "bookvol10.4.pamphlet" 1323227 1323235 1327290 1327295) (-734 "bookvol10.4.pamphlet" 1321102 1321110 1323217 1323222) (-733 "bookvol10.4.pamphlet" 1313548 1313556 1321092 1321097) (-732 "bookvol10.4.pamphlet" 1307704 1307712 1313538 1313543) (-731 "bookvol10.4.pamphlet" 1303534 1303542 1307694 1307699) (-730 "bookvol10.4.pamphlet" 1302046 1302054 1303524 1303529) (-729 "bookvol10.4.pamphlet" 1301344 1301352 1302036 1302041) (-728 "bookvol10.2.pamphlet" 1300850 1300860 1301312 1301339) (-727 NIL 1300376 1300388 1300840 1300845) (-726 "bookvol10.3.pamphlet" 1297597 1297611 1297926 1298079) (-725 "bookvol10.3.pamphlet" 1295716 1295730 1295788 1296008) (-724 "bookvol10.4.pamphlet" 1292700 1292717 1295706 1295711) (-723 "bookvol10.4.pamphlet" 1292098 1292115 1292690 1292695) (-722 "bookvol10.2.pamphlet" 1290132 1290153 1291996 1292093) (-721 "bookvol10.4.pamphlet" 1289789 1289799 1290122 1290127) (-720 "bookvol10.4.pamphlet" 1289229 1289237 1289779 1289784) (-719 "bookvol10.3.pamphlet" 1287234 1287244 1288991 1289030) (-718 "bookvol10.2.pamphlet" 1287067 1287077 1287190 1287229) (-717 "bookvol10.3.pamphlet" 1284020 1284032 1286775 1286842) (-716 "bookvol10.4.pamphlet" 1283580 1283594 1284010 1284015) (-715 "bookvol10.4.pamphlet" 1283141 1283158 1283570 1283575) (-714 "bookvol10.4.pamphlet" 1281186 1281205 1283131 1283136) (-713 "bookvol10.3.pamphlet" 1278636 1278651 1278980 1279107) (-712 "bookvol10.4.pamphlet" 1277915 1277934 1278626 1278631) (-711 "bookvol10.4.pamphlet" 1277723 1277766 1277905 1277910) (-710 "bookvol10.4.pamphlet" 1277467 1277503 1277713 1277718) (-709 "bookvol10.4.pamphlet" 1275802 1275819 1277457 1277462) (-708 "bookvol10.2.pamphlet" 1274666 1274674 1275792 1275797) (-707 NIL 1273528 1273538 1274656 1274661) (-706 "bookvol10.2.pamphlet" 1272274 1272287 1273388 1273523) (-705 NIL 1271042 1271057 1272158 1272163) (-704 "bookvol10.2.pamphlet" 1269048 1269056 1271032 1271037) (-703 NIL 1267052 1267062 1269038 1269043) (-702 "bookvol10.2.pamphlet" 1266196 1266204 1267042 1267047) (-701 NIL 1265338 1265348 1266186 1266191) (-700 "bookvol10.3.pamphlet" 1264017 1264031 1265318 1265333) (-699 "bookvol10.2.pamphlet" 1263698 1263708 1263985 1264012) (-698 NIL 1263399 1263411 1263688 1263693) (-697 "bookvol10.3.pamphlet" 1262712 1262751 1263379 1263394) (-696 "bookvol10.3.pamphlet" 1261354 1261366 1262534 1262601) (-695 "bookvol10.3.pamphlet" 1260865 1260883 1261344 1261349) (-694 "bookvol10.3.pamphlet" 1257525 1257541 1258343 1258496) (-693 "bookvol10.3.pamphlet" 1256886 1256925 1257427 1257520) (-692 "bookvol10.3.pamphlet" 1255673 1255681 1256876 1256881) (-691 "bookvol10.4.pamphlet" 1255413 1255447 1255663 1255668) (-690 "bookvol10.2.pamphlet" 1253855 1253865 1255369 1255408) (-689 "bookvol10.4.pamphlet" 1252427 1252444 1253845 1253850) (-688 "bookvol10.4.pamphlet" 1251897 1251915 1252417 1252422) (-687 "bookvol10.4.pamphlet" 1251483 1251496 1251887 1251892) (-686 "bookvol10.4.pamphlet" 1250798 1250808 1251473 1251478) (-685 "bookvol10.4.pamphlet" 1249691 1249701 1250788 1250793) (-684 "bookvol10.3.pamphlet" 1249467 1249477 1249681 1249686) (-683 "bookvol10.4.pamphlet" 1248928 1248946 1249457 1249462) (-682 "bookvol10.3.pamphlet" 1248367 1248375 1248830 1248923) (-681 "bookvol10.4.pamphlet" 1247006 1247016 1248357 1248362) (-680 "bookvol10.3.pamphlet" 1245450 1245458 1246896 1247001) (-679 "bookvol10.4.pamphlet" 1244850 1244872 1245440 1245445) (-678 "bookvol10.4.pamphlet" 1242712 1242720 1244840 1244845) (-677 "bookvol10.4.pamphlet" 1240953 1240963 1242702 1242707) (-676 "bookvol10.2.pamphlet" 1240228 1240238 1240921 1240948) (-675 "bookvol10.3.pamphlet" 1236202 1236210 1236816 1237017) (-674 "bookvol10.4.pamphlet" 1235410 1235422 1236192 1236197) (-673 "bookvol10.4.pamphlet" 1232518 1232544 1235400 1235405) (-672 "bookvol10.4.pamphlet" 1229794 1229804 1232508 1232513) (-671 "bookvol10.3.pamphlet" 1228685 1228695 1229169 1229196) (-670 "bookvol10.4.pamphlet" 1226011 1226035 1228569 1228574) (-669 "bookvol10.2.pamphlet" 1211222 1211244 1225967 1226006) (-668 NIL 1196281 1196305 1211028 1211033) (-667 "bookvol10.4.pamphlet" 1195549 1195597 1196271 1196276) (-666 "bookvol10.4.pamphlet" 1194269 1194281 1195539 1195544) (-665 "bookvol10.4.pamphlet" 1193168 1193182 1194259 1194264) (-664 "bookvol10.4.pamphlet" 1192502 1192514 1193158 1193163) (-663 "bookvol10.4.pamphlet" 1191320 1191330 1192492 1192497) (-662 "bookvol10.4.pamphlet" 1191128 1191142 1191310 1191315) (-661 "bookvol10.4.pamphlet" 1190893 1190905 1191118 1191123) (-660 "bookvol10.4.pamphlet" 1190523 1190533 1190883 1190888) (-659 "bookvol10.3.pamphlet" 1188467 1188484 1190513 1190518) (-658 "bookvol10.3.pamphlet" 1186386 1186396 1188068 1188073) (-657 "bookvol10.2.pamphlet" 1181842 1181852 1186366 1186381) (-656 NIL 1177306 1177318 1181832 1181837) (-655 "bookvol10.3.pamphlet" 1174112 1174129 1177296 1177301) (-654 "bookvol10.3.pamphlet" 1172370 1172384 1172792 1172843) (-653 "bookvol10.4.pamphlet" 1171903 1171920 1172360 1172365) (-652 "bookvol10.4.pamphlet" 1170743 1170771 1171893 1171898) (-651 "bookvol10.4.pamphlet" 1168547 1168561 1170733 1170738) (-650 "bookvol10.2.pamphlet" 1168204 1168214 1168503 1168542) (-649 NIL 1167893 1167905 1168194 1168199) (-648 "bookvol10.3.pamphlet" 1166907 1166926 1167749 1167818) (-647 "bookvol10.4.pamphlet" 1166164 1166174 1166897 1166902) (-646 "bookvol10.4.pamphlet" 1164609 1164658 1166154 1166159) (-645 "bookvol10.4.pamphlet" 1163248 1163258 1164599 1164604) (-644 "bookvol10.3.pamphlet" 1162649 1162663 1163182 1163209) (-643 "bookvol10.2.pamphlet" 1162251 1162259 1162639 1162644) (-642 NIL 1161851 1161861 1162241 1162246) (-641 "bookvol10.4.pamphlet" 1160769 1160781 1161841 1161846) (-640 "bookvol10.3.pamphlet" 1160156 1160172 1160449 1160488) (-639 "bookvol10.4.pamphlet" 1159200 1159217 1160113 1160118) (-638 "bookvol10.2.pamphlet" 1157817 1157827 1159156 1159195) (-637 NIL 1156432 1156444 1157773 1157778) (-636 "bookvol10.3.pamphlet" 1155708 1155720 1156112 1156151) (-635 "bookvol10.3.pamphlet" 1155111 1155121 1155388 1155427) (-634 "bookvol10.4.pamphlet" 1153883 1153901 1155101 1155106) (-633 "bookvol10.2.pamphlet" 1152258 1152268 1153785 1153878) (-632 "bookvol10.2.pamphlet" 1148006 1148016 1152238 1152253) (-631 NIL 1143728 1143740 1147962 1147967) (-630 "bookvol10.3.pamphlet" 1140464 1140481 1143718 1143723) (-629 "bookvol10.2.pamphlet" 1139947 1139957 1140454 1140459) (-628 "bookvol10.3.pamphlet" 1139047 1139057 1139721 1139748) (-627 "bookvol10.4.pamphlet" 1138478 1138492 1139037 1139042) (-626 "bookvol10.3.pamphlet" 1136419 1136429 1137848 1137875) (-625 "bookvol10.4.pamphlet" 1135710 1135724 1136409 1136414) (-624 "bookvol10.4.pamphlet" 1134350 1134362 1135700 1135705) (-623 "bookvol10.4.pamphlet" 1131223 1131235 1134340 1134345) (-622 "bookvol10.2.pamphlet" 1130655 1130665 1131203 1131218) (-621 "bookvol10.4.pamphlet" 1129432 1129444 1130567 1130572) (-620 "bookvol10.4.pamphlet" 1127346 1127356 1129422 1129427) (-619 "bookvol10.4.pamphlet" 1126229 1126242 1127336 1127341) (-618 "bookvol10.3.pamphlet" 1124243 1124255 1125519 1125664) (-617 "bookvol10.2.pamphlet" 1123768 1123778 1124169 1124238) (-616 NIL 1123321 1123333 1123724 1123729) (-615 "bookvol10.3.pamphlet" 1121854 1121862 1122562 1122577) (-614 "bookvol10.4.pamphlet" 1119222 1119241 1121844 1121849) (-613 "bookvol10.4.pamphlet" 1118141 1118157 1119212 1119217) (-612 "bookvol10.2.pamphlet" 1117160 1117168 1118131 1118136) (-611 "bookvol10.4.pamphlet" 1112812 1112827 1117150 1117155) (-610 "bookvol10.3.pamphlet" 1110875 1110902 1112792 1112807) (-609 "bookvol10.4.pamphlet" 1109259 1109276 1110865 1110870) (-608 "bookvol10.4.pamphlet" 1108317 1108339 1109249 1109254) (-607 "bookvol10.3.pamphlet" 1107089 1107102 1107910 1107979) (-606 "bookvol10.4.pamphlet" 1106662 1106678 1107079 1107084) (-605 "bookvol10.3.pamphlet" 1106102 1106116 1106584 1106623) (-604 "bookvol10.2.pamphlet" 1105878 1105888 1106082 1106097) (-603 NIL 1105662 1105674 1105868 1105873) (-602 "bookvol10.4.pamphlet" 1104375 1104392 1105652 1105657) (-601 "bookvol10.2.pamphlet" 1104097 1104107 1104365 1104370) (-600 "bookvol10.2.pamphlet" 1103834 1103844 1104087 1104092) (-599 "bookvol10.3.pamphlet" 1102369 1102379 1103618 1103623) (-598 "bookvol10.4.pamphlet" 1102072 1102084 1102359 1102364) (-597 "bookvol10.2.pamphlet" 1101163 1101185 1102040 1102067) (-596 NIL 1100274 1100298 1101153 1101158) (-595 "bookvol10.3.pamphlet" 1098896 1098912 1099621 1099648) (-594 "bookvol10.3.pamphlet" 1096873 1096885 1098186 1098331) (-593 "bookvol10.2.pamphlet" 1094955 1094979 1096853 1096868) (-592 NIL 1092902 1092928 1094802 1094807) (-591 "bookvol10.3.pamphlet" 1091911 1091926 1092051 1092078) (-590 "bookvol10.3.pamphlet" 1091071 1091081 1091901 1091906) (-589 "bookvol10.4.pamphlet" 1089882 1089901 1091061 1091066) (-588 "bookvol10.4.pamphlet" 1089376 1089390 1089872 1089877) (-587 "bookvol10.4.pamphlet" 1089106 1089118 1089366 1089371) (-586 "bookvol10.3.pamphlet" 1086898 1086913 1088942 1089067) (-585 "bookvol10.3.pamphlet" 1079324 1079339 1085872 1085969) (-584 "bookvol10.4.pamphlet" 1078807 1078823 1079314 1079319) (-583 "bookvol10.3.pamphlet" 1078037 1078050 1078203 1078230) (-582 "bookvol10.4.pamphlet" 1077117 1077136 1078027 1078032) (-581 "bookvol10.4.pamphlet" 1075081 1075089 1077107 1077112) (-580 "bookvol10.4.pamphlet" 1073604 1073614 1075037 1075042) (-579 "bookvol10.4.pamphlet" 1073205 1073216 1073594 1073599) (-578 "bookvol10.4.pamphlet" 1071551 1071561 1073195 1073200) (-577 "bookvol10.3.pamphlet" 1069296 1069310 1071406 1071433) (-576 "bookvol10.4.pamphlet" 1068432 1068448 1069286 1069291) (-575 "bookvol10.4.pamphlet" 1067573 1067589 1068422 1068427) (-574 "bookvol10.4.pamphlet" 1067333 1067341 1067563 1067568) (-573 "bookvol10.3.pamphlet" 1067026 1067038 1067138 1067231) (-572 "bookvol10.3.pamphlet" 1066787 1066813 1066952 1067021) (-571 "bookvol10.4.pamphlet" 1066396 1066412 1066777 1066782) (-570 "bookvol10.4.pamphlet" 1059642 1059659 1066386 1066391) (-569 "bookvol10.4.pamphlet" 1057501 1057517 1059216 1059221) (-568 "bookvol10.4.pamphlet" 1056807 1056815 1057491 1057496) (-567 "bookvol10.3.pamphlet" 1056583 1056593 1056721 1056802) (-566 "bookvol10.4.pamphlet" 1054947 1054961 1056573 1056578) (-565 "bookvol10.4.pamphlet" 1054436 1054446 1054937 1054942) (-564 "bookvol10.4.pamphlet" 1053081 1053098 1054426 1054431) (-563 "bookvol10.4.pamphlet" 1051444 1051460 1052724 1052729) (-562 "bookvol10.4.pamphlet" 1049171 1049189 1051376 1051381) (-561 "bookvol10.4.pamphlet" 1039278 1039286 1049161 1049166) (-560 "bookvol10.3.pamphlet" 1038639 1038647 1039132 1039273) (-559 "bookvol10.4.pamphlet" 1037905 1037922 1038629 1038634) (-558 "bookvol10.4.pamphlet" 1037570 1037594 1037895 1037900) (-557 "bookvol10.4.pamphlet" 1033971 1033979 1037560 1037565) (-556 "bookvol10.4.pamphlet" 1027351 1027369 1033903 1033908) (-555 "bookvol10.3.pamphlet" 1021349 1021357 1027341 1027346) (-554 "bookvol10.4.pamphlet" 1020449 1020506 1021339 1021344) (-553 "bookvol10.4.pamphlet" 1019523 1019533 1020439 1020444) (-552 "bookvol10.4.pamphlet" 1019391 1019415 1019513 1019518) (-551 "bookvol10.4.pamphlet" 1017705 1017721 1019381 1019386) (-550 "bookvol10.2.pamphlet" 1016329 1016337 1017631 1017700) (-549 NIL 1015015 1015025 1016319 1016324) (-548 "bookvol10.4.pamphlet" 1014145 1014232 1015005 1015010) (-547 "bookvol10.2.pamphlet" 1012608 1012618 1014059 1014140) (-546 "bookvol10.4.pamphlet" 1012111 1012119 1012598 1012603) (-545 "bookvol10.4.pamphlet" 1011293 1011320 1012101 1012106) (-544 "bookvol10.4.pamphlet" 1010785 1010801 1011283 1011288) (-543 "bookvol10.3.pamphlet" 1009865 1009896 1010028 1010055) (-542 "bookvol10.2.pamphlet" 1007261 1007269 1009767 1009860) (-541 NIL 1004743 1004753 1007251 1007256) (-540 "bookvol10.4.pamphlet" 1004177 1004190 1004733 1004738) (-539 "bookvol10.4.pamphlet" 1003243 1003262 1004167 1004172) (-538 "bookvol10.4.pamphlet" 1002301 1002325 1003233 1003238) (-537 "bookvol10.4.pamphlet" 1001287 1001304 1002291 1002296) (-536 "bookvol10.4.pamphlet" 1000434 1000464 1001277 1001282) (-535 "bookvol10.4.pamphlet" 998719 998741 1000424 1000429) (-534 "bookvol10.4.pamphlet" 997769 997788 998709 998714) (-533 "bookvol10.3.pamphlet" 994813 994821 997759 997764) (-532 "bookvol10.4.pamphlet" 994438 994448 994803 994808) (-531 "bookvol10.4.pamphlet" 994026 994034 994428 994433) (-530 "bookvol10.3.pamphlet" 993407 993470 994016 994021) (-529 "bookvol10.3.pamphlet" 992813 992836 993397 993402) (-528 "bookvol10.2.pamphlet" 991436 991499 992803 992808) (-527 "bookvol10.4.pamphlet" 989968 989990 991426 991431) (-526 "bookvol10.3.pamphlet" 989874 989891 989958 989963) (-525 "bookvol10.4.pamphlet" 989295 989305 989864 989869) (-524 "bookvol10.4.pamphlet" 985061 985072 989285 989290) (-523 "bookvol10.3.pamphlet" 984193 984219 984705 984732) (-522 "bookvol10.4.pamphlet" 983283 983327 984149 984154) (-521 "bookvol10.4.pamphlet" 981888 981912 983239 983244) (-520 "bookvol10.3.pamphlet" 980767 980782 981294 981321) (-519 "bookvol10.3.pamphlet" 980492 980530 980597 980624) (-518 "bookvol10.3.pamphlet" 979902 979918 980173 980266) (-517 "bookvol10.3.pamphlet" 976973 976988 979308 979335) (-516 "bookvol10.3.pamphlet" 976811 976828 976929 976934) (-515 "bookvol10.2.pamphlet" 976200 976212 976801 976806) (-514 NIL 975587 975601 976190 976195) (-513 "bookvol10.3.pamphlet" 975400 975412 975577 975582) (-512 "bookvol10.3.pamphlet" 975171 975183 975390 975395) (-511 "bookvol10.3.pamphlet" 974906 974918 975161 975166) (-510 "bookvol10.2.pamphlet" 973840 973852 974896 974901) (-509 "bookvol10.3.pamphlet" 973600 973612 973830 973835) (-508 "bookvol10.3.pamphlet" 973362 973374 973590 973595) (-507 "bookvol10.4.pamphlet" 970614 970632 973352 973357) (-506 "bookvol10.3.pamphlet" 965548 965587 970549 970554) (-505 "bookvol10.3.pamphlet" 964969 964992 965538 965543) (-504 "bookvol10.4.pamphlet" 964120 964136 964959 964964) (-503 "bookvol10.3.pamphlet" 963343 963351 964110 964115) (-502 "bookvol10.4.pamphlet" 961966 961983 963333 963338) (-501 "bookvol10.3.pamphlet" 961244 961257 961660 961687) (-500 "bookvol10.4.pamphlet" 958119 958138 961234 961239) (-499 "bookvol10.4.pamphlet" 957007 957022 958109 958114) (-498 "bookvol10.3.pamphlet" 956738 956764 956837 956864) (-497 "bookvol10.3.pamphlet" 956051 956066 956144 956171) (-496 "bookvol10.3.pamphlet" 954264 954272 955867 955960) (-495 "bookvol10.4.pamphlet" 953819 953852 954254 954259) (-494 "bookvol10.2.pamphlet" 953243 953251 953809 953814) (-493 NIL 952665 952675 953233 953238) (-492 "bookvol10.2.pamphlet" 949915 949925 952645 952660) (-491 NIL 947006 947018 949738 949743) (-490 "bookvol10.3.pamphlet" 944875 944883 945473 945566) (-489 "bookvol10.4.pamphlet" 943729 943740 944865 944870) (-488 "bookvol10.3.pamphlet" 943319 943343 943719 943724) (-487 "bookvol10.3.pamphlet" 939042 939052 943149 943176) (-486 "bookvol10.3.pamphlet" 930895 930911 931257 931388) (-485 "bookvol10.3.pamphlet" 928086 928101 928689 928816) (-484 "bookvol10.4.pamphlet" 926626 926634 928076 928081) (-483 "bookvol10.3.pamphlet" 925658 925689 925869 925896) (-482 "bookvol10.3.pamphlet" 925243 925251 925560 925653) (-481 "bookvol10.4.pamphlet" 911120 911132 925233 925238) (-480 "bookvol10.4.pamphlet" 910865 910873 910965 910970) (-479 "bookvol10.4.pamphlet" 894938 894974 910735 910740) (-478 "bookvol10.4.pamphlet" 894699 894707 894797 894802) (-477 "bookvol10.4.pamphlet" 894520 894534 894633 894638) (-476 "bookvol10.4.pamphlet" 894397 894411 894510 894515) (-475 "bookvol10.4.pamphlet" 894230 894238 894330 894335) (-474 "bookvol10.3.pamphlet" 893422 893438 893932 893959) (-473 "bookvol10.3.pamphlet" 892503 892538 892677 892692) (-472 "bookvol10.3.pamphlet" 889670 889697 890635 890784) (-471 "bookvol10.2.pamphlet" 888636 888644 889650 889665) (-470 NIL 887610 887620 888626 888631) (-469 "bookvol10.4.pamphlet" 886193 886214 887600 887605) (-468 "bookvol10.2.pamphlet" 884771 884783 886183 886188) (-467 NIL 883347 883361 884761 884766) (-466 "bookvol10.3.pamphlet" 875952 875960 883337 883342) (-465 "bookvol10.4.pamphlet" 874331 874339 875942 875947) (-464 "bookvol10.4.pamphlet" 872774 872782 874321 874326) (-463 "bookvol10.2.pamphlet" 871828 871840 872764 872769) (-462 NIL 870880 870894 871818 871823) (-461 "bookvol10.3.pamphlet" 870390 870413 870618 870645) (-460 "bookvol10.4.pamphlet" 865080 865167 870346 870351) (-459 "bookvol10.4.pamphlet" 864341 864359 865070 865075) (-458 "bookvol10.3.pamphlet" 860289 860297 864331 864336) (-457 "bookvol10.4.pamphlet" 857872 857880 860279 860284) (-456 "bookvol10.3.pamphlet" 856979 857006 857840 857867) (-455 "bookvol10.4.pamphlet" 856089 856103 856969 856974) (-454 "bookvol10.4.pamphlet" 852190 852203 856079 856084) (-453 "bookvol10.4.pamphlet" 851794 851804 852180 852185) (-452 "bookvol10.4.pamphlet" 851378 851395 851784 851789) (-451 "bookvol10.4.pamphlet" 850845 850864 851368 851373) (-450 "bookvol10.4.pamphlet" 848835 848848 850835 850840) (-449 "bookvol10.3.pamphlet" 845868 845885 846629 846756) (-448 "bookvol10.3.pamphlet" 839763 839790 845662 845729) (-447 "bookvol10.2.pamphlet" 838691 838699 839689 839758) (-446 NIL 837681 837691 838681 838686) (-445 "bookvol10.4.pamphlet" 831462 831500 837637 837642) (-444 "bookvol10.4.pamphlet" 827560 827598 831452 831457) (-443 "bookvol10.4.pamphlet" 822626 822664 827550 827555) (-442 "bookvol10.4.pamphlet" 818881 818919 822616 822621) (-441 "bookvol10.4.pamphlet" 818178 818186 818871 818876) (-440 "bookvol10.4.pamphlet" 816500 816510 818134 818139) (-439 "bookvol10.4.pamphlet" 814959 814972 816490 816495) (-438 "bookvol10.4.pamphlet" 813124 813143 814949 814954) (-437 "bookvol10.4.pamphlet" 803390 803401 813114 813119) (-436 "bookvol10.2.pamphlet" 800403 800411 803370 803385) (-435 "bookvol10.2.pamphlet" 799445 799453 800383 800398) (-434 "bookvol10.3.pamphlet" 799294 799306 799435 799440) (-433 NIL 797506 797514 799284 799289) (-432 "bookvol10.3.pamphlet" 796669 796677 797496 797501) (-431 "bookvol10.4.pamphlet" 795711 795730 796605 796610) (-430 "bookvol10.3.pamphlet" 793797 793805 795701 795706) (-429 "bookvol10.4.pamphlet" 793219 793235 793787 793792) (-428 "bookvol10.4.pamphlet" 792027 792043 793176 793181) (-427 "bookvol10.4.pamphlet" 789299 789315 792017 792022) (-426 "bookvol10.2.pamphlet" 783333 783343 789062 789294) (-425 NIL 777157 777169 782888 782893) (-424 "bookvol10.4.pamphlet" 776779 776795 777147 777152) (-423 "bookvol10.3.pamphlet" 776087 776099 776599 776698) (-422 "bookvol10.4.pamphlet" 775361 775377 776077 776082) (-421 "bookvol10.2.pamphlet" 774462 774472 775305 775356) (-420 NIL 773537 773549 774382 774387) (-419 "bookvol10.4.pamphlet" 772224 772240 773527 773532) (-418 "bookvol10.4.pamphlet" 766613 766647 772214 772219) (-417 "bookvol10.4.pamphlet" 766223 766239 766603 766608) (-416 "bookvol10.4.pamphlet" 765346 765369 766213 766218) (-415 "bookvol10.4.pamphlet" 764288 764298 765336 765341) (-414 "bookvol10.3.pamphlet" 755712 755722 763312 763381) (-413 "bookvol10.2.pamphlet" 750791 750801 755654 755707) (-412 NIL 745882 745894 750747 750752) (-411 "bookvol10.4.pamphlet" 745328 745346 745872 745877) (-410 "bookvol10.3.pamphlet" 744722 744752 745259 745264) (-409 "bookvol10.3.pamphlet" 743917 743938 744702 744717) (-408 "bookvol10.4.pamphlet" 743653 743685 743907 743912) (-407 "bookvol10.2.pamphlet" 743317 743327 743643 743648) (-406 NIL 742847 742859 743175 743180) (-405 "bookvol10.2.pamphlet" 741175 741188 742803 742842) (-404 NIL 739535 739550 741165 741170) (-403 "bookvol10.3.pamphlet" 736634 736644 737037 737210) (-402 "bookvol10.4.pamphlet" 736237 736249 736624 736629) (-401 "bookvol10.4.pamphlet" 735571 735583 736227 736232) (-400 "bookvol10.2.pamphlet" 732541 732549 735461 735566) (-399 NIL 729539 729549 732461 732466) (-398 "bookvol10.2.pamphlet" 728583 728591 729441 729534) (-397 NIL 727713 727723 728573 728578) (-396 "bookvol10.2.pamphlet" 727465 727475 727693 727708) (-395 "bookvol10.3.pamphlet" 726241 726258 727455 727460) (-394 NIL 724726 724775 726231 726236) (-393 "bookvol10.4.pamphlet" 723655 723663 724716 724721) (-392 "bookvol10.2.pamphlet" 720815 720823 723635 723650) (-391 "bookvol10.2.pamphlet" 720489 720497 720795 720810) (-390 "bookvol10.3.pamphlet" 717827 717835 720479 720484) (-389 "bookvol10.4.pamphlet" 717306 717316 717817 717822) (-388 "bookvol10.4.pamphlet" 717087 717111 717296 717301) (-387 "bookvol10.4.pamphlet" 716288 716296 717077 717082) (-386 "bookvol10.3.pamphlet" 715710 715732 716256 716283) (-385 "bookvol10.2.pamphlet" 714038 714046 715700 715705) (-384 "bookvol10.3.pamphlet" 713930 713938 714028 714033) (-383 "bookvol10.2.pamphlet" 713728 713736 713856 713925) (-382 "bookvol10.3.pamphlet" 710783 710793 713684 713689) (-381 "bookvol10.3.pamphlet" 710478 710490 710717 710744) (-380 "bookvol10.2.pamphlet" 707498 707506 710458 710473) (-379 "bookvol10.2.pamphlet" 706540 706548 707478 707493) (-378 "bookvol10.2.pamphlet" 704244 704262 706508 706535) (-377 "bookvol10.3.pamphlet" 703704 703716 704178 704205) (-376 "bookvol10.4.pamphlet" 701440 701454 703694 703699) (-375 "bookvol10.3.pamphlet" 694861 694869 701306 701435) (-374 "bookvol10.4.pamphlet" 692293 692307 694851 694856) (-373 "bookvol10.2.pamphlet" 692005 692015 692273 692288) (-372 NIL 691671 691683 691941 691946) (-371 "bookvol10.4.pamphlet" 690921 690933 691661 691666) (-370 "bookvol10.2.pamphlet" 688626 688645 690847 690916) (-369 "bookvol10.2.pamphlet" 685624 685634 688594 688621) (-368 NIL 682535 682547 685507 685512) (-367 "bookvol10.4.pamphlet" 681204 681220 682525 682530) (-366 "bookvol10.2.pamphlet" 679237 679250 681160 681199) (-365 NIL 677196 677211 679121 679126) (-364 "bookvol10.2.pamphlet" 676348 676356 677186 677191) (-363 "bookvol10.2.pamphlet" 665277 665287 676290 676343) (-362 NIL 654218 654230 665233 665238) (-361 "bookvol10.3.pamphlet" 653801 653811 654208 654213) (-360 "bookvol10.2.pamphlet" 652230 652247 653791 653796) (-359 "bookvol10.2.pamphlet" 651548 651556 652132 652225) (-358 NIL 650952 650962 651538 651543) (-357 "bookvol10.3.pamphlet" 649561 649571 650932 650947) (-356 "bookvol10.4.pamphlet" 648376 648391 649551 649556) (-355 "bookvol10.3.pamphlet" 647795 647810 648092 648185) (-354 "bookvol10.4.pamphlet" 647660 647677 647785 647790) (-353 "bookvol10.4.pamphlet" 647149 647170 647650 647655) (-352 "bookvol10.4.pamphlet" 638428 638439 647139 647144) (-351 "bookvol10.4.pamphlet" 637474 637491 638418 638423) (-350 "bookvol10.3.pamphlet" 636960 636980 637190 637283) (-349 "bookvol10.3.pamphlet" 636408 636424 636641 636734) (-348 "bookvol10.3.pamphlet" 634926 634946 636124 636217) (-347 "bookvol10.3.pamphlet" 633436 633453 634642 634735) (-346 "bookvol10.3.pamphlet" 631947 631968 633117 633210) (-345 "bookvol10.4.pamphlet" 629309 629328 631937 631942) (-344 "bookvol10.2.pamphlet" 626883 626891 629211 629304) (-343 NIL 624543 624553 626873 626878) (-342 "bookvol10.4.pamphlet" 623288 623305 624533 624538) (-341 "bookvol10.4.pamphlet" 620703 620714 623278 623283) (-340 "bookvol10.4.pamphlet" 613911 613927 620693 620698) (-339 "bookvol10.4.pamphlet" 612526 612545 613901 613906) (-338 "bookvol10.4.pamphlet" 611935 611952 612516 612521) (-337 "bookvol10.3.pamphlet" 610788 610808 611651 611744) (-336 "bookvol10.3.pamphlet" 609683 609703 610504 610597) (-335 "bookvol10.3.pamphlet" 608482 608503 609364 609457) (-334 "bookvol10.2.pamphlet" 597113 597135 608321 608477) (-333 NIL 585823 585847 597033 597038) (-332 "bookvol10.4.pamphlet" 585568 585608 585813 585818) (-331 "bookvol10.3.pamphlet" 578198 578244 585324 585363) (-330 "bookvol10.2.pamphlet" 577904 577914 578188 578193) (-329 NIL 577395 577407 577681 577686) (-328 "bookvol10.3.pamphlet" 576828 576852 577385 577390) (-327 "bookvol10.2.pamphlet" 574870 574894 576818 576823) (-326 NIL 572910 572936 574860 574865) (-325 "bookvol10.4.pamphlet" 572654 572694 572900 572905) (-324 "bookvol10.4.pamphlet" 571175 571183 572644 572649) (-323 "bookvol10.3.pamphlet" 570704 570714 571165 571170) (-322 NIL 560529 560537 570694 570699) (-321 "bookvol10.2.pamphlet" 553402 553416 560431 560524) (-320 NIL 546327 546343 553358 553363) (-319 "bookvol10.3.pamphlet" 544741 544751 545733 545760) (-318 "bookvol10.2.pamphlet" 542861 542873 544639 544736) (-317 NIL 540965 540979 542745 542750) (-316 "bookvol10.4.pamphlet" 540515 540537 540955 540960) (-315 "bookvol10.3.pamphlet" 540165 540175 540469 540474) (-314 "bookvol10.2.pamphlet" 538356 538368 540155 540160) (-313 "bookvol10.3.pamphlet" 537962 537972 538252 538279) (-312 "bookvol10.4.pamphlet" 536158 536175 537952 537957) (-311 "bookvol10.4.pamphlet" 536040 536050 536148 536153) (-310 "bookvol10.4.pamphlet" 535216 535226 536030 536035) (-309 "bookvol10.4.pamphlet" 535098 535108 535206 535211) (-308 "bookvol10.3.pamphlet" 531931 531954 533230 533379) (-307 "bookvol10.4.pamphlet" 529295 529303 531921 531926) (-306 "bookvol10.4.pamphlet" 529197 529226 529285 529290) (-305 "bookvol10.4.pamphlet" 526005 526021 529187 529192) (-304 "bookvol10.3.pamphlet" 521254 521264 521994 522401) (-303 "bookvol10.4.pamphlet" 517314 517327 521244 521249) (-302 "bookvol10.4.pamphlet" 517074 517086 517304 517309) (-301 "bookvol10.3.pamphlet" 514012 514037 514646 514739) (-300 "bookvol10.3.pamphlet" 513679 513687 514002 514007) (-299 "bookvol10.4.pamphlet" 513169 513183 513669 513674) (-298 "bookvol10.2.pamphlet" 512733 512743 513159 513164) (-297 NIL 512295 512307 512723 512728) (-296 "bookvol10.2.pamphlet" 509829 509837 512221 512290) (-295 NIL 507425 507435 509819 509824) (-294 "bookvol10.4.pamphlet" 499265 499273 507415 507420) (-293 "bookvol10.4.pamphlet" 498850 498864 499255 499260) (-292 "bookvol10.4.pamphlet" 498527 498538 498840 498845) (-291 "bookvol10.2.pamphlet" 491074 491082 498517 498522) (-290 NIL 483527 483537 490972 490977) (-289 "bookvol10.4.pamphlet" 480300 480308 483517 483522) (-288 "bookvol10.4.pamphlet" 480041 480053 480290 480295) (-287 "bookvol10.4.pamphlet" 479536 479552 480031 480036) (-286 "bookvol10.4.pamphlet" 479102 479118 479526 479531) (-285 "bookvol10.4.pamphlet" 476476 476484 479092 479097) (-284 "bookvol10.3.pamphlet" 475510 475532 475719 475746) (-283 "bookvol10.3.pamphlet" 470368 470378 473183 473295) (-282 "bookvol10.4.pamphlet" 470084 470096 470358 470363) (-281 "bookvol10.4.pamphlet" 466398 466408 470074 470079) (-280 "bookvol10.2.pamphlet" 465940 465948 466342 466393) (-279 "bookvol10.3.pamphlet" 465120 465161 465866 465935) (-278 "bookvol10.2.pamphlet" 463374 463393 465110 465115) (-277 NIL 461592 461613 463330 463335) (-276 "bookvol10.2.pamphlet" 461056 461074 461582 461587) (-275 "bookvol10.4.pamphlet" 460435 460454 461046 461051) (-274 "bookvol10.2.pamphlet" 460124 460132 460425 460430) (-273 NIL 459811 459821 460114 460119) (-272 "bookvol10.2.pamphlet" 457515 457525 459779 459806) (-271 NIL 455168 455180 457434 457439) (-270 "bookvol10.4.pamphlet" 451959 451989 455124 455129) (-269 "bookvol10.4.pamphlet" 448810 448833 451915 451920) (-268 "bookvol10.4.pamphlet" 446765 446781 448800 448805) (-267 "bookvol10.4.pamphlet" 441531 441547 446755 446760) (-266 "bookvol10.3.pamphlet" 439807 439815 441521 441526) (-265 "bookvol10.3.pamphlet" 439343 439351 439797 439802) (-264 "bookvol10.3.pamphlet" 438920 438928 439333 439338) (-263 "bookvol10.3.pamphlet" 438500 438508 438910 438915) (-262 "bookvol10.3.pamphlet" 438036 438044 438490 438495) (-261 "bookvol10.3.pamphlet" 437572 437580 438026 438031) (-260 "bookvol10.3.pamphlet" 437108 437116 437562 437567) (-259 "bookvol10.3.pamphlet" 436644 436652 437098 437103) (-258 "bookvol10.4.pamphlet" 432260 432268 436634 436639) (-257 "bookvol10.2.pamphlet" 428941 428951 432250 432255) (-256 NIL 425620 425632 428931 428936) (-255 "bookvol10.4.pamphlet" 422600 422687 425610 425615) (-254 "bookvol10.3.pamphlet" 421770 421780 422430 422457) (-253 "bookvol10.2.pamphlet" 421424 421434 421726 421765) (-252 "bookvol10.3.pamphlet" 418867 418881 419160 419287) (-251 "bookvol10.3.pamphlet" 412812 412820 418857 418862) (-250 "bookvol10.4.pamphlet" 412473 412483 412802 412807) (-249 "bookvol10.4.pamphlet" 407298 407306 412463 412468) (-248 "bookvol10.4.pamphlet" 405453 405461 407288 407293) (-247 "bookvol10.4.pamphlet" 398053 398066 405443 405448) (-246 "bookvol10.4.pamphlet" 397306 397316 398043 398048) (-245 "bookvol10.4.pamphlet" 394661 394669 397296 397301) (-244 "bookvol10.4.pamphlet" 394198 394213 394651 394656) (-243 "bookvol10.4.pamphlet" 383370 383378 394188 394193) (-242 "bookvol10.2.pamphlet" 381522 381532 383326 383365) (-241 "bookvol10.2.pamphlet" 376863 376879 381390 381517) (-240 NIL 372290 372308 376819 376824) (-239 "bookvol10.3.pamphlet" 365649 365665 365787 366088) (-238 "bookvol10.3.pamphlet" 359021 359039 359146 359447) (-237 "bookvol10.3.pamphlet" 356258 356273 356815 356942) (-236 "bookvol10.4.pamphlet" 355602 355612 356248 356253) (-235 "bookvol10.3.pamphlet" 354237 354247 355008 355035) (-234 "bookvol10.2.pamphlet" 352630 352640 354217 354232) (-233 "bookvol10.2.pamphlet" 352077 352085 352574 352625) (-232 NIL 351568 351578 352067 352072) (-231 "bookvol10.3.pamphlet" 351421 351431 351500 351527) (-230 "bookvol10.2.pamphlet" 350180 350190 351389 351416) (-229 "bookvol10.4.pamphlet" 348360 348368 350170 350175) (-228 "bookvol10.3.pamphlet" 339950 339966 340575 340706) (-227 "bookvol10.4.pamphlet" 338773 338791 339940 339945) (-226 "bookvol10.2.pamphlet" 337935 337951 338625 338768) (-225 NIL 336838 336856 337530 337535) (-224 "bookvol10.4.pamphlet" 335641 335649 336828 336833) (-223 "bookvol10.2.pamphlet" 334613 334623 335609 335636) (-222 NIL 333571 333583 334569 334574) (-221 "bookvol10.2.pamphlet" 332684 332692 333551 333566) (-220 NIL 331805 331815 332674 332679) (-219 "bookvol10.2.pamphlet" 330964 330974 331785 331800) (-218 NIL 330040 330052 330863 330868) (-217 "bookvol10.2.pamphlet" 329658 329668 330008 330035) (-216 NIL 329296 329308 329648 329653) (-215 "bookvol10.3.pamphlet" 327504 327514 328940 328967) (-214 "bookvol10.4.pamphlet" 318746 318754 327494 327499) (-213 "bookvol10.3.pamphlet" 315023 315031 318636 318741) (-212 "bookvol10.4.pamphlet" 313232 313248 315013 315018) (-211 "bookvol10.3.pamphlet" 311142 311174 313212 313227) (-210 "bookvol10.3.pamphlet" 304816 304826 310972 310999) (-209 "bookvol10.4.pamphlet" 304429 304443 304806 304811) (-208 "bookvol10.4.pamphlet" 301910 301920 304419 304424) (-207 "bookvol10.4.pamphlet" 300406 300422 301900 301905) (-206 "bookvol10.3.pamphlet" 298287 298295 298873 298966) (-205 "bookvol10.4.pamphlet" 296138 296155 298277 298282) (-204 "bookvol10.4.pamphlet" 295736 295760 296128 296133) (-203 "bookvol10.3.pamphlet" 294323 294333 295726 295731) (-202 "bookvol10.3.pamphlet" 294151 294159 294313 294318) (-201 "bookvol10.3.pamphlet" 293971 293979 294141 294146) (-200 "bookvol10.4.pamphlet" 292910 292918 293961 293966) (-199 "bookvol10.3.pamphlet" 292372 292380 292900 292905) (-198 "bookvol10.3.pamphlet" 291850 291858 292362 292367) (-197 "bookvol10.3.pamphlet" 291340 291348 291840 291845) (-196 "bookvol10.3.pamphlet" 290830 290838 291330 291335) (-195 "bookvol10.4.pamphlet" 285672 285680 290820 290825) (-194 "bookvol10.4.pamphlet" 283991 283999 285662 285667) (-193 "bookvol10.3.pamphlet" 283968 283976 283981 283986) (-192 "bookvol10.3.pamphlet" 283490 283498 283958 283963) (-191 "bookvol10.3.pamphlet" 283012 283020 283480 283485) (-190 "bookvol10.3.pamphlet" 282480 282488 283002 283007) (-189 "bookvol10.3.pamphlet" 281965 281973 282470 282475) (-188 "bookvol10.3.pamphlet" 281389 281397 281955 281960) (-187 "bookvol10.3.pamphlet" 280883 280891 281379 281384) (-186 "bookvol10.3.pamphlet" 280393 280401 280873 280878) (-185 "bookvol10.3.pamphlet" 279933 279941 280383 280388) (-184 "bookvol10.3.pamphlet" 279459 279467 279923 279928) (-183 "bookvol10.3.pamphlet" 278982 278990 279449 279454) (-182 "bookvol10.4.pamphlet" 275041 275049 278972 278977) (-181 "bookvol10.4.pamphlet" 274545 274553 275031 275036) (-180 "bookvol10.4.pamphlet" 271362 271370 274535 274540) (-179 "bookvol10.4.pamphlet" 270777 270787 271352 271357) (-178 "bookvol10.4.pamphlet" 269267 269283 270767 270772) (-177 "bookvol10.4.pamphlet" 267936 267949 269257 269262) (-176 "bookvol10.4.pamphlet" 261763 261776 267926 267931) (-175 "bookvol10.4.pamphlet" 260802 260812 261753 261758) (-174 "bookvol10.4.pamphlet" 260302 260317 260727 260732) (-173 "bookvol10.4.pamphlet" 260007 260026 260292 260297) (-172 "bookvol10.4.pamphlet" 254900 254910 259997 260002) (-171 "bookvol10.3.pamphlet" 250635 250645 254802 254895) (-170 "bookvol10.2.pamphlet" 250310 250318 250573 250630) (-169 "bookvol10.3.pamphlet" 249806 249814 250300 250305) (-168 "bookvol10.4.pamphlet" 249573 249588 249796 249801) (-167 "bookvol10.3.pamphlet" 243598 243608 243841 244102) (-166 "bookvol10.4.pamphlet" 243311 243323 243588 243593) (-165 "bookvol10.4.pamphlet" 243107 243121 243301 243306) (-164 "bookvol10.2.pamphlet" 241163 241173 242829 243102) (-163 NIL 238924 238936 240592 240597) (-162 "bookvol10.4.pamphlet" 238670 238688 238914 238919) (-161 "bookvol10.4.pamphlet" 238203 238211 238660 238665) (-160 "bookvol10.3.pamphlet" 238010 238018 238193 238198) (-159 "bookvol10.2.pamphlet" 236915 236923 238000 238005) (-158 "bookvol10.4.pamphlet" 235413 235423 236905 236910) (-157 "bookvol10.4.pamphlet" 232673 232689 235403 235408) (-156 "bookvol10.3.pamphlet" 231510 231518 232663 232668) (-155 "bookvol10.4.pamphlet" 230842 230859 231500 231505) (-154 "bookvol10.4.pamphlet" 226906 226914 230832 230837) (-153 "bookvol10.3.pamphlet" 225559 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. -555) 125278) ((-218 . -556) 125239) ((-218 . -555) 125178) ((-1042 . -33) T) ((-863 . -1104) T) ((-312 . -648) 125123) ((-605 . -25) T) ((-605 . -21) T) ((-441 . -959) T) ((-571 . -386) 125088) ((-549 . -386) 125053) ((-1018 . -1046) T) ((-528 . -260) T) ((-479 . -260) T) ((-1130 . -276) 125032) ((-441 . -206) 124984) ((-441 . -216) 124963) ((-1109 . -276) 124942) ((-983 . -123) T) ((-794 . -727) 124921) ((-131 . -97) T) ((-39 . -1001) T) ((-794 . -722) 124900) ((-578 . -924) 124884) ((-527 . -965) T) ((-501 . -965) T) ((-458 . -965) T) ((-375 . -419) T) ((-327 . -123) T) ((-282 . -368) 124868) ((-281 . -368) 124829) ((-322 . -123) T) ((-314 . -123) T) ((-1109 . -933) NIL) ((-991 . -555) 124796) ((-103 . -123) T) ((-1018 . -37) 124783) ((-839 . -1001) T) ((-701 . -1001) T) ((-606 . -1001) T) ((-632 . -134) T) ((-111 . -134) T) ((-1168 . -21) T) ((-1168 . -25) T) ((-1167 . -21) T) ((-1167 . -25) T) ((-599 . -964) 124767) ((-487 . -777) T) ((-463 . -777) T) ((-323 . -964) 124719) 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. -296) 108821) ((-1147 . -318) 108798) ((-640 . -708) T) ((-1147 . -221) T) ((-101 . -600) 108780) ((-1143 . -622) 108732) ((-488 . -25) T) ((-488 . -21) T) ((-1198 . -1013) 108684) ((-607 . -1039) T) ((-375 . -400) T) ((-386 . -105) T) ((-252 . -887) 108630) ((-237 . -887) 108607) ((-126 . -1039) T) ((-803 . -1094) T) ((-1070 . -708) T) ((-607 . -221) 108586) ((-605 . -105) T) ((-769 . -708) T) ((-767 . -708) T) ((-409 . -1094) T) ((-126 . -233) T) ((-45 . -364) NIL) ((-126 . -221) NIL) ((-449 . -708) T) ((-803 . -23) T) ((-713 . -25) T) ((-713 . -21) T) ((-684 . -834) T) ((-1062 . -276) 108565) ((-83 . -392) T) ((-83 . -391) T) ((-1231 . -994) 108531) ((-675 . -1045) 108481) ((-1227 . -137) T) ((-1220 . -137) T) ((-1199 . -137) T) ((-1193 . -137) T) ((-1151 . -25) T) ((-1119 . -407) 108465) ((-618 . -363) 108397) ((-594 . -363) 108329) ((-1133 . -1126) 108313) ((-106 . -1082) 108291) ((-1151 . -21) T) ((-1150 . -21) T) ((-1150 . -25) T) ((-991 . -699) 108239) ((-211 . -629) 108206) 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. -969) 102185) ((-913 . -1080) T) ((-114 . -152) 102167) ((-78 . -600) 102149) ((-880 . -600) 102131) ((-1065 . -706) 102110) ((-725 . -1039) T) ((-1262 . -1039) T) ((-803 . -622) 102058) ((-283 . -1046) 102000) ((-167 . -1191) 101905) ((-213 . -1094) T) ((-315 . -23) T) ((-1143 . -985) 101857) ((-827 . -1082) T) ((-725 . -233) 101836) ((-1106 . -722) 101815) ((-1221 . -1045) 101704) ((-1219 . -908) 101683) ((-856 . -708) T) ((-167 . -550) 101594) ((-1198 . -908) 101573) ((-572 . -629) 101560) ((-403 . -1082) T) ((-560 . -629) 101547) ((-251 . -1082) T) ((-496 . -629) 101512) ((-213 . -23) T) ((-1198 . -807) 101465) ((-958 . -1082) T) ((-1256 . -105) T) ((-349 . -1253) 101442) ((-1254 . -105) T) ((-1221 . -120) 101292) ((-145 . -600) 101274) ((-986 . -137) T) ((-49 . -105) T) ((-228 . -834) 101225) ((-1208 . -1191) 101204) ((-106 . -492) 101188) ((-1257 . -699) 101158) ((-1070 . -52) 101119) ((-1050 . -1094) T) ((-945 . -1094) T) ((-136 . -39) T) ((-130 . -39) T) ((-769 . -52) 101096) 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. -43) 96493) ((-68 . -436) T) ((-68 . -391) T) ((-1136 . -105) T) ((-857 . -137) T) ((-487 . -105) 96471) ((-1262 . -364) T) ((-726 . -942) 96440) ((-1065 . -105) T) ((-1049 . -105) T) ((-346 . -699) 96385) ((-713 . -148) 96364) ((-713 . -146) 96343) ((-1015 . -629) 96280) ((-523 . -1082) 96258) ((-355 . -105) T) ((-348 . -105) T) ((-337 . -105) T) ((-112 . -105) T) ((-506 . -1082) T) ((-349 . -629) 96203) ((-1149 . -622) 96151) ((-1105 . -622) 96099) ((-381 . -510) 96078) ((-820 . -832) 96057) ((-375 . -1191) T) ((-675 . -708) T) ((-331 . -1046) T) ((-1199 . -985) 96009) ((-171 . -1046) T) ((-106 . -600) 95976) ((-1151 . -146) 95955) ((-1151 . -148) 95934) ((-375 . -550) T) ((-1150 . -148) 95913) ((-1150 . -146) 95892) ((-1143 . -146) 95799) ((-403 . -280) T) ((-1143 . -148) 95706) ((-1106 . -148) 95685) ((-1106 . -146) 95664) ((-308 . -43) 95505) ((-167 . -137) T) ((-301 . -782) NIL) ((-301 . -779) NIL) ((-636 . -1039) T) ((-53 . -629) 95470) ((-986 . -21) T) ((-136 . -1002) 95454) 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. -105) T) ((-187 . -105) T) ((-186 . -105) T) ((-185 . -105) T) ((-184 . -105) T) ((-183 . -105) T) ((-349 . -708) T) ((-694 . -120) 94470) ((-654 . -219) 94454) ((-573 . -296) T) ((-518 . -296) T) ((-283 . -515) 94403) ((-112 . -298) NIL) ((-77 . -391) T) ((-1095 . -105) 94193) ((-820 . -407) 94177) ((-1100 . -782) T) ((-1100 . -779) T) ((-682 . -1082) T) ((-375 . -359) T) ((-167 . -494) 94155) ((-210 . -600) 94122) ((-139 . -1082) T) ((-125 . -1082) T) ((-53 . -708) T) ((-1036 . -492) 94087) ((-142 . -421) 94069) ((-142 . -364) T) ((-1019 . -105) T) ((-513 . -510) 94048) ((-474 . -105) T) ((-461 . -105) T) ((-1026 . -1094) T) ((-726 . -1211) 94032) ((-1151 . -40) 93998) ((-1151 . -98) 93964) ((-1151 . -1176) 93930) ((-1151 . -1173) 93896) ((-1135 . -298) NIL) ((-94 . -392) T) ((-94 . -391) T) ((-1065 . -1128) 93875) ((-1150 . -1173) 93841) ((-1150 . -1176) 93807) ((-1026 . -23) T) ((-1150 . -98) 93773) ((-567 . -494) T) ((-1150 . -40) 93739) ((-1143 . -1173) 93705) ((-1143 . -1176) 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88302) ((-126 . -873) NIL) ((-607 . -1029) 88185) ((-626 . -834) 88164) ((-1246 . -105) T) ((-284 . -105) T) ((-694 . -364) 88143) ((-126 . -1029) 88120) ((-386 . -699) 88104) ((-1147 . -373) 88088) ((-605 . -699) 88072) ((-50 . -298) 87876) ((-803 . -146) 87855) ((-803 . -148) 87834) ((-1257 . -378) 87813) ((-806 . -834) T) ((-1238 . -1082) T) ((-1227 . -40) 87779) ((-1136 . -217) 87726) ((-1227 . -98) 87692) ((-382 . -834) 87671) ((-1227 . -1176) 87637) ((-1227 . -1173) 87603) ((-1220 . -1173) 87569) ((-1220 . -1176) 87535) ((-1220 . -98) 87501) ((-1220 . -40) 87467) ((-1219 . -1094) T) ((-1199 . -1173) 87433) ((-516 . -137) T) ((-1199 . -1176) 87399) ((-1193 . -1176) 87365) ((-1193 . -1173) 87331) ((-1199 . -98) 87297) ((-1199 . -40) 87263) ((-618 . -600) 87232) ((-594 . -600) 87201) ((-33 . -105) T) ((-213 . -834) T) ((-1198 . -1094) T) ((-1193 . -40) 87167) ((-1193 . -98) 87133) ((-1100 . -629) 87120) ((-1147 . -887) 87063) ((-1065 . -344) 87042) ((-583 . -152) 87024) ((-856 . 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. -21) T) ((-897 . -321) 84169) ((-91 . -600) 84151) ((-680 . -1013) T) ((-659 . -834) T) ((-1219 . -137) T) ((-1198 . -137) T) ((-888 . -1002) 84135) ((-821 . -21) T) ((-53 . -1029) 84078) ((-821 . -25) T) ((-814 . -25) T) ((-814 . -21) T) ((-1256 . -1046) T) ((-1254 . -1046) T) ((-636 . -708) T) ((-1147 . -296) 84057) ((-254 . -1002) 84041) ((-1257 . -1045) 84025) ((-1208 . -834) 84004) ((-802 . -407) 83973) ((-106 . -128) 83957) ((-57 . -1082) T) ((-918 . -600) 83939) ((-857 . -985) 83916) ((-810 . -105) T) ((-1257 . -120) 83895) ((-635 . -43) 83865) ((-567 . -834) T) ((-350 . -1094) T) ((-347 . -1094) T) ((-336 . -1094) T) ((-252 . -1094) T) ((-237 . -1094) T) ((-607 . -296) 83844) ((-1127 . -298) 83648) ((-648 . -23) T) ((-486 . -219) 83617) ((-153 . -1046) T) ((-350 . -23) T) ((-347 . -23) T) ((-336 . -23) T) ((-126 . -296) T) ((-252 . -23) T) ((-237 . -23) T) ((-995 . -1039) T) ((-694 . -896) 83596) ((-995 . -221) 83568) ((-995 . -233) T) ((-126 . -1013) NIL) ((-897 . -1094) T) 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. -1029) 78312) ((-852 . -1094) T) ((-2 . -1082) T) ((-2 . |RecordCategory|) T) ((-847 . -1094) T) ((-820 . -600) 78294) ((-1095 . -1046) 78224) ((-572 . -908) T) ((-560 . -807) T) ((-560 . -908) T) ((-496 . -908) T) ((-141 . -1029) 78208) ((-213 . -98) T) ((-80 . -436) T) ((-80 . -391) T) ((0 . -600) 78190) ((-167 . -148) 78169) ((-167 . -146) 78120) ((-213 . -40) T) ((-54 . -600) 78102) ((-852 . -23) T) ((-482 . -1046) T) ((-847 . -23) T) ((-490 . -219) 78084) ((-487 . -961) 78068) ((-486 . -832) 78047) ((-206 . -219) 78029) ((-86 . -436) T) ((-86 . -391) T) ((-1123 . -39) T) ((-802 . -170) 78008) ((-713 . -105) T) ((-1018 . -600) 77975) ((-501 . -276) 77950) ((-304 . -373) 77919) ((-301 . -373) 77880) ((-301 . -330) 77841) ((-803 . -942) 77788) ((-644 . -137) T) ((-1208 . -146) 77767) ((-1208 . -148) 77746) ((-1151 . -105) T) ((-1150 . -105) T) ((-1143 . -105) T) ((-1136 . -1082) T) ((-1106 . -105) T) ((-210 . -39) T) ((-279 . -699) 77733) ((-1136 . -597) 77709) ((-583 . -298) NIL) 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|SystemODESolver| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| |OrderedIntegralDomain| |OpenMath| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| |OnePointCompletion| |OnePointCompletionFunctions2| |Operator| |OperationsQuery| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrdSetInts| |OutputPackage| |OutputForm| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResult| |PatternMatchResultFunctions2| |Pattern| |PatternFunctions1| |PatternFunctions2| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permutation| |Permanent| |PermutationCategory| |PermutationGroup| |PrimeField| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| 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|yCoordinates| |f01ref| |OMreadStr| |exists?| |mightHaveRoots| |rule| |f01rdf| |hessian| |binomThmExpt| |qShiftC| |iipolygamma| |f01rcf| |corrPoly| |factorFraction| |formula| |qShiftAction| |f01qef| |multiple?| |powerAssociative?| |adjoint| |ruleset| |generalInterpolation| |symbNameV| |f01qdf| |clearTheSymbolTable| |order| |extendedEuclidean| |generalCoefficient| |subMultV| |f01qcf| |mainCharacterization| |explicitlyEmpty?| |cLog| |rightRank| |fffg| |f01mcf| |setsymbName!| |getCode| |ScanRoman| |rischNormalize| |ShiftC| |f01maf| |exprex| |even?| |simpsono| |ShiftAction| |coerceS| |f01bsf| |crushedSet| |rk4qc| |exteriorDifferential| |DiffC| |f01brf| |shiftInfoRec| |matrixConcat3D| |setPosition| |DiffAction| |distdfact| |makeViewport2D| |exponential1| |semiSubResultantGcdEuclidean1| |numberOfValuesNeeded| |label| |leftNorm| |OMsend| |getShiftRec| |perfectNthPower?| |mainValue| |rotate!| |getOp| |multiplyExponents| |constantIfCan| |factorUsingYun| |gethi| |getEq| |branchIfCan| |setValue!| |factorUsingMusser| |inGroundField?| |evalRec| |setleft!| |factorCantorZassenhaus| |remove!| |evalADE| |viewDefaults| |infRittWu?| |constant| |groebnerFactorize| |coerceL| |removeDuplicates!| |universe| |setsubmult!| |parametric?| |semiDiscriminantEuclidean| |nextColeman| |leftTrim| |lex| |number?| |readLine!| |dimensionsOf| |cosIfCan| |lazyIntegrate| |gcdPrimitive| |algDsolve| |pushuconst| |sincos| |newLine| |symbolTableOf| |elementary| |intPatternMatch| |print| |setpoint!| |definingPolynomial| |rightDivide| |shallowCopy| |axes| |realEigenvectors| |tubePoints| |hue| |compdegd| |insertTop!| |OMgetApp| |iisinh| |concat!| |splitLinear| |drawToScale| |primitivePart| |setLabelValue| |tracePowMod| |setmult!| |quadraticForm| |tubeRadius| |inconsistent?| |ptFunc| |leftCharacteristicPolynomial| |setlocalPoint!| |weighted| |message| |triangular?| |setProperty| |scalarTypeOf| |screenResolution| |ratDenom| |bright| |palgLODE0| |rk4a| |extendedint| |realEigenvalues| |printStatement| |setlocalParam!| |lazyResidueClass| |splitSquarefree| |toroidal| |output| |mainCoefficients| |permutation| |totalfract| |inverseLaplace| |bumptab| |OMputAtp| |logpart| |iitanh| |doubleComplex?| |characteristicPolynomial| |expandPower| |lSpaceBasis| |bfEntry| |realRoots| |bringDown| |setParam!| |swapRows!| |leviCivitaSymbol| |parabolic| |component| |setexcpDiv!| |setFoundPlacesToEmpty| |key| |any?| |fortranLogical| |setcurve!| |probablyZeroDim?| |stack| |setDegree!| |degree| |prinpolINFO| |gcdcofactprim| |isTimes| |localParam| |removeRoughlyRedundantFactorsInPol| |stiffnessAndStabilityOfODEIF| |goto| |setchart!| |explicitEntries?| |itsALeaf!| |sec2cos| |pointV| |subMatrix| |qroot| |column| |foundPlaces| |setelt!| |multV| |polyred| |open?| |complexSolve| |numberOfComponents| |systemSizeIF| |localPointV| |cyclicGroup| |euler| |acsch| |overlabel| |specialTrigs| |localParamV| |minimumDegree| |noKaratsuba| |removeSuperfluousQuasiComponents| |removeRedundantFactors| |fullOut| |palgint0| |quasiRegular| |nullSpace| |purelyAlgebraicLeadingMonomial?| |e02bdf| |log2| |genericRightNorm| |gcdprim| |replaceKthElement| |minusInfinity| |edf2df| |sayLength| |plenaryPower| |startStats!| |plusInfinity| |excpDivV| |subresultantSequence| |lazyPseudoRemainder| |minset| |gcdcofact| |ramifiedAtInfinity?| |curveV| |addPoint| |countRealRoots| |cCos| |mapmult| |iter| |setFormula!| |OMUnknownSymbol?| |redpps| |generateIrredPoly| |insertRoot!| |rightMinimalPolynomial| |chartV| |variableName| |toseInvertible?| |isAbsolutelyIrreducible?| |leadingIndex| |OMputEndBVar| |float| |resize| |unrankImproperPartitions1| |putGraph| |interpret| |factorset| |sort| |elColumn2!| |hasoln| |collectQuasiMonic| |next| |safety| |deepestTail| |leftFactorIfCan| |sumOfDivisors| |laguerre| |eisensteinIrreducible?| |unvectorise| |maxRowIndex| |maxShift| |algebraicOf| |d01gbf| |getDatabase| |internalAugment| |child?| |suffix?| |select!| |d01gaf| |generate| |maxPower| |shrinkable| |bsolve| |froot| |pointColorPalette| |d01fcf| |incrementBy| |FormatRoman| |extractIfCan| |graphCurves| |subsInVar| |besselY| |map!| |d01bbf| |expand| |reduceBasisAtInfinity| |showRegion| |series| |subs2ndVar| |leftExtendedGcd| |find| |d01asf| |filterWhile| |powerSum| |zCoord| |hspace| |subs1stVar| |readIfCan!| |bivariatePolynomials| |filterUntil| |unitNormalize| |modularFactor| |getMatch| |replaceVarByZero| |bipolar| |d02raf| |select| |nextNormalPrimitivePoly| |replaceVarByOne| |nextLatticePermutation| |create3Space| |printInfo!| |objectOf| |d02kef| |inRadical?| |trapezoidalo| |baseRDEsys| |listVariable| |iicsch| |d02gbf| |wreath| |factorSquareFreePolynomial| |mat| |listAllMonoExp| |coerceImages| |definingInequation| |d02gaf| |dfRange| |quartic| |listAllMono| |minordet| |setStatus| |badValues| |d02ejf| |expPot| |firstExponent| |degreeSubResultant| |cyclotomic| |changeThreshhold| |d02cjf| |makeRecord| |tanQ| |degreeOfMinimalForm| |symmetric?| |initials| |laplacian| |substring?| |d02bhf| |rootKerSimp| |clipBoolean| |htrigs| |degOneCoef| |prefix?| |mathieu24| |d02bbf| |matrix| |rightTraceMatrix| |maxLevel| |po| |key?| |multiEuclidean| |e02ahf| |false| |setErrorBound| |regime| |singRicDE| |maxDerivative| |cAcos| |yellow| |monicLeftDivide| |rowEchLocal| |yRange| |ef2edf| |maxDegree| |primextintfrac| |bandedHessian| |decimal| |getButtonValue| |hermiteH| |combineFeatureCompatibility| |indexName| |makeSeries| |d03faf| |homogeneous| |linSolve| |push!| |indiceSubResultantEuclidean| |curryRight| |d03eef| |curveColorPalette| |aspFilename| |realElementary| |displayAsGF| |OMgetError| |d03edf| |addiag| |cAsec| |complexForm| |expenseOfEvaluationIF| |prindINFO| |argument| |controlPanel| |aLinear| |cyclicSubmodule| |meshPar1Var| |quotedOperators| |double?| |pair?| |sechIfCan| |zerosOf| |sumOfSquares| |checkOptions| |linGenPos| |size?| |possiblyNewVariety?| |tRange| |resultantReduitEuclidean| |transcendent?| |factorSqFree| |rootSimp| |inHallBasis?| |contract| |say| |perfectSqrt| |LyndonBasis| |nthr| |tubePlot| |allDegrees| |weierstrass| |debug| |getVariableOrder| |stripCommentsAndBlanks| |edf2efi| |irreducibleFactor| |firstSubsetGray| |cyclotomicFactorization| |antisymmetricTensors| |iteratedInitials| |rischDEsys| |imagK| |failed?| |replaceDiffs| |singular?| |Vectorise| |isobaric?| |primintegrate| |internalIntegrate| |OMputEndAtp| |c05nbf| |univariate?| |modifyPoint| |subset?| |c05adf| |pushucoef| |ignore?| |OMclose| |script| |c06gsf| |setMaxPoints| |sPol| |numberOfImproperPartitions| |c06gqf| |dictionary| |monicCompleteDecompose| |sbt| |uniform01| |t| |c06gcf| |safeCeiling| |low| |lifting| |c06gbf| |irreducibleRepresentation| |internalLastSubResultant| |removeFirstZeroes| |nodes| |c06fuf| |useSingleFactorBound| |airyAi| |zeroSetSplitIntoTriangularSystems| |posExpnPart| |c06frf| |orderIfNegative| |rewriteIdealWithHeadRemainder| |tensorProduct| |sub| |fortran| |c06fqf| |swap| |setTopPredicate| |monomial2series| |symmetricPower| |pmComplexintegrate| |c06fpf| |cCosh| |e01sbf| |leaf?| |findTerm| |multiplyCoefficients| |eigenvalues| |c06ekf| |open| |generic| |sinIfCan| |rightExactQuotient| |c06ecf| |nonLinearPart| |FormatArabic| |cond| |qPot| |c06ebf| |findCoef| |mindeg| |sinh2csch| |upperCase| |separateFactors| |c06eaf| |f2st| |setStatus!| |filterUpTo| |dimension| |viewSizeDefault| |s17def| |backOldPos| |coefOfFirstNonZeroTerm| |power!| |wrregime| |depth| |reducedForm| |leftQuotient| |s17dcf| |whileLoop| |closedCurve?| |prologue| |reverse!| |imagJ| |s17akf| |f2df| |exponent| |count| |removeCoshSq| |limitedIntegrate| |s17ajf| |rootSplit| |match?| |integral| |pointSizeDefault| |setchildren!| |s17ahf| |fortranDouble| |tab1| |headReduce| |reduceByQuasiMonic| |s17agf| |table| |pseudoDivide| |vspace| |vedf2vef| |s17aff| |rectangularMatrix| |halfExtendedSubResultantGcd2| |ScanFloatIgnoreSpacesIfCan| |OMmakeConn| |radicalOfLeftTraceForm| |sortConstraints| |s17aef| |exactQuotient!| |OMputAttr| |optimize| |fixedPoints| |mindegTerm| |sparsityIF| |strongGenerators| |discriminant| |s17adf| |close| |copyInto!| |algebraicCoefficients?| |predicates| |simplifyPower| |logical?| |s17acf| |putColorInfo| |setColumn!| |exprToXXP| |cAcosh| |graphState| |iiasin| |s15aef| |limitPlus| |factorSquareFreeByRecursion| |stirling1| |increasePrecision| |polCase| |slope| |nextPartition| |iisqrt2| |tex| |delete!| |s15adf| |functionName| |row| |digamma| |minIndex| |lfintegrate| |completeSmith| |s14baf| |insert| |radicalEigenvector| |numFunEvals| |display| |representationType| |minimalPolynomial| |s14abf| |iiasech| |parametrize| |partialFraction| |s14aaf| |printingInfo?| |radicalEigenvectors| |df2st| |point?| |newtonPolygon| |An| |s13adf| |OMputApp| |subst| |fillPascalTriangle| BY |negAndPosEdge| |block| |cardinality| |s13acf| |nthFlag| |dark| |cCoth| |scripted?| |setfirst!| |s13aaf| |lquo| |screenResolution3D| |paraboloidal| |terms| |last| |s01eaf| |theCurve| |adaptive3D?| |multisect| |rootPower| |s21bdf| |ridHack1| |rootNormalize| |setSingularPoints| |s21bcf| |iFTable| |point| |triangularSystems| |zeroSquareMatrix| |setCurve| |s21bbf| |subPolSet?| |exponential| |reshape| |solve| |lintgcd| |rationalPlaces| |construct| |createMultiplicationTable| |csubst| |s21baf| |optional?| |polyRicDE| |pointDominateBy| |nullary?| |dimensionOfIrreducibleRepresentation| |s20adf| |flexible?| |placesOfDegree| |prefixRagits| |linearAssociatedLog| |redPol| |critBonD| |e02agf| |sizeLess?| |leftLcm| |placesAbove| |applyRules| |kroneckerDelta| |bottom!| |s20acf| |monomialIntPoly| |anfactor| |numberRatPlacesExtDeg| |bit?| |infinity| |empty?| |d01aqf| |curveColor| |s19adf| |roughEqualIdeals?| |OMputEndBind| |cot2trig| |frobenius| |d01apf| |removeSquaresIfCan| |OMReadError?| |listLoops| |showTheSymbolTable| |localAbs| |s19acf| |mainSquareFreePart| |OMgetAtp| |cycleEntry| |directSum| |stiffnessAndStabilityFactor| |rangePascalTriangle| |d01anf| |polyRDE| |bivariate?| |OMgetEndApp| |iiperm| |var1Steps| |d01amf| |RittWuCompare| |mainKernel| |presub| |d01alf| |orthonormalBasis| |top| |isOp| |iCompose| SEGMENT |mapUnivariate| |complementaryBasis| |s19abf| |viewPosDefault| |clip| |rightScalarTimes!| |red| |sign| |sample| |d01akf| |OMconnInDevice| |bipolarCylindrical| |has?| |s19aaf| |laurentRep| |OMgetAttr| |acoshIfCan| |selectODEIVPRoutines| |shuffle| |mask| |processTemplate| |LyndonWordsList1| |generator| |d01ajf| |changeBase| |jacobiIdentity?| |subSet| |convert| |Is| |zeroVector| |s18def| |unitVector| |flatten| |surface| |compose| |associatorDependence| |plus| |s18dcf| |complexEigenvectors| |OMgetEndAtp| |integralMatrix| |integralCoordinates| |setPrologue!| |digit| |s18aff| |youngGroup| |preprocess| |pade| |se2rfi| |coHeight| |getStream| |radicalEigenvalues| |semiSubResultantGcdEuclidean2| |s18aef| |nodeOf?| |intersect| |baseRDE| |s18adf| |child| |pushdown| |rombergo| |stoseInvertibleSetsqfreg| |distribute| |test| |mantissa| |OMputBind| |s18acf| |solveLinearlyOverQ| |subCase?| |lambert| |primeFactor| |adaptive| |f04qaf| |null| |fractionPart| |eigenvectors| |uncouplingMatrices| |call| |duplicates?| |f04mcf| |box| |sequences| |remove| |gcdPolynomial| |integers| |groebSolve| |f04mbf| |LiePolyIfCan| |ceiling| |bezoutMatrix| |rewriteIdealWithRemainder| |complexZeros| |multiset| |f04maf| |lo| |setCondition!| |increase| |min| |f04jgf| |mapSolve| |complexElementary| |incr| |truncate| |goodPoint| |selectOptimizationRoutines| |elliptic?| |f04faf| |expandTrigProducts| |hi| |pointLists| |totalDifferential| |rewriteSetWithReduction| |makeVariable| |f04axf| |internalSubQuasiComponent?| |largest| |addmod| |insert!| |ramified?| |f04atf| |leftDivide| |delta| |polynomial| |datalist| |outputFixed| |hash| |f04asf| |viewDeltaXDefault| |equality| |tableForDiscreteLogarithm| |pleskenSplit| |trapezoidal| |iisech| |tube| |tanAn| |divisorCascade| |palgextint| |coerceListOfPairs| |f04arf| |finiteBound| |solveLinearPolynomialEquationByFractions| |readable?| |supRittWu?| |meshFun2Var| |numericIfCan| |badNum| |basis| |logGamma| |generalTwoFactor| |showArrayValues| |infinityNorm| |extension| |scaleRoots| |torsion?| |medialSet| |outputSpacing| |triangulate| |expenseOfEvaluation| |palgLODE| |digit?| |freeOf?| |invmod| |genus| |subspace| |LazardQuotient| |internal?| |padicFraction| |writeLine!| |computePowers| |remainder| |OMencodingSGML| |log| |iiacot| |mulmod| |viewThetaDefault| |operator| |hexDigit?| |powers| |reducedQPowers| |twist| |subResultantGcd| |createIrreduciblePoly| |sort!| |hasHi| |prime| |nextPrime| |changeNameToObjf| |getGraph| |identification| |horizConcat| |makeYoungTableau| |cycles| |aQuadratic| |algint| |round| |outputAsScript| |GospersMethod| |df2fi| |pmintegrate| |intChoose| |OMgetEndError| |lists| |shanksDiscLogAlgorithm| |twoFactor| |cycleTail| |dequeue!| |createMultiplicationMatrix| |Lazard2| |clearDenominator| |modTree| |factorsOfDegree| |mapBivariate| |gcd| |restorePrecision| |real?| ** |expint| |euclideanSize| |leadingIdeal| |expIfCan| |zeroOf| |zag| |eval| |getCurve| |reverseLex| |hconcat| |upperCase!| UP2UTS |linearMatrix| |moebiusMu| |ffactor| |resetAttributeButtons| |entries| |moreAlgebraic?| |selectNonFiniteRoutines| |root| |endOfFile?| |fmecg| |assert| |createLowComplexityTable| |imagi| |printStats!| |factorOfDegree| |OMParseError?| |homogeneous?| |plotPolar| |subscript| |mainVariables| |mr| |lowerPolynomial| |fglmIfCan| |lieAlgebra?| |computeCycleLength| |orbits| |myDegree| |genericLeftTraceForm| |rischDE| |laplace| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|) \ No newline at end of file diff --git a/src/share/algebra/dependents.daase/dependents.daase/index.kaf b/src/share/algebra/dependents.daase/dependents.daase/index.kaf new file mode 100644 index 0000000..3bf70a6 --- /dev/null +++ b/src/share/algebra/dependents.daase/dependents.daase/index.kaf @@ -0,0 +1,274 @@ +76490 (|AbelianGroup&| |FourierSeries| |FreeAbelianGroup| |IndexedDirectProductAbelianGroup| |QuadraticForm|) +(|AbelianMonoid&| |CardinalNumber| |EuclideanModularRing| |GradedAlgebra| |GradedAlgebra&| |GradedModule| |GradedModule&| |IndexedDirectProductAbelianMonoid| |ListMonoidOps| |ModularField| |ModularRing| |RecurrenceOperator|) +(|AbelianMonoidRing&| |FractionFreeFastGaussian|) +(|AbelianSemiGroup&| |Color| |IncrementingMaps| |PositiveInteger|) +(|AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace|) +(|Aggregate&| |SplittingNode| |SplittingTree|) +(|Algebra&| |CliffordAlgebra| |ContinuedFraction| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EvaluateCycleIndicators| |Factored| |FortranExpression| |FourierSeries| |LocalAlgebra| |PartialFraction| |RealClosure| |ResidueRing| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesODESolver|) +(|AlgFactor| |AlgebraicMultFact|) +(|AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicNumber| |AlgebraicallyClosedField&| |ComplexTrigonometricManipulations| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |InnerAlgebraicNumber| |Kovacic| |PatternMatchIntegration| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) +(|AlgebraicallyClosedFunctionSpace&| |ConstantLODE| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultToFunction| |InverseLaplaceTransform| |LaplaceTransform| |NonLinearFirstOrderODESolver| |ODEIntegration|) +(|Library| |Result| |RoutinesTable|) +(|ArcTrigonometricFunctionCategory&|) +(|AssociationList|) +(|SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial|) +(|BagAggregate&|) +(|BalancedPAdicRational|) +(|ModuleOperator| |Operator|) +(|BasicType&|) +(|FreeModule| |OrdinaryDifferentialRing|) +(|BinaryRecursiveAggregate&| |PendantTree|) +(|BalancedBinaryTree| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&|) +(|BitAggregate&| |Bits| |IndexedBits|) +(|BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |IntersectionDivisorPackage| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) +(|GeneralModulePolynomial| |InnerPAdicInteger| |ModuleMonomial| |OrderedDirectProduct|) +(|Kernel| |MakeCachableSet| |SortedCache|) +(|FreeAbelianMonoidCategory| |InnerFreeAbelianMonoid|) +(|CharacterClass|) +(|AlgebraicNumber| |BalancedFactorisation| |ConstantLODE| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |FullPartialFractionExpansion| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |GenusZeroIntegration| |GroebnerFactorizationPackage| |InfiniteProductCharacteristicZero| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerMultFact| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LinearOrdinaryDifferentialOperatorFactorizer| |MRationalFactorize| |MachineFloat| |MultivariateFactorize| |NonLinearFirstOrderODESolver| |ODEIntegration| |ParametricLinearEquations| |PartialFractionPackage| |Pi| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalIntegration| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StreamInfiniteProduct| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |UnivariatePolynomialDecompositionPackage| |ZeroDimensionalSolvePackage|) +(|AssociatedJordanAlgebra| |AssociatedLieAlgebra| |Float| |FortranScalarType| |InfiniteTuple| |LieSquareMatrix| |MakeCachableSet| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |Pi| |QuasiAlgebraicSet| |QueryEquation| |RectangularMatrix| |SquareMatrix| |Switch| |SymbolTable| |TheSymbolTable| |Tuple| |Variable|) +(|Collection&|) +(|FunctionSpaceSum| |Guess| |MyExpression| |RecurrenceOperator|) +(|Algebra| |Algebra&| 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|#1|)) (-15 ** (|#1| |#1| (-701))) (-15 -3948 (|#1| |#1| (-701))) (-15 * (|#1| |#1| |#1|)) (-15 ** (|#1| |#1| (-839))) (-15 -3948 (|#1| |#1| (-839))) (-15 * (|#1| (-501) |#1|)) (-15 * (|#1| (-701) |#1|)) (-15 * (|#1| (-839) |#1|))) -((-3736 (((-107) $ $) 7)) (-3292 (((-107) $) 16)) (-3177 (((-3 $ "failed") $ $) 19)) (-2540 (($) 17 T CONST)) (-2174 (((-3 $ "failed") $) 34)) (-1355 (((-107) $) 31)) (-3460 (((-1053) $) 9)) (-3833 (($ $) 44)) (-3708 (((-1018) $) 10)) (-3691 (((-786) $) 11) (($ (-501)) 28) (($ (-375 (-501))) 49)) (-3965 (((-701)) 29)) (-3948 (($ $ (-839)) 26) (($ $ (-701)) 33) (($ $ (-501)) 45)) (-1850 (($) 18 T CONST)) (-1925 (($) 30 T CONST)) (-3751 (((-107) $ $) 6)) (-3797 (($ $) 22) (($ $ $) 21)) (-3790 (($ $ $) 14)) (** (($ $ (-839)) 25) (($ $ (-701)) 32) (($ $ (-501)) 46)) (* (($ (-839) $) 13) (($ (-701) $) 15) (($ (-501) $) 20) (($ $ $) 24) (($ (-375 (-501)) $) 48) (($ $ (-375 (-501))) 47))) -(((-216) (-1180)) (T -216)) -((** (*1 *1 *1 *2) (-12 (-4 *1 (-216)) (-5 *2 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T) ((-298 |#2|) -12 (|has| |#2| (-298 |#2|)) (|has| |#2| (-1082))) ((-364) |has| |#2| (-364)) ((-373 |#2|) |has| |#2| (-1039)) ((-407 |#2|) |has| |#2| (-1082)) ((-492 |#2|) . T) ((-593 (-560) |#2|) . T) ((-515 |#2| |#2|) -12 (|has| |#2| (-298 |#2|)) (|has| |#2| (-1082))) ((-629 |#2|) -2318 (|has| |#2| (-1039)) (|has| |#2| (-359)) (|has| |#2| (-170))) ((-629 $) -2318 (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-170))) ((-622 (-560)) -12 (|has| |#2| (-622 (-560))) (|has| |#2| (-1039))) ((-622 |#2|) |has| |#2| (-1039)) ((-699 |#2|) -2318 (|has| |#2| (-359)) (|has| |#2| (-170))) ((-708 (SEQ (|:| * (-1 $ |#2| $)) (|exit| 1 (|:| * (-1 $ $ |#2|))))) |has| |#2| (-708)) ((-708) -2318 (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-170))) ((-778) |has| |#2| (-832)) ((-779) -2318 (|has| |#2| (-832)) (|has| |#2| (-780))) ((-780) |has| |#2| (-780)) ((-781) -2318 (|has| |#2| (-832)) (|has| |#2| (-780))) ((-782) -2318 (|has| |#2| (-832)) (|has| |#2| (-780))) ((-832) |has| |#2| (-832)) ((-834) -2318 (|has| |#2| (-832)) (|has| |#2| (-780))) ((-887 (-1153)) -12 (|has| |#2| (-887 (-1153))) (|has| |#2| (-1039))) ((-1029 (-403 (-560))) -12 (|has| |#2| (-1029 (-403 (-560)))) (|has| |#2| (-1082))) ((-1029 (-560)) -12 (|has| |#2| (-1029 (-560))) (|has| |#2| (-1082))) ((-1029 |#2|) |has| |#2| (-1082)) ((-1045 |#2|) -2318 (|has| |#2| (-1039)) (|has| |#2| (-359)) (|has| |#2| (-170))) ((-1045 $) |has| |#2| (-170)) ((-1039) -2318 (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-170))) ((-1046) -2318 (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-170))) ((-1094) -2318 (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-708)) (|has| |#2| (-170))) ((-1082) -2318 (|has| |#2| (-1082)) (|has| |#2| (-1039)) (|has| |#2| (-832)) (|has| |#2| (-780)) (|has| |#2| (-708)) (|has| |#2| (-364)) (|has| |#2| (-359)) (|has| |#2| (-170)) (|has| |#2| (-137)) (|has| |#2| (-25))) ((-1187) . T) ((-1243 |#2|) |has| |#2| (-359))) +((-3469 (((-228 |#1| |#3|) (-1 |#3| |#2| |#3|) (-228 |#1| |#2|) |#3|) 21)) (-2342 ((|#3| (-1 |#3| |#2| |#3|) (-228 |#1| |#2|) |#3|) 23)) (-2803 (((-228 |#1| |#3|) (-1 |#3| |#2|) (-228 |#1| |#2|)) 18))) +(((-227 |#1| |#2| |#3|) (-10 -7 (-15 -3469 ((-228 |#1| |#3|) (-1 |#3| |#2| |#3|) (-228 |#1| |#2|) |#3|)) (-15 -2342 (|#3| (-1 |#3| |#2| |#3|) (-228 |#1| |#2|) |#3|)) (-15 -2803 ((-228 |#1| |#3|) (-1 |#3| |#2|) (-228 |#1| |#2|)))) (-755) (-1187) (-1187)) (T -227)) +((-2803 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-228 *5 *6)) (-14 *5 (-755)) (-4 *6 (-1187)) (-4 *7 (-1187)) (-5 *2 (-228 *5 *7)) (-5 *1 (-227 *5 *6 *7)))) (-2342 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-228 *5 *6)) (-14 *5 (-755)) (-4 *6 (-1187)) (-4 *2 (-1187)) (-5 *1 (-227 *5 *6 *2)))) (-3469 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-228 *6 *7)) (-14 *6 (-755)) (-4 *7 (-1187)) (-4 *5 (-1187)) (-5 *2 (-228 *6 *5)) (-5 *1 (-227 *6 *7 *5))))) +(-10 -7 (-15 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2685229 "STTF" 2687989 NIL STTF (NIL T) -7 NIL NIL) (-1055 2673977 2675844 2677635 "STTAYLOR" 2680865 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1054 2667233 2673841 2673924 "STRTBL" 2673929 NIL STRTBL (NIL T) -8 NIL NIL) (-1053 2662624 2667188 2667219 "STRING" 2667224 T STRING (NIL) -8 NIL NIL) (-1052 2657482 2661967 2661998 "STRICAT" 2662057 T STRICAT (NIL) -9 NIL 2662119) (-1051 2656992 2657069 2657213 "STREAM3" 2657399 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1050 2655974 2656157 2656392 "STREAM2" 2656805 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1049 2655662 2655714 2655807 "STREAM1" 2655916 NIL STREAM1 (NIL T) -7 NIL NIL) (-1048 2648389 2653189 2653807 "STREAM" 2655079 NIL STREAM (NIL T) -8 NIL NIL) (-1047 2647405 2647586 2647817 "STINPROD" 2648205 NIL STINPROD (NIL T) -7 NIL NIL) (-1046 2646983 2647167 2647198 "STEP" 2647278 T STEP (NIL) -9 NIL 2647356) (-1045 2640538 2646882 2646959 "STBL" 2646964 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1044 2635751 2639792 2639836 "STAGG" 2639989 NIL STAGG (NIL T) -9 NIL 2640078) (-1043 2633453 2634055 2634927 "STAGG-" 2634932 NIL STAGG- (NIL T T) -8 NIL NIL) (-1042 2631651 2633223 2633315 "STACK" 2633396 NIL STACK (NIL T) -8 NIL NIL) (-1041 2624382 2629798 2630253 "SREGSET" 2631281 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1040 2616822 2618190 2619702 "SRDCMPK" 2622988 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1039 2609794 2614261 2614292 "SRAGG" 2615595 T SRAGG (NIL) -9 NIL 2616203) (-1038 2608811 2609066 2609445 "SRAGG-" 2609450 NIL SRAGG- (NIL T) -8 NIL NIL) (-1037 2603268 2607738 2608161 "SQMATRIX" 2608434 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1036 2597026 2599988 2600714 "SPLTREE" 2602614 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1035 2593016 2593682 2594328 "SPLNODE" 2596452 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1034 2592062 2592295 2592326 "SPFCAT" 2592770 T SPFCAT (NIL) -9 NIL NIL) (-1033 2590799 2591009 2591273 "SPECOUT" 2591820 T SPECOUT (NIL) -7 NIL NIL) (-1032 2582821 2584568 2584611 "SPACEC" 2588934 NIL SPACEC (NIL T) -9 NIL 2590750) (-1031 2580993 2582754 2582802 "SPACE3" 2582807 NIL SPACE3 (NIL T) -8 NIL NIL) (-1030 2579747 2579918 2580208 "SORTPAK" 2580799 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1029 2577803 2578106 2578524 "SOLVETRA" 2579411 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1028 2576814 2577036 2577310 "SOLVESER" 2577576 NIL SOLVESER (NIL T) -7 NIL NIL) (-1027 2572034 2572915 2573917 "SOLVERAD" 2575866 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1026 2567849 2568458 2569187 "SOLVEFOR" 2571401 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1025 2562148 2567200 2567297 "SNTSCAT" 2567302 NIL SNTSCAT (NIL T T T T) -9 NIL 2567372) (-1024 2556255 2560481 2560870 "SMTS" 2561839 NIL SMTS (NIL T T T) -8 NIL NIL) (-1023 2550665 2556144 2556220 "SMP" 2556225 NIL SMP (NIL T T) -8 NIL NIL) (-1022 2548824 2549125 2549523 "SMITH" 2550362 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1021 2541791 2545987 2546090 "SMATCAT" 2547430 NIL SMATCAT (NIL NIL T T T) -9 NIL 2547976) (-1020 2538732 2539555 2540732 "SMATCAT-" 2540737 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1019 2536486 2538003 2538047 "SKAGG" 2538308 NIL SKAGG (NIL T) -9 NIL 2538443) (-1018 2532544 2535590 2535868 "SINT" 2536230 T SINT (NIL) -8 NIL NIL) (-1017 2532316 2532354 2532420 "SIMPAN" 2532500 T SIMPAN (NIL) -7 NIL NIL) (-1016 2531154 2531375 2531650 "SIGNRF" 2532075 NIL SIGNRF (NIL T) -7 NIL NIL) (-1015 2529963 2530114 2530404 "SIGNEF" 2530983 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1014 2527655 2528109 2528614 "SHP" 2529505 NIL SHP (NIL T NIL) -7 NIL NIL) (-1013 2521514 2527556 2527632 "SHDP" 2527637 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1012 2521003 2521195 2521226 "SGROUP" 2521378 T SGROUP (NIL) -9 NIL 2521465) (-1011 2520773 2520825 2520929 "SGROUP-" 2520934 NIL SGROUP- (NIL T) -8 NIL NIL) (-1010 2517609 2518306 2519029 "SGCF" 2520072 T SGCF (NIL) -7 NIL NIL) (-1009 2512007 2517059 2517156 "SFRTCAT" 2517161 NIL SFRTCAT (NIL T T T T) -9 NIL 2517199) (-1008 2505467 2506482 2507616 "SFRGCD" 2510990 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1007 2498633 2499704 2500888 "SFQCMPK" 2504400 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1006 2498255 2498344 2498454 "SFORT" 2498574 NIL SFORT (NIL T T) -8 NIL NIL) (-1005 2497400 2498095 2498216 "SEXOF" 2498221 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1004 2492176 2492865 2492961 "SEXCAT" 2496732 NIL SEXCAT (NIL T T T T T) -9 NIL 2497351) (-1003 2491310 2492057 2492125 "SEX" 2492130 T SEX (NIL) -8 NIL NIL) (-1002 2489561 2490023 2490328 "SETMN" 2491051 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1001 2489168 2489294 2489325 "SETCAT" 2489442 T SETCAT (NIL) -9 NIL 2489526) (-1000 2488948 2489000 2489099 "SETCAT-" 2489104 NIL SETCAT- (NIL T) -8 NIL NIL) (-999 2485350 2487424 2487466 "SETAGG" 2488323 NIL SETAGG (NIL T) -9 NIL 2488663) (-998 2484811 2484927 2485161 "SETAGG-" 2485166 NIL SETAGG- (NIL T T) -8 NIL NIL) (-997 2481993 2484747 2484793 "SET" 2484798 NIL SET (NIL T) -8 NIL NIL) (-996 2481203 2481496 2481556 "SEGXCAT" 2481839 NIL SEGXCAT (NIL T T) -9 NIL 2481958) (-995 2480120 2480333 2480375 "SEGCAT" 2480948 NIL SEGCAT (NIL T) -9 NIL 2481186) (-994 2479752 2479809 2479918 "SEGBIND2" 2480057 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-993 2478816 2479144 2479339 "SEGBIND" 2479590 NIL SEGBIND (NIL T) -8 NIL NIL) (-992 2478053 2478176 2478374 "SEG2" 2478664 NIL SEG2 (NIL T T) -7 NIL NIL) (-991 2477119 2477729 2477905 "SEG" 2477910 NIL SEG (NIL T) -8 NIL NIL) (-990 2476558 2477056 2477101 "SDVAR" 2477106 NIL SDVAR (NIL T) -8 NIL NIL) (-989 2468864 2476337 2476461 "SDPOL" 2476466 NIL SDPOL (NIL T) -8 NIL NIL) (-988 2467463 2467729 2468046 "SCPKG" 2468579 NIL SCPKG (NIL T) -7 NIL NIL) (-987 2466690 2466823 2467000 "SCACHE" 2467318 NIL SCACHE (NIL T) -7 NIL NIL) (-986 2466133 2466454 2466537 "SAOS" 2466627 T SAOS (NIL) -8 NIL NIL) (-985 2465701 2465736 2465907 "SAERFFC" 2466092 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-984 2465297 2465332 2465489 "SAEFACT" 2465660 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-983 2459193 2465196 2465274 "SAE" 2465279 NIL SAE (NIL T T NIL) -8 NIL NIL) (-982 2457519 2457833 2458232 "RURPK" 2458859 NIL RURPK (NIL T NIL) -7 NIL NIL) (-981 2456172 2456449 2456756 "RULESET" 2457355 NIL RULESET (NIL T T T) -8 NIL NIL) (-980 2455814 2455969 2456050 "RULECOLD" 2456124 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-979 2453022 2453525 2453986 "RULE" 2455496 NIL RULE (NIL T T T) -8 NIL NIL) (-978 2447914 2448708 2449624 "RSETGCD" 2452221 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-977 2437228 2442280 2442375 "RSETCAT" 2446440 NIL RSETCAT (NIL T T T T) -9 NIL 2447537) (-976 2435159 2435698 2436518 "RSETCAT-" 2436523 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-975 2427589 2428964 2430480 "RSDCMPK" 2433758 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-974 2425606 2426047 2426120 "RRCC" 2427196 NIL RRCC (NIL T T) -9 NIL 2427540) (-973 2424960 2425134 2425410 "RRCC-" 2425415 NIL RRCC- (NIL T T T) -8 NIL NIL) (-972 2399290 2408915 2408980 "RPOLCAT" 2419482 NIL RPOLCAT (NIL T T T) -9 NIL 2422629) (-971 2390794 2393132 2396250 "RPOLCAT-" 2396255 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-970 2381872 2389024 2389504 "ROUTINE" 2390334 T ROUTINE (NIL) -8 NIL NIL) (-969 2378577 2381428 2381575 "ROMAN" 2381745 T ROMAN (NIL) -8 NIL NIL) (-968 2376863 2377448 2377705 "ROIRC" 2378383 NIL ROIRC (NIL T T) -8 NIL NIL) (-967 2373211 2375524 2375553 "RNS" 2375849 T RNS (NIL) -9 NIL 2376119) (-966 2371725 2372108 2372639 "RNS-" 2372712 NIL RNS- (NIL T) -8 NIL NIL) (-965 2371150 2371558 2371587 "RNG" 2371592 T RNG (NIL) -9 NIL 2371613) (-964 2370547 2370909 2370950 "RMODULE" 2371010 NIL RMODULE (NIL T) -9 NIL 2371052) (-963 2369399 2369493 2369823 "RMCAT2" 2370448 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-962 2366117 2368586 2368905 "RMATRIX" 2369136 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-961 2359118 2361352 2361465 "RMATCAT" 2364774 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2365751) (-960 2358497 2358644 2358947 "RMATCAT-" 2358952 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-959 2357547 2358111 2358140 "RING" 2358250 T RING (NIL) -9 NIL 2358344) (-958 2357342 2357386 2357480 "RING-" 2357485 NIL RING- (NIL T) -8 NIL NIL) (-957 2356194 2356430 2356685 "RIDIST" 2357107 T RIDIST (NIL) -7 NIL NIL) (-956 2347516 2355668 2355871 "RGCHAIN" 2356043 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-955 2347165 2347228 2347329 "RFFACTOR" 2347447 NIL RFFACTOR (NIL T) -7 NIL NIL) (-954 2346893 2346928 2347023 "RFFACT" 2347124 NIL RFFACT (NIL T) -7 NIL NIL) (-953 2345023 2345387 2345767 "RFDIST" 2346533 T RFDIST (NIL) -7 NIL NIL) (-952 2342028 2342642 2343310 "RF" 2344387 NIL RF (NIL T) -7 NIL NIL) (-951 2341486 2341578 2341738 "RETSOL" 2341930 NIL RETSOL (NIL T T) -7 NIL NIL) (-950 2341078 2341158 2341200 "RETRACT" 2341390 NIL RETRACT (NIL T) -9 NIL NIL) (-949 2340930 2340955 2341039 "RETRACT-" 2341044 NIL RETRACT- (NIL T T) -8 NIL NIL) (-948 2333800 2340587 2340712 "RESULT" 2340825 T RESULT (NIL) -8 NIL NIL) (-947 2332385 2333074 2333271 "RESRING" 2333703 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-946 2332025 2332074 2332170 "RESLATC" 2332322 NIL RESLATC (NIL T) -7 NIL NIL) (-945 2331734 2331768 2331873 "REPSQ" 2331984 NIL REPSQ (NIL T) -7 NIL NIL) (-944 2331435 2331469 2331578 "REPDB" 2331693 NIL REPDB (NIL T) -7 NIL NIL) (-943 2325388 2326767 2327983 "REP2" 2330251 NIL REP2 (NIL T) -7 NIL NIL) (-942 2321798 2322479 2323282 "REP1" 2324617 NIL REP1 (NIL T) -7 NIL NIL) (-941 2319229 2319809 2320409 "REP" 2321218 T REP (NIL) -7 NIL NIL) (-940 2311975 2317390 2317842 "REGSET" 2318860 NIL REGSET (NIL T T T T) -8 NIL NIL) (-939 2310798 2311133 2311380 "REF" 2311761 NIL REF (NIL T) -8 NIL NIL) (-938 2310179 2310282 2310447 "REDORDER" 2310682 NIL REDORDER (NIL T T) -7 NIL NIL) (-937 2306148 2309413 2309634 "RECLOS" 2310010 NIL RECLOS (NIL T) -8 NIL NIL) (-936 2305205 2305386 2305599 "REALSOLV" 2305955 T REALSOLV (NIL) -7 NIL NIL) (-935 2301696 2302498 2303380 "REAL0Q" 2304370 NIL REAL0Q (NIL T) -7 NIL NIL) (-934 2297307 2298295 2299354 "REAL0" 2300677 NIL REAL0 (NIL T) -7 NIL NIL) (-933 2297154 2297195 2297224 "REAL" 2297229 T REAL (NIL) -9 NIL 2297264) (-932 2296562 2296634 2296839 "RDIV" 2297076 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-931 2295639 2295812 2296022 "RDIST" 2296385 NIL RDIST (NIL T) -7 NIL NIL) (-930 2294243 2294530 2294899 "RDETRS" 2295347 NIL RDETRS (NIL T T) -7 NIL NIL) (-929 2292064 2292518 2293053 "RDETR" 2293785 NIL RDETR (NIL T T) -7 NIL NIL) (-928 2290680 2290958 2291359 "RDEEFS" 2291780 NIL RDEEFS (NIL T T) -7 NIL NIL) (-927 2289180 2289486 2289915 "RDEEF" 2290368 NIL RDEEF (NIL T T) -7 NIL NIL) (-926 2283403 2286337 2286366 "RCFIELD" 2287643 T RCFIELD (NIL) -9 NIL 2288373) (-925 2281472 2281976 2282669 "RCFIELD-" 2282742 NIL RCFIELD- (NIL T) -8 NIL NIL) (-924 2277846 2279625 2279667 "RCAGG" 2280738 NIL RCAGG (NIL T) -9 NIL 2281201) (-923 2277477 2277571 2277731 "RCAGG-" 2277736 NIL RCAGG- (NIL T T) -8 NIL NIL) (-922 2276822 2276933 2277095 "RATRET" 2277361 NIL RATRET (NIL T) -7 NIL NIL) (-921 2276379 2276446 2276565 "RATFACT" 2276750 NIL RATFACT (NIL T) -7 NIL NIL) (-920 2275694 2275814 2275964 "RANDSRC" 2276249 T RANDSRC (NIL) -7 NIL NIL) (-919 2275431 2275475 2275546 "RADUTIL" 2275643 T RADUTIL (NIL) -7 NIL NIL) (-918 2268438 2274174 2274491 "RADIX" 2275146 NIL RADIX (NIL NIL) -8 NIL NIL) (-917 2260008 2268282 2268410 "RADFF" 2268415 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-916 2259659 2259734 2259763 "RADCAT" 2259920 T RADCAT (NIL) -9 NIL NIL) (-915 2259444 2259492 2259589 "RADCAT-" 2259594 NIL RADCAT- (NIL T) -8 NIL NIL) (-914 2257601 2259219 2259308 "QUEUE" 2259388 NIL QUEUE (NIL T) -8 NIL NIL) (-913 2257239 2257282 2257409 "QUATCT2" 2257552 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-912 2250993 2254373 2254414 "QUATCAT" 2255193 NIL QUATCAT (NIL T) -9 NIL 2255950) (-911 2247137 2248174 2249561 "QUATCAT-" 2249655 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-910 2243634 2247074 2247119 "QUAT" 2247124 NIL QUAT (NIL T) -8 NIL NIL) (-909 2241195 2242753 2242795 "QUAGG" 2243170 NIL QUAGG (NIL T) -9 NIL 2243345) (-908 2240120 2240593 2240765 "QFORM" 2241067 NIL QFORM (NIL NIL T) -8 NIL NIL) (-907 2239758 2239801 2239928 "QFCAT2" 2240071 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-906 2231019 2236277 2236318 "QFCAT" 2236976 NIL QFCAT (NIL T) -9 NIL 2237957) (-905 2226591 2227792 2229383 "QFCAT-" 2229477 NIL QFCAT- (NIL T T) -8 NIL NIL) (-904 2226051 2226161 2226291 "QEQUAT" 2226481 T QEQUAT (NIL) -8 NIL NIL) (-903 2219237 2220308 2221490 "QCMPACK" 2224984 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-902 2218482 2218656 2218888 "QALGSET2" 2219057 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-901 2216062 2216483 2216909 "QALGSET" 2218139 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-900 2214753 2214976 2215293 "PWFFINTB" 2215835 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-899 2212941 2213109 2213462 "PUSHVAR" 2214567 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-898 2208858 2209912 2209954 "PTRANFN" 2211838 NIL PTRANFN (NIL T) -9 NIL NIL) (-897 2207270 2207561 2207882 "PTPACK" 2208569 NIL PTPACK (NIL T) -7 NIL NIL) (-896 2206906 2206963 2207070 "PTFUNC2" 2207207 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-895 2201412 2205747 2205788 "PTCAT" 2206156 NIL PTCAT (NIL T) -9 NIL 2206318) (-894 2201070 2201105 2201229 "PSQFR" 2201371 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-893 2199665 2199963 2200297 "PSEUDLIN" 2200768 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-892 2186479 2188843 2191163 "PSETPK" 2197428 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-891 2179566 2182280 2182375 "PSETCAT" 2185356 NIL PSETCAT (NIL T T T T) -9 NIL 2186169) (-890 2177404 2178038 2178857 "PSETCAT-" 2178862 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-889 2176761 2176923 2176952 "PSCURVE" 2177217 T PSCURVE (NIL) -9 NIL 2177381) (-888 2173165 2174691 2174756 "PSCAT" 2175592 NIL PSCAT (NIL T T T) -9 NIL 2175832) (-887 2172229 2172445 2172844 "PSCAT-" 2172849 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-886 2170882 2171514 2171728 "PRTITION" 2172035 T PRTITION (NIL) -8 NIL NIL) (-885 2159982 2162188 2164375 "PRS" 2168745 NIL PRS (NIL T T) -7 NIL NIL) (-884 2157881 2159367 2159408 "PRQAGG" 2159591 NIL PRQAGG (NIL T) -9 NIL 2159693) (-883 2151687 2156079 2156883 "PRODUCT" 2157123 NIL PRODUCT (NIL T T) -8 NIL NIL) (-882 2151483 2151515 2151574 "PRINT" 2151648 T PRINT (NIL) -7 NIL NIL) (-881 2150823 2150940 2151092 "PRIMES" 2151363 NIL PRIMES (NIL T) -7 NIL NIL) (-880 2148888 2149289 2149755 "PRIMELT" 2150402 NIL PRIMELT (NIL T) -7 NIL NIL) (-879 2148619 2148667 2148696 "PRIMCAT" 2148819 T PRIMCAT (NIL) -9 NIL NIL) (-878 2147626 2147804 2148032 "PRIMARR2" 2148437 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-877 2143793 2147564 2147609 "PRIMARR" 2147614 NIL PRIMARR (NIL T) -8 NIL NIL) (-876 2143436 2143492 2143603 "PREASSOC" 2143731 NIL PREASSOC (NIL T T) -7 NIL NIL) (-875 2140718 2142902 2143132 "PR" 2143250 NIL PR (NIL T T) -8 NIL NIL) (-874 2140198 2140329 2140358 "PPCURVE" 2140561 T PPCURVE (NIL) -9 NIL 2140695) (-873 2137559 2137958 2138549 "POLYROOT" 2139780 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-872 2136944 2137002 2137235 "POLYLIFT" 2137495 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-871 2133229 2133678 2134306 "POLYCATQ" 2136489 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-870 2120235 2125634 2125699 "POLYCAT" 2129184 NIL POLYCAT (NIL T T T) -9 NIL 2131096) (-869 2113686 2115547 2117930 "POLYCAT-" 2117935 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-868 2113275 2113343 2113462 "POLY2UP" 2113612 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-867 2112911 2112968 2113075 "POLY2" 2113212 NIL POLY2 (NIL T T) -7 NIL NIL) (-866 2106819 2112519 2112677 "POLY" 2112785 NIL POLY (NIL T) -8 NIL NIL) (-865 2105506 2105745 2106020 "POLUTIL" 2106594 NIL POLUTIL (NIL T T) -7 NIL NIL) (-864 2103868 2104145 2104475 "POLTOPOL" 2105228 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-863 2099397 2103805 2103850 "POINT" 2103855 NIL POINT (NIL T) -8 NIL NIL) (-862 2097584 2097941 2098316 "PNTHEORY" 2099042 T PNTHEORY (NIL) -7 NIL NIL) (-861 2096012 2096309 2096718 "PMTOOLS" 2097282 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-860 2095605 2095683 2095800 "PMSYM" 2095928 NIL PMSYM (NIL T) -7 NIL NIL) (-859 2095115 2095184 2095358 "PMQFCAT" 2095530 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-858 2094511 2094597 2094758 "PMPREDFS" 2095016 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-857 2093866 2093976 2094132 "PMPRED" 2094388 NIL PMPRED (NIL T) -7 NIL NIL) (-856 2092514 2092722 2093105 "PMPLCAT" 2093629 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-855 2092046 2092125 2092277 "PMLSAGG" 2092429 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-854 2091523 2091599 2091779 "PMKERNEL" 2091964 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-853 2091140 2091215 2091328 "PMINS" 2091442 NIL PMINS (NIL T) -7 NIL NIL) (-852 2090570 2090639 2090854 "PMFS" 2091065 NIL PMFS (NIL T T T) -7 NIL NIL) (-851 2089801 2089919 2090123 "PMDOWN" 2090447 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-850 2089075 2089186 2089349 "PMASSFS" 2089687 NIL PMASSFS (NIL T T) -7 NIL NIL) (-849 2088238 2088397 2088579 "PMASS" 2088913 T PMASS (NIL) -7 NIL NIL) (-848 2087897 2087964 2088057 "PLOTTOOL" 2088165 T PLOTTOOL (NIL) -7 NIL NIL) (-847 2083770 2084785 2085690 "PLOT3D" 2087012 T PLOT3D (NIL) -8 NIL NIL) (-846 2082694 2082868 2083100 "PLOT1" 2083577 NIL PLOT1 (NIL T) -7 NIL NIL) (-845 2077395 2078561 2079688 "PLOT" 2081587 T PLOT (NIL) -8 NIL NIL) (-844 2053386 2057990 2062768 "PLEQN" 2072734 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-843 2053079 2053126 2053229 "PINTERPA" 2053333 NIL PINTERPA (NIL T T) -7 NIL NIL) (-842 2052397 2052519 2052699 "PINTERP" 2052944 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-841 2050788 2051773 2051802 "PID" 2051984 T PID (NIL) -9 NIL 2052118) (-840 2050513 2050550 2050638 "PICOERCE" 2050745 NIL PICOERCE (NIL T) -7 NIL NIL) (-839 2049740 2050307 2050400 "PI" 2050440 T PI (NIL) -8 NIL NIL) (-838 2049061 2049199 2049375 "PGROEB" 2049596 NIL PGROEB (NIL T) -7 NIL NIL) (-837 2044648 2045462 2046367 "PGE" 2048176 T PGE (NIL) -7 NIL NIL) (-836 2042772 2043018 2043384 "PGCD" 2044365 NIL PGCD (NIL T T T T) -7 NIL NIL) (-835 2042110 2042213 2042374 "PFRPAC" 2042656 NIL PFRPAC (NIL T) -7 NIL NIL) (-834 2038725 2040658 2041011 "PFR" 2041789 NIL PFR (NIL T) -8 NIL NIL) (-833 2037114 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(NIL T) -8 NIL NIL) (-820 2008404 2009182 2009224 "PDRING" 2009881 NIL PDRING (NIL T) -9 NIL 2010166) (-819 2007507 2007725 2008087 "PDRING-" 2008092 NIL PDRING- (NIL T T) -8 NIL NIL) (-818 2004649 2005399 2006090 "PDEPROB" 2006836 T PDEPROB (NIL) -8 NIL NIL) (-817 2002220 2002716 2003265 "PDEPACK" 2004120 T PDEPACK (NIL) -7 NIL NIL) (-816 2001132 2001322 2001573 "PDECOMP" 2002019 NIL PDECOMP (NIL T T) -7 NIL NIL) (-815 1998743 1999558 1999587 "PDECAT" 2000372 T PDECAT (NIL) -9 NIL 2001083) (-814 1998496 1998529 1998618 "PCOMP" 1998704 NIL PCOMP (NIL T T) -7 NIL NIL) (-813 1996703 1997299 1997595 "PBWLB" 1998226 NIL PBWLB (NIL T) -8 NIL NIL) (-812 1996335 1996392 1996501 "PATTERN2" 1996640 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-811 1994092 1994480 1994937 "PATTERN1" 1995924 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-810 1986601 1988169 1989505 "PATTERN" 1992777 NIL PATTERN (NIL T) -8 NIL NIL) (-809 1986165 1986232 1986364 "PATRES2" 1986528 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-808 1983560 1984114 1984595 "PATRES" 1985730 NIL PATRES (NIL T T) -8 NIL NIL) (-807 1981457 1981857 1982262 "PATMATCH" 1983229 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-806 1980993 1981176 1981218 "PATMAB" 1981325 NIL PATMAB (NIL T) -9 NIL 1981408) (-805 1979538 1979847 1980105 "PATLRES" 1980798 NIL PATLRES (NIL T T T) -8 NIL NIL) (-804 1979085 1979208 1979250 "PATAB" 1979255 NIL PATAB (NIL T) -9 NIL 1979425) (-803 1976566 1977098 1977671 "PARTPERM" 1978532 T PARTPERM (NIL) -7 NIL NIL) (-802 1976187 1976250 1976352 "PARSURF" 1976497 NIL PARSURF (NIL T) -8 NIL NIL) (-801 1975819 1975876 1975985 "PARSU2" 1976124 NIL PARSU2 (NIL T T) -7 NIL NIL) (-800 1975440 1975503 1975605 "PARSCURV" 1975750 NIL PARSCURV (NIL T) -8 NIL NIL) (-799 1975072 1975129 1975238 "PARSC2" 1975377 NIL PARSC2 (NIL T T) -7 NIL NIL) (-798 1974711 1974769 1974866 "PARPCURV" 1975008 NIL PARPCURV (NIL T) -8 NIL NIL) (-797 1974343 1974400 1974509 "PARPC2" 1974648 NIL PARPC2 (NIL T T) -7 NIL NIL) (-796 1973863 1973949 1974068 "PAN2EXPR" 1974244 T PAN2EXPR (NIL) -7 NIL NIL) (-795 1972669 1972984 1973212 "PALETTE" 1973655 T PALETTE (NIL) -8 NIL NIL) (-794 1966519 1971928 1972122 "PADICRC" 1972524 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-793 1959727 1965865 1966049 "PADICRAT" 1966367 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-792 1956931 1958505 1958546 "PADICCT" 1959127 NIL PADICCT (NIL NIL) -9 NIL 1959409) (-791 1955235 1956868 1956913 "PADIC" 1956918 NIL PADIC (NIL NIL) -8 NIL NIL) (-790 1954192 1954392 1954660 "PADEPAC" 1955022 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-789 1953404 1953537 1953743 "PADE" 1954054 NIL PADE (NIL T T T) -7 NIL NIL) (-788 1951419 1952251 1952564 "OWP" 1953174 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-787 1950528 1951024 1951196 "OVAR" 1951287 NIL OVAR (NIL NIL) -8 NIL NIL) (-786 1939574 1941753 1943923 "OUTFORM" 1948378 T OUTFORM (NIL) -8 NIL NIL) (-785 1938838 1938959 1939120 "OUT" 1939433 T OUT (NIL) -7 NIL NIL) (-784 1938246 1938567 1938656 "OSI" 1938769 T OSI (NIL) -8 NIL NIL) (-783 1936993 1937220 1937504 "ORTHPOL" 1937994 NIL ORTHPOL (NIL T) -7 NIL NIL) (-782 1934364 1936654 1936792 "OREUP" 1936936 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-781 1931760 1934057 1934183 "ORESUP" 1934306 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-780 1929299 1929799 1930357 "OREPCTO" 1931251 NIL OREPCTO (NIL T T) -7 NIL NIL) (-779 1923212 1925418 1925459 "OREPCAT" 1927780 NIL OREPCAT (NIL T) -9 NIL 1928879) (-778 1920360 1921142 1922199 "OREPCAT-" 1922204 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-777 1919537 1919809 1919838 "ORDSET" 1920147 T ORDSET (NIL) -9 NIL 1920311) (-776 1919056 1919178 1919371 "ORDSET-" 1919376 NIL ORDSET- (NIL T) -8 NIL NIL) (-775 1917669 1918470 1918499 "ORDRING" 1918701 T ORDRING (NIL) -9 NIL 1918825) (-774 1917314 1917408 1917552 "ORDRING-" 1917557 NIL ORDRING- (NIL T) -8 NIL NIL) (-773 1916689 1917170 1917199 "ORDMON" 1917204 T ORDMON (NIL) -9 NIL 1917225) (-772 1915851 1915998 1916193 "ORDFUNS" 1916538 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-771 1915362 1915721 1915750 "ORDFIN" 1915755 T ORDFIN (NIL) -9 NIL 1915776) (-770 1914628 1914755 1914941 "ORDCOMP2" 1915222 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-769 1911146 1913220 1913626 "ORDCOMP" 1914255 NIL ORDCOMP (NIL T) -8 NIL NIL) (-768 1907654 1908536 1909373 "OPTPROB" 1910329 T OPTPROB (NIL) -8 NIL NIL) (-767 1904496 1905125 1905819 "OPTPACK" 1906980 T OPTPACK (NIL) -7 NIL NIL) (-766 1902221 1902957 1902986 "OPTCAT" 1903801 T OPTCAT (NIL) -9 NIL 1904447) (-765 1901989 1902028 1902094 "OPQUERY" 1902175 T OPQUERY (NIL) -7 NIL NIL) (-764 1899131 1900322 1900819 "OP" 1901524 NIL OP (NIL T) -8 NIL NIL) (-763 1898436 1898551 1898725 "ONECOMP2" 1899003 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-762 1895207 1897239 1897605 "ONECOMP" 1898103 NIL ONECOMP (NIL T) -8 NIL NIL) (-761 1894626 1894732 1894862 "OMSERVER" 1895097 T OMSERVER (NIL) -7 NIL NIL) (-760 1891515 1894067 1894108 "OMSAGG" 1894169 NIL OMSAGG (NIL T) -9 NIL 1894233) (-759 1890138 1890401 1890683 "OMPKG" 1891253 T OMPKG (NIL) -7 NIL NIL) (-758 1888679 1889692 1889859 "OMLO" 1890020 NIL OMLO (NIL T T) -8 NIL NIL) (-757 1887609 1887756 1887982 "OMEXPR" 1888505 NIL OMEXPR (NIL T) -7 NIL NIL) (-756 1886787 1887030 1887190 "OMERRK" 1887469 T OMERRK (NIL) -8 NIL NIL) (-755 1886105 1886333 1886469 "OMERR" 1886671 T OMERR (NIL) -8 NIL NIL) (-754 1885583 1885782 1885890 "OMENC" 1886017 T OMENC (NIL) -8 NIL NIL) (-753 1879478 1880663 1881834 "OMDEV" 1884432 T OMDEV (NIL) -8 NIL NIL) (-752 1878547 1878718 1878912 "OMCONN" 1879304 T OMCONN (NIL) -8 NIL NIL) (-751 1877976 1878079 1878108 "OM" 1878407 T OM (NIL) -9 NIL NIL) (-750 1876591 1877577 1877606 "OINTDOM" 1877611 T OINTDOM (NIL) -9 NIL 1877632) (-749 1872353 1873583 1874298 "OFMONOID" 1875908 NIL OFMONOID (NIL T) -8 NIL NIL) (-748 1871791 1872290 1872335 "ODVAR" 1872340 NIL ODVAR (NIL T) -8 NIL NIL) (-747 1868918 1871290 1871474 "ODR" 1871667 NIL ODR (NIL T T NIL) -8 NIL NIL) (-746 1861224 1868697 1868821 "ODPOL" 1868826 NIL ODPOL (NIL T) -8 NIL NIL) (-745 1855053 1861096 1861201 "ODP" 1861206 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-744 1853819 1854034 1854309 "ODETOOLS" 1854827 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-743 1850788 1851444 1852160 "ODESYS" 1853152 NIL ODESYS (NIL T T) -7 NIL NIL) (-742 1845694 1846602 1847624 "ODERTRIC" 1849864 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-741 1845120 1845202 1845396 "ODERED" 1845606 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-740 1842022 1842570 1843245 "ODERAT" 1844543 NIL ODERAT (NIL T T) -7 NIL NIL) (-739 1838990 1839454 1840050 "ODEPRRIC" 1841551 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-738 1836861 1837428 1837937 "ODEPROB" 1838501 T ODEPROB (NIL) -8 NIL NIL) (-737 1833393 1833876 1834522 "ODEPRIM" 1836340 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-736 1832646 1832748 1833006 "ODEPAL" 1833285 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-735 1828848 1829629 1830483 "ODEPACK" 1831812 T ODEPACK (NIL) -7 NIL NIL) (-734 1827885 1827992 1828220 "ODEINT" 1828737 NIL ODEINT (NIL T T) -7 NIL NIL) (-733 1821986 1823411 1824858 "ODEIFTBL" 1826458 T ODEIFTBL (NIL) -8 NIL NIL) (-732 1817330 1818116 1819074 "ODEEF" 1821145 NIL ODEEF (NIL T T) -7 NIL NIL) (-731 1816667 1816756 1816985 "ODECONST" 1817235 NIL ODECONST (NIL T T T) -7 NIL NIL) (-730 1814824 1815457 1815486 "ODECAT" 1816089 T ODECAT (NIL) -9 NIL 1816618) (-729 1814462 1814505 1814632 "OCTCT2" 1814775 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-728 1811334 1814174 1814293 "OCT" 1814375 NIL OCT (NIL T) -8 NIL NIL) (-727 1810712 1811154 1811183 "OCAMON" 1811188 T OCAMON (NIL) -9 NIL 1811209) (-726 1805553 1807991 1808032 "OC" 1809128 NIL OC (NIL T) -9 NIL 1809977) (-725 1802780 1803528 1804518 "OC-" 1804612 NIL OC- (NIL T T) -8 NIL NIL) (-724 1802233 1802640 1802669 "OASGP" 1802674 T OASGP (NIL) -9 NIL 1802694) (-723 1801520 1801983 1802012 "OAMONS" 1802052 T OAMONS (NIL) -9 NIL 1802095) (-722 1800960 1801367 1801396 "OAMON" 1801401 T OAMON (NIL) -9 NIL 1801421) (-721 1800264 1800756 1800785 "OAGROUP" 1800790 T OAGROUP (NIL) -9 NIL 1800810) (-720 1799954 1800004 1800092 "NUMTUBE" 1800208 NIL NUMTUBE (NIL T) -7 NIL NIL) (-719 1793527 1795045 1796581 "NUMQUAD" 1798438 T NUMQUAD (NIL) -7 NIL NIL) (-718 1789283 1790271 1791296 "NUMODE" 1792522 T NUMODE (NIL) -7 NIL NIL) (-717 1786698 1787540 1787569 "NUMINT" 1788482 T NUMINT (NIL) -9 NIL 1789234) (-716 1785646 1785843 1786061 "NUMFMT" 1786500 T NUMFMT (NIL) -7 NIL NIL) (-715 1772044 1774978 1777500 "NUMERIC" 1783163 NIL NUMERIC (NIL T) -7 NIL NIL) (-714 1766444 1771496 1771591 "NTSCAT" 1771596 NIL NTSCAT (NIL T T T T) -9 NIL 1771634) (-713 1765640 1765805 1765997 "NTPOLFN" 1766284 NIL NTPOLFN (NIL T) -7 NIL NIL) (-712 1765276 1765333 1765440 "NSUP2" 1765577 NIL NSUP2 (NIL T T) -7 NIL NIL) (-711 1753134 1762120 1762929 "NSUP" 1764499 NIL NSUP (NIL T) -8 NIL NIL) (-710 1743096 1752913 1753043 "NSMP" 1753048 NIL NSMP (NIL T T) -8 NIL NIL) (-709 1741528 1741829 1742186 "NREP" 1742784 NIL NREP (NIL T) -7 NIL NIL) (-708 1740119 1740371 1740729 "NPCOEF" 1741271 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-707 1739185 1739300 1739516 "NORMRETR" 1740000 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-706 1737238 1737528 1737935 "NORMPK" 1738893 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-705 1736923 1736951 1737075 "NORMMA" 1737204 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-704 1736712 1736741 1736810 "NONE1" 1736887 NIL NONE1 (NIL T) -7 NIL NIL) (-703 1736539 1736669 1736698 "NONE" 1736703 T NONE (NIL) -8 NIL NIL) (-702 1736024 1736086 1736271 "NODE1" 1736471 NIL NODE1 (NIL T T) -7 NIL NIL) (-701 1734318 1735187 1735442 "NNI" 1735789 T NNI (NIL) -8 NIL NIL) (-700 1732738 1733051 1733415 "NLINSOL" 1733986 NIL NLINSOL (NIL T) -7 NIL NIL) (-699 1728930 1729891 1730807 "NIPROB" 1731842 T NIPROB (NIL) -8 NIL NIL) (-698 1727687 1727921 1728223 "NFINTBAS" 1728692 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-697 1726395 1726626 1726907 "NCODIV" 1727455 NIL NCODIV (NIL T T) -7 NIL NIL) (-696 1726157 1726194 1726269 "NCNTFRAC" 1726352 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-695 1724337 1724701 1725121 "NCEP" 1725782 NIL NCEP (NIL T) -7 NIL NIL) (-694 1723248 1723987 1724016 "NASRING" 1724126 T NASRING (NIL) -9 NIL 1724200) (-693 1723043 1723087 1723181 "NASRING-" 1723186 NIL NASRING- (NIL T) -8 NIL NIL) (-692 1722196 1722695 1722724 "NARNG" 1722841 T NARNG (NIL) -9 NIL 1722932) (-691 1721888 1721955 1722089 "NARNG-" 1722094 NIL NARNG- (NIL T) -8 NIL NIL) (-690 1720767 1720974 1721209 "NAGSP" 1721673 T NAGSP (NIL) -7 NIL NIL) (-689 1712191 1713837 1715472 "NAGS" 1719152 T NAGS (NIL) -7 NIL NIL) (-688 1710755 1711059 1711386 "NAGF07" 1711884 T NAGF07 (NIL) -7 NIL NIL) (-687 1705337 1706617 1707913 "NAGF04" 1709479 T NAGF04 (NIL) -7 NIL NIL) (-686 1698369 1699967 1701584 "NAGF02" 1703740 T NAGF02 (NIL) -7 NIL NIL) (-685 1693633 1694723 1695830 "NAGF01" 1697282 T NAGF01 (NIL) -7 NIL NIL) (-684 1687293 1688851 1690428 "NAGE04" 1692076 T NAGE04 (NIL) -7 NIL NIL) (-683 1678534 1680637 1682749 "NAGE02" 1685201 T NAGE02 (NIL) -7 NIL NIL) (-682 1674527 1675464 1676418 "NAGE01" 1677600 T NAGE01 (NIL) -7 NIL NIL) (-681 1672334 1672865 1673420 "NAGD03" 1673992 T NAGD03 (NIL) -7 NIL NIL) (-680 1664120 1666039 1667984 "NAGD02" 1670409 T NAGD02 (NIL) -7 NIL NIL) (-679 1657979 1659392 1660820 "NAGD01" 1662712 T NAGD01 (NIL) -7 NIL NIL) (-678 1654236 1655046 1655871 "NAGC06" 1657174 T NAGC06 (NIL) -7 NIL NIL) (-677 1652713 1653042 1653395 "NAGC05" 1653903 T NAGC05 (NIL) -7 NIL NIL) (-676 1652097 1652214 1652356 "NAGC02" 1652591 T NAGC02 (NIL) -7 NIL NIL) (-675 1651158 1651715 1651756 "NAALG" 1651835 NIL NAALG (NIL T) -9 NIL 1651896) (-674 1650993 1651022 1651112 "NAALG-" 1651117 NIL NAALG- (NIL T T) -8 NIL NIL) (-673 1644943 1646051 1647238 "MULTSQFR" 1649889 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-672 1644262 1644337 1644521 "MULTFACT" 1644855 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-671 1637397 1641315 1641368 "MTSCAT" 1642428 NIL MTSCAT (NIL T T) -9 NIL 1642941) (-670 1637109 1637163 1637255 "MTHING" 1637337 NIL MTHING (NIL T) -7 NIL NIL) (-669 1636901 1636934 1636994 "MSYSCMD" 1637069 T MSYSCMD (NIL) -7 NIL NIL) (-668 1633998 1636464 1636506 "MSETAGG" 1636511 NIL MSETAGG (NIL T) -9 NIL 1636544) (-667 1630110 1632753 1633073 "MSET" 1633711 NIL MSET (NIL T) -8 NIL NIL) (-666 1625978 1627520 1628255 "MRING" 1629419 NIL MRING (NIL T T) -8 NIL NIL) (-665 1625548 1625615 1625744 "MRF2" 1625905 NIL MRF2 (NIL T T T) -7 NIL NIL) (-664 1625166 1625201 1625345 "MRATFAC" 1625507 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-663 1622778 1623073 1623504 "MPRFF" 1624871 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-662 1616798 1622633 1622729 "MPOLY" 1622734 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-661 1616288 1616323 1616531 "MPCPF" 1616757 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-660 1615804 1615847 1616030 "MPC3" 1616239 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-659 1615005 1615086 1615305 "MPC2" 1615719 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-658 1613306 1613643 1614033 "MONOTOOL" 1614665 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-657 1612430 1612765 1612794 "MONOID" 1613071 T MONOID (NIL) -9 NIL 1613243) (-656 1611808 1611971 1612214 "MONOID-" 1612219 NIL MONOID- (NIL T) -8 NIL NIL) (-655 1602744 1608730 1608790 "MONOGEN" 1609464 NIL MONOGEN (NIL T T) -9 NIL 1609917) (-654 1599962 1600697 1601697 "MONOGEN-" 1601816 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-653 1598821 1599241 1599270 "MONADWU" 1599662 T MONADWU (NIL) -9 NIL 1599900) (-652 1598193 1598352 1598600 "MONADWU-" 1598605 NIL MONADWU- (NIL T) -8 NIL NIL) (-651 1597578 1597796 1597825 "MONAD" 1598032 T MONAD (NIL) -9 NIL 1598144) (-650 1597263 1597341 1597473 "MONAD-" 1597478 NIL MONAD- (NIL T) -8 NIL NIL) (-649 1595514 1596176 1596455 "MOEBIUS" 1597016 NIL MOEBIUS (NIL T) -8 NIL NIL) (-648 1594907 1595285 1595326 "MODULE" 1595331 NIL MODULE (NIL T) -9 NIL 1595357) (-647 1594475 1594571 1594761 "MODULE-" 1594766 NIL MODULE- (NIL T T) -8 NIL NIL) (-646 1592146 1592841 1593167 "MODRING" 1594300 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-645 1589108 1590273 1590787 "MODOP" 1591681 NIL MODOP (NIL T T) -8 NIL NIL) (-644 1587295 1587747 1588088 "MODMONOM" 1588907 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-643 1577017 1585503 1585923 "MODMON" 1586925 NIL MODMON (NIL T T) -8 NIL NIL) (-642 1574143 1575861 1576137 "MODFIELD" 1576892 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-641 1573669 1573712 1573891 "MMAP" 1574094 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-640 1571906 1572683 1572724 "MLO" 1573141 NIL MLO (NIL T) -9 NIL 1573381) (-639 1569273 1569788 1570390 "MLIFT" 1571387 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-638 1568664 1568748 1568902 "MKUCFUNC" 1569184 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-637 1568263 1568333 1568456 "MKRECORD" 1568587 NIL MKRECORD (NIL T T) -7 NIL NIL) (-636 1567311 1567472 1567700 "MKFUNC" 1568074 NIL MKFUNC (NIL T) -7 NIL NIL) (-635 1566699 1566803 1566959 "MKFLCFN" 1567194 NIL MKFLCFN (NIL T) -7 NIL NIL) (-634 1566125 1566492 1566581 "MKCHSET" 1566643 NIL MKCHSET (NIL T) -8 NIL NIL) (-633 1565402 1565504 1565689 "MKBCFUNC" 1566018 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-632 1562086 1564956 1565092 "MINT" 1565286 T MINT (NIL) -8 NIL NIL) (-631 1560898 1561141 1561418 "MHROWRED" 1561841 NIL MHROWRED (NIL T) -7 NIL NIL) (-630 1556169 1559343 1559767 "MFLOAT" 1560494 T MFLOAT (NIL) -8 NIL NIL) (-629 1555526 1555602 1555773 "MFINFACT" 1556081 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-628 1551873 1552712 1553587 "MESH" 1554671 T MESH (NIL) -7 NIL NIL) (-627 1550263 1550575 1550928 "MDDFACT" 1551560 NIL MDDFACT (NIL T) -7 NIL NIL) (-626 1547146 1549457 1549499 "MDAGG" 1549754 NIL MDAGG (NIL T) -9 NIL 1549897) (-625 1536844 1546439 1546646 "MCMPLX" 1546959 T MCMPLX (NIL) -8 NIL NIL) (-624 1535985 1536131 1536331 "MCDEN" 1536693 NIL MCDEN (NIL T T) -7 NIL NIL) (-623 1533875 1534145 1534525 "MCALCFN" 1535715 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-622 1531497 1532020 1532581 "MATSTOR" 1533346 NIL MATSTOR (NIL T) -7 NIL NIL) (-621 1527515 1530876 1531121 "MATRIX" 1531284 NIL MATRIX (NIL T) -8 NIL NIL) (-620 1523291 1523994 1524727 "MATLIN" 1526875 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-619 1521893 1522046 1522377 "MATCAT2" 1523126 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1512137 1515269 1515346 "MATCAT" 1520184 NIL MATCAT (NIL T T T) -9 NIL 1521595) (-617 1508502 1509515 1510870 "MATCAT-" 1510875 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-616 1506614 1506938 1507322 "MAPPKG3" 1508177 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-615 1505595 1505768 1505990 "MAPPKG2" 1506438 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-614 1504094 1504378 1504705 "MAPPKG1" 1505301 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-613 1503705 1503763 1503886 "MAPHACK3" 1504030 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-612 1503297 1503358 1503472 "MAPHACK2" 1503637 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-611 1502735 1502838 1502980 "MAPHACK1" 1503188 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-610 1500843 1501437 1501740 "MAGMA" 1502464 NIL MAGMA (NIL T) -8 NIL NIL) (-609 1497326 1499089 1499548 "M3D" 1500417 NIL M3D (NIL T) -8 NIL NIL) (-608 1491519 1495728 1495770 "LZSTAGG" 1496552 NIL LZSTAGG (NIL T) -9 NIL 1496847) (-607 1487493 1488650 1490107 "LZSTAGG-" 1490112 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-606 1484609 1485386 1485872 "LWORD" 1487039 NIL LWORD (NIL T) -8 NIL NIL) (-605 1477769 1484380 1484514 "LSQM" 1484519 NIL LSQM (NIL NIL T) -8 NIL NIL) (-604 1476993 1477132 1477360 "LSPP" 1477624 NIL LSPP (NIL T T T T) -7 NIL NIL) (-603 1473772 1474446 1475176 "LSMP1" 1476295 NIL LSMP1 (NIL T) -7 NIL NIL) (-602 1471584 1471885 1472341 "LSMP" 1473461 NIL LSMP (NIL T T T T) -7 NIL NIL) (-601 1465540 1470776 1470818 "LSAGG" 1470880 NIL LSAGG (NIL T) -9 NIL 1470958) (-600 1462235 1463159 1464372 "LSAGG-" 1464377 NIL LSAGG- (NIL T T) -8 NIL NIL) (-599 1459861 1461379 1461628 "LPOLY" 1462030 NIL LPOLY (NIL T T) -8 NIL NIL) (-598 1459443 1459528 1459651 "LPEFRAC" 1459770 NIL LPEFRAC (NIL T) -7 NIL NIL) (-597 1459096 1459208 1459237 "LOGIC" 1459348 T LOGIC (NIL) -9 NIL 1459428) (-596 1458958 1458981 1459052 "LOGIC-" 1459057 NIL LOGIC- (NIL T) -8 NIL NIL) (-595 1458151 1458291 1458484 "LODOOPS" 1458814 NIL LODOOPS (NIL T T) -7 NIL NIL) (-594 1456699 1456934 1457284 "LODOF" 1457899 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1453119 1455555 1455596 "LODOCAT" 1456028 NIL LODOCAT (NIL T) -9 NIL 1456238) (-592 1452853 1452911 1453037 "LODOCAT-" 1453042 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1450167 1452694 1452812 "LODO2" 1452817 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1447596 1450104 1450149 "LODO1" 1450154 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1445014 1447513 1447578 "LODO" 1447583 NIL LODO (NIL T NIL) -8 NIL NIL) (-588 1443877 1444042 1444353 "LODEEF" 1444837 NIL LODEEF (NIL T T T) -7 NIL NIL) (-587 1442226 1442973 1443225 "LO" 1443710 NIL LO (NIL T T T) -8 NIL NIL) (-586 1437551 1440389 1440431 "LNAGG" 1441378 NIL LNAGG (NIL T) -9 NIL 1441821) (-585 1436698 1436912 1437254 "LNAGG-" 1437259 NIL LNAGG- (NIL T T) -8 NIL NIL) (-584 1432863 1433625 1434263 "LMOPS" 1436114 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-583 1432260 1432622 1432663 "LMODULE" 1432723 NIL LMODULE (NIL T) -9 NIL 1432765) (-582 1429512 1431905 1432028 "LMDICT" 1432170 NIL LMDICT (NIL T) -8 NIL NIL) (-581 1429037 1429111 1429250 "LIST3" 1429432 NIL LIST3 (NIL T T T) -7 NIL NIL) (-580 1427171 1427483 1427882 "LIST2MAP" 1428684 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1426178 1426356 1426584 "LIST2" 1426989 NIL LIST2 (NIL T T) -7 NIL NIL) (-578 1419415 1425128 1425424 "LIST" 1425915 NIL LIST (NIL T) -8 NIL NIL) (-577 1418127 1418807 1418848 "LINEXP" 1419101 NIL LINEXP (NIL T) -9 NIL 1419249) (-576 1416774 1417034 1417331 "LINDEP" 1417879 NIL LINDEP (NIL T T) -7 NIL NIL) (-575 1413541 1414260 1415037 "LIMITRF" 1416029 NIL LIMITRF (NIL T) -7 NIL NIL) (-574 1411822 1412116 1412531 "LIMITPS" 1413236 NIL LIMITPS (NIL T T) -7 NIL NIL) (-573 1410873 1411316 1411357 "LIECAT" 1411497 NIL LIECAT (NIL T) -9 NIL 1411647) (-572 1410714 1410741 1410829 "LIECAT-" 1410834 NIL LIECAT- (NIL T T) -8 NIL NIL) (-571 1405173 1410229 1410455 "LIE" 1410537 NIL LIE (NIL T T) -8 NIL NIL) (-570 1397797 1404622 1404787 "LIB" 1405028 T LIB (NIL) -8 NIL NIL) (-569 1393434 1394315 1395250 "LGROBP" 1396914 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-568 1392274 1392965 1392994 "LFCAT" 1393201 T LFCAT (NIL) -9 NIL 1393340) (-567 1390144 1390417 1390778 "LF" 1391996 NIL LF (NIL T T) -7 NIL NIL) (-566 1387056 1387682 1388368 "LEXTRIPK" 1389510 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-565 1383762 1384626 1385129 "LEXP" 1386636 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-564 1382160 1382473 1382874 "LEADCDET" 1383444 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-563 1381356 1381430 1381657 "LAZM3PK" 1382081 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-562 1376279 1379441 1379975 "LAUPOL" 1380872 NIL LAUPOL (NIL T T) -8 NIL NIL) (-561 1375846 1375890 1376057 "LAPLACE" 1376229 NIL LAPLACE (NIL T T) -7 NIL NIL) (-560 1374908 1375502 1375543 "LALG" 1375604 NIL LALG (NIL T) -9 NIL 1375662) (-559 1374623 1374682 1374817 "LALG-" 1374822 NIL LALG- (NIL T T) -8 NIL NIL) (-558 1372553 1373726 1373976 "LA" 1374457 NIL LA (NIL T T T) -8 NIL NIL) (-557 1371463 1371650 1371947 "KOVACIC" 1372353 NIL KOVACIC (NIL T T) -7 NIL NIL) (-556 1371297 1371321 1371363 "KONVERT" 1371425 NIL KONVERT (NIL T) -9 NIL NIL) (-555 1371131 1371155 1371197 "KOERCE" 1371259 NIL KOERCE (NIL T) -9 NIL NIL) (-554 1370633 1370714 1370844 "KERNEL2" 1371045 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-553 1368369 1369129 1369521 "KERNEL" 1370273 NIL KERNEL (NIL T) -8 NIL NIL) (-552 1362053 1366735 1366790 "KDAGG" 1367167 NIL KDAGG (NIL T T) -9 NIL 1367373) (-551 1361582 1361706 1361911 "KDAGG-" 1361916 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-550 1354757 1361243 1361398 "KAFILE" 1361460 NIL KAFILE (NIL T) -8 NIL NIL) (-549 1349216 1354272 1354498 "JORDAN" 1354580 NIL JORDAN (NIL T T) -8 NIL NIL) (-548 1345560 1347460 1347515 "IXAGG" 1348444 NIL IXAGG (NIL T T) -9 NIL 1348899) (-547 1344479 1344785 1345204 "IXAGG-" 1345209 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-546 1340070 1344401 1344460 "IVECTOR" 1344465 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-545 1338836 1339073 1339339 "ITUPLE" 1339837 NIL ITUPLE (NIL T) -8 NIL NIL) (-544 1337272 1337449 1337755 "ITRIGMNP" 1338658 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-543 1336017 1336221 1336504 "ITFUN3" 1337048 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-542 1335649 1335706 1335815 "ITFUN2" 1335954 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-541 1333453 1334524 1334820 "ITAYLOR" 1335385 NIL ITAYLOR (NIL T) -8 NIL NIL) (-540 1322447 1327641 1328799 "ISUPS" 1332327 NIL ISUPS (NIL T) -8 NIL NIL) (-539 1321555 1321694 1321929 "ISUMP" 1322295 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-538 1316825 1321356 1321435 "ISTRING" 1321508 NIL ISTRING (NIL NIL) -8 NIL NIL) (-537 1316038 1316119 1316334 "IRURPK" 1316739 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-536 1314974 1315175 1315415 "IRSN" 1315818 T IRSN (NIL) -7 NIL NIL) (-535 1313011 1313366 1313800 "IRRF2F" 1314613 NIL IRRF2F (NIL T) -7 NIL NIL) (-534 1312758 1312796 1312872 "IRREDFFX" 1312967 NIL IRREDFFX (NIL T) -7 NIL NIL) (-533 1311373 1311632 1311931 "IROOT" 1312491 NIL IROOT (NIL T) -7 NIL NIL) (-532 1310449 1310562 1310782 "IR2F" 1311256 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1308062 1308557 1309123 "IR2" 1309927 NIL IR2 (NIL T T) -7 NIL NIL) (-530 1304704 1305755 1306443 "IR" 1307406 NIL IR (NIL T) -8 NIL NIL) (-529 1304495 1304529 1304589 "IPRNTPK" 1304664 T IPRNTPK (NIL) -7 NIL NIL) (-528 1301049 1304384 1304453 "IPF" 1304458 NIL IPF (NIL NIL) -8 NIL NIL) (-527 1299366 1300974 1301031 "IPADIC" 1301036 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-526 1298865 1298923 1299112 "INVLAPLA" 1299302 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-525 1288514 1290867 1293253 "INTTR" 1296529 NIL INTTR (NIL T T) -7 NIL NIL) (-524 1284876 1285617 1286473 "INTTOOLS" 1287707 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-523 1284462 1284553 1284670 "INTSLPE" 1284779 T INTSLPE (NIL) -7 NIL NIL) (-522 1282412 1284385 1284444 "INTRVL" 1284449 NIL INTRVL (NIL T) -8 NIL NIL) (-521 1280019 1280531 1281105 "INTRF" 1281897 NIL INTRF (NIL T) -7 NIL NIL) (-520 1279434 1279531 1279672 "INTRET" 1279917 NIL INTRET (NIL T) -7 NIL NIL) (-519 1277436 1277825 1278294 "INTRAT" 1279042 NIL INTRAT (NIL T T) -7 NIL NIL) (-518 1274677 1275260 1275881 "INTPM" 1276925 NIL INTPM (NIL T T) -7 NIL NIL) (-517 1271388 1271987 1272730 "INTPAF" 1274064 NIL INTPAF (NIL T T T) -7 NIL NIL) (-516 1266671 1267607 1268632 "INTPACK" 1270383 T INTPACK (NIL) -7 NIL NIL) (-515 1265923 1266075 1266283 "INTHERTR" 1266513 NIL INTHERTR (NIL T T) -7 NIL NIL) (-514 1265362 1265442 1265630 "INTHERAL" 1265837 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-513 1263208 1263651 1264108 "INTHEORY" 1264925 T INTHEORY (NIL) -7 NIL NIL) (-512 1254533 1256153 1257930 "INTG0" 1261561 NIL INTG0 (NIL T T T) -7 NIL NIL) (-511 1235130 1239914 1244718 "INTFTBL" 1249749 T INTFTBL (NIL) -8 NIL NIL) (-510 1234379 1234517 1234690 "INTFACT" 1234989 NIL INTFACT (NIL T) -7 NIL NIL) (-509 1231770 1232216 1232779 "INTEF" 1233933 NIL INTEF (NIL T T) -7 NIL NIL) (-508 1230231 1230980 1231009 "INTDOM" 1231310 T INTDOM (NIL) -9 NIL 1231517) (-507 1229600 1229774 1230016 "INTDOM-" 1230021 NIL INTDOM- (NIL T) -8 NIL NIL) (-506 1226092 1228024 1228079 "INTCAT" 1228878 NIL INTCAT (NIL T) -9 NIL 1229197) (-505 1225565 1225667 1225795 "INTBIT" 1225984 T INTBIT (NIL) -7 NIL NIL) (-504 1224240 1224394 1224707 "INTALG" 1225410 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-503 1223697 1223787 1223957 "INTAF" 1224144 NIL INTAF (NIL T T) -7 NIL NIL) (-502 1217163 1223507 1223647 "INTABL" 1223652 NIL INTABL (NIL T T T) -8 NIL NIL) (-501 1214017 1216892 1217019 "INT" 1217056 T INT (NIL) -8 NIL NIL) (-500 1208952 1211696 1211725 "INS" 1212693 T INS (NIL) -9 NIL 1213374) (-499 1206192 1206963 1207937 "INS-" 1208010 NIL INS- (NIL T) -8 NIL NIL) (-498 1204971 1205198 1205495 "INPSIGN" 1205945 NIL INPSIGN (NIL T T) -7 NIL NIL) (-497 1204089 1204206 1204403 "INPRODPF" 1204851 NIL INPRODPF (NIL T T) -7 NIL NIL) (-496 1202983 1203100 1203337 "INPRODFF" 1203969 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-495 1201983 1202135 1202395 "INNMFACT" 1202819 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-494 1201180 1201277 1201465 "INMODGCD" 1201882 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-493 1199689 1199933 1200257 "INFSP" 1200925 NIL INFSP (NIL T T T) -7 NIL NIL) (-492 1198873 1198990 1199173 "INFPROD0" 1199569 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-491 1198483 1198543 1198641 "INFORM1" 1198808 NIL INFORM1 (NIL T) -7 NIL NIL) (-490 1195493 1196652 1197143 "INFORM" 1198000 T INFORM (NIL) -8 NIL NIL) (-489 1195016 1195105 1195219 "INFINITY" 1195399 T INFINITY (NIL) -7 NIL NIL) (-488 1193634 1193882 1194203 "INEP" 1194764 NIL INEP (NIL T T T) -7 NIL NIL) (-487 1192910 1193531 1193596 "INDE" 1193601 NIL INDE (NIL T) -8 NIL NIL) (-486 1192474 1192542 1192659 "INCRMAPS" 1192837 NIL INCRMAPS (NIL T) -7 NIL NIL) (-485 1187785 1188710 1189654 "INBFF" 1191562 NIL INBFF (NIL T) -7 NIL NIL) (-484 1184286 1187630 1187733 "IMATRIX" 1187738 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-483 1183000 1183123 1183437 "IMATQF" 1184143 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-482 1181222 1181449 1181785 "IMATLIN" 1182757 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-481 1175854 1181146 1181204 "ILIST" 1181209 NIL ILIST (NIL T NIL) -8 NIL NIL) (-480 1173813 1175714 1175827 "IIARRAY2" 1175832 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-479 1169181 1173724 1173788 "IFF" 1173793 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-478 1164230 1168473 1168661 "IFARRAY" 1169038 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-477 1163437 1164134 1164207 "IFAMON" 1164212 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-476 1163020 1163085 1163140 "IEVALAB" 1163347 NIL IEVALAB (NIL T T) -9 NIL NIL) (-475 1162695 1162763 1162923 "IEVALAB-" 1162928 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-474 1161972 1162584 1162659 "IDPOAMS" 1162664 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-473 1161306 1161861 1161936 "IDPOAM" 1161941 NIL IDPOAM (NIL T T) -8 NIL NIL) (-472 1160964 1161220 1161283 "IDPO" 1161288 NIL IDPO (NIL T T) -8 NIL NIL) (-471 1160049 1160299 1160353 "IDPC" 1160766 NIL IDPC (NIL T T) -9 NIL 1160915) (-470 1159545 1159941 1160014 "IDPAM" 1160019 NIL IDPAM (NIL T T) -8 NIL NIL) (-469 1158948 1159437 1159510 "IDPAG" 1159515 NIL IDPAG (NIL T T) -8 NIL NIL) (-468 1155203 1156051 1156946 "IDECOMP" 1158105 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-467 1148079 1149128 1150174 "IDEAL" 1154240 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-466 1147243 1147355 1147554 "ICDEN" 1147963 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-465 1146342 1146723 1146870 "ICARD" 1147116 T ICARD (NIL) -8 NIL NIL) (-464 1144414 1144727 1145130 "IBPTOOLS" 1146019 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-463 1140028 1144034 1144147 "IBITS" 1144333 NIL IBITS (NIL NIL) -8 NIL NIL) (-462 1136751 1137327 1138022 "IBATOOL" 1139445 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-461 1134531 1134992 1135525 "IBACHIN" 1136286 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-460 1132414 1134377 1134480 "IARRAY2" 1134485 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-459 1128573 1132340 1132397 "IARRAY1" 1132402 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-458 1122513 1126991 1127469 "IAN" 1128115 T IAN (NIL) -8 NIL NIL) (-457 1122024 1122081 1122254 "IALGFACT" 1122450 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-456 1121551 1121664 1121693 "HYPCAT" 1121900 T HYPCAT (NIL) -9 NIL NIL) (-455 1121089 1121206 1121392 "HYPCAT-" 1121397 NIL HYPCAT- (NIL T) -8 NIL NIL) (-454 1117879 1119204 1119246 "HOAGG" 1120227 NIL HOAGG (NIL T) -9 NIL 1120836) (-453 1116473 1116872 1117398 "HOAGG-" 1117403 NIL HOAGG- (NIL T T) -8 NIL NIL) (-452 1110304 1115914 1116080 "HEXADEC" 1116327 T HEXADEC (NIL) -8 NIL NIL) (-451 1109052 1109274 1109537 "HEUGCD" 1110081 NIL HEUGCD (NIL T) -7 NIL NIL) (-450 1108155 1108889 1109019 "HELLFDIV" 1109024 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-449 1106389 1107932 1108020 "HEAP" 1108099 NIL HEAP (NIL T) -8 NIL NIL) (-448 1100262 1106304 1106366 "HDP" 1106371 NIL HDP (NIL NIL T) -8 NIL NIL) (-447 1093974 1099899 1100050 "HDMP" 1100163 NIL HDMP (NIL NIL T) -8 NIL NIL) (-446 1093299 1093438 1093602 "HB" 1093830 T HB (NIL) -7 NIL NIL) (-445 1086808 1093145 1093249 "HASHTBL" 1093254 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-444 1084561 1086436 1086615 "HACKPI" 1086649 T HACKPI (NIL) -8 NIL NIL) (-443 1080257 1084415 1084527 "GTSET" 1084532 NIL GTSET (NIL T T T T) -8 NIL NIL) (-442 1073795 1080135 1080233 "GSTBL" 1080238 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-441 1066033 1072833 1073096 "GSERIES" 1073587 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-440 1065055 1065508 1065537 "GROUP" 1065798 T GROUP (NIL) -9 NIL 1065957) (-439 1064171 1064394 1064738 "GROUP-" 1064743 NIL GROUP- (NIL T) -8 NIL NIL) (-438 1062540 1062859 1063246 "GROEBSOL" 1063848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-437 1061480 1061742 1061794 "GRMOD" 1062323 NIL GRMOD (NIL T T) -9 NIL 1062491) (-436 1061248 1061284 1061412 "GRMOD-" 1061417 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-435 1056588 1057610 1058607 "GRIMAGE" 1060271 T GRIMAGE (NIL) -8 NIL NIL) (-434 1055055 1055315 1055639 "GRDEF" 1056284 T GRDEF (NIL) -7 NIL NIL) (-433 1054499 1054615 1054756 "GRAY" 1054934 T GRAY (NIL) -7 NIL NIL) (-432 1053732 1054112 1054164 "GRALG" 1054317 NIL GRALG (NIL T T) -9 NIL 1054409) (-431 1053393 1053466 1053629 "GRALG-" 1053634 NIL GRALG- (NIL T T T) -8 NIL NIL) (-430 1050201 1052982 1053158 "GPOLSET" 1053300 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-429 1049557 1049614 1049871 "GOSPER" 1050138 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-428 1045316 1045995 1046521 "GMODPOL" 1049256 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-427 1044321 1044505 1044743 "GHENSEL" 1045128 NIL GHENSEL (NIL T T) -7 NIL NIL) (-426 1038387 1039230 1040256 "GENUPS" 1043405 NIL GENUPS (NIL T T) -7 NIL NIL) (-425 1038084 1038135 1038224 "GENUFACT" 1038330 NIL GENUFACT (NIL T) -7 NIL NIL) (-424 1037496 1037573 1037738 "GENPGCD" 1038002 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-423 1036970 1037005 1037218 "GENMFACT" 1037455 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-422 1035538 1035793 1036100 "GENEEZ" 1036713 NIL GENEEZ (NIL T T) -7 NIL NIL) (-421 1029412 1035151 1035312 "GDMP" 1035461 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-420 1018796 1023185 1024290 "GCNAALG" 1028396 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-419 1017217 1018089 1018118 "GCDDOM" 1018373 T GCDDOM (NIL) -9 NIL 1018530) (-418 1016687 1016814 1017029 "GCDDOM-" 1017034 NIL GCDDOM- (NIL T) -8 NIL NIL) (-417 1005307 1007633 1010025 "GBINTERN" 1014378 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-416 1003144 1003436 1003857 "GBF" 1004982 NIL GBF (NIL T T T T) -7 NIL NIL) (-415 1001925 1002090 1002357 "GBEUCLID" 1002960 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-414 1000599 1000784 1001087 "GB" 1001705 NIL GB (NIL T T T T) -7 NIL NIL) (-413 999948 1000073 1000222 "GAUSSFAC" 1000470 T GAUSSFAC (NIL) -7 NIL NIL) (-412 998327 998629 998941 "GALUTIL" 999668 NIL GALUTIL (NIL T) -7 NIL NIL) (-411 996644 996918 997241 "GALPOLYU" 998054 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-410 994033 994323 994728 "GALFACTU" 996341 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-409 985843 987341 988948 "GALFACT" 992466 NIL GALFACT (NIL T) -7 NIL NIL) (-408 983230 983888 983917 "FVFUN" 985073 T FVFUN (NIL) -9 NIL 985793) (-407 982495 982677 982706 "FVC" 982997 T FVC (NIL) -9 NIL 983180) (-406 982137 982292 982373 "FUNCTION" 982447 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-405 980955 981438 981641 "FTEM" 981954 T FTEM (NIL) -8 NIL NIL) (-404 978625 979176 979665 "FT" 980486 T FT (NIL) -8 NIL NIL) (-403 976892 977180 977581 "FSUPFACT" 978318 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-402 975289 975578 975910 "FST" 976580 T FST (NIL) -8 NIL NIL) (-401 974464 974570 974764 "FSRED" 975171 NIL FSRED (NIL T T) -7 NIL NIL) (-400 973145 973400 973753 "FSPRMELT" 974180 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-399 970230 970668 971167 "FSPECF" 972708 NIL FSPECF (NIL T T) -7 NIL NIL) (-398 969746 969800 969976 "FSINT" 970171 NIL FSINT (NIL T T) -7 NIL NIL) (-397 968031 968743 969044 "FSERIES" 969527 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 967049 967165 967395 "FSCINT" 967911 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 966091 966234 966461 "FSAGG2" 966902 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-394 962329 965039 965081 "FSAGG" 965451 NIL FSAGG (NIL T) -9 NIL 965707) (-393 960091 960692 961488 "FSAGG-" 961583 NIL FSAGG- (NIL T T) -8 NIL NIL) (-392 957750 958029 958582 "FS2UPS" 959809 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 956610 956781 957089 "FS2EXPXP" 957575 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-390 956196 956239 956392 "FS2" 956561 NIL FS2 (NIL T T T T) -7 NIL NIL) (-389 938533 947090 947131 "FS" 950969 NIL FS (NIL T) -9 NIL 953240) (-388 927183 930173 934229 "FS-" 934526 NIL FS- (NIL T T) -8 NIL NIL) (-387 926609 926724 926876 "FRUTIL" 927063 NIL FRUTIL (NIL T) -7 NIL NIL) (-386 921686 924329 924370 "FRNAALG" 925766 NIL FRNAALG (NIL T) -9 NIL 926372) (-385 917365 918435 919710 "FRNAALG-" 920460 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-384 917003 917046 917173 "FRNAAF2" 917316 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-383 915370 915862 916155 "FRMOD" 916817 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-382 914569 914656 914943 "FRIDEAL2" 915277 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 912292 912960 913276 "FRIDEAL" 914360 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-380 911551 911959 912001 "FRETRCT" 912006 NIL FRETRCT (NIL T) -9 NIL 912175) (-379 910663 910894 911245 "FRETRCT-" 911250 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-378 907872 909092 909152 "FRAMALG" 910034 NIL FRAMALG (NIL T T) -9 NIL 910326) (-377 906005 906461 907091 "FRAMALG-" 907314 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-376 905641 905698 905805 "FRAC2" 905942 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 899553 905126 905397 "FRAC" 905402 NIL FRAC (NIL T) -8 NIL NIL) (-374 899189 899246 899353 "FR2" 899490 NIL FR2 (NIL T T) -7 NIL NIL) (-373 890626 894704 896052 "FR" 897873 NIL FR (NIL T) -8 NIL NIL) (-372 885255 888168 888197 "FPS" 889316 T FPS (NIL) -9 NIL 889869) (-371 884704 884813 884977 "FPS-" 885123 NIL FPS- (NIL T) -8 NIL NIL) (-370 882105 883802 883831 "FPC" 884056 T FPC (NIL) -9 NIL 884198) (-369 881898 881938 882035 "FPC-" 882040 NIL FPC- (NIL T) -8 NIL NIL) (-368 880778 881388 881430 "FPATMAB" 881435 NIL FPATMAB (NIL T) -9 NIL 881585) (-367 878478 878954 879380 "FPARFRAC" 880415 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-366 873873 874370 875052 "FORTRAN" 877910 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-365 871548 872110 872139 "FORTFN" 873199 T FORTFN (NIL) -9 NIL 873823) (-364 871311 871361 871390 "FORTCAT" 871449 T FORTCAT (NIL) -9 NIL 871511) (-363 869027 869527 870066 "FORT" 870792 T FORT (NIL) -7 NIL NIL) (-362 868815 868845 868914 "FORMULA1" 868991 NIL FORMULA1 (NIL T) -7 NIL NIL) (-361 866875 867358 867757 "FORMULA" 868436 T FORMULA (NIL) -8 NIL NIL) (-360 866398 866450 866623 "FORDER" 866817 NIL FORDER (NIL T T T T) -7 NIL NIL) (-359 865494 865658 865851 "FOP" 866225 T FOP (NIL) -7 NIL NIL) (-358 864102 864774 864948 "FNLA" 865376 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-357 862770 863159 863188 "FNCAT" 863760 T FNCAT (NIL) -9 NIL 864053) (-356 862336 862729 862757 "FNAME" 862762 T FNAME (NIL) -8 NIL NIL) (-355 860995 861968 861997 "FMTC" 862002 T FMTC (NIL) -9 NIL 862037) (-354 857315 858522 859149 "FMONOID" 860401 NIL FMONOID (NIL T) -8 NIL NIL) (-353 854738 855384 855413 "FMFUN" 856557 T FMFUN (NIL) -9 NIL 857265) (-352 851968 852802 852856 "FMCAT" 854038 NIL FMCAT (NIL T T) -9 NIL 854531) (-351 851236 851417 851446 "FMC" 851736 T FMC (NIL) -9 NIL 851918) (-350 850131 851004 851103 "FM1" 851181 NIL FM1 (NIL T T) -8 NIL NIL) (-349 849353 849876 850023 "FM" 850028 NIL FM (NIL T T) -8 NIL NIL) (-348 847127 847543 848037 "FLOATRP" 848904 NIL FLOATRP (NIL T) -7 NIL NIL) (-347 844565 845065 845643 "FLOATCP" 846594 NIL FLOATCP (NIL T) -7 NIL NIL) (-346 838053 842221 842851 "FLOAT" 843955 T FLOAT (NIL) -8 NIL NIL) (-345 836842 837690 837731 "FLINEXP" 837736 NIL FLINEXP (NIL T) -9 NIL 837828) (-344 835997 836232 836559 "FLINEXP-" 836564 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-343 835073 835217 835441 "FLASORT" 835849 NIL FLASORT (NIL T T) -7 NIL NIL) (-342 832291 833133 833186 "FLALG" 834413 NIL FLALG (NIL T T) -9 NIL 834880) (-341 831333 831476 831703 "FLAGG2" 832144 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 825151 828847 828889 "FLAGG" 830151 NIL FLAGG (NIL T) -9 NIL 830799) (-339 823877 824216 824706 "FLAGG-" 824711 NIL FLAGG- (NIL T T) -8 NIL NIL) (-338 820852 821870 821930 "FINRALG" 823058 NIL FINRALG (NIL T T) -9 NIL 823563) (-337 820012 820241 820580 "FINRALG-" 820585 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-336 819418 819631 819660 "FINITE" 819856 T FINITE (NIL) -9 NIL 819963) (-335 811878 814039 814080 "FINAALG" 817747 NIL FINAALG (NIL T) -9 NIL 819199) (-334 807219 808260 809404 "FINAALG-" 810783 NIL FINAALG- (NIL T T) -8 NIL NIL) (-333 805903 806215 806270 "FILECAT" 806954 NIL FILECAT (NIL T T) -9 NIL 807170) (-332 805298 805658 805761 "FILE" 805833 NIL FILE (NIL T) -8 NIL NIL) (-331 803113 804669 804698 "FIELD" 804738 T FIELD (NIL) -9 NIL 804818) (-330 801733 802118 802629 "FIELD-" 802634 NIL FIELD- (NIL T) -8 NIL NIL) (-329 799548 800370 800716 "FGROUP" 801420 NIL FGROUP (NIL T) -8 NIL NIL) (-328 798638 798802 799022 "FGLMICPK" 799380 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-327 794440 798563 798620 "FFX" 798625 NIL FFX (NIL T NIL) -8 NIL NIL) (-326 794041 794102 794237 "FFSLPE" 794373 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-325 793545 793581 793790 "FFPOLY2" 793999 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-324 789541 790317 791113 "FFPOLY" 792781 NIL FFPOLY (NIL T) -7 NIL NIL) (-323 785363 789460 789523 "FFP" 789528 NIL FFP (NIL T NIL) -8 NIL NIL) (-322 780459 784706 784896 "FFNBX" 785217 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-321 775369 779594 779852 "FFNBP" 780313 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-320 769972 774653 774864 "FFNB" 775202 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-319 768804 769002 769317 "FFINTBAS" 769769 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-318 764980 767220 767249 "FFIELDC" 767869 T FFIELDC (NIL) -9 NIL 768245) (-317 763643 764013 764510 "FFIELDC-" 764515 NIL FFIELDC- (NIL T) -8 NIL NIL) (-316 763213 763258 763382 "FFHOM" 763585 NIL FFHOM (NIL T T T) -7 NIL NIL) (-315 760911 761395 761912 "FFF" 762728 NIL FFF (NIL T) -7 NIL NIL) (-314 756499 760653 760754 "FFCGX" 760854 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-313 752101 756231 756338 "FFCGP" 756442 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-312 747254 751828 751936 "FFCG" 752037 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-311 746665 746708 746943 "FFCAT2" 747205 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-310 728464 737587 737674 "FFCAT" 742839 NIL FFCAT (NIL T T T) -9 NIL 744324) (-309 723662 724709 726023 "FFCAT-" 727253 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-308 719030 723573 723637 "FF" 723642 NIL FF (NIL NIL NIL) -8 NIL NIL) (-307 708234 712024 713239 "FEXPR" 717887 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-306 707236 707671 707713 "FEVALAB" 707797 NIL FEVALAB (NIL T) -9 NIL 708055) (-305 706395 706605 706943 "FEVALAB-" 706948 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-304 703461 704176 704292 "FDIVCAT" 705860 NIL FDIVCAT (NIL T T T T) -9 NIL 706297) (-303 703223 703250 703420 "FDIVCAT-" 703425 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-302 702443 702530 702807 "FDIV2" 703130 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-301 701036 701826 702029 "FDIV" 702342 NIL FDIV (NIL T T T T) -8 NIL NIL) (-300 699729 699986 700273 "FCPAK1" 700769 T FCPAK1 (NIL) -7 NIL NIL) (-299 698857 699229 699370 "FCOMP" 699620 NIL FCOMP (NIL T) -8 NIL NIL) (-298 682497 685909 689469 "FC" 695317 T FC (NIL) -8 NIL NIL) (-297 675045 679092 679133 "FAXF" 680935 NIL FAXF (NIL T) -9 NIL 681625) (-296 672324 672979 673804 "FAXF-" 674269 NIL FAXF- (NIL T T) -8 NIL NIL) (-295 667430 671700 671876 "FARRAY" 672181 NIL FARRAY (NIL T) -8 NIL NIL) (-294 662776 664847 664900 "FAMR" 665912 NIL FAMR (NIL T T) -9 NIL 666369) (-293 661667 661969 662403 "FAMR-" 662408 NIL FAMR- (NIL T T T) -8 NIL NIL) (-292 660863 661589 661642 "FAMONOID" 661647 NIL FAMONOID (NIL T) -8 NIL NIL) (-291 658696 659380 659434 "FAMONC" 660375 NIL FAMONC (NIL T T) -9 NIL 660759) (-290 657390 658452 658588 "FAGROUP" 658593 NIL FAGROUP (NIL T) -8 NIL NIL) (-289 655193 655512 655914 "FACUTIL" 657071 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-288 654292 654477 654699 "FACTFUNC" 655003 NIL FACTFUNC (NIL T) -7 NIL NIL) (-287 646615 653543 653755 "EXPUPXS" 654148 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-286 644114 644650 645232 "EXPRTUBE" 646053 T EXPRTUBE (NIL) -7 NIL NIL) (-285 640308 640900 641637 "EXPRODE" 643453 NIL EXPRODE (NIL T T) -7 NIL NIL) (-284 634736 635323 636135 "EXPR2UPS" 639606 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-283 634372 634429 634536 "EXPR2" 634673 NIL EXPR2 (NIL T T) -7 NIL NIL) (-282 619540 633037 633460 "EXPR" 633981 NIL EXPR (NIL T) -8 NIL NIL) (-281 610894 618677 618972 "EXPEXPAN" 619378 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-280 610721 610851 610880 "EXIT" 610885 T EXIT (NIL) -8 NIL NIL) (-279 610348 610410 610523 "EVALCYC" 610653 NIL EVALCYC (NIL T) -7 NIL NIL) (-278 609888 610006 610048 "EVALAB" 610218 NIL EVALAB (NIL T) -9 NIL 610322) (-277 609369 609491 609712 "EVALAB-" 609717 NIL EVALAB- (NIL T T) -8 NIL NIL) (-276 606831 608143 608172 "EUCDOM" 608727 T EUCDOM (NIL) -9 NIL 609077) (-275 605236 605678 606268 "EUCDOM-" 606273 NIL EUCDOM- (NIL T) -8 NIL NIL) (-274 604872 604929 605036 "ESTOOLS2" 605173 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-273 604623 604665 604745 "ESTOOLS1" 604824 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-272 592236 594975 597706 "ESTOOLS" 601912 T ESTOOLS (NIL) -7 NIL NIL) (-271 591981 592013 592095 "ESCONT1" 592198 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-270 588388 589140 589912 "ESCONT" 591229 T ESCONT (NIL) -7 NIL NIL) (-269 588063 588113 588213 "ES2" 588332 NIL ES2 (NIL T T) -7 NIL NIL) (-268 587693 587751 587860 "ES1" 587999 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581632 583356 583385 "ES" 586149 T ES (NIL) -9 NIL 587553) (-266 576580 577866 579683 "ES-" 579847 NIL ES- (NIL T) -8 NIL NIL) (-265 575796 575925 576101 "ERROR" 576424 T ERROR (NIL) -7 NIL NIL) (-264 569311 575655 575746 "EQTBL" 575751 NIL EQTBL (NIL T T) -8 NIL NIL) (-263 568943 569000 569109 "EQ2" 569248 NIL EQ2 (NIL T T) -7 NIL NIL) (-262 561408 564289 565722 "EQ" 567543 NIL -2373 (NIL T) -8 NIL NIL) (-261 556700 557746 558839 "EP" 560347 NIL EP (NIL T) -7 NIL NIL) (-260 555859 556423 556452 "ENTIRER" 556457 T ENTIRER (NIL) -9 NIL 556502) (-259 552315 553814 554184 "EMR" 555658 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-258 551459 551644 551699 "ELTAGG" 552079 NIL ELTAGG (NIL T T) -9 NIL 552289) (-257 551178 551240 551381 "ELTAGG-" 551386 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-256 550966 550995 551050 "ELTAB" 551134 NIL ELTAB (NIL T T) -9 NIL NIL) (-255 550092 550238 550437 "ELFUTS" 550817 NIL ELFUTS (NIL T T) -7 NIL NIL) (-254 549833 549889 549918 "ELEMFUN" 550023 T ELEMFUN (NIL) -9 NIL NIL) (-253 549703 549724 549792 "ELEMFUN-" 549797 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-252 544634 547837 547879 "ELAGG" 548819 NIL ELAGG (NIL T) -9 NIL 549280) (-251 542919 543353 544016 "ELAGG-" 544021 NIL ELAGG- (NIL T T) -8 NIL NIL) (-250 535789 537588 538414 "EFUPXS" 542196 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-249 529241 531042 531851 "EFULS" 535066 NIL EFULS (NIL T T T) -8 NIL NIL) (-248 526672 527030 527508 "EFSTRUC" 528873 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-247 515744 517309 518869 "EF" 525187 NIL EF (NIL T T) -7 NIL NIL) (-246 514845 515229 515378 "EAB" 515615 T EAB (NIL) -8 NIL NIL) (-245 514058 514804 514832 "E04UCFA" 514837 T E04UCFA (NIL) -8 NIL NIL) (-244 513271 514017 514045 "E04NAFA" 514050 T E04NAFA (NIL) -8 NIL NIL) (-243 512484 513230 513258 "E04MBFA" 513263 T E04MBFA (NIL) -8 NIL NIL) (-242 511697 512443 512471 "E04JAFA" 512476 T E04JAFA (NIL) -8 NIL NIL) (-241 510912 511656 511684 "E04GCFA" 511689 T E04GCFA (NIL) -8 NIL NIL) (-240 510127 510871 510899 "E04FDFA" 510904 T E04FDFA (NIL) -8 NIL NIL) (-239 509340 510086 510114 "E04DGFA" 510119 T E04DGFA (NIL) -8 NIL NIL) (-238 503526 504870 506232 "E04AGNT" 507998 T E04AGNT (NIL) -7 NIL NIL) (-237 502252 502732 502773 "DVARCAT" 503248 NIL DVARCAT (NIL T) -9 NIL 503446) (-236 501456 501668 501982 "DVARCAT-" 501987 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-235 494318 501258 501385 "DSMP" 501390 NIL DSMP (NIL T T T) -8 NIL NIL) (-234 493983 494042 494140 "DROPT1" 494253 NIL DROPT1 (NIL T) -7 NIL NIL) (-233 489105 490229 491364 "DROPT0" 492868 T DROPT0 (NIL) -7 NIL NIL) (-232 483931 485062 486126 "DROPT" 488061 T DROPT (NIL) -8 NIL NIL) (-231 482276 482601 482987 "DRAWPT" 483565 T DRAWPT (NIL) -7 NIL NIL) (-230 481917 481968 482084 "DRAWHACK" 482219 NIL DRAWHACK (NIL T) -7 NIL NIL) (-229 480662 480927 481214 "DRAWCX" 481650 T DRAWCX (NIL) -7 NIL NIL) (-228 480180 480248 480398 "DRAWCURV" 480588 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-227 470784 472706 474785 "DRAWCFUN" 478121 T DRAWCFUN (NIL) -7 NIL NIL) (-226 465459 466358 467413 "DRAW" 469782 NIL DRAW (NIL T) -7 NIL NIL) (-225 462313 464189 464231 "DQAGG" 464860 NIL DQAGG (NIL T) -9 NIL 465133) (-224 450773 457511 457594 "DPOLCAT" 459432 NIL DPOLCAT (NIL T T T T) -9 NIL 459975) (-223 445613 446959 448916 "DPOLCAT-" 448921 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-222 439697 445475 445572 "DPMO" 445577 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-221 433684 439478 439644 "DPMM" 439649 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-220 427396 433321 433472 "DMP" 433585 NIL DMP (NIL NIL T) -8 NIL NIL) (-219 426996 427052 427196 "DLP" 427334 NIL DLP (NIL T) -7 NIL NIL) (-218 420646 426097 426324 "DLIST" 426801 NIL DLIST (NIL T) -8 NIL NIL) (-217 417534 419537 419579 "DLAGG" 420129 NIL DLAGG (NIL T) -9 NIL 420357) (-216 416196 416888 416917 "DIVRING" 417067 T DIVRING (NIL) -9 NIL 417175) (-215 415184 415437 415830 "DIVRING-" 415835 NIL DIVRING- (NIL T) -8 NIL NIL) (-214 413286 413643 414049 "DISPLAY" 414798 T DISPLAY (NIL) -7 NIL NIL) (-213 412134 412337 412602 "DIRPROD2" 413079 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 406029 412048 412111 "DIRPROD" 412116 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-211 395700 401699 401753 "DIRPCAT" 402161 NIL DIRPCAT (NIL NIL T) -9 NIL 402977) (-210 393026 393668 394549 "DIRPCAT-" 394886 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-209 392313 392473 392659 "DIOSP" 392860 T DIOSP (NIL) -7 NIL NIL) (-208 389057 391261 391303 "DIOPS" 391737 NIL DIOPS (NIL T) -9 NIL 391965) (-207 388606 388720 388911 "DIOPS-" 388916 NIL DIOPS- (NIL T T) -8 NIL NIL) (-206 387477 388115 388144 "DIFRING" 388331 T DIFRING (NIL) -9 NIL 388440) (-205 387123 387200 387352 "DIFRING-" 387357 NIL DIFRING- (NIL T) -8 NIL NIL) (-204 384914 386196 386237 "DIFEXT" 386596 NIL DIFEXT (NIL T) -9 NIL 386887) (-203 383200 383628 384293 "DIFEXT-" 384298 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-202 380563 382767 382809 "DIAGG" 382814 NIL DIAGG (NIL T) -9 NIL 382834) (-201 379947 380104 380356 "DIAGG-" 380361 NIL DIAGG- (NIL T T) -8 NIL NIL) (-200 375559 376468 377478 "DFSFUN" 378957 T DFSFUN (NIL) -7 NIL NIL) (-199 370493 374389 374724 "DFLOAT" 375244 T DFLOAT (NIL) -8 NIL NIL) (-198 368726 369007 369402 "DFINTTLS" 370201 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 365759 366761 367159 "DERHAM" 368393 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363614 365534 365623 "DEQUEUE" 365703 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 362832 362965 363160 "DEGRED" 363476 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359248 359989 360837 "DEFINTRF" 362064 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 356787 357254 357850 "DEFINTEF" 358769 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350618 356228 356394 "DECIMAL" 356641 T DECIMAL (NIL) -8 NIL NIL) (-191 348130 348588 349094 "DDFACT" 350162 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 347726 347769 347920 "DBLRESP" 348081 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345436 345770 346139 "DBASE" 347484 NIL DBASE (NIL T) -8 NIL NIL) (-188 344571 345395 345423 "D03FAFA" 345428 T D03FAFA (NIL) -8 NIL NIL) (-187 343707 344530 344558 "D03EEFA" 344563 T D03EEFA (NIL) -8 NIL NIL) (-186 341657 342123 342612 "D03AGNT" 343238 T D03AGNT (NIL) -7 NIL NIL) (-185 340975 341616 341644 "D02EJFA" 341649 T D02EJFA (NIL) -8 NIL NIL) (-184 340293 340934 340962 "D02CJFA" 340967 T D02CJFA (NIL) -8 NIL NIL) (-183 339611 340252 340280 "D02BHFA" 340285 T D02BHFA (NIL) -8 NIL NIL) (-182 338929 339570 339598 "D02BBFA" 339603 T D02BBFA (NIL) -8 NIL NIL) (-181 332128 333715 335321 "D02AGNT" 337343 T D02AGNT (NIL) -7 NIL NIL) (-180 329909 330428 330971 "D01WGTS" 331605 T D01WGTS (NIL) -7 NIL NIL) (-179 329016 329868 329896 "D01TRNS" 329901 T D01TRNS (NIL) -8 NIL NIL) (-178 328123 328975 329003 "D01GBFA" 329008 T D01GBFA (NIL) -8 NIL NIL) (-177 327230 328082 328110 "D01FCFA" 328115 T D01FCFA (NIL) -8 NIL NIL) (-176 326337 327189 327217 "D01ASFA" 327222 T D01ASFA (NIL) -8 NIL NIL) (-175 325444 326296 326324 "D01AQFA" 326329 T D01AQFA (NIL) -8 NIL NIL) (-174 324551 325403 325431 "D01APFA" 325436 T D01APFA (NIL) -8 NIL NIL) (-173 323658 324510 324538 "D01ANFA" 324543 T D01ANFA (NIL) -8 NIL NIL) (-172 322765 323617 323645 "D01AMFA" 323650 T D01AMFA (NIL) -8 NIL NIL) (-171 321872 322724 322752 "D01ALFA" 322757 T D01ALFA (NIL) -8 NIL NIL) (-170 320979 321831 321859 "D01AKFA" 321864 T D01AKFA (NIL) -8 NIL NIL) (-169 320086 320938 320966 "D01AJFA" 320971 T D01AJFA (NIL) -8 NIL NIL) (-168 313418 314960 316512 "D01AGNT" 318554 T D01AGNT (NIL) -7 NIL NIL) (-167 312755 312883 313035 "CYCLOTOM" 313286 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309490 310203 310930 "CYCLES" 312048 T CYCLES (NIL) -7 NIL NIL) (-165 308802 308936 309107 "CVMP" 309351 NIL CVMP (NIL T) -7 NIL NIL) (-164 306584 306841 307216 "CTRIGMNP" 308530 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 305958 306057 306210 "CSTTOOLS" 306481 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 301757 302414 303172 "CRFP" 305270 NIL CRFP (NIL T T) -7 NIL NIL) (-161 300804 300989 301217 "CRAPACK" 301561 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 300190 300291 300494 "CPMATCH" 300681 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 299915 299943 300049 "CPIMA" 300156 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 296279 296951 297669 "COORDSYS" 299250 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 292140 294282 294774 "CONTFRAC" 295819 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291293 291857 291886 "COMRING" 291891 T COMRING (NIL) -9 NIL 291942) (-155 290374 290651 290835 "COMPPROP" 291129 T COMPPROP (NIL) -8 NIL NIL) (-154 290035 290070 290198 "COMPLPAT" 290333 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 289671 289728 289835 "COMPLEX2" 289972 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-152 279654 289482 289590 "COMPLEX" 289595 NIL COMPLEX (NIL T) -8 NIL NIL) (-151 279372 279407 279505 "COMPFACT" 279613 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263652 273946 273987 "COMPCAT" 274989 NIL COMPCAT (NIL T) -9 NIL 276365) (-149 253168 256091 259718 "COMPCAT-" 260074 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 252899 252927 253029 "COMMUPC" 253134 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252694 252727 252786 "COMMONOP" 252860 T COMMONOP (NIL) -7 NIL NIL) (-146 252277 252445 252532 "COMM" 252627 T COMM (NIL) -8 NIL NIL) (-145 251531 251723 251752 "COMBOPC" 252088 T COMBOPC (NIL) -9 NIL 252261) (-144 250427 250637 250879 "COMBINAT" 251321 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246633 247204 247842 "COMBF" 249851 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245419 245749 245984 "COLOR" 246418 T COLOR (NIL) -8 NIL NIL) (-141 245059 245106 245231 "CMPLXRT" 245366 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240617 241631 242697 "CLIP" 244013 T CLIP (NIL) -7 NIL NIL) (-139 238955 239725 239963 "CLIF" 240445 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 235221 237139 237181 "CLAGG" 238110 NIL CLAGG (NIL T) -9 NIL 238643) (-137 233643 234100 234683 "CLAGG-" 234688 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 233187 233272 233412 "CINTSLPE" 233552 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230688 231159 231707 "CHVAR" 232715 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 229910 230474 230503 "CHARZ" 230508 T CHARZ (NIL) -9 NIL 230522) (-133 229664 229704 229782 "CHARPOL" 229864 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 228770 229367 229396 "CHARNZ" 229443 T CHARNZ (NIL) -9 NIL 229498) (-131 226793 227460 227795 "CHAR" 228455 T CHAR (NIL) -8 NIL NIL) (-130 226518 226579 226608 "CFCAT" 226719 T CFCAT (NIL) -9 NIL NIL) (-129 225763 225874 226056 "CDEN" 226402 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 221755 224916 225196 "CCLASS" 225503 T CCLASS (NIL) -8 NIL NIL) (-127 220863 221011 221232 "CARTEN2" 221602 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 215916 216892 217645 "CARTEN" 220166 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-125 214213 215068 215324 "CARD" 215680 T CARD (NIL) -8 NIL NIL) (-124 213585 213913 213942 "CACHSET" 214074 T CACHSET (NIL) -9 NIL 214151) (-123 213081 213377 213406 "CABMON" 213456 T CABMON (NIL) -9 NIL 213512) (-122 210644 212773 212880 "BTREE" 213007 NIL BTREE (NIL T) -8 NIL NIL) (-121 208148 210292 210414 "BTOURN" 210554 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205607 207654 207696 "BTCAT" 207764 NIL BTCAT (NIL T) -9 NIL 207841) (-119 205274 205354 205503 "BTCAT-" 205508 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200464 204335 204364 "BTAGG" 204620 T BTAGG (NIL) -9 NIL 204799) (-117 199887 200031 200261 "BTAGG-" 200266 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 196937 199165 199380 "BSTREE" 199704 NIL BSTREE (NIL T) -8 NIL NIL) (-115 196075 196201 196385 "BRILL" 196793 NIL BRILL (NIL T) -7 NIL NIL) (-114 192818 194839 194881 "BRAGG" 195530 NIL BRAGG (NIL T) -9 NIL 195786) (-113 191347 191753 192308 "BRAGG-" 192313 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184555 190693 190877 "BPADICRT" 191195 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 182859 184492 184537 "BPADIC" 184542 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182559 182589 182702 "BOUNDZRO" 182823 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 180182 180626 181145 "BOP1" 182073 NIL BOP1 (NIL T) -7 NIL NIL) (-108 175697 176788 177655 "BOP" 179335 T BOP (NIL) -8 NIL NIL) (-107 174050 174740 175034 "BOOLEAN" 175423 T BOOLEAN (NIL) -8 NIL NIL) (-106 173416 173794 173847 "BMODULE" 173852 NIL BMODULE (NIL T T) -9 NIL 173916) (-105 169226 173214 173287 "BITS" 173363 T BITS (NIL) -8 NIL NIL) (-104 168323 168758 168910 "BINFILE" 169094 T BINFILE (NIL) -8 NIL NIL) (-103 162158 167767 167932 "BINARY" 168178 T BINARY (NIL) -8 NIL NIL) (-102 160026 161448 161490 "BGAGG" 161750 NIL BGAGG (NIL T) -9 NIL 161887) (-101 159857 159889 159980 "BGAGG-" 159985 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158955 159241 159446 "BFUNCT" 159672 T BFUNCT (NIL) -8 NIL NIL) (-99 157658 157836 158120 "BEZOUT" 158780 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154189 156518 156846 "BBTREE" 157361 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153926 153979 154006 "BASTYPE" 154123 T BASTYPE (NIL) -9 NIL NIL) (-96 153782 153810 153880 "BASTYPE-" 153885 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153220 153296 153446 "BALFACT" 153693 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 152042 152639 152824 "AUTOMOR" 153065 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151767 151772 151799 "ATTREG" 151804 T ATTREG (NIL) -9 NIL NIL) (-92 150046 150464 150816 "ATTRBUT" 151433 T ATTRBUT (NIL) -8 NIL NIL) (-91 149581 149694 149721 "ATRIG" 149922 T ATRIG (NIL) -9 NIL NIL) (-90 149390 149431 149518 "ATRIG-" 149523 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147593 149166 149254 "ASTACK" 149333 NIL ASTACK (NIL T) -8 NIL NIL) (-88 146100 146397 146761 "ASSOCEQ" 147276 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 145132 145759 145883 "ASP9" 146007 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144002 144737 144879 "ASP80" 145021 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 143766 143950 143989 "ASP8" 143994 NIL ASP8 (NIL NIL) -8 NIL NIL) (-84 142722 143443 143561 "ASP78" 143679 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 141693 142402 142519 "ASP77" 142636 NIL ASP77 (NIL NIL) -8 NIL NIL) (-82 140608 141331 141462 "ASP74" 141593 NIL ASP74 (NIL NIL) -8 NIL NIL) (-81 139509 140243 140375 "ASP73" 140507 NIL ASP73 (NIL NIL) -8 NIL NIL) (-80 138408 139144 139276 "ASP7" 139408 NIL ASP7 (NIL NIL) -8 NIL NIL) (-79 137363 138085 138203 "ASP6" 138321 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136312 137040 137158 "ASP55" 137276 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135262 135986 136105 "ASP50" 136224 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134350 134963 135073 "ASP49" 135183 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 133135 133889 134057 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URAGG- (NIL T T) -8 NIL NIL) (-1221 3417905 3420841 3421313 "UPXSSING" 3421891 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1220 3409792 3417022 3417303 "UPXS" 3417682 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1219 3402820 3409696 3409768 "UPXSCONS" 3409773 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1218 3393033 3399858 3399921 "UPXSCCA" 3400577 NIL UPXSCCA (NIL T T) -9 NIL 3400819) (-1217 3392671 3392756 3392930 "UPXSCCA-" 3392935 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1216 3382817 3389415 3389459 "UPXSCAT" 3390107 NIL UPXSCAT (NIL T) -9 NIL 3390708) (-1215 3382247 3382326 3382505 "UPXS2" 3382732 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1214 3380901 3381154 3381505 "UPSQFREE" 3381990 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1213 3374736 3377786 3377842 "UPSCAT" 3379003 NIL UPSCAT (NIL T T) -9 NIL 3379771) (-1212 3373940 3374147 3374474 "UPSCAT-" 3374479 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1211 3359929 3367969 3368013 "UPOLYC" 3370114 NIL UPOLYC (NIL T) -9 NIL 3371329) (-1210 3351258 3353683 3356830 "UPOLYC-" 3356835 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1209 3350885 3350928 3351061 "UPOLYC2" 3351209 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1208 3342296 3350451 3350589 "UP" 3350795 NIL UP (NIL NIL T) -8 NIL NIL) (-1207 3341635 3341742 3341906 "UPMP" 3342185 NIL UPMP (NIL T T) -7 NIL NIL) (-1206 3341188 3341269 3341408 "UPDIVP" 3341548 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1205 3339756 3340005 3340321 "UPDECOMP" 3340937 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1204 3338991 3339103 3339288 "UPCDEN" 3339640 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1203 3338510 3338579 3338728 "UP2" 3338916 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1202 3337031 3337718 3337993 "UNISEG" 3338270 NIL UNISEG (NIL T) -8 NIL NIL) (-1201 3336248 3336375 3336579 "UNISEG2" 3336875 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1200 3335308 3335488 3335714 "UNIFACT" 3336064 NIL UNIFACT (NIL T) -7 NIL NIL) (-1199 3319192 3334487 3334737 "ULS" 3335116 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1198 3307147 3319096 3319168 "ULSCONS" 3319173 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1197 3289815 3301832 3301895 "ULSCCAT" 3302615 NIL ULSCCAT (NIL T T) -9 NIL 3302911) (-1196 3288865 3289110 3289498 "ULSCCAT-" 3289503 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1195 3278803 3285315 3285359 "ULSCAT" 3286222 NIL ULSCAT (NIL T) -9 NIL 3286944) (-1194 3278233 3278312 3278491 "ULS2" 3278718 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1193 3270371 3276224 3276724 "UFPS" 3277768 NIL UFPS (NIL T) -8 NIL NIL) (-1192 3270068 3270125 3270223 "UFPS1" 3270308 NIL UFPS1 (NIL T) -7 NIL NIL) (-1191 3268461 3269428 3269459 "UFD" 3269671 T UFD (NIL) -9 NIL 3269785) (-1190 3268255 3268301 3268396 "UFD-" 3268401 NIL UFD- (NIL T) -8 NIL NIL) (-1189 3267337 3267520 3267736 "UDVO" 3268061 T UDVO (NIL) -7 NIL NIL) (-1188 3265155 3265564 3266034 "UDPO" 3266902 NIL UDPO (NIL T) -7 NIL NIL) (-1187 3265087 3265092 3265123 "TYPE" 3265128 T TYPE (NIL) -9 NIL NIL) (-1186 3264058 3264260 3264500 "TWOFACT" 3264881 NIL TWOFACT (NIL T) -7 NIL NIL) (-1185 3263130 3263461 3263660 "TUPLE" 3263894 NIL TUPLE (NIL T) -8 NIL NIL) (-1184 3260821 3261340 3261879 "TUBETOOL" 3262613 T TUBETOOL (NIL) -7 NIL NIL) (-1183 3259670 3259875 3260116 "TUBE" 3260614 NIL TUBE (NIL T) -8 NIL NIL) (-1182 3254390 3258644 3258926 "TS" 3259423 NIL TS (NIL T) -8 NIL NIL) (-1181 3243064 3247149 3247247 "TSETCAT" 3252516 NIL TSETCAT (NIL T T T T) -9 NIL 3254046) (-1180 3237799 3239396 3241287 "TSETCAT-" 3241292 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1179 3232070 3232916 3233854 "TRMANIP" 3236939 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1178 3231511 3231574 3231737 "TRIMAT" 3232002 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1177 3229307 3229544 3229908 "TRIGMNIP" 3231260 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1176 3228826 3228939 3228970 "TRIGCAT" 3229183 T TRIGCAT (NIL) -9 NIL NIL) (-1175 3228495 3228574 3228715 "TRIGCAT-" 3228720 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1174 3225398 3227353 3227634 "TREE" 3228249 NIL TREE (NIL T) -8 NIL NIL) (-1173 3224671 3225199 3225230 "TRANFUN" 3225265 T TRANFUN (NIL) -9 NIL 3225331) (-1172 3223950 3224141 3224421 "TRANFUN-" 3224426 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1171 3223754 3223786 3223847 "TOPSP" 3223911 T TOPSP (NIL) -7 NIL NIL) (-1170 3223102 3223217 3223371 "TOOLSIGN" 3223635 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1169 3221737 3222279 3222518 "TEXTFILE" 3222885 T TEXTFILE (NIL) -8 NIL NIL) (-1168 3219602 3220116 3220554 "TEX" 3221321 T TEX (NIL) -8 NIL NIL) (-1167 3219383 3219414 3219486 "TEX1" 3219565 NIL TEX1 (NIL T) -7 NIL NIL) (-1166 3219031 3219094 3219184 "TEMUTL" 3219315 T TEMUTL (NIL) -7 NIL NIL) (-1165 3217185 3217465 3217790 "TBCMPPK" 3218754 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1164 3208930 3215190 3215247 "TBAGG" 3215647 NIL TBAGG (NIL T T) -9 NIL 3215858) (-1163 3204000 3205488 3207242 "TBAGG-" 3207247 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1162 3203384 3203491 3203636 "TANEXP" 3203889 NIL TANEXP (NIL T) -7 NIL NIL) (-1161 3196897 3203241 3203334 "TABLE" 3203339 NIL TABLE (NIL T T) -8 NIL NIL) (-1160 3196310 3196408 3196546 "TABLEAU" 3196794 NIL TABLEAU (NIL T) -8 NIL NIL) (-1159 3190918 3192138 3193386 "TABLBUMP" 3195096 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1158 3187381 3188076 3188859 "SYSSOLP" 3190169 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1157 3184515 3185123 3185761 "SYMTAB" 3186765 T SYMTAB (NIL) -8 NIL NIL) (-1156 3179764 3180666 3181649 "SYMS" 3183554 T SYMS (NIL) -8 NIL NIL) (-1155 3176996 3179228 3179455 "SYMPOLY" 3179572 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1154 3176513 3176588 3176711 "SYMFUNC" 3176908 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1153 3172491 3173750 3174572 "SYMBOL" 3175713 T SYMBOL (NIL) -8 NIL NIL) (-1152 3166030 3167719 3169439 "SWITCH" 3170793 T SWITCH (NIL) -8 NIL NIL) (-1151 3159256 3164853 3165155 "SUTS" 3165786 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1150 3151142 3158373 3158654 "SUPXS" 3159033 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1149 3142627 3150760 3150886 "SUP" 3151051 NIL SUP (NIL T) -8 NIL NIL) (-1148 3141786 3141913 3142130 "SUPFRACF" 3142495 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1147 3132358 3141588 3141702 "SUPEXPR" 3141707 NIL SUPEXPR (NIL T) -8 NIL NIL) (-1146 3131979 3132038 3132151 "SUP2" 3132293 NIL SUP2 (NIL T T) -7 NIL NIL) (-1145 3130392 3130666 3131029 "SUMRF" 3131678 NIL SUMRF (NIL T) -7 NIL NIL) (-1144 3129706 3129772 3129971 "SUMFS" 3130313 NIL SUMFS (NIL T T) -7 NIL NIL) (-1143 3113630 3128885 3129135 "SULS" 3129514 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1142 3112952 3113155 3113295 "SUCH" 3113538 NIL SUCH (NIL T T) -8 NIL NIL) (-1141 3106846 3107858 3108817 "SUBSPACE" 3112040 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1140 3106278 3106368 3106531 "SUBRESP" 3106735 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1139 3099647 3100943 3102254 "STTF" 3105014 NIL STTF (NIL T) -7 NIL NIL) (-1138 3093820 3094940 3096087 "STTFNC" 3098547 NIL STTFNC (NIL T) -7 NIL NIL) (-1137 3085139 3087006 3088798 "STTAYLOR" 3092063 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1136 3078395 3085003 3085086 "STRTBL" 3085091 NIL STRTBL (NIL T) -8 NIL NIL) (-1135 3073786 3078350 3078381 "STRING" 3078386 T STRING (NIL) -8 NIL NIL) (-1134 3068650 3073128 3073159 "STRICAT" 3073218 T STRICAT (NIL) -9 NIL 3073280) (-1133 3061377 3066177 3066795 "STREAM" 3068067 NIL STREAM (NIL T) -8 NIL NIL) (-1132 3060887 3060964 3061108 "STREAM3" 3061294 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1131 3059869 3060052 3060287 "STREAM2" 3060700 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1130 3059557 3059609 3059702 "STREAM1" 3059811 NIL STREAM1 (NIL T) -7 NIL NIL) (-1129 3058573 3058754 3058985 "STINPROD" 3059373 NIL STINPROD (NIL T) -7 NIL NIL) (-1128 3058150 3058334 3058365 "STEP" 3058445 T STEP (NIL) -9 NIL 3058523) (-1127 3051705 3058049 3058126 "STBL" 3058131 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1126 3046919 3050957 3051001 "STAGG" 3051154 NIL STAGG (NIL T) -9 NIL 3051243) (-1125 3044621 3045223 3046095 "STAGG-" 3046100 NIL STAGG- (NIL T T) -8 NIL NIL) (-1124 3038113 3039682 3040797 "STACK" 3043541 NIL STACK (NIL T) -8 NIL NIL) (-1123 3030838 3036254 3036710 "SREGSET" 3037743 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1122 3023264 3024632 3026145 "SRDCMPK" 3029444 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1121 3016242 3020702 3020733 "SRAGG" 3022036 T SRAGG (NIL) -9 NIL 3022644) (-1120 3015259 3015514 3015893 "SRAGG-" 3015898 NIL SRAGG- (NIL T) -8 NIL NIL) (-1119 3009707 3014182 3014606 "SQMATRIX" 3014882 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1118 3003463 3006425 3007152 "SPLTREE" 3009052 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1117 2999453 3000119 3000765 "SPLNODE" 3002889 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1116 2998499 2998732 2998763 "SPFCAT" 2999207 T SPFCAT (NIL) -9 NIL NIL) (-1115 2997236 2997446 2997710 "SPECOUT" 2998257 T SPECOUT (NIL) -7 NIL NIL) (-1114 2989206 2990953 2990997 "SPACEC" 2995370 NIL SPACEC (NIL T) -9 NIL 2997186) (-1113 2987377 2989138 2989187 "SPACE3" 2989192 NIL SPACE3 (NIL T) -8 NIL NIL) (-1112 2986131 2986302 2986592 "SORTPAK" 2987183 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1111 2984181 2984484 2984903 "SOLVETRA" 2985795 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1110 2983192 2983414 2983688 "SOLVESER" 2983954 NIL SOLVESER (NIL T) -7 NIL NIL) (-1109 2978412 2979293 2980295 "SOLVERAD" 2982244 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1108 2974227 2974836 2975565 "SOLVEFOR" 2977779 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1107 2968530 2973575 2973673 "SNTSCAT" 2973678 NIL SNTSCAT (NIL T T T T) -9 NIL 2973748) (-1106 2962628 2966855 2967245 "SMTS" 2968221 NIL SMTS (NIL T T T) -8 NIL NIL) (-1105 2957032 2962516 2962593 "SMP" 2962598 NIL SMP (NIL T T) -8 NIL NIL) (-1104 2955191 2955492 2955890 "SMITH" 2956729 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1103 2948133 2952331 2952435 "SMATCAT" 2953786 NIL SMATCAT (NIL NIL T T T) -9 NIL 2954333) (-1102 2945073 2945896 2947074 "SMATCAT-" 2947079 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1101 2942826 2944343 2944387 "SKAGG" 2944648 NIL SKAGG (NIL T) -9 NIL 2944783) (-1100 2938884 2941930 2942208 "SINT" 2942570 T SINT (NIL) -8 NIL NIL) (-1099 2938656 2938694 2938760 "SIMPAN" 2938840 T SIMPAN (NIL) -7 NIL NIL) (-1098 2937494 2937715 2937990 "SIGNRF" 2938415 NIL SIGNRF (NIL T) -7 NIL NIL) (-1097 2936299 2936450 2936741 "SIGNEF" 2937323 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1096 2933991 2934445 2934950 "SHP" 2935841 NIL SHP (NIL T NIL) -7 NIL NIL) (-1095 2927815 2933892 2933968 "SHDP" 2933973 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1094 2927303 2927495 2927526 "SGROUP" 2927678 T SGROUP (NIL) -9 NIL 2927765) (-1093 2927073 2927125 2927229 "SGROUP-" 2927234 NIL SGROUP- (NIL T) -8 NIL NIL) (-1092 2923909 2924606 2925329 "SGCF" 2926372 T SGCF (NIL) -7 NIL NIL) (-1091 2918310 2923355 2923453 "SFRTCAT" 2923458 NIL SFRTCAT (NIL T T T T) -9 NIL 2923497) (-1090 2911734 2912749 2913885 "SFRGCD" 2917293 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1089 2904862 2905933 2907119 "SFQCMPK" 2910667 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1088 2904484 2904573 2904683 "SFORT" 2904803 NIL SFORT (NIL T T) -8 NIL NIL) (-1087 2903629 2904324 2904445 "SEXOF" 2904450 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1086 2902763 2903510 2903578 "SEX" 2903583 T SEX (NIL) -8 NIL NIL) (-1085 2897538 2898227 2898323 "SEXCAT" 2902094 NIL SEXCAT (NIL T T T T T) -9 NIL 2902713) (-1084 2894718 2897472 2897520 "SET" 2897525 NIL SET (NIL T) -8 NIL NIL) (-1083 2892969 2893431 2893736 "SETMN" 2894459 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1082 2892574 2892700 2892731 "SETCAT" 2892848 T SETCAT (NIL) -9 NIL 2892933) (-1081 2892354 2892406 2892505 "SETCAT-" 2892510 NIL SETCAT- (NIL T) -8 NIL NIL) (-1080 2892017 2892167 2892198 "SETCATD" 2892257 T SETCATD (NIL) -9 NIL 2892304) (-1079 2888403 2890477 2890521 "SETAGG" 2891391 NIL SETAGG (NIL T) -9 NIL 2891731) (-1078 2887861 2887977 2888214 "SETAGG-" 2888219 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1077 2887064 2887357 2887419 "SEGXCAT" 2887705 NIL SEGXCAT (NIL T T) -9 NIL 2887825) (-1076 2886124 2886734 2886914 "SEG" 2886919 NIL SEG (NIL T) -8 NIL NIL) (-1075 2885030 2885243 2885287 "SEGCAT" 2885869 NIL SEGCAT (NIL T) -9 NIL 2886107) (-1074 2884081 2884411 2884610 "SEGBIND" 2884866 NIL SEGBIND (NIL T) -8 NIL NIL) (-1073 2883702 2883761 2883874 "SEGBIND2" 2884016 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1072 2882923 2883049 2883252 "SEG2" 2883547 NIL SEG2 (NIL T T) -7 NIL NIL) (-1071 2882360 2882858 2882905 "SDVAR" 2882910 NIL SDVAR (NIL T) -8 NIL NIL) (-1070 2874604 2882130 2882260 "SDPOL" 2882265 NIL SDPOL (NIL T) -8 NIL NIL) (-1069 2873197 2873463 2873782 "SCPKG" 2874319 NIL SCPKG (NIL T) -7 NIL NIL) (-1068 2872418 2872551 2872730 "SCACHE" 2873052 NIL SCACHE (NIL T) -7 NIL NIL) (-1067 2871857 2872178 2872263 "SAOS" 2872355 T SAOS (NIL) -8 NIL NIL) (-1066 2871422 2871457 2871630 "SAERFFC" 2871816 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1065 2865311 2871319 2871399 "SAE" 2871404 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1064 2864904 2864939 2865098 "SAEFACT" 2865270 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1063 2863225 2863539 2863940 "RURPK" 2864570 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1062 2861861 2862140 2862452 "RULESET" 2863059 NIL RULESET (NIL T T T) -8 NIL NIL) (-1061 2859048 2859551 2860016 "RULE" 2861542 NIL RULE (NIL T T T) -8 NIL NIL) (-1060 2858687 2858842 2858925 "RULECOLD" 2859000 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1059 2853536 2854330 2855250 "RSETGCD" 2857886 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1058 2842799 2847844 2847942 "RSETCAT" 2852061 NIL RSETCAT (NIL T T T T) -9 NIL 2853158) (-1057 2840726 2841265 2842089 "RSETCAT-" 2842094 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1056 2833113 2834488 2836008 "RSDCMPK" 2839325 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1055 2831117 2831558 2831633 "RRCC" 2832719 NIL RRCC (NIL T T) -9 NIL 2833063) (-1054 2830468 2830642 2830921 "RRCC-" 2830926 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1053 2804615 2814244 2814312 "RPOLCAT" 2824976 NIL RPOLCAT (NIL T T T) -9 NIL 2828124) (-1052 2796115 2798453 2801575 "RPOLCAT-" 2801580 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1051 2787174 2794326 2794808 "ROUTINE" 2795655 T ROUTINE (NIL) -8 NIL NIL) (-1050 2783874 2786725 2786874 "ROMAN" 2787047 T ROMAN (NIL) -8 NIL NIL) (-1049 2782149 2782734 2782994 "ROIRC" 2783679 NIL ROIRC (NIL T T) -8 NIL NIL) (-1048 2778489 2780789 2780820 "RNS" 2781124 T RNS (NIL) -9 NIL 2781397) (-1047 2776998 2777381 2777915 "RNS-" 2777990 NIL RNS- (NIL T) -8 NIL NIL) (-1046 2776420 2776828 2776859 "RNG" 2776864 T RNG (NIL) -9 NIL 2776885) (-1045 2775811 2776173 2776217 "RMODULE" 2776279 NIL RMODULE (NIL T) -9 NIL 2776321) (-1044 2774647 2774741 2775077 "RMCAT2" 2775712 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1043 2771356 2773825 2774148 "RMATRIX" 2774383 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1042 2764302 2766536 2766652 "RMATCAT" 2770011 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2770988) (-1041 2763677 2763824 2764131 "RMATCAT-" 2764136 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1040 2763244 2763319 2763447 "RINTERP" 2763596 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1039 2762287 2762851 2762882 "RING" 2762994 T RING (NIL) -9 NIL 2763089) (-1038 2762079 2762123 2762220 "RING-" 2762225 NIL RING- (NIL T) -8 NIL NIL) (-1037 2760920 2761157 2761415 "RIDIST" 2761843 T RIDIST (NIL) -7 NIL NIL) (-1036 2752236 2760388 2760594 "RGCHAIN" 2760768 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1035 2751036 2751277 2751556 "RFP" 2751991 NIL RFP (NIL T) -7 NIL NIL) (-1034 2748030 2748644 2749314 "RF" 2750400 NIL RF (NIL T) -7 NIL NIL) (-1033 2747676 2747739 2747842 "RFFACTOR" 2747961 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1032 2747401 2747436 2747533 "RFFACT" 2747635 NIL RFFACT (NIL T) -7 NIL NIL) (-1031 2745518 2745882 2746264 "RFDIST" 2747041 T RFDIST (NIL) -7 NIL NIL) (-1030 2744971 2745063 2745226 "RETSOL" 2745420 NIL RETSOL (NIL T T) -7 NIL NIL) (-1029 2744558 2744638 2744682 "RETRACT" 2744875 NIL RETRACT (NIL T) -9 NIL NIL) (-1028 2744407 2744432 2744519 "RETRACT-" 2744524 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1027 2737273 2744060 2744187 "RESULT" 2744302 T RESULT (NIL) -8 NIL NIL) (-1026 2735853 2736542 2736741 "RESRING" 2737176 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1025 2735489 2735538 2735636 "RESLATC" 2735790 NIL RESLATC (NIL T) -7 NIL NIL) (-1024 2735195 2735229 2735336 "REPSQ" 2735448 NIL REPSQ (NIL T) -7 NIL NIL) (-1023 2732617 2733197 2733799 "REP" 2734615 T REP (NIL) -7 NIL NIL) (-1022 2732315 2732349 2732460 "REPDB" 2732576 NIL REPDB (NIL T) -7 NIL NIL) (-1021 2726233 2727612 2728831 "REP2" 2731131 NIL REP2 (NIL T) -7 NIL NIL) (-1020 2722614 2723295 2724101 "REP1" 2725462 NIL REP1 (NIL T) -7 NIL NIL) (-1019 2715340 2720755 2721211 "REGSET" 2722244 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1018 2714155 2714490 2714739 "REF" 2715126 NIL REF (NIL T) -8 NIL NIL) (-1017 2713532 2713635 2713802 "REDORDER" 2714039 NIL REDORDER (NIL T T) -7 NIL NIL) (-1016 2710394 2710860 2711469 "RECOP" 2713066 NIL RECOP (NIL T T) -7 NIL NIL) (-1015 2706334 2709607 2709834 "RECLOS" 2710222 NIL RECLOS (NIL T) -8 NIL NIL) (-1014 2705386 2705567 2705782 "REALSOLV" 2706141 T REALSOLV (NIL) -7 NIL NIL) (-1013 2705231 2705272 2705303 "REAL" 2705308 T REAL (NIL) -9 NIL 2705343) (-1012 2701714 2702516 2703400 "REAL0Q" 2704396 NIL REAL0Q (NIL T) -7 NIL NIL) (-1011 2697315 2698303 2699364 "REAL0" 2700695 NIL REAL0 (NIL T) -7 NIL NIL) (-1010 2696720 2696792 2696999 "RDIV" 2697237 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1009 2695788 2695962 2696175 "RDIST" 2696542 NIL RDIST (NIL T) -7 NIL NIL) (-1008 2694385 2694672 2695044 "RDETRS" 2695496 NIL RDETRS (NIL T T) -7 NIL NIL) (-1007 2692197 2692651 2693189 "RDETR" 2693927 NIL RDETR (NIL T T) -7 NIL NIL) (-1006 2690808 2691086 2691490 "RDEEFS" 2691913 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1005 2689303 2689609 2690041 "RDEEF" 2690496 NIL RDEEF (NIL T T) -7 NIL NIL) (-1004 2683496 2686431 2686462 "RCFIELD" 2687757 T RCFIELD (NIL) -9 NIL 2688487) (-1003 2681560 2682064 2682760 "RCFIELD-" 2682835 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1002 2677918 2679697 2679741 "RCAGG" 2680825 NIL RCAGG (NIL T) -9 NIL 2681288) (-1001 2677546 2677640 2677803 "RCAGG-" 2677808 NIL RCAGG- (NIL T T) -8 NIL NIL) (-1000 2676882 2676993 2677158 "RATRET" 2677430 NIL RATRET (NIL T) -7 NIL NIL) (-999 2676439 2676506 2676625 "RATFACT" 2676810 NIL RATFACT (NIL T) -7 NIL NIL) (-998 2675754 2675874 2676024 "RANDSRC" 2676309 T RANDSRC (NIL) -7 NIL NIL) (-997 2675491 2675535 2675606 "RADUTIL" 2675703 T RADUTIL (NIL) -7 NIL NIL) (-996 2668489 2674234 2674551 "RADIX" 2675206 NIL RADIX (NIL NIL) -8 NIL NIL) (-995 2660054 2668333 2668461 "RADFF" 2668466 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-994 2659705 2659780 2659809 "RADCAT" 2659966 T RADCAT (NIL) -9 NIL NIL) (-993 2659490 2659538 2659635 "RADCAT-" 2659640 NIL RADCAT- (NIL T) -8 NIL NIL) (-992 2652773 2654391 2655542 "QUEUE" 2658372 NIL QUEUE (NIL T) -8 NIL NIL) (-991 2649264 2652710 2652755 "QUAT" 2652760 NIL QUAT (NIL T) -8 NIL NIL) (-990 2648902 2648945 2649072 "QUATCT2" 2649215 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-989 2642639 2646023 2646064 "QUATCAT" 2646844 NIL QUATCAT (NIL T) -9 NIL 2647602) (-988 2638783 2639820 2641207 "QUATCAT-" 2641301 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-987 2636343 2637901 2637943 "QUAGG" 2638318 NIL QUAGG (NIL T) -9 NIL 2638493) (-986 2635268 2635741 2635913 "QFORM" 2636215 NIL QFORM (NIL NIL T) -8 NIL NIL) (-985 2626495 2631762 2631803 "QFCAT" 2632461 NIL QFCAT (NIL T) -9 NIL 2633450) (-984 2622067 2623268 2624859 "QFCAT-" 2624953 NIL QFCAT- (NIL T T) -8 NIL NIL) (-983 2621705 2621748 2621875 "QFCAT2" 2622018 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-982 2621165 2621275 2621405 "QEQUAT" 2621595 T QEQUAT (NIL) -8 NIL NIL) (-981 2614313 2615384 2616568 "QCMPACK" 2620098 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-980 2611893 2612314 2612740 "QALGSET" 2613970 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-979 2611138 2611312 2611544 "QALGSET2" 2611713 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-978 2609829 2610052 2610369 "PWFFINTB" 2610911 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-977 2608011 2608179 2608533 "PUSHVAR" 2609643 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-976 2603928 2604982 2605024 "PTRANFN" 2606908 NIL PTRANFN (NIL T) -9 NIL NIL) (-975 2602330 2602621 2602943 "PTPACK" 2603639 NIL PTPACK (NIL T) -7 NIL NIL) (-974 2601962 2602019 2602128 "PTFUNC2" 2602267 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-973 2596464 2600796 2600838 "PTCAT" 2601211 NIL PTCAT (NIL T) -9 NIL 2601373) (-972 2596122 2596157 2596281 "PSQFR" 2596423 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-971 2594709 2595009 2595345 "PSEUDLIN" 2595818 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-970 2581485 2583849 2586170 "PSETPK" 2592472 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-969 2574529 2577243 2577340 "PSETCAT" 2580361 NIL PSETCAT (NIL T T T T) -9 NIL 2581174) (-968 2572365 2572999 2573820 "PSETCAT-" 2573825 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-967 2571714 2571878 2571907 "PSCURVE" 2572175 T PSCURVE (NIL) -9 NIL 2572342) (-966 2568103 2569629 2569695 "PSCAT" 2570539 NIL PSCAT (NIL T T T) -9 NIL 2570779) (-965 2567166 2567382 2567782 "PSCAT-" 2567787 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-964 2565819 2566451 2566665 "PRTITION" 2566972 T PRTITION (NIL) -8 NIL NIL) (-963 2562983 2563632 2563673 "PRSPCAT" 2565187 NIL PRSPCAT (NIL T) -9 NIL 2565755) (-962 2552083 2554289 2556476 "PRS" 2560846 NIL PRS (NIL T T) -7 NIL NIL) (-961 2549981 2551467 2551508 "PRQAGG" 2551691 NIL PRQAGG (NIL T) -9 NIL 2551793) (-960 2549250 2549906 2549963 "PROJSP" 2549968 NIL PROJSP (NIL NIL T) -8 NIL NIL) (-959 2548432 2549173 2549225 "PROJPLPS" 2549230 NIL PROJPLPS (NIL T) -8 NIL NIL) (-958 2547691 2548369 2548414 "PROJPL" 2548419 NIL PROJPL (NIL T) -8 NIL NIL) (-957 2541497 2545889 2546693 "PRODUCT" 2546933 NIL PRODUCT (NIL T T) -8 NIL NIL) (-956 2538772 2540961 2541192 "PR" 2541311 NIL PR (NIL T T) -8 NIL NIL) (-955 2537324 2537481 2537776 "PRJALGPK" 2538612 NIL PRJALGPK (NIL T NIL T T T) -7 NIL NIL) (-954 2537120 2537152 2537211 "PRINT" 2537285 T PRINT (NIL) -7 NIL NIL) (-953 2536460 2536577 2536729 "PRIMES" 2537000 NIL PRIMES (NIL T) -7 NIL NIL) (-952 2534525 2534926 2535392 "PRIMELT" 2536039 NIL PRIMELT (NIL T) -7 NIL NIL) (-951 2534253 2534302 2534331 "PRIMCAT" 2534455 T PRIMCAT (NIL) -9 NIL NIL) (-950 2530420 2534191 2534236 "PRIMARR" 2534241 NIL PRIMARR (NIL T) -8 NIL NIL) (-949 2529427 2529605 2529833 "PRIMARR2" 2530238 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-948 2529070 2529126 2529237 "PREASSOC" 2529365 NIL PREASSOC (NIL T T) -7 NIL NIL) (-947 2528545 2528677 2528706 "PPCURVE" 2528911 T PPCURVE (NIL) -9 NIL 2529047) (-946 2525906 2526305 2526896 "POLYROOT" 2528127 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-945 2519807 2525512 2525671 "POLY" 2525780 NIL POLY (NIL T) -8 NIL NIL) (-944 2519190 2519248 2519482 "POLYLIFT" 2519743 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-943 2515465 2515914 2516543 "POLYCATQ" 2518735 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-942 2502427 2507827 2507893 "POLYCAT" 2511407 NIL POLYCAT (NIL T T T) -9 NIL 2513320) (-941 2495877 2497738 2500122 "POLYCAT-" 2500127 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-940 2495464 2495532 2495652 "POLY2UP" 2495803 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-939 2495096 2495153 2495262 "POLY2" 2495401 NIL POLY2 (NIL T T) -7 NIL NIL) (-938 2493783 2494022 2494297 "POLUTIL" 2494871 NIL POLUTIL (NIL T T) -7 NIL NIL) (-937 2492138 2492415 2492746 "POLTOPOL" 2493505 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-936 2487662 2492074 2492120 "POINT" 2492125 NIL POINT (NIL T) -8 NIL NIL) (-935 2485849 2486206 2486581 "PNTHEORY" 2487307 T PNTHEORY (NIL) -7 NIL NIL) (-934 2484268 2484565 2484977 "PMTOOLS" 2485547 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-933 2483861 2483939 2484056 "PMSYM" 2484184 NIL PMSYM (NIL T) -7 NIL NIL) (-932 2483371 2483440 2483614 "PMQFCAT" 2483786 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-931 2482726 2482836 2482992 "PMPRED" 2483248 NIL PMPRED (NIL T) -7 NIL NIL) (-930 2482122 2482208 2482369 "PMPREDFS" 2482627 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-929 2480767 2480975 2481359 "PMPLCAT" 2481885 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-928 2480299 2480378 2480530 "PMLSAGG" 2480682 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-927 2479774 2479850 2480031 "PMKERNEL" 2480217 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-926 2479391 2479466 2479579 "PMINS" 2479693 NIL PMINS (NIL T) -7 NIL NIL) (-925 2478819 2478888 2479104 "PMFS" 2479316 NIL PMFS (NIL T T T) -7 NIL NIL) (-924 2478047 2478165 2478370 "PMDOWN" 2478696 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-923 2477210 2477369 2477551 "PMASS" 2477885 T PMASS (NIL) -7 NIL NIL) (-922 2476484 2476595 2476758 "PMASSFS" 2477096 NIL PMASSFS (NIL T T) -7 NIL NIL) (-921 2474244 2474497 2474880 "PLPKCRV" 2476208 NIL PLPKCRV (NIL T T T NIL T) -7 NIL NIL) (-920 2473899 2473967 2474061 "PLOTTOOL" 2474170 T PLOTTOOL (NIL) -7 NIL NIL) (-919 2468521 2469710 2470858 "PLOT" 2472771 T PLOT (NIL) -8 NIL NIL) (-918 2464335 2465369 2466290 "PLOT3D" 2467620 T PLOT3D (NIL) -8 NIL NIL) (-917 2463247 2463424 2463659 "PLOT1" 2464139 NIL PLOT1 (NIL T) -7 NIL NIL) (-916 2438642 2443313 2448164 "PLEQN" 2458513 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-915 2437882 2438552 2438619 "PLCS" 2438624 NIL PLCS (NIL T T) -8 NIL NIL) (-914 2437033 2437767 2437838 "PLACESPS" 2437843 NIL PLACESPS (NIL T) -8 NIL NIL) (-913 2436240 2436946 2437003 "PLACES" 2437008 NIL PLACES (NIL T) -8 NIL NIL) (-912 2433306 2433970 2434029 "PLACESC" 2435605 NIL PLACESC (NIL T T) -9 NIL 2436176) (-911 2432624 2432746 2432926 "PINTERP" 2433171 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-910 2432317 2432364 2432467 "PINTERPA" 2432571 NIL PINTERPA (NIL T T) -7 NIL NIL) (-909 2431544 2432111 2432204 "PI" 2432244 T PI (NIL) -8 NIL NIL) (-908 2429931 2430916 2430945 "PID" 2431127 T PID (NIL) -9 NIL 2431261) (-907 2429656 2429693 2429781 "PICOERCE" 2429888 NIL PICOERCE (NIL T) -7 NIL NIL) (-906 2428977 2429115 2429291 "PGROEB" 2429512 NIL PGROEB (NIL T) -7 NIL NIL) (-905 2424564 2425378 2426283 "PGE" 2428092 T PGE (NIL) -7 NIL NIL) (-904 2422688 2422934 2423300 "PGCD" 2424281 NIL PGCD (NIL T T T T) -7 NIL NIL) (-903 2422026 2422129 2422290 "PFRPAC" 2422572 NIL PFRPAC (NIL T) -7 NIL NIL) (-902 2418641 2420574 2420927 "PFR" 2421705 NIL PFR (NIL T) -8 NIL NIL) (-901 2417030 2417274 2417599 "PFOTOOLS" 2418388 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-900 2411895 2412560 2413309 "PFORP" 2416372 NIL PFORP (NIL T T T NIL) -7 NIL NIL) (-899 2410428 2410667 2411018 "PFOQ" 2411652 NIL PFOQ (NIL T T T) -7 NIL NIL) (-898 2408901 2409113 2409476 "PFO" 2410212 NIL PFO (NIL T T T T T) -7 NIL NIL) (-897 2405424 2408790 2408859 "PF" 2408864 NIL PF (NIL NIL) -8 NIL NIL) (-896 2402849 2404130 2404159 "PFECAT" 2404744 T PFECAT (NIL) -9 NIL 2405127) (-895 2402294 2402448 2402662 "PFECAT-" 2402667 NIL PFECAT- (NIL T) -8 NIL NIL) (-894 2400898 2401149 2401450 "PFBRU" 2402043 NIL PFBRU (NIL T T) -7 NIL NIL) (-893 2398765 2399116 2399548 "PFBR" 2400549 NIL PFBR (NIL T T T T) -7 NIL NIL) (-892 2394621 2396145 2396819 "PERM" 2398124 NIL PERM (NIL T) -8 NIL NIL) (-891 2389888 2390828 2391698 "PERMGRP" 2393784 NIL PERMGRP (NIL T) -8 NIL NIL) (-890 2387959 2388952 2388994 "PERMCAT" 2389440 NIL PERMCAT (NIL T) -9 NIL 2389743) (-889 2387612 2387653 2387777 "PERMAN" 2387912 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-888 2385058 2387181 2387312 "PENDTREE" 2387514 NIL PENDTREE (NIL T) -8 NIL NIL) (-887 2383126 2383904 2383946 "PDRING" 2384603 NIL PDRING (NIL T) -9 NIL 2384889) (-886 2382229 2382447 2382809 "PDRING-" 2382814 NIL PDRING- (NIL T T) -8 NIL NIL) (-885 2379371 2380121 2380812 "PDEPROB" 2381558 T PDEPROB (NIL) -8 NIL NIL) (-884 2376918 2377420 2377975 "PDEPACK" 2378836 T PDEPACK (NIL) -7 NIL NIL) (-883 2375830 2376020 2376271 "PDECOMP" 2376717 NIL PDECOMP (NIL T T) -7 NIL NIL) (-882 2373434 2374251 2374280 "PDECAT" 2375067 T PDECAT (NIL) -9 NIL 2375780) (-881 2373185 2373218 2373308 "PCOMP" 2373395 NIL PCOMP (NIL T T) -7 NIL NIL) (-880 2371390 2371986 2372283 "PBWLB" 2372914 NIL PBWLB (NIL T) -8 NIL NIL) (-879 2363895 2365463 2366801 "PATTERN" 2370073 NIL PATTERN (NIL T) -8 NIL NIL) (-878 2363527 2363584 2363693 "PATTERN2" 2363832 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-877 2361284 2361672 2362129 "PATTERN1" 2363116 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-876 2358679 2359233 2359714 "PATRES" 2360849 NIL PATRES (NIL T T) -8 NIL NIL) (-875 2358243 2358310 2358442 "PATRES2" 2358606 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-874 2356126 2356531 2356938 "PATMATCH" 2357910 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-873 2355661 2355844 2355886 "PATMAB" 2355993 NIL PATMAB (NIL T) -9 NIL 2356076) (-872 2354206 2354515 2354773 "PATLRES" 2355466 NIL PATLRES (NIL T T T) -8 NIL NIL) (-871 2353753 2353876 2353918 "PATAB" 2353923 NIL PATAB (NIL T) -9 NIL 2354093) (-870 2351234 2351766 2352339 "PARTPERM" 2353200 T PARTPERM (NIL) -7 NIL NIL) (-869 2350855 2350918 2351020 "PARSURF" 2351165 NIL PARSURF (NIL T) -8 NIL NIL) (-868 2350487 2350544 2350653 "PARSU2" 2350792 NIL PARSU2 (NIL T T) -7 NIL NIL) (-867 2350108 2350171 2350273 "PARSCURV" 2350418 NIL PARSCURV (NIL T) -8 NIL NIL) (-866 2349740 2349797 2349906 "PARSC2" 2350045 NIL PARSC2 (NIL T T) -7 NIL NIL) (-865 2349379 2349437 2349534 "PARPCURV" 2349676 NIL PARPCURV (NIL T) -8 NIL NIL) (-864 2349011 2349068 2349177 "PARPC2" 2349316 NIL PARPC2 (NIL T T) -7 NIL NIL) (-863 2347491 2347609 2347928 "PARAMP" 2348866 NIL PARAMP (NIL T NIL T T T T T) -7 NIL NIL) (-862 2347011 2347097 2347216 "PAN2EXPR" 2347392 T PAN2EXPR (NIL) -7 NIL NIL) (-861 2345817 2346132 2346360 "PALETTE" 2346803 T PALETTE (NIL) -8 NIL NIL) (-860 2333450 2335616 2337732 "PAFF" 2343765 NIL PAFF (NIL T NIL T) -7 NIL NIL) (-859 2320446 2322774 2324985 "PAFFFF" 2331303 NIL PAFFFF (NIL T NIL T) -7 NIL NIL) (-858 2314287 2319705 2319899 "PADICRC" 2320301 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-857 2307486 2313633 2313817 "PADICRAT" 2314135 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-856 2305790 2307423 2307468 "PADIC" 2307473 NIL PADIC (NIL NIL) -8 NIL NIL) (-855 2302990 2304564 2304605 "PADICCT" 2305186 NIL PADICCT (NIL NIL) -9 NIL 2305468) (-854 2301947 2302147 2302415 "PADEPAC" 2302777 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-853 2301159 2301292 2301498 "PADE" 2301809 NIL PADE (NIL T T T) -7 NIL NIL) (-852 2297636 2300777 2300896 "PACRAT" 2301060 T PACRAT (NIL) -8 NIL NIL) (-851 2293697 2296747 2296776 "PACRATC" 2296781 T PACRATC (NIL) -9 NIL 2296861) (-850 2289819 2291784 2291813 "PACPERC" 2292759 T PACPERC (NIL) -9 NIL 2293199) (-849 2286489 2289593 2289684 "PACOFF" 2289760 NIL PACOFF (NIL T) -8 NIL NIL) (-848 2283184 2285844 2285873 "PACFFC" 2285878 T PACFFC (NIL) -9 NIL 2285899) (-847 2279274 2282867 2282968 "PACEXT" 2283115 NIL PACEXT (NIL NIL) -8 NIL NIL) (-846 2274652 2278169 2278198 "PACEXTC" 2278203 T PACEXTC (NIL) -9 NIL 2278247) (-845 2272660 2273492 2273807 "OWP" 2274421 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-844 2271769 2272265 2272437 "OVAR" 2272528 NIL OVAR (NIL NIL) -8 NIL NIL) (-843 2271033 2271154 2271315 "OUT" 2271628 T OUT (NIL) -7 NIL NIL) (-842 2260079 2262258 2264428 "OUTFORM" 2268883 T OUTFORM (NIL) -8 NIL NIL) (-841 2259487 2259808 2259897 "OSI" 2260010 T OSI (NIL) -8 NIL NIL) (-840 2258234 2258461 2258745 "ORTHPOL" 2259235 NIL ORTHPOL (NIL T) -7 NIL NIL) (-839 2255596 2257891 2258031 "OREUP" 2258177 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-838 2252983 2255285 2255413 "ORESUP" 2255538 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-837 2250491 2250997 2251562 "OREPCTO" 2252468 NIL OREPCTO (NIL T T) -7 NIL NIL) (-836 2244361 2246572 2246614 "OREPCAT" 2248962 NIL OREPCAT (NIL T) -9 NIL 2250062) (-835 2241508 2242290 2243348 "OREPCAT-" 2243353 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-834 2240684 2240956 2240985 "ORDSET" 2241294 T ORDSET (NIL) -9 NIL 2241458) (-833 2240203 2240325 2240518 "ORDSET-" 2240523 NIL ORDSET- (NIL T) -8 NIL NIL) (-832 2238812 2239613 2239642 "ORDRING" 2239844 T ORDRING (NIL) -9 NIL 2239969) (-831 2238457 2238551 2238695 "ORDRING-" 2238700 NIL ORDRING- (NIL T) -8 NIL NIL) (-830 2237831 2238312 2238341 "ORDMON" 2238346 T ORDMON (NIL) -9 NIL 2238367) (-829 2236993 2237140 2237335 "ORDFUNS" 2237680 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-828 2236503 2236862 2236891 "ORDFIN" 2236896 T ORDFIN (NIL) -9 NIL 2236917) (-827 2233015 2235095 2235501 "ORDCOMP" 2236130 NIL ORDCOMP (NIL T) -8 NIL NIL) (-826 2232281 2232408 2232594 "ORDCOMP2" 2232875 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-825 2228789 2229671 2230508 "OPTPROB" 2231464 T OPTPROB (NIL) -8 NIL NIL) (-824 2225591 2226230 2226934 "OPTPACK" 2228105 T OPTPACK (NIL) -7 NIL NIL) (-823 2223303 2224043 2224072 "OPTCAT" 2224891 T OPTCAT (NIL) -9 NIL 2225541) (-822 2223071 2223110 2223176 "OPQUERY" 2223257 T OPQUERY (NIL) -7 NIL NIL) (-821 2220197 2221388 2221889 "OP" 2222603 NIL OP (NIL T) -8 NIL NIL) (-820 2216962 2219000 2219366 "ONECOMP" 2219864 NIL ONECOMP (NIL T) -8 NIL NIL) (-819 2216267 2216382 2216556 "ONECOMP2" 2216834 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-818 2215686 2215792 2215922 "OMSERVER" 2216157 T OMSERVER (NIL) -7 NIL NIL) (-817 2212573 2215125 2215166 "OMSAGG" 2215227 NIL OMSAGG (NIL T) -9 NIL 2215291) (-816 2211196 2211459 2211741 "OMPKG" 2212311 T OMPKG (NIL) -7 NIL NIL) (-815 2210625 2210728 2210757 "OM" 2211056 T OM (NIL) -9 NIL NIL) (-814 2209163 2210176 2210344 "OMLO" 2210507 NIL OMLO (NIL T T) -8 NIL NIL) (-813 2208088 2208235 2208462 "OMEXPR" 2208989 NIL OMEXPR (NIL T) -7 NIL NIL) (-812 2207406 2207634 2207770 "OMERR" 2207972 T OMERR (NIL) -8 NIL NIL) (-811 2206584 2206827 2206987 "OMERRK" 2207266 T OMERRK (NIL) -8 NIL NIL) (-810 2206062 2206261 2206369 "OMENC" 2206496 T OMENC (NIL) -8 NIL NIL) (-809 2199957 2201142 2202313 "OMDEV" 2204911 T OMDEV (NIL) -8 NIL NIL) (-808 2199026 2199197 2199391 "OMCONN" 2199783 T OMCONN (NIL) -8 NIL NIL) (-807 2197637 2198623 2198652 "OINTDOM" 2198657 T OINTDOM (NIL) -9 NIL 2198678) (-806 2193288 2194543 2195287 "OFMONOID" 2196925 NIL OFMONOID (NIL T) -8 NIL NIL) (-805 2192726 2193225 2193270 "ODVAR" 2193275 NIL ODVAR (NIL T) -8 NIL NIL) (-804 2189853 2192225 2192409 "ODR" 2192602 NIL ODR (NIL T T NIL) -8 NIL NIL) (-803 2182151 2189629 2189755 "ODPOL" 2189760 NIL ODPOL (NIL T) -8 NIL NIL) (-802 2175945 2182023 2182128 "ODP" 2182133 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-801 2174711 2174926 2175201 "ODETOOLS" 2175719 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-800 2171680 2172336 2173052 "ODESYS" 2174044 NIL ODESYS (NIL T T) -7 NIL NIL) (-799 2166564 2167472 2168496 "ODERTRIC" 2170756 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-798 2165990 2166072 2166266 "ODERED" 2166476 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-797 2162878 2163426 2164103 "ODERAT" 2165413 NIL ODERAT (NIL T T) -7 NIL NIL) (-796 2159838 2160302 2160899 "ODEPRRIC" 2162407 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-795 2157709 2158276 2158785 "ODEPROB" 2159349 T ODEPROB (NIL) -8 NIL NIL) (-794 2154231 2154714 2155361 "ODEPRIM" 2157188 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-793 2153480 2153582 2153842 "ODEPAL" 2154123 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-792 2149642 2150433 2151297 "ODEPACK" 2152636 T ODEPACK (NIL) -7 NIL NIL) (-791 2148675 2148782 2149011 "ODEINT" 2149531 NIL ODEINT (NIL T T) -7 NIL NIL) (-790 2142776 2144201 2145648 "ODEIFTBL" 2147248 T ODEIFTBL (NIL) -8 NIL NIL) (-789 2138111 2138897 2139856 "ODEEF" 2141935 NIL ODEEF (NIL T T) -7 NIL NIL) (-788 2137446 2137535 2137765 "ODECONST" 2138016 NIL ODECONST (NIL T T T) -7 NIL NIL) (-787 2135596 2136231 2136260 "ODECAT" 2136865 T ODECAT (NIL) -9 NIL 2137396) (-786 2132457 2135308 2135427 "OCT" 2135509 NIL OCT (NIL T) -8 NIL NIL) (-785 2132095 2132138 2132265 "OCTCT2" 2132408 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-784 2126919 2129363 2129404 "OC" 2130501 NIL OC (NIL T) -9 NIL 2131351) (-783 2124146 2124894 2125884 "OC-" 2125978 NIL OC- (NIL T T) -8 NIL NIL) (-782 2123523 2123965 2123994 "OCAMON" 2123999 T OCAMON (NIL) -9 NIL 2124020) (-781 2122975 2123382 2123411 "OASGP" 2123416 T OASGP (NIL) -9 NIL 2123436) (-780 2122261 2122724 2122753 "OAMONS" 2122793 T OAMONS (NIL) -9 NIL 2122836) (-779 2121700 2122107 2122136 "OAMON" 2122141 T OAMON (NIL) -9 NIL 2122161) (-778 2121003 2121495 2121524 "OAGROUP" 2121529 T OAGROUP (NIL) -9 NIL 2121549) (-777 2120693 2120743 2120831 "NUMTUBE" 2120947 NIL NUMTUBE (NIL T) -7 NIL NIL) (-776 2114266 2115784 2117320 "NUMQUAD" 2119177 T NUMQUAD (NIL) -7 NIL NIL) (-775 2110022 2111010 2112035 "NUMODE" 2113261 T NUMODE (NIL) -7 NIL NIL) (-774 2107402 2108256 2108285 "NUMINT" 2109208 T NUMINT (NIL) -9 NIL 2109972) (-773 2106350 2106547 2106765 "NUMFMT" 2107204 T NUMFMT (NIL) -7 NIL NIL) (-772 2092728 2095670 2098194 "NUMERIC" 2103865 NIL NUMERIC (NIL T) -7 NIL NIL) (-771 2087131 2092176 2092272 "NTSCAT" 2092277 NIL NTSCAT (NIL T T T T) -9 NIL 2092316) (-770 2086327 2086492 2086684 "NTPOLFN" 2086971 NIL NTPOLFN (NIL T) -7 NIL NIL) (-769 2074123 2083154 2083965 "NSUP" 2085549 NIL NSUP (NIL T) -8 NIL NIL) (-768 2073755 2073812 2073921 "NSUP2" 2074060 NIL NSUP2 (NIL T T) -7 NIL NIL) (-767 2063706 2073529 2073662 "NSMP" 2073667 NIL NSMP (NIL T T) -8 NIL NIL) (-766 2051798 2063288 2063452 "NSDPS" 2063574 NIL NSDPS (NIL T) -8 NIL NIL) (-765 2050230 2050531 2050888 "NREP" 2051486 NIL NREP (NIL T) -7 NIL NIL) (-764 2047319 2047867 2048516 "NPOLYGON" 2049672 NIL NPOLYGON (NIL T T T NIL) -7 NIL NIL) (-763 2045910 2046162 2046520 "NPCOEF" 2047062 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-762 2045192 2045694 2045778 "NOTTING" 2045858 NIL NOTTING (NIL T) -8 NIL NIL) (-761 2044258 2044373 2044589 "NORMRETR" 2045073 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-760 2042299 2042589 2042998 "NORMPK" 2043966 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-759 2041984 2042012 2042136 "NORMMA" 2042265 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-758 2041811 2041941 2041970 "NONE" 2041975 T NONE (NIL) -8 NIL NIL) (-757 2041600 2041629 2041698 "NONE1" 2041775 NIL NONE1 (NIL T) -7 NIL NIL) (-756 2041083 2041145 2041331 "NODE1" 2041532 NIL NODE1 (NIL T T) -7 NIL NIL) (-755 2039377 2040246 2040501 "NNI" 2040848 T NNI (NIL) -8 NIL NIL) (-754 2037797 2038110 2038474 "NLINSOL" 2039045 NIL NLINSOL (NIL T) -7 NIL NIL) (-753 2033965 2034932 2035854 "NIPROB" 2036895 T NIPROB (NIL) -8 NIL NIL) (-752 2032722 2032956 2033258 "NFINTBAS" 2033727 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-751 2032451 2032494 2032575 "NEWTON" 2032673 NIL NEWTON (NIL T) -7 NIL NIL) (-750 2031159 2031390 2031671 "NCODIV" 2032219 NIL NCODIV (NIL T T) -7 NIL NIL) (-749 2030921 2030958 2031033 "NCNTFRAC" 2031116 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-748 2029101 2029465 2029885 "NCEP" 2030546 NIL NCEP (NIL T) -7 NIL NIL) (-747 2028011 2028750 2028779 "NASRING" 2028889 T NASRING (NIL) -9 NIL 2028963) (-746 2027806 2027850 2027944 "NASRING-" 2027949 NIL NASRING- (NIL T) -8 NIL NIL) (-745 2026958 2027457 2027486 "NARNG" 2027603 T NARNG (NIL) -9 NIL 2027694) (-744 2026650 2026717 2026851 "NARNG-" 2026856 NIL NARNG- (NIL T) -8 NIL NIL) (-743 2025529 2025736 2025971 "NAGSP" 2026435 T NAGSP (NIL) -7 NIL NIL) (-742 2016801 2018485 2020158 "NAGS" 2023876 T NAGS (NIL) -7 NIL NIL) (-741 2015349 2015657 2015988 "NAGF07" 2016490 T NAGF07 (NIL) -7 NIL NIL) (-740 2009887 2011178 2012485 "NAGF04" 2014062 T NAGF04 (NIL) -7 NIL NIL) (-739 2002855 2004469 2006102 "NAGF02" 2008274 T NAGF02 (NIL) -7 NIL NIL) (-738 1998079 1999179 2000296 "NAGF01" 2001758 T NAGF01 (NIL) -7 NIL NIL) (-737 1991707 1993273 1994858 "NAGE04" 1996514 T NAGE04 (NIL) -7 NIL NIL) (-736 1982876 1984997 1987127 "NAGE02" 1989597 T NAGE02 (NIL) -7 NIL NIL) (-735 1978829 1979776 1980740 "NAGE01" 1981932 T NAGE01 (NIL) -7 NIL NIL) (-734 1976624 1977158 1977716 "NAGD03" 1978291 T NAGD03 (NIL) -7 NIL NIL) (-733 1968374 1970302 1972256 "NAGD02" 1974690 T NAGD02 (NIL) -7 NIL NIL) (-732 1962185 1963610 1965050 "NAGD01" 1966954 T NAGD01 (NIL) -7 NIL NIL) (-731 1958394 1959216 1960053 "NAGC06" 1961368 T NAGC06 (NIL) -7 NIL NIL) (-730 1956859 1957191 1957547 "NAGC05" 1958058 T NAGC05 (NIL) -7 NIL NIL) (-729 1956235 1956354 1956498 "NAGC02" 1956735 T NAGC02 (NIL) -7 NIL NIL) (-728 1955294 1955851 1955892 "NAALG" 1955971 NIL NAALG (NIL T) -9 NIL 1956032) (-727 1955129 1955158 1955248 "NAALG-" 1955253 NIL NAALG- (NIL T T) -8 NIL NIL) (-726 1946005 1954245 1954520 "MYUP" 1954900 NIL MYUP (NIL NIL T) -8 NIL NIL) (-725 1936368 1944461 1944832 "MYEXPR" 1945700 NIL MYEXPR (NIL NIL T) -8 NIL NIL) (-724 1930318 1931426 1932613 "MULTSQFR" 1935264 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-723 1929637 1929712 1929896 "MULTFACT" 1930230 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-722 1922764 1926673 1926727 "MTSCAT" 1927797 NIL MTSCAT (NIL T T) -9 NIL 1928310) (-721 1922476 1922530 1922622 "MTHING" 1922704 NIL MTHING (NIL T) -7 NIL NIL) (-720 1922268 1922301 1922361 "MSYSCMD" 1922436 T MSYSCMD (NIL) -7 NIL NIL) (-719 1918380 1921023 1921343 "MSET" 1921981 NIL MSET (NIL T) -8 NIL NIL) (-718 1915474 1917940 1917982 "MSETAGG" 1917987 NIL MSETAGG (NIL T) -9 NIL 1918021) (-717 1911323 1912865 1913604 "MRING" 1914780 NIL MRING (NIL T T) -8 NIL NIL) (-716 1910889 1910956 1911087 "MRF2" 1911250 NIL MRF2 (NIL T T T) -7 NIL NIL) (-715 1910507 1910542 1910686 "MRATFAC" 1910848 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-714 1908119 1908414 1908845 "MPRFF" 1910212 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-713 1902133 1907973 1908070 "MPOLY" 1908075 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-712 1901623 1901658 1901866 "MPCPF" 1902092 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-711 1901137 1901180 1901364 "MPC3" 1901574 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-710 1900332 1900413 1900634 "MPC2" 1901052 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-709 1898633 1898970 1899360 "MONOTOOL" 1899992 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-708 1897756 1898091 1898120 "MONOID" 1898397 T MONOID (NIL) -9 NIL 1898569) (-707 1897134 1897297 1897540 "MONOID-" 1897545 NIL MONOID- (NIL T) -8 NIL NIL) (-706 1888060 1894045 1894105 "MONOGEN" 1894779 NIL MONOGEN (NIL T T) -9 NIL 1895232) (-705 1885278 1886013 1887013 "MONOGEN-" 1887132 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-704 1884136 1884556 1884585 "MONADWU" 1884977 T MONADWU (NIL) -9 NIL 1885215) (-703 1883508 1883667 1883915 "MONADWU-" 1883920 NIL MONADWU- (NIL T) -8 NIL NIL) (-702 1882892 1883110 1883139 "MONAD" 1883346 T MONAD (NIL) -9 NIL 1883458) (-701 1882577 1882655 1882787 "MONAD-" 1882792 NIL MONAD- (NIL T) -8 NIL NIL) (-700 1880828 1881490 1881769 "MOEBIUS" 1882330 NIL MOEBIUS (NIL T) -8 NIL NIL) (-699 1880219 1880597 1880638 "MODULE" 1880643 NIL MODULE (NIL T) -9 NIL 1880669) (-698 1879787 1879883 1880073 "MODULE-" 1880078 NIL MODULE- (NIL T T) -8 NIL NIL) (-697 1877456 1878151 1878478 "MODRING" 1879611 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-696 1874402 1875567 1876085 "MODOP" 1876988 NIL MODOP (NIL T T) -8 NIL NIL) (-695 1872589 1873041 1873382 "MODMONOM" 1874201 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-694 1862254 1870785 1871206 "MODMON" 1872219 NIL MODMON (NIL T T) -8 NIL NIL) (-693 1859380 1861098 1861374 "MODFIELD" 1862129 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-692 1858384 1858661 1858851 "MMLFORM" 1859210 T MMLFORM (NIL) -8 NIL NIL) (-691 1857910 1857953 1858132 "MMAP" 1858335 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-690 1856135 1856912 1856954 "MLO" 1857377 NIL MLO (NIL T) -9 NIL 1857618) (-689 1853502 1854017 1854619 "MLIFT" 1855616 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-688 1852893 1852977 1853131 "MKUCFUNC" 1853413 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-687 1852492 1852562 1852685 "MKRECORD" 1852816 NIL MKRECORD (NIL T T) -7 NIL NIL) (-686 1851540 1851701 1851929 "MKFUNC" 1852303 NIL MKFUNC (NIL T) -7 NIL NIL) (-685 1850928 1851032 1851188 "MKFLCFN" 1851423 NIL MKFLCFN (NIL T) -7 NIL NIL) (-684 1850354 1850721 1850810 "MKCHSET" 1850872 NIL MKCHSET (NIL T) -8 NIL NIL) (-683 1849631 1849733 1849918 "MKBCFUNC" 1850247 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-682 1846315 1849185 1849321 "MINT" 1849515 T MINT (NIL) -8 NIL NIL) (-681 1845127 1845370 1845647 "MHROWRED" 1846070 NIL MHROWRED (NIL T) -7 NIL NIL) (-680 1840394 1843568 1843994 "MFLOAT" 1844721 T MFLOAT (NIL) -8 NIL NIL) (-679 1839751 1839827 1839998 "MFINFACT" 1840306 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-678 1836066 1836914 1837798 "MESH" 1838887 T MESH (NIL) -7 NIL NIL) (-677 1834456 1834768 1835121 "MDDFACT" 1835753 NIL MDDFACT (NIL T) -7 NIL NIL) (-676 1831338 1833649 1833691 "MDAGG" 1833946 NIL MDAGG (NIL T) -9 NIL 1834089) (-675 1821029 1830631 1830838 "MCMPLX" 1831151 T MCMPLX (NIL) -8 NIL NIL) (-674 1820170 1820316 1820516 "MCDEN" 1820878 NIL MCDEN (NIL T T) -7 NIL NIL) (-673 1818060 1818330 1818710 "MCALCFN" 1819900 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-672 1815672 1816195 1816757 "MATSTOR" 1817531 NIL MATSTOR (NIL T) -7 NIL NIL) (-671 1811586 1815048 1815294 "MATRIX" 1815459 NIL MATRIX (NIL T) -8 NIL NIL) (-670 1807362 1808065 1808798 "MATLIN" 1810946 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-669 1797127 1800348 1800426 "MATCAT" 1805556 NIL MATCAT (NIL T T T) -9 NIL 1807063) (-668 1793326 1794394 1795805 "MATCAT-" 1795810 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-667 1791920 1792073 1792406 "MATCAT2" 1793161 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-666 1790660 1790926 1791241 "MAPPKG4" 1791651 NIL MAPPKG4 (NIL T T) -7 NIL NIL) (-665 1788772 1789096 1789480 "MAPPKG3" 1790335 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-664 1787753 1787926 1788148 "MAPPKG2" 1788596 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-663 1786252 1786536 1786863 "MAPPKG1" 1787459 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-662 1785863 1785921 1786044 "MAPHACK3" 1786188 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-661 1785455 1785516 1785630 "MAPHACK2" 1785795 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-660 1784893 1784996 1785138 "MAPHACK1" 1785346 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-659 1782999 1783593 1783897 "MAGMA" 1784621 NIL MAGMA (NIL T) -8 NIL NIL) (-658 1779474 1781240 1781700 "M3D" 1782572 NIL M3D (NIL T) -8 NIL NIL) (-657 1773668 1777874 1777916 "LZSTAGG" 1778698 NIL LZSTAGG (NIL T) -9 NIL 1778993) (-656 1769642 1770799 1772256 "LZSTAGG-" 1772261 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-655 1766756 1767533 1768020 "LWORD" 1769187 NIL LWORD (NIL T) -8 NIL NIL) (-654 1759911 1766527 1766661 "LSQM" 1766666 NIL LSQM (NIL NIL T) -8 NIL NIL) (-653 1759135 1759274 1759502 "LSPP" 1759766 NIL LSPP (NIL T T T T) -7 NIL NIL) (-652 1756947 1757248 1757704 "LSMP" 1758824 NIL LSMP (NIL T T T T) -7 NIL NIL) (-651 1753726 1754400 1755130 "LSMP1" 1756249 NIL LSMP1 (NIL T) -7 NIL NIL) (-650 1747683 1752916 1752958 "LSAGG" 1753020 NIL LSAGG (NIL T) -9 NIL 1753098) (-649 1744378 1745302 1746515 "LSAGG-" 1746520 NIL LSAGG- (NIL T T) -8 NIL NIL) (-648 1742004 1743522 1743771 "LPOLY" 1744173 NIL LPOLY (NIL T T) -8 NIL NIL) (-647 1741586 1741671 1741794 "LPEFRAC" 1741913 NIL LPEFRAC (NIL T) -7 NIL NIL) (-646 1739150 1739399 1739831 "LPARSPT" 1741328 NIL LPARSPT (NIL T NIL T T T T T) -7 NIL NIL) (-645 1737625 1737952 1738312 "LOP" 1738822 NIL LOP (NIL T) -7 NIL NIL) (-644 1735974 1736721 1736973 "LO" 1737458 NIL LO (NIL T T T) -8 NIL NIL) (-643 1735625 1735737 1735766 "LOGIC" 1735877 T LOGIC (NIL) -9 NIL 1735958) (-642 1735487 1735510 1735581 "LOGIC-" 1735586 NIL LOGIC- (NIL T) -8 NIL NIL) (-641 1734680 1734820 1735013 "LODOOPS" 1735343 NIL LODOOPS (NIL T T) -7 NIL NIL) (-640 1732092 1734596 1734662 "LODO" 1734667 NIL LODO (NIL T NIL) -8 NIL NIL) (-639 1730632 1730867 1731219 "LODOF" 1731840 NIL LODOF (NIL T T) -7 NIL NIL) (-638 1727031 1729472 1729514 "LODOCAT" 1729952 NIL LODOCAT (NIL T) -9 NIL 1730162) (-637 1726764 1726822 1726949 "LODOCAT-" 1726954 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-636 1724073 1726605 1726723 "LODO2" 1726728 NIL LODO2 (NIL T T) -8 NIL NIL) (-635 1721497 1724010 1724055 "LODO1" 1724060 NIL LODO1 (NIL T) -8 NIL NIL) (-634 1720357 1720522 1720834 "LODEEF" 1721320 NIL LODEEF (NIL T T T) -7 NIL NIL) (-633 1713184 1717349 1717390 "LOCPOWC" 1718852 NIL LOCPOWC (NIL T) -9 NIL 1719429) (-632 1708508 1711346 1711388 "LNAGG" 1712335 NIL LNAGG (NIL T) -9 NIL 1712778) (-631 1707655 1707869 1708211 "LNAGG-" 1708216 NIL LNAGG- (NIL T T) -8 NIL NIL) (-630 1703818 1704580 1705219 "LMOPS" 1707070 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-629 1703212 1703574 1703616 "LMODULE" 1703677 NIL LMODULE (NIL T) -9 NIL 1703719) (-628 1700464 1702857 1702980 "LMDICT" 1703122 NIL LMDICT (NIL T) -8 NIL NIL) (-627 1699621 1699755 1699942 "LISYSER" 1700326 NIL LISYSER (NIL T T) -7 NIL NIL) (-626 1692858 1698571 1698867 "LIST" 1699358 NIL LIST (NIL T) -8 NIL NIL) (-625 1692383 1692457 1692596 "LIST3" 1692778 NIL LIST3 (NIL T T T) -7 NIL NIL) (-624 1691390 1691568 1691796 "LIST2" 1692201 NIL LIST2 (NIL T T) -7 NIL NIL) (-623 1689524 1689836 1690235 "LIST2MAP" 1691037 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-622 1688229 1688909 1688951 "LINEXP" 1689206 NIL LINEXP (NIL T) -9 NIL 1689355) (-621 1686876 1687136 1687433 "LINDEP" 1687981 NIL LINDEP (NIL T T) -7 NIL NIL) (-620 1683643 1684362 1685139 "LIMITRF" 1686131 NIL LIMITRF (NIL T) -7 NIL NIL) (-619 1681920 1682214 1682630 "LIMITPS" 1683338 NIL LIMITPS (NIL T T) -7 NIL NIL) (-618 1676379 1681435 1681661 "LIE" 1681743 NIL LIE (NIL T T) -8 NIL NIL) (-617 1675428 1675871 1675912 "LIECAT" 1676052 NIL LIECAT (NIL T) -9 NIL 1676202) (-616 1675269 1675296 1675384 "LIECAT-" 1675389 NIL LIECAT- (NIL T T) -8 NIL NIL) (-615 1667803 1674648 1674831 "LIB" 1675106 T LIB (NIL) -8 NIL NIL) (-614 1663440 1664321 1665256 "LGROBP" 1666920 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-613 1661306 1661580 1661942 "LF" 1663161 NIL LF (NIL T T) -7 NIL NIL) (-612 1660145 1660837 1660866 "LFCAT" 1661073 T LFCAT (NIL) -9 NIL 1661212) (-611 1657049 1657677 1658365 "LEXTRIPK" 1659509 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-610 1653755 1654619 1655122 "LEXP" 1656629 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-609 1652153 1652466 1652867 "LEADCDET" 1653437 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-608 1651343 1651417 1651646 "LAZM3PK" 1652074 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-607 1646259 1649426 1649961 "LAUPOL" 1650858 NIL LAUPOL (NIL T T) -8 NIL NIL) (-606 1645824 1645868 1646036 "LAPLACE" 1646209 NIL LAPLACE (NIL T T) -7 NIL NIL) (-605 1643754 1644927 1645177 "LA" 1645658 NIL LA (NIL T T T) -8 NIL NIL) (-604 1642810 1643404 1643446 "LALG" 1643508 NIL LALG (NIL T) -9 NIL 1643567) (-603 1642524 1642583 1642719 "LALG-" 1642724 NIL LALG- (NIL T T) -8 NIL NIL) (-602 1641428 1641615 1641914 "KOVACIC" 1642324 NIL KOVACIC (NIL T T) -7 NIL NIL) (-601 1641262 1641286 1641328 "KONVERT" 1641390 NIL KONVERT (NIL T) -9 NIL NIL) (-600 1641096 1641120 1641162 "KOERCE" 1641224 NIL KOERCE (NIL T) -9 NIL NIL) (-599 1638832 1639592 1639984 "KERNEL" 1640736 NIL KERNEL (NIL T) -8 NIL NIL) (-598 1638334 1638415 1638545 "KERNEL2" 1638746 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-597 1632017 1636699 1636754 "KDAGG" 1637131 NIL KDAGG (NIL T T) -9 NIL 1637337) (-596 1631546 1631670 1631875 "KDAGG-" 1631880 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-595 1624695 1631207 1631362 "KAFILE" 1631424 NIL KAFILE (NIL T) -8 NIL NIL) (-594 1619154 1624210 1624436 "JORDAN" 1624518 NIL JORDAN (NIL T T) -8 NIL NIL) (-593 1615497 1617397 1617452 "IXAGG" 1618381 NIL IXAGG (NIL T T) -9 NIL 1618836) (-592 1614416 1614722 1615141 "IXAGG-" 1615146 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-591 1610002 1614338 1614397 "IVECTOR" 1614402 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-590 1608768 1609005 1609271 "ITUPLE" 1609769 NIL ITUPLE (NIL T) -8 NIL NIL) (-589 1607204 1607381 1607687 "ITRIGMNP" 1608590 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-588 1605949 1606153 1606436 "ITFUN3" 1606980 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-587 1605581 1605638 1605747 "ITFUN2" 1605886 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-586 1603374 1604445 1604743 "ITAYLOR" 1605316 NIL ITAYLOR (NIL T) -8 NIL NIL) (-585 1592313 1597513 1598675 "ISUPS" 1602245 NIL ISUPS (NIL T) -8 NIL NIL) (-584 1591417 1591557 1591793 "ISUMP" 1592160 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-583 1586687 1591218 1591297 "ISTRING" 1591370 NIL ISTRING (NIL NIL) -8 NIL NIL) (-582 1585897 1585978 1586194 "IRURPK" 1586601 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-581 1584833 1585034 1585274 "IRSN" 1585677 T IRSN (NIL) -7 NIL NIL) (-580 1582864 1583219 1583654 "IRRF2F" 1584472 NIL IRRF2F (NIL T) -7 NIL NIL) (-579 1582611 1582649 1582725 "IRREDFFX" 1582820 NIL IRREDFFX (NIL T) -7 NIL NIL) (-578 1581226 1581485 1581784 "IROOT" 1582344 NIL IROOT (NIL T) -7 NIL NIL) (-577 1577862 1578914 1579604 "IR" 1580568 NIL IR (NIL T) -8 NIL NIL) (-576 1575475 1575970 1576536 "IR2" 1577340 NIL IR2 (NIL T T) -7 NIL NIL) (-575 1574547 1574660 1574881 "IR2F" 1575358 NIL IR2F (NIL T T) -7 NIL NIL) (-574 1574338 1574372 1574432 "IPRNTPK" 1574507 T IPRNTPK (NIL) -7 NIL NIL) (-573 1570892 1574227 1574296 "IPF" 1574301 NIL IPF (NIL NIL) -8 NIL NIL) (-572 1569209 1570817 1570874 "IPADIC" 1570879 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-571 1568706 1568764 1568954 "INVLAPLA" 1569145 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-570 1558355 1560708 1563094 "INTTR" 1566370 NIL INTTR (NIL T T) -7 NIL NIL) (-569 1554713 1555455 1556312 "INTTOOLS" 1557547 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-568 1554299 1554390 1554507 "INTSLPE" 1554616 T INTSLPE (NIL) -7 NIL NIL) (-567 1552249 1554222 1554281 "INTRVL" 1554286 NIL INTRVL (NIL T) -8 NIL NIL) (-566 1549851 1550363 1550938 "INTRF" 1551734 NIL INTRF (NIL T) -7 NIL NIL) (-565 1549262 1549359 1549501 "INTRET" 1549749 NIL INTRET (NIL T) -7 NIL NIL) (-564 1547259 1547648 1548118 "INTRAT" 1548870 NIL INTRAT (NIL T T) -7 NIL NIL) (-563 1544495 1545078 1545700 "INTPM" 1546748 NIL INTPM (NIL T T) -7 NIL NIL) (-562 1541200 1541799 1542543 "INTPAF" 1543882 NIL INTPAF (NIL T T T) -7 NIL NIL) (-561 1536379 1537341 1538392 "INTPACK" 1540169 T INTPACK (NIL) -7 NIL NIL) (-560 1533233 1536108 1536235 "INT" 1536272 T INT (NIL) -8 NIL NIL) (-559 1532485 1532637 1532845 "INTHERTR" 1533075 NIL INTHERTR (NIL T T) -7 NIL NIL) (-558 1531924 1532004 1532192 "INTHERAL" 1532399 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-557 1529770 1530213 1530670 "INTHEORY" 1531487 T INTHEORY (NIL) -7 NIL NIL) (-556 1521081 1522701 1524479 "INTG0" 1528123 NIL INTG0 (NIL T T T) -7 NIL NIL) (-555 1501654 1506444 1511254 "INTFTBL" 1516291 T INTFTBL (NIL) -8 NIL NIL) (-554 1499691 1499898 1500299 "INTFRSP" 1501444 NIL INTFRSP (NIL T NIL T T T T T T) -7 NIL NIL) (-553 1498940 1499078 1499251 "INTFACT" 1499550 NIL INTFACT (NIL T) -7 NIL NIL) (-552 1498530 1498572 1498723 "INTERGB" 1498892 NIL INTERGB (NIL T NIL T T T) -7 NIL NIL) (-551 1495915 1496361 1496925 "INTEF" 1498084 NIL INTEF (NIL T T) -7 NIL NIL) (-550 1494372 1495121 1495150 "INTDOM" 1495451 T INTDOM (NIL) -9 NIL 1495658) (-549 1493741 1493915 1494157 "INTDOM-" 1494162 NIL INTDOM- (NIL T) -8 NIL NIL) (-548 1492345 1492450 1492840 "INTDIVP" 1493631 NIL INTDIVP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-547 1488833 1490763 1490818 "INTCAT" 1491617 NIL INTCAT (NIL T) -9 NIL 1491937) (-546 1488306 1488408 1488536 "INTBIT" 1488725 T INTBIT (NIL) -7 NIL NIL) (-545 1486977 1487131 1487445 "INTALG" 1488151 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-544 1486434 1486524 1486694 "INTAF" 1486881 NIL INTAF (NIL T T) -7 NIL NIL) (-543 1479900 1486244 1486384 "INTABL" 1486389 NIL INTABL (NIL T T T) -8 NIL NIL) (-542 1474845 1477571 1477600 "INS" 1478568 T INS (NIL) -9 NIL 1479251) (-541 1472085 1472856 1473830 "INS-" 1473903 NIL INS- (NIL T) -8 NIL NIL) (-540 1470860 1471087 1471385 "INPSIGN" 1471838 NIL INPSIGN (NIL T T) -7 NIL NIL) (-539 1469978 1470095 1470292 "INPRODPF" 1470740 NIL INPRODPF (NIL T T) -7 NIL NIL) (-538 1468872 1468989 1469226 "INPRODFF" 1469858 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-537 1467872 1468024 1468284 "INNMFACT" 1468708 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-536 1467069 1467166 1467354 "INMODGCD" 1467771 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-535 1465578 1465822 1466146 "INFSP" 1466814 NIL INFSP (NIL T T T) -7 NIL NIL) (-534 1464762 1464879 1465062 "INFPROD0" 1465458 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-533 1461643 1462827 1463342 "INFORM" 1464255 T INFORM (NIL) -8 NIL NIL) (-532 1461253 1461313 1461411 "INFORM1" 1461578 NIL INFORM1 (NIL T) -7 NIL NIL) (-531 1460776 1460865 1460979 "INFINITY" 1461159 T INFINITY (NIL) -7 NIL NIL) (-530 1458459 1459456 1459799 "INFCLSPT" 1460636 NIL INFCLSPT (NIL T NIL T T T T T T T) -8 NIL NIL) (-529 1456336 1457581 1457875 "INFCLSPS" 1458229 NIL INFCLSPS (NIL T NIL T) -8 NIL NIL) (-528 1449264 1450187 1450408 "INFCLCT" 1455461 NIL INFCLCT (NIL T NIL T T T T T T T) -9 NIL 1456272) (-527 1447882 1448130 1448451 "INEP" 1449012 NIL INEP (NIL T T T) -7 NIL NIL) (-526 1447158 1447779 1447844 "INDE" 1447849 NIL INDE (NIL T) -8 NIL NIL) (-525 1446722 1446790 1446907 "INCRMAPS" 1447085 NIL INCRMAPS (NIL T) -7 NIL NIL) (-524 1442033 1442958 1443902 "INBFF" 1445810 NIL INBFF (NIL T) -7 NIL NIL) (-523 1438428 1441877 1441981 "IMATRIX" 1441986 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-522 1437142 1437265 1437579 "IMATQF" 1438285 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-521 1435364 1435591 1435927 "IMATLIN" 1436899 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-520 1429996 1435288 1435346 "ILIST" 1435351 NIL ILIST (NIL T NIL) -8 NIL NIL) (-519 1427955 1429856 1429969 "IIARRAY2" 1429974 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-518 1423323 1427866 1427930 "IFF" 1427935 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-517 1418372 1422615 1422803 "IFARRAY" 1423180 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-516 1417579 1418276 1418349 "IFAMON" 1418354 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-515 1417162 1417227 1417282 "IEVALAB" 1417489 NIL IEVALAB (NIL T T) -9 NIL NIL) (-514 1416837 1416905 1417065 "IEVALAB-" 1417070 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-513 1416495 1416751 1416814 "IDPO" 1416819 NIL IDPO (NIL T T) -8 NIL NIL) (-512 1415772 1416384 1416459 "IDPOAMS" 1416464 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-511 1415106 1415661 1415736 "IDPOAM" 1415741 NIL IDPOAM (NIL T T) -8 NIL NIL) (-510 1414190 1414440 1414494 "IDPC" 1414907 NIL IDPC (NIL T T) -9 NIL 1415056) (-509 1413686 1414082 1414155 "IDPAM" 1414160 NIL IDPAM (NIL T T) -8 NIL NIL) (-508 1413089 1413578 1413651 "IDPAG" 1413656 NIL IDPAG (NIL T T) -8 NIL NIL) (-507 1409344 1410192 1411087 "IDECOMP" 1412246 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-506 1402220 1403269 1404315 "IDEAL" 1408381 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-505 1400237 1401384 1401657 "ICP" 1402011 NIL ICP (NIL T NIL T) -8 NIL NIL) (-504 1399401 1399513 1399712 "ICDEN" 1400121 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-503 1398500 1398881 1399028 "ICARD" 1399274 T ICARD (NIL) -8 NIL NIL) (-502 1396560 1396873 1397278 "IBPTOOLS" 1398177 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-501 1392174 1396180 1396293 "IBITS" 1396479 NIL IBITS (NIL NIL) -8 NIL NIL) (-500 1388897 1389473 1390168 "IBATOOL" 1391591 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-499 1386677 1387138 1387671 "IBACHIN" 1388432 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-498 1384560 1386523 1386626 "IARRAY2" 1386631 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-497 1380719 1384486 1384543 "IARRAY1" 1384548 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-496 1374649 1379131 1379612 "IAN" 1380258 T IAN (NIL) -8 NIL NIL) (-495 1374160 1374217 1374390 "IALGFACT" 1374586 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-494 1373687 1373800 1373829 "HYPCAT" 1374036 T HYPCAT (NIL) -9 NIL NIL) (-493 1373225 1373342 1373528 "HYPCAT-" 1373533 NIL HYPCAT- (NIL T) -8 NIL NIL) (-492 1370014 1371339 1371381 "HOAGG" 1372362 NIL HOAGG (NIL T) -9 NIL 1372971) (-491 1368608 1369007 1369533 "HOAGG-" 1369538 NIL HOAGG- (NIL T T) -8 NIL NIL) (-490 1362430 1368049 1368215 "HEXADEC" 1368462 T HEXADEC (NIL) -8 NIL NIL) (-489 1361178 1361400 1361663 "HEUGCD" 1362207 NIL HEUGCD (NIL T) -7 NIL NIL) (-488 1360281 1361015 1361145 "HELLFDIV" 1361150 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-487 1353998 1355541 1356622 "HEAP" 1359232 NIL HEAP (NIL T) -8 NIL NIL) (-486 1347836 1353913 1353975 "HDP" 1353980 NIL HDP (NIL NIL T) -8 NIL NIL) (-485 1341541 1347471 1347623 "HDMP" 1347737 NIL HDMP (NIL NIL T) -8 NIL NIL) (-484 1340866 1341005 1341169 "HB" 1341397 T HB (NIL) -7 NIL NIL) (-483 1334375 1340712 1340816 "HASHTBL" 1340821 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-482 1332122 1333997 1334179 "HACKPI" 1334213 T HACKPI (NIL) -8 NIL NIL) (-481 1314270 1318139 1322142 "GUESSUP" 1328152 NIL GUESSUP (NIL NIL) -7 NIL NIL) (-480 1285367 1292408 1299104 "GUESSP" 1307594 T GUESSP (NIL) -7 NIL NIL) (-479 1252182 1257453 1262837 "GUESS" 1280311 NIL GUESS (NIL T T T T NIL NIL) -7 NIL NIL) (-478 1225687 1232084 1238220 "GUESSINT" 1246066 T GUESSINT (NIL) -7 NIL NIL) (-477 1201058 1206508 1212075 "GUESSF" 1220172 NIL GUESSF (NIL T) -7 NIL NIL) (-476 1200780 1200817 1200912 "GUESSF1" 1201015 NIL GUESSF1 (NIL T) -7 NIL NIL) (-475 1176941 1182475 1188090 "GUESSAN" 1195185 T GUESSAN (NIL) -7 NIL NIL) (-474 1172636 1176794 1176907 "GTSET" 1176912 NIL GTSET (NIL T T T T) -8 NIL NIL) (-473 1166174 1172514 1172612 "GSTBL" 1172617 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-472 1158404 1165207 1165471 "GSERIES" 1165966 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-471 1157425 1157878 1157907 "GROUP" 1158168 T GROUP (NIL) -9 NIL 1158327) (-470 1156541 1156764 1157108 "GROUP-" 1157113 NIL GROUP- (NIL T) -8 NIL NIL) (-469 1154910 1155229 1155616 "GROEBSOL" 1156218 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-468 1153849 1154111 1154163 "GRMOD" 1154692 NIL GRMOD (NIL T T) -9 NIL 1154860) (-467 1153617 1153653 1153781 "GRMOD-" 1153786 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-466 1148946 1149971 1150971 "GRIMAGE" 1152637 T GRIMAGE (NIL) -8 NIL NIL) (-465 1147413 1147673 1147997 "GRDEF" 1148642 T GRDEF (NIL) -7 NIL NIL) (-464 1146857 1146973 1147114 "GRAY" 1147292 T GRAY (NIL) -7 NIL NIL) (-463 1146087 1146467 1146519 "GRALG" 1146672 NIL GRALG (NIL T T) -9 NIL 1146765) (-462 1145748 1145821 1145984 "GRALG-" 1145989 NIL GRALG- (NIL T T T) -8 NIL NIL) (-461 1142552 1145333 1145511 "GPOLSET" 1145655 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-460 1124755 1126245 1127834 "GPAFF" 1141243 NIL GPAFF (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-459 1124109 1124166 1124424 "GOSPER" 1124692 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-458 1121502 1122096 1122585 "GOPT" 1123640 T GOPT (NIL) -8 NIL NIL) (-457 1118723 1119364 1119901 "GOPT0" 1120985 T GOPT0 (NIL) -8 NIL NIL) (-456 1114482 1115161 1115687 "GMODPOL" 1118422 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-455 1113487 1113671 1113909 "GHENSEL" 1114294 NIL GHENSEL (NIL T T) -7 NIL NIL) (-454 1107538 1108381 1109408 "GENUPS" 1112571 NIL GENUPS (NIL T T) -7 NIL NIL) (-453 1107235 1107286 1107375 "GENUFACT" 1107481 NIL GENUFACT (NIL T) -7 NIL NIL) (-452 1106647 1106724 1106889 "GENPGCD" 1107153 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-451 1106121 1106156 1106369 "GENMFACT" 1106606 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-450 1104689 1104944 1105251 "GENEEZ" 1105864 NIL GENEEZ (NIL T T) -7 NIL NIL) (-449 1098556 1104300 1104462 "GDMP" 1104612 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-448 1087940 1092329 1093434 "GCNAALG" 1097540 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-447 1086357 1087229 1087258 "GCDDOM" 1087513 T GCDDOM (NIL) -9 NIL 1087670) (-446 1085827 1085954 1086169 "GCDDOM-" 1086174 NIL GCDDOM- (NIL T) -8 NIL NIL) (-445 1084501 1084686 1084989 "GB" 1085607 NIL GB (NIL T T T T) -7 NIL NIL) (-444 1073121 1075447 1077839 "GBINTERN" 1082192 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-443 1070958 1071250 1071671 "GBF" 1072796 NIL GBF (NIL T T T T) -7 NIL NIL) (-442 1069739 1069904 1070171 "GBEUCLID" 1070774 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-441 1069088 1069213 1069362 "GAUSSFAC" 1069610 T GAUSSFAC (NIL) -7 NIL NIL) (-440 1067457 1067759 1068072 "GALUTIL" 1068808 NIL GALUTIL (NIL T) -7 NIL NIL) (-439 1065765 1066039 1066363 "GALPOLYU" 1067184 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-438 1063130 1063420 1063827 "GALFACTU" 1065462 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-437 1054936 1056435 1058043 "GALFACT" 1061562 NIL GALFACT (NIL T) -7 NIL NIL) (-436 1052324 1052981 1053010 "FVFUN" 1054166 T FVFUN (NIL) -9 NIL 1054886) (-435 1051590 1051771 1051800 "FVC" 1052091 T FVC (NIL) -9 NIL 1052274) (-434 1051232 1051387 1051468 "FUNCTION" 1051542 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-433 1048902 1049453 1049942 "FT" 1050763 T FT (NIL) -8 NIL NIL) (-432 1047694 1048203 1048406 "FTEM" 1048719 T FTEM (NIL) -8 NIL NIL) (-431 1045952 1046241 1046644 "FSUPFACT" 1047386 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-430 1044349 1044638 1044970 "FST" 1045640 T FST (NIL) -8 NIL NIL) (-429 1043520 1043626 1043821 "FSRED" 1044231 NIL FSRED (NIL T T) -7 NIL NIL) (-428 1042201 1042456 1042809 "FSPRMELT" 1043236 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-427 1037567 1038272 1039029 "FSPECF" 1041506 NIL FSPECF (NIL T T) -7 NIL NIL) (-426 1019825 1028414 1028455 "FS" 1032303 NIL FS (NIL T) -9 NIL 1034581) (-425 1008475 1011465 1015521 "FS-" 1015818 NIL FS- (NIL T T) -8 NIL NIL) (-424 1007989 1008043 1008220 "FSINT" 1008416 NIL FSINT (NIL T T) -7 NIL NIL) (-423 1006274 1006986 1007287 "FSERIES" 1007770 NIL FSERIES (NIL T T) -8 NIL NIL) (-422 1005288 1005404 1005635 "FSCINT" 1006154 NIL FSCINT (NIL T T) -7 NIL NIL) (-421 1001523 1004233 1004275 "FSAGG" 1004645 NIL FSAGG (NIL T) -9 NIL 1004902) (-420 999285 999886 1000682 "FSAGG-" 1000777 NIL FSAGG- (NIL T T) -8 NIL NIL) (-419 998327 998470 998697 "FSAGG2" 999138 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-418 995982 996261 996815 "FS2UPS" 998045 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-417 995564 995607 995762 "FS2" 995933 NIL FS2 (NIL T T T T) -7 NIL NIL) (-416 994421 994592 994901 "FS2EXPXP" 995389 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-415 993847 993962 994114 "FRUTIL" 994301 NIL FRUTIL (NIL T) -7 NIL NIL) (-414 985273 989358 990708 "FR" 992529 NIL FR (NIL T) -8 NIL NIL) (-413 980353 982991 983032 "FRNAALG" 984428 NIL FRNAALG (NIL T) -9 NIL 985034) (-412 976032 977102 978377 "FRNAALG-" 979127 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-411 975670 975713 975840 "FRNAAF2" 975983 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-410 974033 974526 974820 "FRMOD" 975483 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-409 971748 972416 972733 "FRIDEAL" 973824 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-408 970943 971030 971319 "FRIDEAL2" 971655 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-407 970186 970600 970642 "FRETRCT" 970647 NIL FRETRCT (NIL T) -9 NIL 970821) (-406 969298 969529 969880 "FRETRCT-" 969885 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-405 966503 967723 967783 "FRAMALG" 968665 NIL FRAMALG (NIL T T) -9 NIL 968957) (-404 964636 965092 965722 "FRAMALG-" 965945 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-403 958539 964121 964392 "FRAC" 964397 NIL FRAC (NIL T) -8 NIL NIL) (-402 958175 958232 958339 "FRAC2" 958476 NIL FRAC2 (NIL T T) -7 NIL NIL) (-401 957811 957868 957975 "FR2" 958112 NIL FR2 (NIL T T) -7 NIL NIL) (-400 952434 955343 955372 "FPS" 956491 T FPS (NIL) -9 NIL 957045) (-399 951883 951992 952156 "FPS-" 952302 NIL FPS- (NIL T) -8 NIL NIL) (-398 949279 950976 951005 "FPC" 951230 T FPC (NIL) -9 NIL 951372) (-397 949072 949112 949209 "FPC-" 949214 NIL FPC- (NIL T) -8 NIL NIL) (-396 947951 948561 948603 "FPATMAB" 948608 NIL FPATMAB (NIL T) -9 NIL 948758) (-395 945651 946127 946553 "FPARFRAC" 947588 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-394 941046 941543 942225 "FORTRAN" 945083 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-393 938762 939262 939801 "FORT" 940527 T FORT (NIL) -7 NIL NIL) (-392 936438 936999 937028 "FORTFN" 938088 T FORTFN (NIL) -9 NIL 938712) (-391 936201 936251 936280 "FORTCAT" 936339 T FORTCAT (NIL) -9 NIL 936401) (-390 934261 934744 935143 "FORMULA" 935822 T FORMULA (NIL) -8 NIL NIL) (-389 934049 934079 934148 "FORMULA1" 934225 NIL FORMULA1 (NIL T) -7 NIL NIL) (-388 933572 933624 933797 "FORDER" 933991 NIL FORDER (NIL T T T T) -7 NIL NIL) (-387 932668 932832 933025 "FOP" 933399 T FOP (NIL) -7 NIL NIL) (-386 931276 931948 932122 "FNLA" 932550 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-385 929943 930332 930361 "FNCAT" 930933 T FNCAT (NIL) -9 NIL 931226) (-384 929509 929902 929930 "FNAME" 929935 T FNAME (NIL) -8 NIL NIL) (-383 928162 929135 929164 "FMTC" 929169 T FMTC (NIL) -9 NIL 929205) (-382 924480 925687 926315 "FMONOID" 927567 NIL FMONOID (NIL T) -8 NIL NIL) (-381 923701 924224 924372 "FM" 924377 NIL FM (NIL T T) -8 NIL NIL) (-380 921125 921770 921799 "FMFUN" 922943 T FMFUN (NIL) -9 NIL 923651) (-379 920394 920574 920603 "FMC" 920893 T FMC (NIL) -9 NIL 921075) (-378 917606 918440 918495 "FMCAT" 919690 NIL FMCAT (NIL T T) -9 NIL 920184) (-377 916499 917372 917472 "FM1" 917551 NIL FM1 (NIL T T) -8 NIL NIL) (-376 914273 914689 915183 "FLOATRP" 916050 NIL FLOATRP (NIL T) -7 NIL NIL) (-375 907760 911929 912559 "FLOAT" 913663 T FLOAT (NIL) -8 NIL NIL) (-374 905198 905698 906276 "FLOATCP" 907227 NIL FLOATCP (NIL T) -7 NIL NIL) (-373 903983 904831 904873 "FLINEXP" 904878 NIL FLINEXP (NIL T) -9 NIL 904970) (-372 903137 903372 903700 "FLINEXP-" 903705 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-371 902213 902357 902581 "FLASORT" 902989 NIL FLASORT (NIL T T) -7 NIL NIL) (-370 899429 900271 900324 "FLALG" 901551 NIL FLALG (NIL T T) -9 NIL 902018) (-369 893248 896942 896984 "FLAGG" 898246 NIL FLAGG (NIL T) -9 NIL 898894) (-368 891974 892313 892803 "FLAGG-" 892808 NIL FLAGG- (NIL T T) -8 NIL NIL) (-367 891016 891159 891386 "FLAGG2" 891827 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-366 887987 889005 889065 "FINRALG" 890193 NIL FINRALG (NIL T T) -9 NIL 890698) (-365 887147 887376 887715 "FINRALG-" 887720 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-364 886552 886765 886794 "FINITE" 886990 T FINITE (NIL) -9 NIL 887097) (-363 879010 881171 881212 "FINAALG" 884879 NIL FINAALG (NIL T) -9 NIL 886331) (-362 874350 875392 876536 "FINAALG-" 877915 NIL FINAALG- (NIL T T) -8 NIL NIL) (-361 873720 874105 874208 "FILE" 874280 NIL FILE (NIL T) -8 NIL NIL) (-360 872260 872597 872652 "FILECAT" 873430 NIL FILECAT (NIL T T) -9 NIL 873670) (-359 870070 871626 871655 "FIELD" 871695 T FIELD (NIL) -9 NIL 871775) (-358 868690 869075 869586 "FIELD-" 869591 NIL FIELD- (NIL T) -8 NIL NIL) (-357 866503 867325 867672 "FGROUP" 868376 NIL FGROUP (NIL T) -8 NIL NIL) (-356 865593 865757 865977 "FGLMICPK" 866335 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-355 861395 865518 865575 "FFX" 865580 NIL FFX (NIL T NIL) -8 NIL NIL) (-354 860935 861002 861124 "FFSQFR" 861323 NIL FFSQFR (NIL T T) -7 NIL NIL) (-353 860536 860597 860732 "FFSLPE" 860868 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-352 856532 857308 858104 "FFPOLY" 859772 NIL FFPOLY (NIL T) -7 NIL NIL) (-351 856036 856072 856281 "FFPOLY2" 856490 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-350 851858 855955 856018 "FFP" 856023 NIL FFP (NIL T NIL) -8 NIL NIL) (-349 847226 851769 851833 "FF" 851838 NIL FF (NIL NIL NIL) -8 NIL NIL) (-348 842322 846569 846759 "FFNBX" 847080 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-347 837232 841457 841715 "FFNBP" 842176 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-346 831835 836516 836727 "FFNB" 837065 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-345 830667 830865 831180 "FFINTBAS" 831632 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-344 826843 829078 829107 "FFIELDC" 829727 T FFIELDC (NIL) -9 NIL 830103) (-343 825506 825876 826373 "FFIELDC-" 826378 NIL FFIELDC- (NIL T) -8 NIL NIL) (-342 825076 825121 825245 "FFHOM" 825448 NIL FFHOM (NIL T T T) -7 NIL NIL) (-341 822774 823258 823775 "FFF" 824591 NIL FFF (NIL T) -7 NIL NIL) (-340 818470 819235 820079 "FFFG" 821998 NIL FFFG (NIL T T) -7 NIL NIL) (-339 817196 817405 817727 "FFFGF" 818248 NIL FFFGF (NIL T T T) -7 NIL NIL) (-338 815947 816144 816392 "FFFACTSE" 816998 NIL FFFACTSE (NIL T T) -7 NIL NIL) (-337 811535 815689 815790 "FFCGX" 815890 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-336 807137 811267 811374 "FFCGP" 811478 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-335 802290 806864 806972 "FFCG" 807073 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-334 784079 793201 793288 "FFCAT" 798453 NIL FFCAT (NIL T T T) -9 NIL 799938) (-333 779277 780324 781638 "FFCAT-" 782868 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-332 778688 778731 778966 "FFCAT2" 779228 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-331 767858 771664 772882 "FEXPR" 777542 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-330 766860 767295 767337 "FEVALAB" 767421 NIL FEVALAB (NIL T) -9 NIL 767679) (-329 766019 766229 766567 "FEVALAB-" 766572 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-328 764612 765402 765605 "FDIV" 765918 NIL FDIV (NIL T T T T) -8 NIL NIL) (-327 761677 762392 762508 "FDIVCAT" 764076 NIL FDIVCAT (NIL T T T T) -9 NIL 764513) (-326 761439 761466 761636 "FDIVCAT-" 761641 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-325 760659 760746 761023 "FDIV2" 761346 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-324 759345 759604 759893 "FCPAK1" 760390 T FCPAK1 (NIL) -7 NIL NIL) (-323 758473 758845 758986 "FCOMP" 759236 NIL FCOMP (NIL T) -8 NIL NIL) (-322 742101 745516 749079 "FC" 754930 T FC (NIL) -8 NIL NIL) (-321 734645 738688 738729 "FAXF" 740531 NIL FAXF (NIL T) -9 NIL 741222) (-320 731925 732579 733404 "FAXF-" 733869 NIL FAXF- (NIL T T) -8 NIL NIL) (-319 727031 731301 731477 "FARRAY" 731782 NIL FARRAY (NIL T) -8 NIL NIL) (-318 722349 724425 724479 "FAMR" 725502 NIL FAMR (NIL T T) -9 NIL 725959) (-317 721239 721541 721976 "FAMR-" 721981 NIL FAMR- (NIL T T T) -8 NIL NIL) (-316 720827 720870 721021 "FAMR2" 721190 NIL FAMR2 (NIL T T T T T) -7 NIL NIL) (-315 720023 720749 720802 "FAMONOID" 720807 NIL FAMONOID (NIL T) -8 NIL NIL) (-314 717853 718537 718591 "FAMONC" 719532 NIL FAMONC (NIL T T) -9 NIL 719917) (-313 716547 717609 717745 "FAGROUP" 717750 NIL FAGROUP (NIL T) -8 NIL NIL) (-312 714342 714661 715064 "FACUTIL" 716228 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-311 713758 713867 714013 "FACTRN" 714228 NIL FACTRN (NIL T) -7 NIL NIL) (-310 712857 713042 713264 "FACTFUNC" 713568 NIL FACTFUNC (NIL T) -7 NIL NIL) (-309 712273 712382 712528 "FACTEXT" 712743 NIL FACTEXT (NIL T) -7 NIL NIL) (-308 704593 711524 711736 "EXPUPXS" 712129 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-307 702076 702616 703202 "EXPRTUBE" 704027 T EXPRTUBE (NIL) -7 NIL NIL) (-306 701247 701342 701562 "EXPRSOL" 701976 NIL EXPRSOL (NIL T T T T) -7 NIL NIL) (-305 697441 698033 698770 "EXPRODE" 700586 NIL EXPRODE (NIL T T) -7 NIL NIL) (-304 682542 696102 696527 "EXPR" 697048 NIL EXPR (NIL T) -8 NIL NIL) (-303 676949 677536 678349 "EXPR2UPS" 681840 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-302 676585 676642 676749 "EXPR2" 676886 NIL EXPR2 (NIL T T) -7 NIL NIL) (-301 667925 675717 676014 "EXPEXPAN" 676422 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-300 667752 667882 667911 "EXIT" 667916 T EXIT (NIL) -8 NIL NIL) (-299 667379 667441 667554 "EVALCYC" 667684 NIL EVALCYC (NIL T) -7 NIL NIL) (-298 666921 667037 667079 "EVALAB" 667249 NIL EVALAB (NIL T) -9 NIL 667353) (-297 666402 666524 666745 "EVALAB-" 666750 NIL EVALAB- (NIL T T) -8 NIL NIL) (-296 663860 665172 665201 "EUCDOM" 665756 T EUCDOM (NIL) -9 NIL 666106) (-295 662265 662707 663297 "EUCDOM-" 663302 NIL EUCDOM- (NIL T) -8 NIL NIL) (-294 649805 652563 655313 "ESTOOLS" 659535 T ESTOOLS (NIL) -7 NIL NIL) (-293 649437 649494 649603 "ESTOOLS2" 649742 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-292 649188 649230 649310 "ESTOOLS1" 649389 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-291 643114 644842 644871 "ES" 647639 T ES (NIL) -9 NIL 649046) (-290 638062 639348 641165 "ES-" 641329 NIL ES- (NIL T) -8 NIL NIL) (-289 634437 635197 635977 "ESCONT" 637302 T ESCONT (NIL) -7 NIL NIL) (-288 634182 634214 634296 "ESCONT1" 634399 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-287 633857 633907 634007 "ES2" 634126 NIL ES2 (NIL T T) -7 NIL NIL) (-286 633487 633545 633654 "ES1" 633793 NIL ES1 (NIL T T) -7 NIL NIL) (-285 632703 632832 633008 "ERROR" 633331 T ERROR (NIL) -7 NIL NIL) (-284 626218 632562 632653 "EQTBL" 632658 NIL EQTBL (NIL T T) -8 NIL NIL) (-283 618677 621560 622995 "EQ" 624816 NIL -3211 (NIL T) -8 NIL NIL) (-282 618309 618366 618475 "EQ2" 618614 NIL EQ2 (NIL T T) -7 NIL NIL) (-281 613601 614647 615740 "EP" 617248 NIL EP (NIL T) -7 NIL NIL) (-280 612755 613319 613348 "ENTIRER" 613353 T ENTIRER (NIL) -9 NIL 613399) (-279 609211 610710 611080 "EMR" 612554 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-278 608357 608540 608595 "ELTAGG" 608975 NIL ELTAGG (NIL T T) -9 NIL 609185) (-277 608076 608138 608279 "ELTAGG-" 608284 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-276 607864 607893 607948 "ELTAB" 608032 NIL ELTAB (NIL T T) -9 NIL NIL) (-275 606990 607136 607335 "ELFUTS" 607715 NIL ELFUTS (NIL T T) -7 NIL NIL) (-274 606731 606787 606816 "ELEMFUN" 606921 T ELEMFUN (NIL) -9 NIL NIL) (-273 606601 606622 606690 "ELEMFUN-" 606695 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-272 601531 604734 604776 "ELAGG" 605716 NIL ELAGG (NIL T) -9 NIL 606177) (-271 599816 600250 600913 "ELAGG-" 600918 NIL ELAGG- (NIL T T) -8 NIL NIL) (-270 592686 594485 595311 "EFUPXS" 599093 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-269 586138 587939 588748 "EFULS" 591963 NIL EFULS (NIL T T T) -8 NIL NIL) (-268 583560 583918 584397 "EFSTRUC" 585770 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-267 572632 574197 575757 "EF" 582075 NIL EF (NIL T T) -7 NIL NIL) (-266 571733 572117 572266 "EAB" 572503 T EAB (NIL) -8 NIL NIL) (-265 570942 571692 571720 "E04UCFA" 571725 T E04UCFA (NIL) -8 NIL NIL) (-264 570151 570901 570929 "E04NAFA" 570934 T E04NAFA (NIL) -8 NIL NIL) (-263 569360 570110 570138 "E04MBFA" 570143 T E04MBFA (NIL) -8 NIL NIL) (-262 568569 569319 569347 "E04JAFA" 569352 T E04JAFA (NIL) -8 NIL NIL) (-261 567780 568528 568556 "E04GCFA" 568561 T E04GCFA (NIL) -8 NIL NIL) (-260 566991 567739 567767 "E04FDFA" 567772 T E04FDFA (NIL) -8 NIL NIL) (-259 566200 566950 566978 "E04DGFA" 566983 T E04DGFA (NIL) -8 NIL NIL) (-258 560379 561725 563089 "E04AGNT" 564856 T E04AGNT (NIL) -7 NIL NIL) (-257 559102 559582 559623 "DVARCAT" 560098 NIL DVARCAT (NIL T) -9 NIL 560297) (-256 558306 558518 558832 "DVARCAT-" 558837 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-255 551275 551757 552506 "DTP" 557837 NIL DTP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-254 548724 550697 550854 "DSTREE" 551151 NIL DSTREE (NIL T) -8 NIL NIL) (-253 546193 548038 548080 "DSTRCAT" 548299 NIL DSTRCAT (NIL T) -9 NIL 548433) (-252 539047 545992 546121 "DSMP" 546126 NIL DSMP (NIL T T T) -8 NIL NIL) (-251 533857 534992 536060 "DROPT" 537999 T DROPT (NIL) -8 NIL NIL) (-250 533522 533581 533679 "DROPT1" 533792 NIL DROPT1 (NIL T) -7 NIL NIL) (-249 528637 529763 530900 "DROPT0" 532405 T DROPT0 (NIL) -7 NIL NIL) (-248 526982 527307 527693 "DRAWPT" 528271 T DRAWPT (NIL) -7 NIL NIL) (-247 521569 522492 523571 "DRAW" 525956 NIL DRAW (NIL T) -7 NIL NIL) (-246 521202 521255 521373 "DRAWHACK" 521510 NIL DRAWHACK (NIL T) -7 NIL NIL) (-245 519933 520202 520493 "DRAWCX" 520931 T DRAWCX (NIL) -7 NIL NIL) (-244 519449 519517 519668 "DRAWCURV" 519859 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-243 509921 511879 513994 "DRAWCFUN" 517354 T DRAWCFUN (NIL) -7 NIL NIL) (-242 506774 508650 508692 "DQAGG" 509321 NIL DQAGG (NIL T) -9 NIL 509594) (-241 495202 501943 502027 "DPOLCAT" 503879 NIL DPOLCAT (NIL T T T T) -9 NIL 504423) (-240 490041 491387 493345 "DPOLCAT-" 493350 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-239 482780 489902 490000 "DPMO" 490005 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-238 475422 482560 482727 "DPMM" 482732 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-237 469127 475057 475209 "DMP" 475323 NIL DMP (NIL NIL T) -8 NIL NIL) (-236 468727 468783 468927 "DLP" 469065 NIL DLP (NIL T) -7 NIL NIL) (-235 462377 467828 468055 "DLIST" 468532 NIL DLIST (NIL T) -8 NIL NIL) (-234 459262 461265 461307 "DLAGG" 461857 NIL DLAGG (NIL T) -9 NIL 462086) (-233 457919 458611 458640 "DIVRING" 458790 T DIVRING (NIL) -9 NIL 458898) (-232 456907 457160 457553 "DIVRING-" 457558 NIL DIVRING- (NIL T) -8 NIL NIL) (-231 455335 456500 456636 "DIV" 456804 NIL DIV (NIL T) -8 NIL NIL) (-230 452829 453897 453939 "DIVCAT" 454773 NIL DIVCAT (NIL T) -9 NIL 455104) (-229 450931 451288 451694 "DISPLAY" 452443 T DISPLAY (NIL) -7 NIL NIL) (-228 444791 450845 450908 "DIRPROD" 450913 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-227 443639 443842 444107 "DIRPROD2" 444584 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-226 433203 439232 439286 "DIRPCAT" 439544 NIL DIRPCAT (NIL NIL T) -9 NIL 440388) (-225 430529 431171 432052 "DIRPCAT-" 432389 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-224 429816 429976 430162 "DIOSP" 430363 T DIOSP (NIL) -7 NIL NIL) (-223 426559 428763 428805 "DIOPS" 429239 NIL DIOPS (NIL T) -9 NIL 429467) (-222 426108 426222 426413 "DIOPS-" 426418 NIL DIOPS- (NIL T T) -8 NIL NIL) (-221 424975 425613 425642 "DIFRING" 425829 T DIFRING (NIL) -9 NIL 425939) (-220 424621 424698 424850 "DIFRING-" 424855 NIL DIFRING- (NIL T) -8 NIL NIL) (-219 422403 423685 423727 "DIFEXT" 424090 NIL DIFEXT (NIL T) -9 NIL 424382) (-218 420688 421116 421782 "DIFEXT-" 421787 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-217 418050 420254 420296 "DIAGG" 420301 NIL DIAGG (NIL T) -9 NIL 420321) (-216 417434 417591 417843 "DIAGG-" 417848 NIL DIAGG- (NIL T T) -8 NIL NIL) (-215 412804 416393 416670 "DHMATRIX" 417203 NIL DHMATRIX (NIL T) -8 NIL NIL) (-214 406688 407977 409358 "DFSFUN" 411443 T DFSFUN (NIL) -7 NIL NIL) (-213 400965 405142 405575 "DFLOAT" 406275 T DFLOAT (NIL) -8 NIL NIL) (-212 399193 399474 399870 "DFINTTLS" 400673 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-211 396212 397214 397614 "DERHAM" 398859 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-210 387825 389742 391177 "DEQUEUE" 394810 NIL DEQUEUE (NIL T) -8 NIL NIL) (-209 387040 387173 387369 "DEGRED" 387687 NIL DEGRED (NIL T T) -7 NIL NIL) (-208 383435 384180 385033 "DEFINTRF" 386268 NIL DEFINTRF (NIL T) -7 NIL NIL) (-207 380962 381431 382030 "DEFINTEF" 382954 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-206 374784 380403 380569 "DECIMAL" 380816 T DECIMAL (NIL) -8 NIL NIL) (-205 372296 372754 373260 "DDFACT" 374328 NIL DDFACT (NIL T T) -7 NIL NIL) (-204 371892 371935 372086 "DBLRESP" 372247 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-203 369602 369936 370305 "DBASE" 371650 NIL DBASE (NIL T) -8 NIL NIL) (-202 368735 369561 369589 "D03FAFA" 369594 T D03FAFA (NIL) -8 NIL NIL) (-201 367869 368694 368722 "D03EEFA" 368727 T D03EEFA (NIL) -8 NIL NIL) (-200 365819 366285 366774 "D03AGNT" 367400 T D03AGNT (NIL) -7 NIL NIL) (-199 365135 365778 365806 "D02EJFA" 365811 T D02EJFA (NIL) -8 NIL NIL) (-198 364451 365094 365122 "D02CJFA" 365127 T D02CJFA (NIL) -8 NIL NIL) (-197 363767 364410 364438 "D02BHFA" 364443 T D02BHFA (NIL) -8 NIL NIL) (-196 363083 363726 363754 "D02BBFA" 363759 T D02BBFA (NIL) -8 NIL NIL) (-195 356282 357869 359475 "D02AGNT" 361497 T D02AGNT (NIL) -7 NIL NIL) (-194 354051 354573 355119 "D01WGTS" 355756 T D01WGTS (NIL) -7 NIL NIL) (-193 353146 354010 354038 "D01TRNS" 354043 T D01TRNS (NIL) -8 NIL NIL) (-192 352241 353105 353133 "D01GBFA" 353138 T D01GBFA (NIL) -8 NIL NIL) (-191 351336 352200 352228 "D01FCFA" 352233 T D01FCFA (NIL) -8 NIL NIL) (-190 350431 351295 351323 "D01ASFA" 351328 T D01ASFA (NIL) -8 NIL NIL) (-189 349526 350390 350418 "D01AQFA" 350423 T D01AQFA (NIL) -8 NIL NIL) (-188 348621 349485 349513 "D01APFA" 349518 T D01APFA (NIL) -8 NIL NIL) (-187 347716 348580 348608 "D01ANFA" 348613 T D01ANFA (NIL) -8 NIL NIL) (-186 346811 347675 347703 "D01AMFA" 347708 T D01AMFA (NIL) -8 NIL NIL) (-185 345906 346770 346798 "D01ALFA" 346803 T D01ALFA (NIL) -8 NIL NIL) (-184 345001 345865 345893 "D01AKFA" 345898 T D01AKFA (NIL) -8 NIL NIL) (-183 344096 344960 344988 "D01AJFA" 344993 T D01AJFA (NIL) -8 NIL NIL) (-182 337393 338944 340505 "D01AGNT" 342555 T D01AGNT (NIL) -7 NIL NIL) (-181 336730 336858 337010 "CYCLOTOM" 337261 T CYCLOTOM (NIL) -7 NIL NIL) (-180 333465 334178 334905 "CYCLES" 336023 T CYCLES (NIL) -7 NIL NIL) (-179 332777 332911 333082 "CVMP" 333326 NIL CVMP (NIL T) -7 NIL NIL) (-178 330549 330806 331182 "CTRIGMNP" 332505 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-177 329923 330022 330175 "CSTTOOLS" 330446 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-176 325722 326379 327137 "CRFP" 329235 NIL CRFP (NIL T T) -7 NIL NIL) (-175 324769 324954 325182 "CRAPACK" 325526 NIL CRAPACK (NIL T) -7 NIL NIL) (-174 324155 324256 324459 "CPMATCH" 324646 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-173 323880 323908 324014 "CPIMA" 324121 NIL CPIMA (NIL T T T) -7 NIL NIL) (-172 320244 320916 321634 "COORDSYS" 323215 NIL COORDSYS (NIL T) -7 NIL NIL) (-171 316105 318247 318739 "CONTFRAC" 319784 NIL CONTFRAC (NIL T) -8 NIL NIL) (-170 315253 315817 315846 "COMRING" 315851 T COMRING (NIL) -9 NIL 315903) (-169 314334 314611 314795 "COMPPROP" 315089 T COMPPROP (NIL) -8 NIL NIL) (-168 313995 314030 314158 "COMPLPAT" 314293 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-167 303969 313806 313914 "COMPLEX" 313919 NIL COMPLEX (NIL T) -8 NIL NIL) (-166 303605 303662 303769 "COMPLEX2" 303906 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-165 303323 303358 303456 "COMPFACT" 303564 NIL COMPFACT (NIL T T) -7 NIL NIL) (-164 287582 297879 297920 "COMPCAT" 298924 NIL COMPCAT (NIL T) -9 NIL 300303) (-163 277098 280021 283648 "COMPCAT-" 284004 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-162 276827 276855 276958 "COMMUPC" 277064 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-161 276622 276655 276714 "COMMONOP" 276788 T COMMONOP (NIL) -7 NIL NIL) (-160 276205 276373 276460 "COMM" 276555 T COMM (NIL) -8 NIL NIL) (-159 275453 275647 275676 "COMBOPC" 276014 T COMBOPC (NIL) -9 NIL 276189) (-158 274349 274559 274801 "COMBINAT" 275243 NIL COMBINAT (NIL T) -7 NIL NIL) (-157 270547 271120 271760 "COMBF" 273771 NIL COMBF (NIL T T) -7 NIL NIL) (-156 269333 269663 269898 "COLOR" 270332 T COLOR (NIL) -8 NIL NIL) (-155 268973 269020 269145 "CMPLXRT" 269280 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-154 264475 265503 266583 "CLIP" 267913 T CLIP (NIL) -7 NIL NIL) (-153 262811 263581 263820 "CLIF" 264302 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-152 259076 260994 261036 "CLAGG" 261965 NIL CLAGG (NIL T) -9 NIL 262498) (-151 257498 257955 258538 "CLAGG-" 258543 NIL CLAGG- (NIL T T) -8 NIL NIL) (-150 257042 257127 257267 "CINTSLPE" 257407 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-149 254543 255014 255562 "CHVAR" 256570 NIL CHVAR (NIL T T T) -7 NIL NIL) (-148 253761 254325 254354 "CHARZ" 254359 T CHARZ (NIL) -9 NIL 254374) (-147 253515 253555 253633 "CHARPOL" 253715 NIL CHARPOL (NIL T) -7 NIL NIL) (-146 252617 253214 253243 "CHARNZ" 253290 T CHARNZ (NIL) -9 NIL 253346) (-145 250640 251307 251642 "CHAR" 252302 T CHAR (NIL) -8 NIL NIL) (-144 250365 250426 250455 "CFCAT" 250566 T CFCAT (NIL) -9 NIL NIL) (-143 249610 249721 249903 "CDEN" 250249 NIL CDEN (NIL T T T) -7 NIL NIL) (-142 245602 248763 249043 "CCLASS" 249350 T CCLASS (NIL) -8 NIL NIL) (-141 240655 241631 242384 "CARTEN" 244905 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-140 239763 239911 240132 "CARTEN2" 240502 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-139 238058 238913 239170 "CARD" 239526 T CARD (NIL) -8 NIL NIL) (-138 237429 237757 237786 "CACHSET" 237918 T CACHSET (NIL) -9 NIL 237995) (-137 236924 237220 237249 "CABMON" 237299 T CABMON (NIL) -9 NIL 237355) (-136 234487 236616 236723 "BTREE" 236850 NIL BTREE (NIL T) -8 NIL NIL) (-135 231991 234135 234257 "BTOURN" 234397 NIL BTOURN (NIL T) -8 NIL NIL) (-134 229448 231495 231537 "BTCAT" 231605 NIL BTCAT (NIL T) -9 NIL 231682) (-133 229115 229195 229344 "BTCAT-" 229349 NIL BTCAT- (NIL T T) -8 NIL NIL) (-132 224305 228175 228204 "BTAGG" 228460 T BTAGG (NIL) -9 NIL 228639) (-131 223728 223872 224102 "BTAGG-" 224107 NIL BTAGG- (NIL T) -8 NIL NIL) (-130 220778 223006 223221 "BSTREE" 223545 NIL BSTREE (NIL T) -8 NIL NIL) (-129 219916 220042 220226 "BRILL" 220634 NIL BRILL (NIL T) -7 NIL NIL) (-128 216656 218677 218719 "BRAGG" 219368 NIL BRAGG (NIL T) -9 NIL 219625) (-127 215185 215591 216146 "BRAGG-" 216151 NIL BRAGG- (NIL T T) -8 NIL NIL) (-126 208384 214531 214715 "BPADICRT" 215033 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-125 206688 208321 208366 "BPADIC" 208371 NIL BPADIC (NIL NIL) -8 NIL NIL) (-124 206386 206416 206530 "BOUNDZRO" 206652 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-123 201901 202992 203859 "BOP" 205539 T BOP (NIL) -8 NIL NIL) (-122 199524 199968 200487 "BOP1" 201415 NIL BOP1 (NIL T) -7 NIL NIL) (-121 197877 198567 198861 "BOOLEAN" 199250 T BOOLEAN (NIL) -8 NIL NIL) (-120 197238 197616 197671 "BMODULE" 197676 NIL BMODULE (NIL T T) -9 NIL 197741) (-119 193581 194251 195037 "BLUPPACK" 196570 NIL BLUPPACK (NIL T NIL T T T) -7 NIL NIL) (-118 192973 193458 193527 "BLQT" 193532 T BLQT (NIL) -8 NIL NIL) (-117 191402 191877 191906 "BLMETCT" 192551 T BLMETCT (NIL) -9 NIL 192923) (-116 190801 191283 191350 "BLHN" 191355 T BLHN (NIL) -8 NIL NIL) (-115 189619 189878 190161 "BLAS1" 190538 T BLAS1 (NIL) -7 NIL NIL) (-114 185429 189417 189490 "BITS" 189566 T BITS (NIL) -8 NIL NIL) (-113 184500 184961 185113 "BINFILE" 185297 T BINFILE (NIL) -8 NIL NIL) (-112 178326 183944 184109 "BINARY" 184355 T BINARY (NIL) -8 NIL NIL) (-111 176193 177615 177657 "BGAGG" 177917 NIL BGAGG (NIL T) -9 NIL 178054) (-110 176024 176056 176147 "BGAGG-" 176152 NIL BGAGG- (NIL T T) -8 NIL NIL) (-109 175122 175408 175613 "BFUNCT" 175839 T BFUNCT (NIL) -8 NIL NIL) (-108 173814 173992 174279 "BEZOUT" 174947 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-107 172777 172999 173258 "BEZIER" 173588 NIL BEZIER (NIL T) -7 NIL NIL) (-106 169300 171629 171959 "BBTREE" 172480 NIL BBTREE (NIL T) -8 NIL NIL) (-105 169033 169086 169115 "BASTYPE" 169234 T BASTYPE (NIL) -9 NIL NIL) (-104 168886 168914 168987 "BASTYPE-" 168992 NIL BASTYPE- (NIL T) -8 NIL NIL) (-103 168320 168396 168548 "BALFACT" 168797 NIL BALFACT (NIL T T) -7 NIL NIL) (-102 167684 167807 167955 "AXSERV" 168192 T AXSERV (NIL) -7 NIL NIL) (-101 166497 167094 167282 "AUTOMOR" 167529 NIL AUTOMOR (NIL T) -8 NIL NIL) (-100 166209 166214 166243 "ATTREG" 166248 T ATTREG (NIL) -9 NIL NIL) (-99 164488 164906 165258 "ATTRBUT" 165875 T ATTRBUT (NIL) -8 NIL NIL) (-98 164023 164136 164163 "ATRIG" 164364 T ATRIG (NIL) -9 NIL NIL) (-97 163832 163873 163960 "ATRIG-" 163965 NIL ATRIG- (NIL T) -8 NIL NIL) (-96 157392 158961 160072 "ASTACK" 162752 NIL ASTACK (NIL T) -8 NIL NIL) (-95 155899 156196 156560 "ASSOCEQ" 157075 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-94 154931 155558 155682 "ASP9" 155806 NIL ASP9 (NIL NIL) -8 NIL NIL) (-93 154695 154879 154918 "ASP8" 154923 NIL ASP8 (NIL NIL) -8 NIL NIL) (-92 153565 154300 154442 "ASP80" 154584 NIL ASP80 (NIL NIL) -8 NIL NIL) (-91 152464 153200 153332 "ASP7" 153464 NIL ASP7 (NIL NIL) -8 NIL NIL) (-90 151420 152141 152259 "ASP78" 152377 NIL ASP78 (NIL NIL) -8 NIL NIL) (-89 150391 151100 151217 "ASP77" 151334 NIL ASP77 (NIL NIL) -8 NIL NIL) (-88 149306 150029 150160 "ASP74" 150291 NIL ASP74 (NIL NIL) -8 NIL NIL) (-87 148207 148941 149073 "ASP73" 149205 NIL ASP73 (NIL NIL) -8 NIL NIL) (-86 147162 147884 148002 "ASP6" 148120 NIL ASP6 (NIL NIL) -8 NIL NIL) (-85 146111 146839 146957 "ASP55" 147075 NIL ASP55 (NIL NIL) -8 NIL NIL) (-84 145061 145785 145904 "ASP50" 146023 NIL ASP50 (NIL NIL) -8 NIL NIL) (-83 144149 144762 144872 "ASP4" 144982 NIL ASP4 (NIL NIL) -8 NIL NIL) (-82 143237 143850 143960 "ASP49" 144070 NIL ASP49 (NIL NIL) -8 NIL NIL) (-81 142022 142776 142944 "ASP42" 143126 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-80 140800 141555 141725 "ASP41" 141909 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-79 139752 140477 140595 "ASP35" 140713 NIL ASP35 (NIL NIL) -8 NIL NIL) (-78 139517 139700 139739 "ASP34" 139744 NIL ASP34 (NIL NIL) -8 NIL NIL) (-77 139254 139321 139397 "ASP33" 139472 NIL ASP33 (NIL NIL) -8 NIL NIL) (-76 138150 138889 139021 "ASP31" 139153 NIL ASP31 (NIL NIL) -8 NIL NIL) (-75 137915 138098 138137 "ASP30" 138142 NIL ASP30 (NIL NIL) -8 NIL NIL) (-74 137650 137719 137795 "ASP29" 137870 NIL ASP29 (NIL NIL) -8 NIL NIL) (-73 137415 137598 137637 "ASP28" 137642 NIL ASP28 (NIL NIL) -8 NIL NIL) (-72 137180 137363 137402 "ASP27" 137407 NIL ASP27 (NIL NIL) -8 NIL NIL) (-71 136264 136878 136989 "ASP24" 137100 NIL ASP24 (NIL NIL) -8 NIL NIL) (-70 135181 135905 136035 "ASP20" 136165 NIL ASP20 (NIL NIL) -8 NIL NIL) (-69 134269 134882 134992 "ASP1" 135102 NIL ASP1 (NIL NIL) -8 NIL NIL) (-68 133213 133943 134062 "ASP19" 134181 NIL ASP19 (NIL NIL) -8 NIL NIL) (-67 132950 133017 133093 "ASP12" 133168 NIL ASP12 (NIL NIL) -8 NIL NIL) (-66 131803 132549 132693 "ASP10" 132837 NIL ASP10 (NIL NIL) -8 NIL NIL) (-65 129708 131647 131738 "ARRAY2" 131743 NIL ARRAY2 (NIL T) -8 NIL NIL) (-64 125530 129356 129470 "ARRAY1" 129625 NIL ARRAY1 (NIL T) -8 NIL NIL) (-63 124562 124735 124956 "ARRAY12" 125353 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-62 118961 120826 120902 "ARR2CAT" 123532 NIL ARR2CAT (NIL T T T) -9 NIL 124290) (-61 116395 117139 118093 "ARR2CAT-" 118098 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-60 115143 115295 115601 "APPRULE" 116231 NIL APPRULE (NIL T T T) -7 NIL NIL) (-59 114794 114842 114961 "APPLYORE" 115089 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-58 114318 114406 114516 "API" 114702 T API (NIL) -7 NIL NIL) (-57 113292 113583 113778 "ANY" 114141 T ANY (NIL) -8 NIL NIL) (-56 112570 112693 112850 "ANY1" 113166 NIL ANY1 (NIL T) -7 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12669 14625 14652 "ACF" 15531 T ACF (NIL) -9 NIL 15943) (-26 11373 11707 12200 "ACF-" 12205 NIL ACF- (NIL T) -8 NIL NIL) (-25 10970 11139 11166 "ABELSG" 11258 T ABELSG (NIL) -9 NIL 11323) (-24 10837 10862 10928 "ABELSG-" 10933 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10205 10466 10493 "ABELMON" 10663 T ABELMON (NIL) -9 NIL 10775) (-22 9869 9953 10091 "ABELMON-" 10096 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9202 9548 9575 "ABELGRP" 9700 T ABELGRP (NIL) -9 NIL 9782) (-20 8665 8794 9010 "ABELGRP-" 9015 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8027 8067 "A1AGG" 8072 NIL A1AGG (NIL T) -9 NIL 8112) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) \ No newline at end of file diff --git a/src/share/algebra/libdb.text b/src/share/algebra/libdb.text index d3ad6ca..867502c 100755 --- a/src/share/algebra/libdb.text +++ b/src/share/algebra/libdb.text @@ -1,41 +1,38 @@ -aJacobiIdentity`0`x``cAttributeRegistry``0 -aJacobiIdentity`0`x``cLieAlgebra``0 -aNullSquare`0`x``cAttributeRegistry``0 -aNullSquare`0`x``cLieAlgebra``0 aadditiveValuation`0`x``cAttributeRegistry``3 aadditiveValuation`0`x``cComplexCategory`has(R,ATTRIBUTE(additiveValuation))`0 -aadditiveValuation`0`x``cUnivariatePolynomialCategory`has(R,Field)`101 -aapproximate`0`x``cFloatingPointSystem``169 +aadditiveValuation`0`x``cUnivariatePolynomialCategory`has(R,Field)`99 +aapproximate`0`x``cAttributeRegistry``167 +aapproximate`0`x``cFloatingPointSystem``239 aapproximate`0`x``cIntervalCategory``0 aarbitraryExponent`0`x``dFloat``0 -aarbitraryPrecision`0`x``cAttributeRegistry``241 +aarbitraryPrecision`0`x``cAttributeRegistry``311 aarbitraryPrecision`0`x``dFloat``0 -acanonicalUnitNormal`0`n``dPolynomialRing`has(R,ATTRIBUTE(canonicalUnitNormal))`337 +acanonical`0`x``cAttributeRegistry``407 +acanonical`0`x``dFourierSeries`AND(has(R,ATTRIBUTE(canonical)),has(E,ATTRIBUTE(canonical)))`0 +acanonical`0`x``dFraction`AND(has(S,ATTRIBUTE(canonicalUnitNormal)),has(S,ATTRIBUTE(canonical)),has(S,GcdDomain))`692 +acanonical`0`x``dInteger``762 +acanonical`0`x``dRomanNumeral``816 +acanonical`0`x``dSingleInteger``870 +acanonicalsClosed`0`x``cAttributeRegistry``963 +acanonicalsClosed`0`x``cField``1072 +acanonicalsClosed`0`x``dInteger``1111 +acanonicalsClosed`0`x``dRomanNumeral``1156 +acanonicalsClosed`0`x``dSingleInteger``1201 +acanonicalUnitNormal`0`n``dPolynomialRing`has(R,ATTRIBUTE(canonicalUnitNormal))`1275 acanonicalUnitNormal`0`n``dSymmetricPolynomial`has(R,ATTRIBUTE(canonicalUnitNormal))`0 -acanonicalUnitNormal`0`n``dXPolynomialRing`has(R,ATTRIBUTE(canonicalUnitNormal))`482 -acanonicalUnitNormal`0`x``cAttributeRegistry``627 -acanonicalUnitNormal`0`x``cField``870 +acanonicalUnitNormal`0`n``dXPolynomialRing`has(R,ATTRIBUTE(canonicalUnitNormal))`1420 +acanonicalUnitNormal`0`x``cAttributeRegistry``1566 +acanonicalUnitNormal`0`x``cField``1810 acanonicalUnitNormal`0`x``cIntegerNumberSystem``0 -acanonicalUnitNormal`0`x``cPolynomialCategory`has(R,ATTRIBUTE(canonicalUnitNormal))`889 -acanonical`0`x``cAttributeRegistry``1043 -acanonical`0`x``dFourierSeries`AND(has(R,ATTRIBUTE(canonical)),has(E,ATTRIBUTE(canonical)))`0 -acanonical`0`x``dFraction`AND(has(S,ATTRIBUTE(canonicalUnitNormal)),has(S,ATTRIBUTE(canonical)),has(S,GcdDomain))`1329 -acanonical`0`x``dInteger``1400 -acanonical`0`x``dRomanNumeral``1455 -acanonical`0`x``dSingleInteger``1510 -acanonicalsClosed`0`x``cAttributeRegistry``1604 -acanonicalsClosed`0`x``cField``1714 -acanonicalsClosed`0`x``dInteger``1754 -acanonicalsClosed`0`x``dRomanNumeral``1800 -acanonicalsClosed`0`x``dSingleInteger``1846 -acentral`0`n``dSquareMatrix`has(R,ATTRIBUTE(commutative("*")))`1921 -acentral`0`x``cAttributeRegistry``2092 -acommutative`1`x`("*")`cAttributeRegistry``2361 -acommutative`1`x`("*")`cCommutativeRing``2475 -acommutative`1`x`("*")`dCardinalNumber``2511 -acommutative`1`x`("*")`dNonNegativeInteger``2632 -acommutative`1`x`("*")`dPositiveInteger``2717 -acomplex`0`x``cComplexCategory``2801 +acanonicalUnitNormal`0`x``cPolynomialCategory`has(R,ATTRIBUTE(canonicalUnitNormal))`1830 +acentral`0`n``dSquareMatrix`has(R,ATTRIBUTE(commutative("*")))`1985 +acentral`0`x``cAttributeRegistry``2156 +acommutative`1`x`("*")`cAttributeRegistry``2425 +acommutative`1`x`("*")`cCommutativeRing``2539 +acommutative`1`x`("*")`dCardinalNumber``2575 +acommutative`1`x`("*")`dNonNegativeInteger``2696 +acommutative`1`x`("*")`dPositiveInteger``2793 +acomplex`0`x``cComplexCategory``2877 afiniteAggregate`0`n``dEqTable``0 afiniteAggregate`0`n``dGeneralPolynomialSet``0 afiniteAggregate`0`n``dHashTable``0 @@ -44,19 +41,20 @@ afiniteAggregate`0`n``dListMultiDictionary``0 afiniteAggregate`0`n``dSplittingTree``0 afiniteAggregate`0`n``dStringTable``0 afiniteAggregate`0`n``dTable``0 -afiniteAggregate`0`x``cAttributeRegistry``2844 -afiniteAggregate`0`x``cBinaryTreeCategory``2943 -afiniteAggregate`0`x``cDirectProductCategory``2996 +afiniteAggregate`0`x``cAttributeRegistry``2920 +afiniteAggregate`0`x``cBinaryTreeCategory``3019 +afiniteAggregate`0`x``cDesingTreeCategory``0 +afiniteAggregate`0`x``cDirectProductCategory``3072 afiniteAggregate`0`x``cFiniteLinearAggregate``0 afiniteAggregate`0`x``cFiniteSetAggregate``0 -afiniteAggregate`0`x``cMatrixCategory``3051 +afiniteAggregate`0`x``cMatrixCategory``3127 afiniteAggregate`0`x``cPolynomialSetCategory``0 afiniteAggregate`0`x``cPriorityQueueAggregate``0 afiniteAggregate`0`x``cQueueAggregate``0 -afiniteAggregate`0`x``cRectangularMatrixCategory``3076 +afiniteAggregate`0`x``cRectangularMatrixCategory``3152 afiniteAggregate`0`x``cStackAggregate``0 afiniteAggregate`0`x``cTriangularSetCategory``0 -afiniteAggregate`0`x``cTwoDimensionalArrayCategory``3101 +afiniteAggregate`0`x``cTwoDimensionalArrayCategory``3177 afiniteAggregate`0`x``dAttributeButtons``0 afiniteAggregate`0`x``dBalancedBinaryTree``0 afiniteAggregate`0`x``dBasicFunctions``0 @@ -66,713 +64,773 @@ afiniteAggregate`0`x``dMultiset``0 afiniteAggregate`0`x``dResult``0 afiniteAggregate`0`x``dRoutinesTable``0 afiniteAggregate`0`x``dTree``0 -ainfinite`0`x``dInteger``3140 -aleftUnitary`0`x``cAttributeRegistry``3178 -aleftUnitary`0`x``cBiModule``3255 -amultiplicativeValuation`0`x``cAttributeRegistry``3277 +aHamburgerNoether`0`x``dBlowUpWithHamburgerNoether``0 +ainfinite`0`x``dInteger``3216 +aJacobiIdentity`0`x``cAttributeRegistry``0 +aJacobiIdentity`0`x``cLieAlgebra``0 +aleftUnitary`0`x``cAttributeRegistry``3254 +aleftUnitary`0`x``cBiModule``3331 +amultiplicativeValuation`0`x``cAttributeRegistry``3353 amultiplicativeValuation`0`x``cComplexCategory`has(R,ATTRIBUTE(multiplicativeValuation))`0 -amultiplicativeValuation`0`x``cIntegerNumberSystem``3381 +amultiplicativeValuation`0`x``cIntegerNumberSystem``3458 anil`0`x``cType``0 +anoetherian`0`x``cAttributeRegistry``3532 +anoetherian`0`x``dInteger``3615 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-dFiniteDivisor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->Join(FiniteDivisorCategory(F,UP,UPUP,R),etc)`(F,UP,UPUP,R)`FDIV`84785 -dFiniteFieldCyclicGroupExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,SparseUnivariatePolynomial(GF))->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,defpol)`FFCGP`85014 -dFiniteFieldCyclicGroupExtension`2`n`(FiniteFieldCategory,PositiveInteger)->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,extdeg)`FFCGX`85621 -dFiniteFieldCyclicGroup`2`x`(PositiveInteger,PositiveInteger)->Join(FiniteAlgebraicExtensionField(PrimeField(p)),etc)`(p,extdeg)`FFCG`86258 -dFiniteFieldExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,SparseUnivariatePolynomial(GF))->FiniteAlgebraicExtensionField(GF)`(GF,defpol)`FFP`86914 -dFiniteFieldExtension`2`n`(FiniteFieldCategory,PositiveInteger)->FiniteAlgebraicExtensionField(GF)`(GF,n)`FFX`87188 -dFiniteFieldNormalBasisExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value:GF,index:SingleInteger)))))->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,uni)`FFNBP`87487 -dFiniteFieldNormalBasisExtension`2`n`(FiniteFieldCategory,PositiveInteger)->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,extdeg)`FFNBX`88004 -dFiniteFieldNormalBasis`2`x`(PositiveInteger,PositiveInteger)->Join(FiniteAlgebraicExtensionField(PrimeField(p)),etc)`(p,extdeg)`FFNB`88518 -dFiniteField`2`x`(PositiveInteger,PositiveInteger)->FiniteAlgebraicExtensionField(PrimeField(p))`(p,n)`FF`89014 -dFlexibleArray`1`x`(Type)->Join(OneDimensionalArrayAggregate(S),etc)`(S)`FARRAY`0 -dFloat`0`x`()->Join(FloatingPointSystem,etc)``FLOAT`89206 -dFortranCode`0`x`()->Join(SetCategory,etc)``FC`92990 -dFortranExpression`3`x`(List(Symbol),List(Symbol),R:FortranMachineTypeCategory)->Join(ExpressionSpace,etc)`(basicSymbols,subscriptedSymbols,R)`FEXPR`93096 -dFortranProgram`4`x`(Symbol,Union(fst:FortranScalarType,void:"void"),List(Symbol),SymbolTable)->Join(FortranProgramCategory,etc)`(name,returnType,arguments,symbols)`FORTRAN`93255 -dFortranScalarType`0`x`()->Join(CoercibleTo(OutputForm),etc)``FST`93426 -dFortranTemplate`0`x`()->Join(FileCategory(FileName,String),etc)``FTEM`93566 -dFortranType`0`x`()->Join(SetCategory,etc)``FT`93609 -dFourierComponent`1`n`(OrderedSet)->Join(OrderedSet,etc)`(E)`FCOMP`93717 -dFourierSeries`2`x`(Join(CommutativeRing,etc),E:Join(OrderedSet,etc))->Join(Algebra(R),etc)`(R,E)`FSERIES`93926 -dFraction`1`x`(IntegralDomain)->Join(QuotientFieldCategory(S),etc)`(S)`FRAC`94122 -dFractionalIdeal`4`n`(R:EuclideanDomain,F:QuotientFieldCategory(R),UP:UnivariatePolynomialCategory(F),A:Join(FramedAlgebra(F,UP),etc))->Join(Group,etc)`(R,F,UP,A)`FRIDEAL`94390 -dFramedModule`5`n`(R:EuclideanDomain,F:QuotientFieldCategory(R),UP:UnivariatePolynomialCategory(F),A:FramedAlgebra(F,UP),Vector(A))->Join(Monoid,etc)`(R,F,UP,A,ibasis)`FRMOD`94435 -dFreeAbelianGroup`1`n`(SetCategory)->Join(AbelianGroup,etc)`(S)`FAGROUP`94485 -dFreeAbelianMonoid`1`n`(SetCategory)->FreeAbelianMonoidCategory(S,NonNegativeInteger)`(S)`FAMONOID`94735 -dFreeGroup`1`n`(SetCategory)->Join(Group,etc)`(S)`FGROUP`94999 -dFreeModule1`2`n`(Ring,S:OrderedSet)->Join(FreeModuleCat(R,S),etc)`(R,S)`FM1`95254 -dFreeModule`2`n`(Ring,S:OrderedSet)->Join(BiModule(R,R),etc)`(R,S)`FM`95682 -dFreeMonoid`1`n`(SetCategory)->Join(Monoid,etc)`(S)`FMONOID`95887 -dFreeNilpotentLie`3`x`(NonNegativeInteger,NonNegativeInteger,R:CommutativeRing)->Join(NonAssociativeAlgebra(R),etc)`(n,class,R)`FNLA`96156 -dFullPartialFractionExpansion`2`x`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->Join(SetCategory,etc)`(F,UP)`FPARFRAC`96296 -dFunctionCalled`1`n`(Symbol)->Join(SetCategory,etc)`(f)`FUNCTION`96657 -dGeneralDistributedMultivariatePolynomial`3`n`(vl:List(Symbol),R:Ring,E:DirectProductCategory(#(vl),NonNegativeInteger))->Join(PolynomialCategory(R,E,OrderedVariableList(vl)),etc)`(vl,R,E)`GDMP`96702 -dGeneralModulePolynomial`6`n`(vl:List(Symbol),R:CommutativeRing,IS:OrderedSet,E:DirectProductCategory(#(vl),NonNegativeInteger),ff:(Record(index:IS,exponent:E),Record(index:IS,exponent:E))->Boolean,P:PolynomialCategory(R,E,OrderedVariableList(vl)))->Join(Module(P),etc)`(vl,R,IS,E,ff,P)`GMODPOL`97263 -dGeneralPolynomialSet`4`n`(R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,P:RecursivePolynomialCategory(R,E,VarSet))->Join(PolynomialSetCategory(R,E,VarSet,P),etc)`(R,E,VarSet,P)`GPOLSET`97296 -dGeneralSparseTable`4`n`(Key:SetCategory,Entry:SetCategory,TableAggregate(Key,Entry),Entry)->TableAggregate(Key,Entry)`(Key,Entry,Tbl,dent)`GSTBL`97332 -dGeneralTriangularSet`4`n`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->TriangularSetCategory(R,E,V,P)`(R,E,V,P)`GTSET`97450 -dGeneralUnivariatePowerSeries`3`x`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesCategory(Coef),etc)`(Coef,var,cen)`GSERIES`98117 -dGenericNonAssociativeAlgebra`4`n`(R:CommutativeRing,n:PositiveInteger,List(Symbol),Vector(Matrix(R)))->Join(FramedNonAssociativeAlgebra(Fraction(Polynomial(R))),etc)`(R,n,ls,gamma)`GCNAALG`98416 -dGraphImage`0`n`()->Join(SetCategory,etc)``GRIMAGE`0 -dHashTable`3`n`(SetCategory,Entry:SetCategory,String)->Join(TableAggregate(Key,Entry),etc)`(Key,Entry,hashfn)`HASHTBL`98582 -dHeap`1`x`(OrderedSet)->Join(PriorityQueueAggregate(S),etc)`(S)`HEAP`0 -dHexadecimalExpansion`0`x`()->Join(QuotientFieldCategory(Integer),etc)``HEXADEC`98741 -dHomogeneousDirectProduct`2`n`(NonNegativeInteger,S:OrderedAbelianMonoidSup)->DirectProductCategory(dim,S)`(dim,S)`HDP`98836 -dHomogeneousDistributedMultivariatePolynomial`2`n`(List(Symbol),R:Ring)->Join(PolynomialCategory(R,HomogeneousDirectProduct(#(vl),NonNegativeInteger),OrderedVariableList(vl)),etc)`(vl,R)`HDMP`0 -dHyperellipticFiniteDivisor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->FiniteDivisorCategory(F,UP,UPUP,R)`(F,UP,UPUP,R)`HELLFDIV`99174 -dIndexCard`0`x`()->Join(OrderedSet,etc)``ICARD`99528 -dIndexedBits`1`n`(Integer)->Join(BitAggregate,etc)`(mn)`IBITS`99622 -dIndexedDirectProductAbelianGroup`2`n`(AbelianGroup,S:OrderedSet)->Join(AbelianGroup,etc)`(A,S)`IDPAG`99720 -dIndexedDirectProductAbelianMonoid`2`n`(AbelianMonoid,S:OrderedSet)->Join(AbelianMonoid,etc)`(A,S)`IDPAM`99927 -dIndexedDirectProductObject`2`n`(SetCategory,S:OrderedSet)->IndexedDirectProductCategory(A,S)`(A,S)`IDPO`100136 -dIndexedDirectProductOrderedAbelianMonoidSup`2`n`(OrderedAbelianMonoidSup,S:OrderedSet)->Join(OrderedAbelianMonoidSup,etc)`(A,S)`IDPOAMS`100292 -dIndexedDirectProductOrderedAbelianMonoid`2`n`(OrderedAbelianMonoid,S:OrderedSet)->Join(OrderedAbelianMonoid,etc)`(A,S)`IDPOAM`100490 -dIndexedExponents`1`n`(OrderedSet)->Join(OrderedAbelianMonoidSup,etc)`(Varset)`INDE`100724 -dIndexedFlexibleArray`2`n`(Type,Integer)->Join(OneDimensionalArrayAggregate(S),etc)`(S,mn)`IFARRAY`100770 -dIndexedList`2`n`(Type,Integer)->ListAggregate(S)`(S,mn)`ILIST`0 -dIndexedMatrix`3`n`(Ring,mnRow:Integer,mnCol:Integer)->MatrixCategory(R,IndexedVector(R,mnCol),IndexedVector(R,mnRow))`(R,mnRow,mnCol)`IMATRIX`101859 -dIndexedOneDimensionalArray`2`n`(Type,Integer)->OneDimensionalArrayAggregate(S)`(S,mn)`IARRAY1`102330 -dIndexedString`1`n`(Integer)->Join(StringAggregate,etc)`(mn)`ISTRING`0 -dIndexedTwoDimensionalArray`3`n`(Type,mnRow:Integer,mnCol:Integer)->TwoDimensionalArrayCategory(R,IndexedOneDimensionalArray(R,mnCol),IndexedOneDimensionalArray(R,mnRow))`(R,mnRow,mnCol)`IARRAY2`102438 -dIndexedVector`2`n`(Type,Integer)->VectorCategory(R)`(R,mn)`IVECTOR`0 -dInfiniteTuple`1`x`(Type)->Join(CoercibleTo(OutputForm),etc)`(S)`ITUPLE`103017 -dInnerAlgebraicNumber`0`n`()->Join(ExpressionSpace,etc)``IAN`103132 -dInnerFiniteField`2`n`(PositiveInteger,PositiveInteger)->FiniteAlgebraicExtensionField(InnerPrimeField(p))`(p,n)`IFF`103181 -dInnerFreeAbelianMonoid`3`n`(SetCategory,E:CancellationAbelianMonoid,E)->FreeAbelianMonoidCategory(S,E)`(S,E,un)`IFAMON`103409 -dInnerIndexedTwoDimensionalArray`5`n`(R:Type,Integer,Integer,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->TwoDimensionalArrayCategory(R,Row,Col)`(R,mnRow,mnCol,Row,Col)`IIARRAY2`103465 -dInnerPAdicInteger`2`n`(Integer,Boolean)->PAdicIntegerCategory(p)`(p,unBalanced?)`IPADIC`103622 -dInnerPrimeField`1`n`(PositiveInteger)->Join(FiniteFieldCategory,etc)`(p)`IPF`103738 -dInnerSparseUnivariatePowerSeries`1`n`(Ring)->Join(UnivariatePowerSeriesCategory(Coef,Integer),etc)`(Coef)`ISUPS`103941 -dInnerTable`3`n`(Key:SetCategory,Entry:SetCategory,Join(TableAggregate(Key,Entry),etc))->Join(TableAggregate(Key,Entry),etc)`(Key,Entry,addDom)`INTABL`104068 -dInnerTaylorSeries`1`n`(Ring)->Join(Ring,etc)`(Coef)`ITAYLOR`104176 -dInputForm`0`n`()->Join(SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm),etc)``INFORM`104552 -dIntegerMod`1`n`(PositiveInteger)->Join(CommutativeRing,etc)`(p)`ZMOD`104704 -dInteger`0`x`()->Join(IntegerNumberSystem,etc)``INT`104797 -dIntegrationFunctionsTable`0`x`()->etc``INTFTBL`0 -dIntegrationResult`1`n`(Field)->Join(Module(Fraction(Integer)),etc)`(F)`IR`104875 -dInterval`1`x`(Join(FloatingPointSystem,etc))->IntervalCategory(R)`(R)`INTRVL`105381 -dKernel`1`n`(OrderedSet)->Join(CachableSet,etc)`(S)`KERNEL`105697 -dKeyedAccessFile`1`x`(SetCategory)->Join(FileCategory(FileName,Record(key:String,entry:Entry)),etc)`(Entry)`KAFILE`105799 -dLaurentPolynomial`2`n`(R:IntegralDomain,UP:UnivariatePolynomialCategory(R))->Join(DifferentialExtension(UP),etc)`(R,UP)`LAUPOL`105896 -dLibrary`0`x`()->Join(TableAggregate(String,Any),etc)``LIB`106056 -dLieExponentials`3`n`(OrderedSet,R:Join(CommutativeRing,etc),PositiveInteger)->Join(Group,etc)`(VarSet,R,Order)`LEXP`106121 -dLiePolynomial`2`n`(OrderedSet,R:CommutativeRing)->Join(FreeLieAlgebra(VarSet,R),etc)`(VarSet,R)`LPOLY`106490 -dLieSquareMatrix`2`x`(PositiveInteger,R:CommutativeRing)->Join(SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),etc)`(n,R)`LSQM`106682 -dLinearOrdinaryDifferentialOperator1`1`n`(DifferentialRing)->LinearOrdinaryDifferentialOperatorCategory(A)`(A)`LODO1`107033 -dLinearOrdinaryDifferentialOperator2`2`n`(A:DifferentialRing,M:Join(LeftModule(A),etc))->Join(LinearOrdinaryDifferentialOperatorCategory(A),etc)`(A,M)`LODO2`107279 -dLinearOrdinaryDifferentialOperator`2`x`(A:Ring,(A)->A)->LinearOrdinaryDifferentialOperatorCategory(A)`(A,diff)`LODO`107560 -dListMonoidOps`3`n`(SetCategory,E:AbelianMonoid,E)->Join(SetCategory,etc)`(S,E,un)`LMOPS`107816 -dListMultiDictionary`1`n`(SetCategory)->Join(MultiDictionary(S),etc)`(S)`LMDICT`0 -dList`1`x`(Type)->Join(ListAggregate(S),etc)`(S)`LIST`0 -dLocalAlgebra`3`n`(Algebra(R),R:CommutativeRing,S:SubsetCategory(Monoid,R))->Join(Algebra(R),etc)`(A,R,S)`LA`107987 -dLocalize`3`n`(Module(R),R:CommutativeRing,S:SubsetCategory(Monoid,R))->Join(Module(R),etc)`(M,R,S)`LO`108127 -dLyndonWord`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`LWORD`108313 -dMachineComplex`0`x`()->Join(FortranMachineTypeCategory,etc)``MCMPLX`109186 -dMachineFloat`0`x`()->Join(FloatingPointSystem,etc)``MFLOAT`109288 -dMachineInteger`0`x`()->Join(FortranMachineTypeCategory,etc)``MINT`109390 -dMagma`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`MAGMA`109485 -dMakeCachableSet`1`n`(SetCategory)->Join(CachableSet,etc)`(S)`MKCHSET`109684 -dMapping`1`x`special`(T,S)`MAPPING`109776 -dMatrix`1`x`(Ring)->Join(MatrixCategory(R,Vector(R),Vector(R)),etc)`(R)`MATRIX`110015 -dModMonic`2`n`(R:Ring,Rep:UnivariatePolynomialCategory(R))->Join(UnivariatePolynomialCategory(R),etc)`(R,Rep)`MODMON`110116 -dModularField`5`n`(R:CommutativeRing,Mod:AbelianMonoid,(R,Mod)->R,(Mod,Mod)->Union(Mod,"failed"),(R,R,Mod)->Union(R,"failed"))->Join(Field,etc)`(R,Mod,reduction,merge,exactQuo)`MODFIELD`110149 -dModularRing`5`n`(R:CommutativeRing,Mod:AbelianMonoid,(R,Mod)->R,(Mod,Mod)->Union(Mod,"failed"),(R,R,Mod)->Union(R,"failed"))->Join(Ring,etc)`(R,Mod,reduction,merge,exactQuo)`MODRING`110371 -dModuleMonomial`3`n`(IS:OrderedSet,E:SetCategory,(Record(index:IS,exponent:E),Record(index:IS,exponent:E))->Boolean)->Join(OrderedSet,etc)`(IS,E,ff)`MODMONOM`110580 -dModuleOperator`2`x`(R:Ring,M:LeftModule(R))->Join(Ring,etc)`(R,M)`MODOP`110613 -dMoebiusTransform`1`n`(Field)->Join(Group,etc)`(F)`MOEBIUS`110662 -dMonoidRing`2`n`(Ring,M:Monoid)->Join(Ring,etc)`(R,M)`MRING`110785 -dMultiset`1`x`(SetCategory)->Join(MultisetAggregate(S),etc)`(S)`MSET`111737 -dMultivariatePolynomial`2`x`(List(Symbol),R:Ring)->PolynomialCategory(R,IndexedExponents(OrderedVariableList(vl)),OrderedVariableList(vl))`(vl,R)`MPOLY`111784 -dNewSparseMultivariatePolynomial`2`n`(Ring,VarSet:OrderedSet)->Join(RecursivePolynomialCategory(R,IndexedExponents(VarSet),VarSet),etc)`(R,VarSet)`NSMP`112106 -dNewSparseUnivariatePolynomial`1`n`(Ring)->Join(UnivariatePolynomialCategory(R),etc)`(R)`NSUP`112369 -dNonNegativeInteger`0`x`()->Join(OrderedAbelianMonoidSup,etc)``NNI`112558 -dNone`0`n`()->SetCategory``NONE`112654 -dNumericalIntegrationProblem`0`x`()->Join(SetCategory,etc)``NIPROB`0 -dNumericalODEProblem`0`x`()->Join(SetCategory,etc)``ODEPROB`0 -dNumericalOptimizationProblem`0`x`()->Join(SetCategory,etc)``OPTPROB`0 -dNumericalPDEProblem`0`x`()->Join(SetCategory,etc)``PDEPROB`0 -dODEIntensityFunctionsTable`0`x`()->etc``ODEIFTBL`0 -dOctonion`1`x`(CommutativeRing)->Join(OctonionCategory(R),etc)`(R)`OCT`112871 -dOneDimensionalArray`1`x`(Type)->Join(OneDimensionalArrayAggregate(S),etc)`(S)`ARRAY1`0 -dOnePointCompletion`1`x`(SetCategory)->Join(SetCategory,etc)`(R)`ONECOMP`113394 -dOpenMathConnection`0`x`()->etc``OMCONN`113498 -dOpenMathDevice`0`x`()->etc``OMDEV`113635 -dOpenMathEncoding`0`x`()->Join(SetCategory,etc)``OMENC`113827 -dOpenMathErrorKind`0`x`()->Join(SetCategory,etc)``OMERRK`113901 -dOpenMathError`0`x`()->Join(SetCategory,etc)``OMERR`114067 -dOperator`1`n`(Ring)->Join(Ring,etc)`(R)`OP`114132 -dOppositeMonogenicLinearOperator`2`n`(MonogenicLinearOperator(R),R:Ring)->Join(MonogenicLinearOperator(R),etc)`(P,R)`OMLO`114181 -dOrdSetInts`0`x`()->Join(OrderedSet,etc)``OSI`114419 -dOrderedCompletion`1`x`(SetCategory)->Join(SetCategory,etc)`(R)`ORDCOMP`114712 -dOrderedDirectProduct`3`n`(NonNegativeInteger,S:OrderedAbelianMonoidSup,(Vector(S),Vector(S))->Boolean)->DirectProductCategory(dim,S)`(dim,S,f)`ODP`114827 -dOrderedFreeMonoid`1`n`(OrderedSet)->Join(OrderedMonoid,etc)`(S)`OFMONOID`115157 -dOrderedVariableList`1`n`(List(Symbol))->Join(OrderedFinite,etc)`(VariableList)`OVAR`115779 -dOrderlyDifferentialPolynomial`1`n`(Ring)->Join(DifferentialPolynomialCategory(R,Symbol,OrderlyDifferentialVariable(Symbol),IndexedExponents(OrderlyDifferentialVariable(Symbol))),etc)`(R)`ODPOL`0 -dOrderlyDifferentialVariable`1`n`(OrderedSet)->DifferentialVariableCategory(S)`(S)`ODVAR`0 -dOrdinaryDifferentialRing`3`x`(Kernels:SetCategory,R:PartialDifferentialRing(Kernels),Kernels)->Join(BiModule(_$,_$),etc)`(Kernels,R,var)`ODR`115826 -dOrdinaryWeightedPolynomials`4`n`(Ring,List(Symbol),List(NonNegativeInteger),NonNegativeInteger)->Join(Ring,etc)`(R,vl,wl,wtlevel)`OWP`115947 -dOutputForm`0`n`()->Join(SetCategory,etc)``OUTFORM`116175 -dPAdicInteger`1`n`(Integer)->PAdicIntegerCategory(p)`(p)`PADIC`116437 -dPAdicRationalConstructor`2`n`(p:Integer,PADIC:PAdicIntegerCategory(p))->Join(QuotientFieldCategory(PADIC),etc)`(p,PADIC)`PADICRC`116629 -dPAdicRational`1`n`(Integer)->Join(QuotientFieldCategory(PAdicInteger(p)),etc)`(p)`PADICRAT`116702 -dPalette`0`x`()->Join(SetCategory,etc)``PALETTE`0 -dParametricPlaneCurve`1`x`(Type)->etc`(ComponentFunction)`PARPCURV`116884 -dParametricSpaceCurve`1`x`(Type)->etc`(ComponentFunction)`PARSCURV`116977 -dParametricSurface`1`x`(Type)->etc`(ComponentFunction)`PARSURF`117068 -dPartialFraction`1`x`(EuclideanDomain)->Join(Field,etc)`(R)`PFR`117152 -dPartition`0`n`()->Join(OrderedCancellationAbelianMonoid,etc)``PRTITION`118006 -dPatternMatchListResult`3`n`(SetCategory,S:SetCategory,L:ListAggregate(S))->Join(SetCategory,etc)`(R,S,L)`PATLRES`118252 -dPatternMatchResult`2`n`(SetCategory,S:SetCategory)->Join(SetCategory,etc)`(R,S)`PATRES`118488 -dPattern`1`n`(SetCategory)->Join(SetCategory,etc)`(R)`PATTERN`118709 -dPendantTree`1`x`(SetCategory)->Join(BinaryRecursiveAggregate(S),etc)`(S)`PENDTREE`0 -dPermutationGroup`1`x`(SetCategory)->Join(SetCategory,etc)`(S)`PERMGRP`118756 -dPermutation`1`x`(SetCategory)->Join(PermutationCategory(S),etc)`(S)`PERM`119225 -dPi`0`x`()->Join(Field,etc)``HACKPI`119718 -dPlaneAlgebraicCurvePlot`0`n`()->Join(PlottablePlaneCurveCategory,etc)``ACPLOT`120029 -dPlot3D`0`n`()->Join(PlottableSpaceCurveCategory,etc)``PLOT3D`120292 -dPlot`0`n`()->Join(PlottablePlaneCurveCategory,etc)``PLOT`120628 -dPoincareBirkhoffWittLyndonBasis`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`PBWLB`120993 -dPoint`1`n`(Ring)->PointCategory(R)`(R)`POINT`0 -dPolynomialIdeals`4`x`(F:Field,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,DPoly:PolynomialCategory(F,Expon,VarSet))->Join(SetCategory,etc)`(F,Expon,VarSet,DPoly)`IDEAL`121328 -dPolynomialRing`2`n`(Ring,E:OrderedAbelianMonoid)->Join(FiniteAbelianMonoidRing(R,E),etc)`(R,E)`PR`121836 -dPolynomial`1`x`(Ring)->Join(PolynomialCategory(R,IndexedExponents(Symbol),Symbol),etc)`(R)`POLY`122200 -dPositiveInteger`0`x`()->Join(AbelianSemiGroup,etc)``PI`122489 -dPrimeField`1`x`(PositiveInteger)->Join(FiniteFieldCategory,etc)`(p)`PF`122578 -dPrimitiveArray`1`n`(Type)->OneDimensionalArrayAggregate(S)`(S)`PRIMARR`122772 -dProduct`2`n`(SetCategory,B:SetCategory)->Join(SetCategory,etc)`(A,B)`PRODUCT`122917 -dQuadraticForm`2`x`(PositiveInteger,K:Field)->Join(AbelianGroup,etc)`(n,K)`QFORM`122964 -dQuasiAlgebraicSet`4`n`(R:GcdDomain,Var:OrderedSet,Expon:OrderedAbelianMonoidSup,Dpoly:PolynomialCategory(R,Expon,Var))->Join(SetCategory,etc)`(R,Var,Expon,Dpoly)`QALGSET`123027 -dQuaternion`1`x`(CommutativeRing)->QuaternionCategory(R)`(R)`QUAT`124746 -dQueryEquation`0`x`()->Join(CoercibleTo(OutputForm),etc)``QEQUAT`125049 -dQueue`1`x`(SetCategory)->Join(QueueAggregate(S),etc)`(S)`QUEUE`0 -dRadicalFunctionField`5`n`(F:UniqueFactorizationDomain,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),Fraction(UP),NonNegativeInteger)->FunctionFieldCategory(F,UP,UPUP)`(F,UP,UPUP,radicnd,n)`RADFF`125102 -dRadixExpansion`1`x`(Integer)->Join(QuotientFieldCategory(Integer),etc)`(bb)`RADIX`125161 -dRealClosure`1`x`(Join(OrderedRing,etc))->Join(RealClosedField,etc)`(TheField)`RECLOS`125306 -dRecord`1`x`special`(a:A,b:B,...,c:C)`RECORD`125373 -dRectangularMatrix`3`n`(NonNegativeInteger,n:NonNegativeInteger,R:Ring)->Join(RectangularMatrixCategory(m,n,R,DirectProduct(n,R),DirectProduct(m,R)),etc)`(m,n,R)`RMATRIX`125609 -dReference`1`n`(Type)->Join(Type,etc)`(S)`REF`125744 -dRegularChain`2`x`(GcdDomain,ls:List(Symbol))->Join(RegularTriangularSetCategory(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),etc)`(R,ls)`RGCHAIN`125835 -dRegularTriangularSet`4`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(RegularTriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`REGSET`126057 -dResidueRing`5`n`(F:Field,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,FPol:PolynomialCategory(F,Expon,VarSet),List(FPol))->Join(CommutativeRing,etc)`(F,Expon,VarSet,FPol,LFPol)`RESRING`126488 -dResult`0`x`()->Join(TableAggregate(Symbol,Any),etc)``RESULT`126690 -dRewriteRule`3`x`(Base:SetCategory,R:Join(Ring,etc),F:Join(FunctionSpace(R),etc))->Join(SetCategory,etc)`(Base,R,F)`RULE`126886 -dRightOpenIntervalRootCharacterization`2`x`(TheField:Join(OrderedRing,etc),ThePolDom:UnivariatePolynomialCategory(TheField))->Join(RealRootCharacterizationCategory(TheField,ThePolDom),etc)`(TheField,ThePolDom)`ROIRC`127061 -dRomanNumeral`0`x`()->Join(IntegerNumberSystem,etc)``ROMAN`127158 -dRoutinesTable`0`x`()->Join(TableAggregate(Symbol,Any),etc)``ROUTINE`0 -dRuleCalled`1`n`(Symbol)->Join(SetCategory,etc)`(f)`RULECOLD`127264 -dRuleset`3`x`(Base:SetCategory,R:Join(Ring,etc),F:Join(FunctionSpace(R),etc))->Join(SetCategory,etc)`(Base,R,F)`RULESET`127305 -dSExpressionOf`5`n`(SetCategory,Sym:SetCategory,Int:SetCategory,Flt:SetCategory,Expr:SetCategory)->SExpressionCategory(Str,Sym,Int,Flt,Expr)`(Str,Sym,Int,Flt,Expr)`SEXOF`127374 -dSExpression`0`n`()->SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm)``SEX`127460 -dScriptFormulaFormat`0`x`()->Join(SetCategory,etc)``FORMULA`127528 -dSegmentBinding`1`x`(Type)->Join(Type,etc)`(S)`SEGBIND`128229 -dSegment`1`x`(Type)->Join(SegmentCategory(S),etc)`(S)`SEG`128384 -dSequentialDifferentialPolynomial`1`n`(Ring)->Join(DifferentialPolynomialCategory(R,Symbol,SequentialDifferentialVariable(Symbol),IndexedExponents(SequentialDifferentialVariable(Symbol))),etc)`(R)`SDPOL`0 -dSequentialDifferentialVariable`1`n`(OrderedSet)->DifferentialVariableCategory(S)`(S)`SDVAR`0 -dSetOfMIntegersInOneToN`2`n`(PositiveInteger,PositiveInteger)->Join(Finite,etc)`(m,n)`SETMN`128457 -dSet`1`x`(SetCategory)->FiniteSetAggregate(S)`(S)`SET`128571 -dSimpleAlgebraicExtension`3`n`(R:CommutativeRing,UP:UnivariatePolynomialCategory(R),UP)->MonogenicAlgebra(R,UP)`(R,UP,M)`SAE`129649 -dSimpleFortranProgram`2`x`(R:OrderedSet,FS:FunctionSpace(R))->Join(FortranProgramCategory,etc)`(R,FS)`SFORT`130228 -dSingleInteger`0`x`()->Join(IntegerNumberSystem,etc)``SINT`130500 -dSingletonAsOrderedSet`0`n`()->Join(OrderedSet,etc)``SAOS`130571 -dSparseMultivariatePolynomial`2`n`(Ring,VarSet:OrderedSet)->PolynomialCategory(R,IndexedExponents(VarSet),VarSet)`(R,VarSet)`SMP`130659 -dSparseMultivariateTaylorSeries`3`n`(Coef:Ring,Var:OrderedSet,SMP:PolynomialCategory(Coef,IndexedExponents(Var),Var))->Join(MultivariateTaylorSeriesCategory(Coef,Var),etc)`(Coef,Var,SMP)`SMTS`131007 -dSparseTable`3`n`(SetCategory,Ent:SetCategory,Ent)->TableAggregate(Key,Ent)`(Key,Ent,dent)`STBL`131299 -dSparseUnivariateLaurentSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariateLaurentSeriesConstructorCategory(Coef,SparseUnivariateTaylorSeries(Coef,var,cen)),etc)`(Coef,var,cen)`SULS`131417 -dSparseUnivariatePolynomial`1`n`(Ring)->Join(UnivariatePolynomialCategory(R),etc)`(R)`SUP`131981 -dSparseUnivariatePuiseuxSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,SparseUnivariateLaurentSeries(Coef,var,cen)),etc)`(Coef,var,cen)`SUPXS`132355 -dSparseUnivariateSkewPolynomial`3`n`(R:Ring,Automorphism(R),(R)->R)->Join(UnivariateSkewPolynomialCategory(R),etc)`(R,sigma,delta)`ORESUP`132930 -dSparseUnivariateTaylorSeries`3`n`(Coef:Ring,var:Symbol,Coef)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef,var,cen)`SUTS`133092 -dSplitHomogeneousDirectProduct`3`n`(NonNegativeInteger,NonNegativeInteger,S:OrderedAbelianMonoidSup)->DirectProductCategory(dimtot,S)`(dimtot,dim1,S)`SHDP`133673 -dSplittingNode`2`n`(Join(SetCategory,etc),C:Join(SetCategory,etc))->Join(SetCategory,etc)`(V,C)`SPLNODE`134147 -dSplittingTree`2`n`(Join(SetCategory,etc),C:Join(SetCategory,etc))->Join(RecursiveAggregate(SplittingNode(V,C)),etc)`(V,C)`SPLTREE`134770 -dSquareFreeRegularTriangularSet`4`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(SquareFreeRegularTriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`SREGSET`135812 -dSquareMatrix`2`n`(NonNegativeInteger,R:Ring)->Join(SquareMatrixCategory(ndim,R,DirectProduct(ndim,R),DirectProduct(ndim,R)),etc)`(ndim,R)`SQMATRIX`136290 -dStack`1`x`(SetCategory)->Join(StackAggregate(S),etc)`(S)`STACK`0 -dStream`1`x`(Type)->Join(LazyStreamAggregate(S),etc)`(S)`STREAM`136436 -dStringTable`1`n`(SetCategory)->Join(TableAggregate(String,Entry),etc)`(Entry)`STRTBL`136606 -dString`0`x`()->StringCategory``STRING`0 -dSubSpaceComponentProperty`0`n`()->Join(SetCategory,etc)``COMPPROP`0 -dSubSpace`2`n`(PositiveInteger,R:Ring)->Join(SetCategory,etc)`(n,R)`SUBSPACE`0 -dSuchThat`2`n`(SetCategory,S2:SetCategory)->Join(SetCategory,etc)`(S1,S2)`SUCH`136717 -dSwitch`0`x`()->Join(CoercibleTo(OutputForm),etc)``SWITCH`136764 -dSymbolTable`0`x`()->Join(CoercibleTo(OutputForm),etc)``SYMTAB`136877 -dSymbol`0`x`()->Join(OrderedSet,etc)``SYMBOL`136947 -dSymmetricPolynomial`1`n`(Ring)->Join(FiniteAbelianMonoidRing(R,Partition),etc)`(R)`SYMPOLY`136981 -dTable`2`n`(SetCategory,Entry:SetCategory)->Join(TableAggregate(Key,Entry),etc)`(Key,Entry)`TABLE`137031 -dTableau`1`x`(SetCategory)->etc`(S)`TABLEAU`137255 -dTaylorSeries`1`x`(Ring)->Join(MultivariateTaylorSeriesCategory(Coef,Symbol),etc)`(Coef)`TS`137398 -dTexFormat`0`x`()->Join(SetCategory,etc)``TEX`137529 -dTextFile`0`x`()->Join(FileCategory(FileName,String),etc)``TEXTFILE`138281 -dTheSymbolTable`0`x`()->Join(CoercibleTo(OutputForm),etc)``SYMS`138419 -dThreeDimensionalMatrix`1`x`(SetCategory)->Join(HomogeneousAggregate(R),etc)`(R)`M3D`138569 -dThreeDimensionalViewport`0`x`()->Join(SetCategory,etc)``VIEW3D`0 -dThreeSpace`1`x`(Ring)->ThreeSpaceCategory(R)`(R)`SPACE3`0 -dTree`1`x`(SetCategory)->Join(RecursiveAggregate(S),etc)`(S)`TREE`0 -dTubePlot`1`n`(PlottableSpaceCurveCategory)->etc`(Curve)`TUBE`138652 -dTuple`1`n`(Type)->Join(CoercibleTo(PrimitiveArray(S)),etc)`(S)`TUPLE`138799 -dTwoDimensionalArray`1`n`(Type)->Join(TwoDimensionalArrayCategory(R,OneDimensionalArray(R),OneDimensionalArray(R)),etc)`(R)`ARRAY2`138929 -dTwoDimensionalViewport`0`n`()->Join(SetCategory,etc)``VIEW2D`0 -dUnion`1`x`special`(A,B,...,C)`UNION`139047 -dUnivariateLaurentSeriesConstructor`2`n`(Coef:Ring,UTS:UnivariateTaylorSeriesCategory(Coef))->UnivariateLaurentSeriesConstructorCategory(Coef,UTS)`(Coef,UTS)`ULSCONS`139195 -dUnivariateLaurentSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariateLaurentSeriesConstructorCategory(Coef,UnivariateTaylorSeries(Coef,var,cen)),etc)`(Coef,var,cen)`ULS`139522 -dUnivariatePolynomial`2`x`(Symbol,R:Ring)->Join(UnivariatePolynomialCategory(R),etc)`(x,R)`UP`140073 -dUnivariatePuiseuxSeriesConstructor`2`n`(Coef:Ring,ULS:UnivariateLaurentSeriesCategory(Coef))->UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)`(Coef,ULS)`UPXSCONS`140288 -dUnivariatePuiseuxSeriesWithExponentialSingularity`4`n`(R:Join(OrderedSet,etc),FE:Join(AlgebraicallyClosedField,etc),var:Symbol,cen:FE)->Join(FiniteAbelianMonoidRing(UnivariatePuiseuxSeries(FE,var,cen),ExponentialOfUnivariatePuiseuxSeries(FE,var,cen)),etc)`(R,FE,var,cen)`UPXSSING`140618 -dUnivariatePuiseuxSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,UnivariateLaurentSeries(Coef,var,cen)),etc)`(Coef,var,cen)`UPXS`141147 -dUnivariateSkewPolynomial`4`n`(Symbol,R:Ring,Automorphism(R),(R)->R)->Join(UnivariateSkewPolynomialCategory(R),etc)`(x,R,sigma,delta)`OREUP`141709 -dUnivariateTaylorSeries`3`n`(Coef:Ring,var:Symbol,Coef)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef,var,cen)`UTS`141884 -dUniversalSegment`1`x`(Type)->Join(SegmentCategory(S),etc)`(S)`UNISEG`142352 -dVariable`1`n`(Symbol)->Join(SetCategory,etc)`(sym)`VARIABLE`142469 -dVector`1`x`(Type)->Join(VectorCategory(R),etc)`(R)`VECTOR`0 -dVoid`0`x`()->etc``VOID`142508 -dWeightedPolynomials`7`n`(R:Ring,VarSet:OrderedSet,E:OrderedAbelianMonoidSup,P:PolynomialCategory(R,E,VarSet),List(VarSet),List(NonNegativeInteger),NonNegativeInteger)->Join(Ring,etc)`(R,VarSet,E,P,vl,wl,wtlevel)`WP`142732 -dWuWenTsunTriangularSet`4`x`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(TriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`WUTSET`142994 -dXDistributedPolynomial`2`n`(OrderedSet,R:Ring)->Join(FreeModuleCat(R,OrderedFreeMonoid(vl)),etc)`(vl,R)`XDPOLY`144038 -dXPBWPolynomial`2`n`(OrderedSet,R:CommutativeRing)->Join(XPolynomialsCat(VarSet,R),etc)`(VarSet,R)`XPBWPOLY`144242 -dXPolynomialRing`2`n`(Ring,E:OrderedMonoid)->Join(Ring,etc)`(R,E)`XPR`144526 -dXPolynomial`1`n`(Ring)->Join(XPolynomialsCat(Symbol,R),etc)`(R)`XPOLY`144827 -dXRecursivePolynomial`2`n`(OrderedSet,R:Ring)->Join(XPolynomialsCat(VarSet,R),etc)`(VarSet,R)`XRPOLY`145094 +aunitsKnown`0`x``cFiniteRankNonAssociativeAlgebra`has(R,IntegralDomain)`5101 +aunitsKnown`0`x``cGroup``5365 +aunitsKnown`0`x``cRing``5437 +cAbelianGroup`0`x`()->Category``ABELGRP`5537 +cAbelianMonoid`0`x`()->Category``ABELMON`5739 +cAbelianMonoidRing`2`x`(Ring,OrderedAbelianMonoid)->Category`(R,E)`AMR`6028 +cAbelianSemiGroup`0`x`()->Category``ABELSG`6601 +cAffineSpaceCategory`1`x`(Field)->Category`(K)`AFSPCAT`6927 +cAggregate`0`x`()->Category``AGG`7037 +cAlgebra`1`x`(CommutativeRing)->Category`(R)`ALGEBRA`7561 +cAlgebraicallyClosedField`0`x`()->Category``ACF`7902 +cAlgebraicallyClosedFunctionSpace`1`x`(Join(OrderedSet,etc))->Category`(R)`ACFS`7946 +cArcHyperbolicFunctionCategory`0`x`()->Category``AHYP`7999 +cArcTrigonometricFunctionCategory`0`x`()->Category``ATRIG`8065 +cAssociationListAggregate`2`x`(SetCategory,SetCategory)->Category`(Key,Entry)`ALAGG`8120 +cAttributeRegistry`0`x`()->Category``ATTREG`8287 +cBagAggregate`1`x`(Type)->Category`(S)`BGAGG`8350 +cBasicType`0`x`()->Category``BASTYPE`8576 +cBiModule`2`x`(Ring,Ring)->Category`(R,S)`BMODULE`8692 +cBinaryRecursiveAggregate`1`x`(Type)->Category`(S)`BRAGG`8857 +cBinaryTreeCategory`1`x`(SetCategory)->Category`(S)`BTCAT`8995 +cBitAggregate`0`x`()->Category``BTAGG`9208 +cBlowUpMethodCategory`0`x`()->Category``BLMETCT`0 +cCachableSet`0`x`()->Category``CACHSET`9305 +cCancellationAbelianMonoid`0`x`()->Category``CABMON`9393 +cCharacteristicNonZero`0`x`()->Category``CHARNZ`9659 +cCharacteristicZero`0`x`()->Category``CHARZ`9697 +cCoercibleTo`1`x`(Type)->Category`(S)`KOERCE`9732 +cCollection`1`x`(Type)->Category`(S)`CLAGG`9866 +cCombinatorialFunctionCategory`0`x`()->Category``CFCAT`10300 +cCombinatorialOpsCategory`0`x`()->Category``COMBOPC`10353 +cCommutativeRing`0`x`()->Category``COMRING`10485 +cComplexCategory`1`x`(CommutativeRing)->Category`(R)`COMPCAT`10647 +cConvertibleTo`1`x`(Type)->Category`(S)`KONVERT`10732 +cDequeueAggregate`1`x`(Type)->Category`(S)`DQAGG`10879 +cDesingTreeCategory`1`x`(SetCategory)->Category`(S)`DSTRCAT`11057 +cDictionary`1`x`(SetCategory)->Category`(S)`DIAGG`11104 +cDictionaryOperations`1`x`(SetCategory)->Category`(S)`DIOPS`11422 +cDifferentialExtension`1`x`(Ring)->Category`(R)`DIFEXT`11550 +cDifferentialPolynomialCategory`4`x`(Ring,S:OrderedSet,DifferentialVariableCategory(S),OrderedAbelianMonoidSup)->Category`(R,S,V,E)`DPOLCAT`11676 +cDifferentialRing`0`x`()->Category``DIFRING`12985 +cDifferentialVariableCategory`1`x`(OrderedSet)->Category`(S)`DVARCAT`13266 +cDirectProductCategory`2`x`(NonNegativeInteger,Type)->Category`(dim,R)`DIRPCAT`15642 +cDivisionRing`0`x`()->Category``DIVRING`15783 +cDivisorCategory`1`x`(SetCategory)->Category`(S)`DIVCAT`15950 +cDoublyLinkedAggregate`1`x`(Type)->Category`(S)`DLAGG`16002 +cElementaryFunctionCategory`0`x`()->Category``ELEMFUN`16207 +cEltable`2`x`(SetCategory,Type)->Category`(S,Index)`ELTAB`16251 +cEltableAggregate`2`x`(SetCategory,Type)->Category`(Dom,Im)`ELTAGG`16542 +cEntireRing`0`x`()->Category``ENTIRER`16889 +cEuclideanDomain`0`x`()->Category``EUCDOM`17160 +cEvalable`1`x`(SetCategory)->Category`(R)`EVALAB`17552 +cExpressionSpace`0`x`()->Category``ES`17707 +cExtensibleLinearAggregate`1`x`(Type)->Category`(S)`ELAGG`17782 +cExtensionField`1`x`(Field)->Category`(F)`XF`18187 +cField`0`x`()->Category``FIELD`18274 +cFieldOfPrimeCharacteristic`0`x`()->Category``FPC`18574 +cFileCategory`2`x`(SetCategory,SetCategory)->Category`(Name,S)`FILECAT`18814 +cFileNameCategory`0`x`()->Category``FNCAT`19049 +cFinite`0`x`()->Category``FINITE`19119 +cFiniteAbelianMonoidRing`2`x`(Ring,OrderedAbelianMonoid)->Category`(R,E)`FAMR`19347 +cFiniteAlgebraicExtensionField`1`x`(Field)->Category`(F)`FAXF`19516 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+cFortranVectorFunctionCategory`0`x`()->Category``FVFUN`23863 +cFramedAlgebra`2`x`(R:CommutativeRing,UnivariatePolynomialCategory(R))->Category`(R,UP)`FRAMALG`24012 +cFramedNonAssociativeAlgebra`1`x`(CommutativeRing)->Category`(R)`FRNAALG`24124 +cFreeAbelianMonoidCategory`2`x`(SetCategory,CancellationAbelianMonoid)->Category`(S,E)`FAMONC`24401 +cFreeLieAlgebra`2`x`(OrderedSet,CommutativeRing)->Category`(VarSet,R)`FLALG`24667 +cFreeModuleCat`2`x`(Ring,SetCategory)->Category`(R,Basis)`FMCAT`24814 +cFullyEvalableOver`1`x`(SetCategory)->Category`(R)`FEVALAB`25292 +cFullyLinearlyExplicitRingOver`1`x`(Ring)->Category`(R)`FLINEXP`25413 +cFullyPatternMatchable`1`x`(Type)->Category`(R)`FPATMAB`25643 +cFullyRetractableTo`1`x`(Type)->Category`(S)`FRETRCT`25836 +cFunctionFieldCategory`3`x`(F:UniqueFactorizationDomain,UP:UnivariatePolynomialCategory(F),UnivariatePolynomialCategory(Fraction(UP)))->Category`(F,UP,UPUP)`FFCAT`26126 +cFunctionSpace`1`x`(OrderedSet)->Category`(R)`FS`26208 +cGcdDomain`0`x`()->Category``GCDDOM`26286 +cGradedAlgebra`2`x`(CommutativeRing,AbelianMonoid)->Category`(R,E)`GRALG`26592 +cGradedModule`2`x`(CommutativeRing,AbelianMonoid)->Category`(R,E)`GRMOD`26939 +cGroup`0`x`()->Category``GROUP`27481 +cHomogeneousAggregate`1`x`(Type)->Category`(S)`HOAGG`27778 +cHyperbolicFunctionCategory`0`x`()->Category``HYPCAT`28191 +cIndexedAggregate`2`x`(SetCategory,Type)->Category`(Index,Entry)`IXAGG`28250 +cIndexedDirectProductCategory`2`x`(SetCategory,OrderedSet)->Category`(A,S)`IDPC`28508 +cInfinitlyClosePointCategory`9`x`(K:Field,symb:List(Symbol),PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DivisorCategory(Plc),BlowUpMethodCategory)->Category`(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)`INFCLCT`28611 +cInnerEvalable`2`x`(SetCategory,Type)->Category`(A,B)`IEVALAB`28659 +cIntegerNumberSystem`0`x`()->Category``INS`28983 +cIntegralDomain`0`x`()->Category``INTDOM`29048 +cIntervalCategory`1`x`(Join(FloatingPointSystem,etc))->Category`(R)`INTCAT`29365 +cKeyedDictionary`2`x`(SetCategory,SetCategory)->Category`(Key,Entry)`KDAGG`29464 +cLazyStreamAggregate`1`x`(Type)->Category`(S)`LZSTAGG`29572 +cLeftAlgebra`1`x`(Ring)->Category`(R)`LALG`29885 +cLeftModule`1`x`(Rng)->Category`(R)`LMODULE`29949 +cLieAlgebra`1`x`(CommutativeRing)->Category`(R)`LIECAT`30284 +cLinearAggregate`1`x`(Type)->Category`(S)`LNAGG`30410 +cLinearlyExplicitRingOver`1`x`(Ring)->Category`(R)`LINEXP`31037 +cLinearOrdinaryDifferentialOperatorCategory`1`x`(Ring)->Category`(A)`LODOCAT`31102 +cLiouvillianFunctionCategory`0`x`()->Category``LFCAT`31402 +cListAggregate`1`x`(Type)->Category`(S)`LSAGG`31463 +cLocalPowerSeriesCategory`1`x`(Field)->Category`(K)`LOCPOWC`0 +cLogic`0`x`()->Category``LOGIC`31650 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+dFileName`0`x`()->FileNameCategory``FNAME`140279 +dFiniteDivisor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->Join(FiniteDivisorCategory(F,UP,UPUP,R),etc)`(F,UP,UPUP,R)`FDIV`140348 +dFiniteField`2`x`(PositiveInteger,PositiveInteger)->FiniteAlgebraicExtensionField(PrimeField(p))`(p,n)`FF`140577 +dFiniteFieldCyclicGroup`2`x`(PositiveInteger,PositiveInteger)->Join(FiniteAlgebraicExtensionField(PrimeField(p)),etc)`(p,extdeg)`FFCG`140769 +dFiniteFieldCyclicGroupExtension`2`n`(FiniteFieldCategory,PositiveInteger)->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,extdeg)`FFCGX`141419 +dFiniteFieldCyclicGroupExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,SparseUnivariatePolynomial(GF))->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,defpol)`FFCGP`142051 +dFiniteFieldExtension`2`n`(FiniteFieldCategory,PositiveInteger)->FiniteAlgebraicExtensionField(GF)`(GF,n)`FFX`142653 +dFiniteFieldExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,SparseUnivariatePolynomial(GF))->FiniteAlgebraicExtensionField(GF)`(GF,defpol)`FFP`142909 +dFiniteFieldNormalBasis`2`x`(PositiveInteger,PositiveInteger)->Join(FiniteAlgebraicExtensionField(PrimeField(p)),etc)`(p,extdeg)`FFNB`143096 +dFiniteFieldNormalBasisExtension`2`n`(FiniteFieldCategory,PositiveInteger)->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,extdeg)`FFNBX`143547 +dFiniteFieldNormalBasisExtensionByPolynomial`2`n`(GF:FiniteFieldCategory,Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value:GF,index:SingleInteger)))))->Join(FiniteAlgebraicExtensionField(GF),etc)`(GF,uni)`FFNBP`144056 +dFlexibleArray`1`x`(Type)->Join(OneDimensionalArrayAggregate(S),etc)`(S)`FARRAY`144576 +dFloat`0`x`()->Join(FloatingPointSystem,etc)``FLOAT`145546 +dFortranCode`0`x`()->Join(SetCategory,etc)``FC`149077 +dFortranExpression`3`x`(List(Symbol),List(Symbol),R:FortranMachineTypeCategory)->Join(ExpressionSpace,etc)`(basicSymbols,subscriptedSymbols,R)`FEXPR`149183 +dFortranProgram`4`x`(Symbol,Union(fst:FortranScalarType,void:"void"),List(Symbol),SymbolTable)->Join(FortranProgramCategory,etc)`(name,returnType,arguments,symbols)`FORTRAN`149342 +dFortranScalarType`0`x`()->Join(CoercibleTo(OutputForm),etc)``FST`149513 +dFortranTemplate`0`x`()->Join(FileCategory(FileName,String),etc)``FTEM`149653 +dFortranType`0`x`()->Join(SetCategory,etc)``FT`149696 +dFourierComponent`1`n`(OrderedSet)->Join(OrderedSet,etc)`(E)`FCOMP`149804 +dFourierSeries`2`x`(Join(CommutativeRing,etc),E:Join(OrderedSet,etc))->Join(Algebra(R),etc)`(R,E)`FSERIES`149864 +dFraction`1`x`(IntegralDomain)->Join(QuotientFieldCategory(S),etc)`(S)`FRAC`149917 +dFractionalIdeal`4`n`(R:EuclideanDomain,F:QuotientFieldCategory(R),UP:UnivariatePolynomialCategory(F),A:Join(FramedAlgebra(F,UP),etc))->Join(Group,etc)`(R,F,UP,A)`FRIDEAL`150185 +dFramedModule`5`n`(R:EuclideanDomain,F:QuotientFieldCategory(R),UP:UnivariatePolynomialCategory(F),A:FramedAlgebra(F,UP),Vector(A))->Join(Monoid,etc)`(R,F,UP,A,ibasis)`FRMOD`150230 +dFreeAbelianGroup`1`n`(SetCategory)->Join(AbelianGroup,etc)`(S)`FAGROUP`150280 +dFreeAbelianMonoid`1`n`(SetCategory)->FreeAbelianMonoidCategory(S,NonNegativeInteger)`(S)`FAMONOID`150530 +dFreeGroup`1`n`(SetCategory)->Join(Group,etc)`(S)`FGROUP`150794 +dFreeModule1`2`n`(Ring,S:OrderedSet)->Join(FreeModuleCat(R,S),etc)`(R,S)`FM1`151049 +dFreeModule`2`n`(Ring,S:OrderedSet)->Join(BiModule(R,R),etc)`(R,S)`FM`151379 +dFreeMonoid`1`n`(SetCategory)->Join(Monoid,etc)`(S)`FMONOID`151584 +dFreeNilpotentLie`3`x`(NonNegativeInteger,NonNegativeInteger,R:CommutativeRing)->Join(NonAssociativeAlgebra(R),etc)`(n,class,R)`FNLA`151853 +dFullPartialFractionExpansion`2`x`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->Join(SetCategory,etc)`(F,UP)`FPARFRAC`151993 +dFunctionCalled`1`n`(Symbol)->Join(SetCategory,etc)`(f)`FUNCTION`152053 +dGeneralDistributedMultivariatePolynomial`3`n`(vl:List(Symbol),R:Ring,E:DirectProductCategory(#(vl),NonNegativeInteger))->Join(PolynomialCategory(R,E,OrderedVariableList(vl)),etc)`(vl,R,E)`GDMP`152098 +dGeneralModulePolynomial`6`n`(vl:List(Symbol),R:CommutativeRing,IS:OrderedSet,E:DirectProductCategory(#(vl),NonNegativeInteger),ff:(Record(index:IS,exponent:E),Record(index:IS,exponent:E))->Boolean,P:PolynomialCategory(R,E,OrderedVariableList(vl)))->Join(Module(P),etc)`(vl,R,IS,E,ff,P)`GMODPOL`152645 +dGeneralPolynomialSet`4`n`(R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,P:RecursivePolynomialCategory(R,E,VarSet))->Join(PolynomialSetCategory(R,E,VarSet,P),etc)`(R,E,VarSet,P)`GPOLSET`152680 +dGeneralSparseTable`4`n`(Key:SetCategory,Entry:SetCategory,TableAggregate(Key,Entry),Entry)->TableAggregate(Key,Entry)`(Key,Entry,Tbl,dent)`GSTBL`152716 +dGeneralTriangularSet`4`n`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->TriangularSetCategory(R,E,V,P)`(R,E,V,P)`GTSET`152834 +dGeneralUnivariatePowerSeries`3`x`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesCategory(Coef),etc)`(Coef,var,cen)`GSERIES`153312 +dGenericNonAssociativeAlgebra`4`n`(R:CommutativeRing,n:PositiveInteger,List(Symbol),Vector(Matrix(R)))->Join(FramedNonAssociativeAlgebra(Fraction(Polynomial(R))),etc)`(R,n,ls,gamma)`GCNAALG`153611 +dGraphImage`0`n`()->Join(SetCategory,etc)``GRIMAGE`153777 +dGuessOption`0`x`()->Join(SetCategory,etc)``GOPT`153888 +dGuessOptionFunctions0`0`x`()->Join(SetCategory,etc)``GOPT0`153979 +dHashTable`3`n`(SetCategory,Entry:SetCategory,String)->Join(TableAggregate(Key,Entry),etc)`(Key,Entry,hashfn)`HASHTBL`154091 +dHeap`1`x`(OrderedSet)->Join(PriorityQueueAggregate(S),etc)`(S)`HEAP`154250 +dHexadecimalExpansion`0`x`()->Join(QuotientFieldCategory(Integer),etc)``HEXADEC`154317 +dHomogeneousDirectProduct`2`n`(NonNegativeInteger,S:OrderedAbelianMonoidSup)->DirectProductCategory(dim,S)`(dim,S)`HDP`154412 +dHomogeneousDistributedMultivariatePolynomial`2`n`(List(Symbol),R:Ring)->Join(PolynomialCategory(R,HomogeneousDirectProduct(#(vl),NonNegativeInteger),OrderedVariableList(vl)),etc)`(vl,R)`HDMP`154736 +dHyperellipticFiniteDivisor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->FiniteDivisorCategory(F,UP,UPUP,R)`(F,UP,UPUP,R)`HELLFDIV`155131 +dIndexCard`0`x`()->Join(OrderedSet,etc)``ICARD`155485 +dIndexedBits`1`n`(Integer)->Join(BitAggregate,etc)`(mn)`IBITS`155565 +dIndexedDirectProductAbelianGroup`2`n`(AbelianGroup,S:OrderedSet)->Join(AbelianGroup,etc)`(A,S)`IDPAG`155663 +dIndexedDirectProductAbelianMonoid`2`n`(AbelianMonoid,S:OrderedSet)->Join(AbelianMonoid,etc)`(A,S)`IDPAM`155856 +dIndexedDirectProductObject`2`n`(SetCategory,S:OrderedSet)->IndexedDirectProductCategory(A,S)`(A,S)`IDPO`156051 +dIndexedDirectProductOrderedAbelianMonoid`2`n`(OrderedAbelianMonoid,S:OrderedSet)->Join(OrderedAbelianMonoid,etc)`(A,S)`IDPOAM`156193 +dIndexedDirectProductOrderedAbelianMonoidSup`2`n`(OrderedAbelianMonoidSup,S:OrderedSet)->Join(OrderedAbelianMonoidSup,etc)`(A,S)`IDPOAMS`156413 +dIndexedExponents`1`n`(OrderedSet)->Join(OrderedAbelianMonoidSup,etc)`(Varset)`INDE`156597 +dIndexedFlexibleArray`2`n`(Type,Integer)->Join(OneDimensionalArrayAggregate(S),etc)`(S,mn)`IFARRAY`156643 +dIndexedList`2`n`(Type,Integer)->ListAggregate(S)`(S,mn)`ILIST`157643 +dIndexedMatrix`3`n`(Ring,mnRow:Integer,mnCol:Integer)->MatrixCategory(R,IndexedVector(R,mnCol),IndexedVector(R,mnRow))`(R,mnRow,mnCol)`IMATRIX`158138 +dIndexedOneDimensionalArray`2`n`(Type,Integer)->OneDimensionalArrayAggregate(S)`(S,mn)`IARRAY1`158609 +dIndexedString`1`n`(Integer)->Join(StringAggregate,etc)`(mn)`ISTRING`158666 +dIndexedTwoDimensionalArray`3`n`(Type,mnRow:Integer,mnCol:Integer)->TwoDimensionalArrayCategory(R,IndexedOneDimensionalArray(R,mnCol),IndexedOneDimensionalArray(R,mnRow))`(R,mnRow,mnCol)`IARRAY2`158713 +dIndexedVector`2`n`(Type,Integer)->VectorCategory(R)`(R,mn)`IVECTOR`158765 +dInfClsPt`3`x`(Field,symb:List(Symbol),BLMET:BlowUpMethodCategory)->Join(InfinitlyClosePointCategory(K,symb,DistributedMultivariatePolynomial(symb,K),DirectProduct(#(symb),NonNegativeInteger),ProjectivePlane(K),NeitherSparseOrDensePowerSeries(K),Places(K),Divisor(Places(K)),BLMET),etc)`(K,symb,BLMET)`ICP`158869 +dInfiniteTuple`1`x`(Type)->Join(CoercibleTo(OutputForm),etc)`(S)`ITUPLE`158915 +dInfinitlyClosePoint`9`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),E:DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DIVISOR:DivisorCategory(Plc),BLMET:BlowUpMethodCategory)->Join(InfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET),etc)`(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)`INFCLSPT`159016 +dInfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField`3`x`(FiniteFieldCategory,symb:List(Symbol),BLMET:BlowUpMethodCategory)->Join(InfinitlyClosePointCategory(PseudoAlgebraicClosureOfFiniteField(K),symb,DistributedMultivariatePolynomial(symb,PseudoAlgebraicClosureOfFiniteField(K)),DirectProduct(#(symb),NonNegativeInteger),ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K),NeitherSparseOrDensePowerSeries(PseudoAlgebraicClosureOfFiniteField(K)),PlacesOverPseudoAlgebraicClosureOfFinite--Field(K),Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),BLMET),etc)`(K,symb,BLMET)`INFCLSPS`159062 +dInnerAlgebraicNumber`0`n`()->Join(ExpressionSpace,etc)``IAN`159108 +dInnerFiniteField`2`n`(PositiveInteger,PositiveInteger)->FiniteAlgebraicExtensionField(InnerPrimeField(p))`(p,n)`IFF`159157 +dInnerFreeAbelianMonoid`3`n`(SetCategory,E:CancellationAbelianMonoid,E)->FreeAbelianMonoidCategory(S,E)`(S,E,un)`IFAMON`159385 +dInnerIndexedTwoDimensionalArray`5`n`(R:Type,Integer,Integer,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->TwoDimensionalArrayCategory(R,Row,Col)`(R,mnRow,mnCol,Row,Col)`IIARRAY2`159465 +dInnerPAdicInteger`2`n`(Integer,Boolean)->PAdicIntegerCategory(p)`(p,unBalanced?)`IPADIC`159511 +dInnerPrimeField`1`n`(PositiveInteger)->Join(FiniteFieldCategory,etc)`(p)`IPF`159627 +dInnerSparseUnivariatePowerSeries`1`n`(Ring)->Join(UnivariatePowerSeriesCategory(Coef,Integer),etc)`(Coef)`ISUPS`159704 +dInnerTable`3`n`(Key:SetCategory,Entry:SetCategory,Join(TableAggregate(Key,Entry),etc))->Join(TableAggregate(Key,Entry),etc)`(Key,Entry,addDom)`INTABL`159817 +dInnerTaylorSeries`1`n`(Ring)->Join(Ring,etc)`(Coef)`ITAYLOR`159925 +dInputForm`0`n`()->Join(SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm),etc)``INFORM`160301 +dInteger`0`x`()->Join(IntegerNumberSystem,etc)``INT`160453 +dIntegerMod`1`n`(PositiveInteger)->Join(CommutativeRing,etc)`(p)`ZMOD`160531 +dIntegrationFunctionsTable`0`x`()->etc``INTFTBL`160624 +dIntegrationResult`1`n`(Field)->Join(Module(Fraction(Integer)),etc)`(F)`IR`160670 +dInterval`1`x`(Join(FloatingPointSystem,etc))->IntervalCategory(R)`(R)`INTRVL`161220 +dKernel`1`n`(OrderedSet)->Join(CachableSet,etc)`(S)`KERNEL`161327 +dKeyedAccessFile`1`x`(SetCategory)->Join(FileCategory(FileName,Record(key:String,entry:Entry)),etc)`(Entry)`KAFILE`161429 +dLaurentPolynomial`2`n`(R:IntegralDomain,UP:UnivariatePolynomialCategory(R))->Join(DifferentialExtension(UP),etc)`(R,UP)`LAUPOL`162023 +dLibrary`0`x`()->Join(TableAggregate(String,Any),etc)``LIB`162090 +dLieExponentials`3`n`(OrderedSet,R:Join(CommutativeRing,etc),PositiveInteger)->Join(Group,etc)`(VarSet,R,Order)`LEXP`162155 +dLiePolynomial`2`n`(OrderedSet,R:CommutativeRing)->Join(FreeLieAlgebra(VarSet,R),etc)`(VarSet,R)`LPOLY`162466 +dLieSquareMatrix`2`x`(PositiveInteger,R:CommutativeRing)->Join(SquareMatrixCategory(n,R,DirectProduct(n,R),DirectProduct(n,R)),etc)`(n,R)`LSQM`162600 +dLinearOrdinaryDifferentialOperator1`1`n`(DifferentialRing)->LinearOrdinaryDifferentialOperatorCategory(A)`(A)`LODO1`162980 +dLinearOrdinaryDifferentialOperator2`2`n`(A:DifferentialRing,M:Join(LeftModule(A),etc))->Join(LinearOrdinaryDifferentialOperatorCategory(A),etc)`(A,M)`LODO2`163222 +dLinearOrdinaryDifferentialOperator`2`x`(A:Ring,(A)->A)->LinearOrdinaryDifferentialOperatorCategory(A)`(A,diff)`LODO`163499 +dList`1`x`(Type)->Join(ListAggregate(S),etc)`(S)`LIST`163751 +dListMonoidOps`3`n`(SetCategory,E:AbelianMonoid,E)->Join(SetCategory,etc)`(S,E,un)`LMOPS`164036 +dListMultiDictionary`1`n`(SetCategory)->Join(MultiDictionary(S),etc)`(S)`LMDICT`164207 +dLocalAlgebra`3`n`(Algebra(R),R:CommutativeRing,S:SubsetCategory(Monoid,R))->Join(Algebra(R),etc)`(A,R,S)`LA`164594 +dLocalize`3`n`(Module(R),R:CommutativeRing,S:SubsetCategory(Monoid,R))->Join(Module(R),etc)`(M,R,S)`LO`164734 +dLyndonWord`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`LWORD`164920 +dMachineComplex`0`x`()->Join(FortranMachineTypeCategory,etc)``MCMPLX`165754 +dMachineFloat`0`x`()->Join(FloatingPointSystem,etc)``MFLOAT`165856 +dMachineInteger`0`x`()->Join(FortranMachineTypeCategory,etc)``MINT`165958 +dMagma`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`MAGMA`166053 +dMakeCachableSet`1`n`(SetCategory)->Join(CachableSet,etc)`(S)`MKCHSET`166194 +dMapping`1`x`special`(T,S)`MAPPING`166286 +dMathMLFormat`0`x`()->Join(SetCategory,etc)``MMLFORM`166525 +dMatrix`1`x`(Ring)->Join(MatrixCategory(R,Vector(R),Vector(R)),etc)`(R)`MATRIX`166692 +dModMonic`2`n`(R:Ring,Rep:UnivariatePolynomialCategory(R))->Join(UnivariatePolynomialCategory(R),etc)`(R,Rep)`MODMON`166793 +dModularField`5`n`(R:CommutativeRing,Mod:AbelianMonoid,(R,Mod)->R,(Mod,Mod)->Union(Mod,"failed"),(R,R,Mod)->Union(R,"failed"))->Join(Field,etc)`(R,Mod,reduction,merge,exactQuo)`MODFIELD`166836 +dModularRing`5`n`(R:CommutativeRing,Mod:AbelianMonoid,(R,Mod)->R,(Mod,Mod)->Union(Mod,"failed"),(R,R,Mod)->Union(R,"failed"))->Join(Ring,etc)`(R,Mod,reduction,merge,exactQuo)`MODRING`167044 +dModuleMonomial`3`n`(IS:OrderedSet,E:SetCategory,(Record(index:IS,exponent:E),Record(index:IS,exponent:E))->Boolean)->Join(OrderedSet,etc)`(IS,E,ff)`MODMONOM`167253 +dModuleOperator`2`x`(R:Ring,M:LeftModule(R))->Join(Ring,etc)`(R,M)`MODOP`167293 +dMoebiusTransform`1`n`(Field)->Join(Group,etc)`(F)`MOEBIUS`167342 +dMonoidRing`2`n`(Ring,M:Monoid)->Join(Ring,etc)`(R,M)`MRING`167515 +dMultiset`1`x`(SetCategory)->Join(MultisetAggregate(S),etc)`(S)`MSET`168492 +dMultivariatePolynomial`2`x`(List(Symbol),R:Ring)->PolynomialCategory(R,IndexedExponents(OrderedVariableList(vl)),OrderedVariableList(vl))`(vl,R)`MPOLY`168539 +dMyExpression`2`x`(Symbol,R:Join(Ring,etc))->Join(FunctionSpace(R),etc)`(q,R)`MYEXPR`168847 +dMyUnivariatePolynomial`2`x`(Symbol,R:Ring)->Join(UnivariatePolynomialCategory(R),etc)`(x,R)`MYUP`168884 +dNeitherSparseOrDensePowerSeries`1`x`(Field)->Join(LocalPowerSeriesCategory(K),etc)`(K)`NSDPS`168921 +dNewSparseMultivariatePolynomial`2`n`(Ring,VarSet:OrderedSet)->Join(RecursivePolynomialCategory(R,IndexedExponents(VarSet),VarSet),etc)`(R,VarSet)`NSMP`168967 +dNewSparseUnivariatePolynomial`1`n`(Ring)->Join(UnivariatePolynomialCategory(R),etc)`(R)`NSUP`169230 +dNone`0`n`()->SetCategory``NONE`169419 +dNonNegativeInteger`0`x`()->Join(OrderedAbelianMonoidSup,etc)``NNI`169636 +dNottinghamGroup`1`x`(FiniteFieldCategory)->Join(Group,etc)`(F)`NOTTING`169718 +dNumericalIntegrationProblem`0`x`()->Join(SetCategory,etc)``NIPROB`169775 +dNumericalODEProblem`0`x`()->Join(SetCategory,etc)``ODEPROB`170612 +dNumericalOptimizationProblem`0`x`()->Join(SetCategory,etc)``OPTPROB`171187 +dNumericalPDEProblem`0`x`()->Join(SetCategory,etc)``PDEPROB`172038 +dOctonion`1`x`(CommutativeRing)->Join(OctonionCategory(R),etc)`(R)`OCT`172838 +dODEIntensityFunctionsTable`0`x`()->etc``ODEIFTBL`173355 +dOneDimensionalArray`1`x`(Type)->Join(OneDimensionalArrayAggregate(S),etc)`(S)`ARRAY1`173501 +dOnePointCompletion`1`x`(SetCategory)->Join(SetCategory,etc)`(R)`ONECOMP`173560 +dOpenMathConnection`0`x`()->etc``OMCONN`173635 +dOpenMathDevice`0`x`()->etc``OMDEV`173772 +dOpenMathEncoding`0`x`()->Join(SetCategory,etc)``OMENC`173964 +dOpenMathError`0`x`()->Join(SetCategory,etc)``OMERR`174038 +dOpenMathErrorKind`0`x`()->Join(SetCategory,etc)``OMERRK`174103 +dOperator`1`n`(Ring)->Join(Ring,etc)`(R)`OP`174269 +dOppositeMonogenicLinearOperator`2`n`(MonogenicLinearOperator(R),R:Ring)->Join(MonogenicLinearOperator(R),etc)`(P,R)`OMLO`174318 +dOrderedCompletion`1`x`(SetCategory)->Join(SetCategory,etc)`(R)`ORDCOMP`174556 +dOrderedDirectProduct`3`n`(NonNegativeInteger,S:OrderedAbelianMonoidSup,(Vector(S),Vector(S))->Boolean)->DirectProductCategory(dim,S)`(dim,S,f)`ODP`174650 +dOrderedFreeMonoid`1`n`(OrderedSet)->Join(OrderedMonoid,etc)`(S)`OFMONOID`174966 +dOrderedVariableList`1`n`(List(Symbol))->Join(OrderedFinite,etc)`(VariableList)`OVAR`175574 +dOrderlyDifferentialPolynomial`1`n`(Ring)->Join(DifferentialPolynomialCategory(R,Symbol,OrderlyDifferentialVariable(Symbol),IndexedExponents(OrderlyDifferentialVariable(Symbol))),etc)`(R)`ODPOL`175621 +dOrderlyDifferentialVariable`1`n`(OrderedSet)->DifferentialVariableCategory(S)`(S)`ODVAR`175916 +dOrdinaryDifferentialRing`3`x`(Kernels:SetCategory,R:PartialDifferentialRing(Kernels),Kernels)->Join(BiModule(_$,_$),etc)`(Kernels,R,var)`ODR`176604 +dOrdinaryWeightedPolynomials`4`n`(Ring,List(Symbol),List(NonNegativeInteger),NonNegativeInteger)->Join(Ring,etc)`(R,vl,wl,wtlevel)`OWP`176725 +dOrdSetInts`0`x`()->Join(OrderedSet,etc)``OSI`176953 +dOutputForm`0`n`()->Join(SetCategory,etc)``OUTFORM`177133 +dPAdicInteger`1`n`(Integer)->PAdicIntegerCategory(p)`(p)`PADIC`177395 +dPAdicRational`1`n`(Integer)->Join(QuotientFieldCategory(PAdicInteger(p)),etc)`(p)`PADICRAT`177587 +dPAdicRationalConstructor`2`n`(p:Integer,PADIC:PAdicIntegerCategory(p))->Join(QuotientFieldCategory(PADIC),etc)`(p,PADIC)`PADICRC`177769 +dPalette`0`x`()->Join(SetCategory,etc)``PALETTE`177842 +dParametricPlaneCurve`1`x`(Type)->etc`(ComponentFunction)`PARPCURV`177910 +dParametricSpaceCurve`1`x`(Type)->etc`(ComponentFunction)`PARSCURV`178003 +dParametricSurface`1`x`(Type)->etc`(ComponentFunction)`PARSURF`178094 +dPartialFraction`1`x`(EuclideanDomain)->Join(Field,etc)`(R)`PFR`178178 +dPartition`0`n`()->Join(OrderedCancellationAbelianMonoid,etc)``PRTITION`178971 +dPattern`1`n`(SetCategory)->Join(SetCategory,etc)`(R)`PATTERN`179246 +dPatternMatchListResult`3`n`(SetCategory,S:SetCategory,L:ListAggregate(S))->Join(SetCategory,etc)`(R,S,L)`PATLRES`179293 +dPatternMatchResult`2`n`(SetCategory,S:SetCategory)->Join(SetCategory,etc)`(R,S)`PATRES`179529 +dPendantTree`1`x`(SetCategory)->Join(BinaryRecursiveAggregate(S),etc)`(S)`PENDTREE`179750 +dPermutation`1`x`(SetCategory)->Join(PermutationCategory(S),etc)`(S)`PERM`179787 +dPermutationGroup`1`x`(SetCategory)->Join(SetCategory,etc)`(S)`PERMGRP`180245 +dPi`0`x`()->Join(Field,etc)``HACKPI`180714 +dPlaces`1`x`(Field)->PlacesCategory(K,NeitherSparseOrDensePowerSeries(K))`(K)`PLACES`180926 +dPlacesOverPseudoAlgebraicClosureOfFiniteField`1`x`(FiniteFieldCategory)->PlacesCategory(PseudoAlgebraicClosureOfFiniteField(K),NeitherSparseOrDensePowerSeries(PseudoAlgebraicClosureOfFiniteField(K)))`(K)`PLACESPS`180974 +dPlaneAlgebraicCurvePlot`0`n`()->Join(PlottablePlaneCurveCategory,etc)``ACPLOT`181022 +dPlcs`2`x`(K:Field,PCS:LocalPowerSeriesCategory(K))->PlacesCategory(K,PCS)`(K,PCS)`PLCS`181105 +dPlot`0`n`()->Join(PlottablePlaneCurveCategory,etc)``PLOT`181153 +dPlot3D`0`n`()->Join(PlottableSpaceCurveCategory,etc)``PLOT3D`181518 +dPoincareBirkhoffWittLyndonBasis`1`n`(OrderedSet)->Join(OrderedSet,etc)`(VarSet)`PBWLB`181854 +dPoint`1`n`(Ring)->PointCategory(R)`(R)`POINT`182131 +dPolynomial`1`x`(Ring)->Join(PolynomialCategory(R,IndexedExponents(Symbol),Symbol),etc)`(R)`POLY`182187 +dPolynomialIdeals`4`x`(F:Field,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,DPoly:PolynomialCategory(F,Expon,VarSet))->Join(SetCategory,etc)`(F,Expon,VarSet,DPoly)`IDEAL`182462 +dPolynomialRing`2`n`(Ring,E:OrderedAbelianMonoid)->Join(FiniteAbelianMonoidRing(R,E),etc)`(R,E)`PR`182970 +dPositiveInteger`0`x`()->Join(AbelianSemiGroup,etc)``PI`183334 +dPrimeField`1`x`(PositiveInteger)->Join(FiniteFieldCategory,etc)`(p)`PF`183409 +dPrimitiveArray`1`n`(Type)->OneDimensionalArrayAggregate(S)`(S)`PRIMARR`183511 +dProduct`2`n`(SetCategory,B:SetCategory)->Join(SetCategory,etc)`(A,B)`PRODUCT`183642 +dProjectivePlane`1`x`(Field)->ProjectiveSpaceCategory(K)`(K)`PROJPL`183689 +dProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField`1`x`(FiniteFieldCategory)->ProjectiveSpaceCategory(PseudoAlgebraicClosureOfFiniteField(K))`(K)`PROJPLPS`183760 +dProjectiveSpace`2`x`(NonNegativeInteger,K:Field)->ProjectiveSpaceCategory(K)`(dim,K)`PROJSP`183831 +dPseudoAlgebraicClosureOfAlgExtOfRationalNumber`1`x`(PseudoAlgebraicClosureOfRationalNumber)->Join(PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory,etc)`(downLevel)`PACEXT`183902 +dPseudoAlgebraicClosureOfFiniteField`1`x`(FiniteFieldCategory)->Join(PseudoAlgebraicClosureOfFiniteFieldCategory,etc)`(K)`PACOFF`184927 +dPseudoAlgebraicClosureOfRationalNumber`0`x`()->Join(PseudoAlgebraicClosureOfRationalNumberCategory,etc)``PACRAT`185948 +dQuadraticForm`2`x`(PositiveInteger,K:Field)->Join(AbelianGroup,etc)`(n,K)`QFORM`186970 +dQuasiAlgebraicSet`4`n`(R:GcdDomain,Var:OrderedSet,Expon:OrderedAbelianMonoidSup,Dpoly:PolynomialCategory(R,Expon,Var))->Join(SetCategory,etc)`(R,Var,Expon,Dpoly)`QALGSET`187033 +dQuaternion`1`x`(CommutativeRing)->QuaternionCategory(R)`(R)`QUAT`188752 +dQueryEquation`0`x`()->Join(CoercibleTo(OutputForm),etc)``QEQUAT`189013 +dQueue`1`x`(SetCategory)->Join(QueueAggregate(S),etc)`(S)`QUEUE`189066 +dRadicalFunctionField`5`n`(F:UniqueFactorizationDomain,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),Fraction(UP),NonNegativeInteger)->FunctionFieldCategory(F,UP,UPUP)`(F,UP,UPUP,radicnd,n)`RADFF`189110 +dRadixExpansion`1`x`(Integer)->Join(QuotientFieldCategory(Integer),etc)`(bb)`RADIX`189169 +dRealClosure`1`x`(Join(OrderedRing,etc))->Join(RealClosedField,etc)`(TheField)`RECLOS`189314 +dRecord`1`x`special`(a:A,b:B,...,c:C)`RECORD`189381 +dRectangularMatrix`3`n`(NonNegativeInteger,n:NonNegativeInteger,R:Ring)->Join(RectangularMatrixCategory(m,n,R,DirectProduct(n,R),DirectProduct(m,R)),etc)`(m,n,R)`RMATRIX`189617 +dReference`1`n`(Type)->Join(Type,etc)`(S)`REF`189752 +dRegularChain`2`x`(GcdDomain,ls:List(Symbol))->Join(RegularTriangularSetCategory(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),etc)`(R,ls)`RGCHAIN`189829 +dRegularTriangularSet`4`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(RegularTriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`REGSET`190051 +dResidueRing`5`n`(F:Field,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,FPol:PolynomialCategory(F,Expon,VarSet),List(FPol))->Join(CommutativeRing,etc)`(F,Expon,VarSet,FPol,LFPol)`RESRING`190253 +dResult`0`x`()->Join(TableAggregate(Symbol,Any),etc)``RESULT`190455 +dRewriteRule`3`x`(Base:SetCategory,R:Join(Ring,etc),F:Join(FunctionSpace(R),etc))->Join(SetCategory,etc)`(Base,R,F)`RULE`190651 +dRightOpenIntervalRootCharacterization`2`x`(TheField:Join(OrderedRing,etc),ThePolDom:UnivariatePolynomialCategory(TheField))->Join(RealRootCharacterizationCategory(TheField,ThePolDom),etc)`(TheField,ThePolDom)`ROIRC`190687 +dRomanNumeral`0`x`()->Join(IntegerNumberSystem,etc)``ROMAN`190784 +dRoutinesTable`0`x`()->Join(TableAggregate(Symbol,Any),etc)``ROUTINE`190876 +dRuleCalled`1`n`(Symbol)->Join(SetCategory,etc)`(f)`RULECOLD`190995 +dRuleset`3`x`(Base:SetCategory,R:Join(Ring,etc),F:Join(FunctionSpace(R),etc))->Join(SetCategory,etc)`(Base,R,F)`RULESET`191036 +dScriptFormulaFormat`0`x`()->Join(SetCategory,etc)``FORMULA`191144 +dSegment`1`x`(Type)->Join(SegmentCategory(S),etc)`(S)`SEG`191845 +dSegmentBinding`1`x`(Type)->Join(Type,etc)`(S)`SEGBIND`191918 +dSequentialDifferentialPolynomial`1`n`(Ring)->Join(DifferentialPolynomialCategory(R,Symbol,SequentialDifferentialVariable(Symbol),IndexedExponents(SequentialDifferentialVariable(Symbol))),etc)`(R)`SDPOL`192073 +dSequentialDifferentialVariable`1`n`(OrderedSet)->DifferentialVariableCategory(S)`(S)`SDVAR`192319 +dSet`1`x`(SetCategory)->FiniteSetAggregate(S)`(S)`SET`192994 +dSetOfMIntegersInOneToN`2`n`(PositiveInteger,PositiveInteger)->Join(Finite,etc)`(m,n)`SETMN`194105 +dSExpression`0`n`()->SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm)``SEX`194219 +dSExpressionOf`5`n`(SetCategory,Sym:SetCategory,Int:SetCategory,Flt:SetCategory,Expr:SetCategory)->SExpressionCategory(Str,Sym,Int,Flt,Expr)`(Str,Sym,Int,Flt,Expr)`SEXOF`194287 +dSimpleAlgebraicExtension`3`n`(R:CommutativeRing,UP:UnivariatePolynomialCategory(R),UP)->MonogenicAlgebra(R,UP)`(R,UP,M)`SAE`194373 +dSimpleFortranProgram`2`x`(R:OrderedSet,FS:FunctionSpace(R))->Join(FortranProgramCategory,etc)`(R,FS)`SFORT`195006 +dSingleInteger`0`x`()->Join(IntegerNumberSystem,etc)``SINT`195278 +dSingletonAsOrderedSet`0`n`()->Join(OrderedSet,etc)``SAOS`195349 +dSparseMultivariatePolynomial`2`n`(Ring,VarSet:OrderedSet)->PolynomialCategory(R,IndexedExponents(VarSet),VarSet)`(R,VarSet)`SMP`195437 +dSparseMultivariateTaylorSeries`3`n`(Coef:Ring,Var:OrderedSet,SMP:PolynomialCategory(Coef,IndexedExponents(Var),Var))->Join(MultivariateTaylorSeriesCategory(Coef,Var),etc)`(Coef,Var,SMP)`SMTS`195771 +dSparseTable`3`n`(SetCategory,Ent:SetCategory,Ent)->TableAggregate(Key,Ent)`(Key,Ent,dent)`STBL`196063 +dSparseUnivariateLaurentSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariateLaurentSeriesConstructorCategory(Coef,SparseUnivariateTaylorSeries(Coef,var,cen)),etc)`(Coef,var,cen)`SULS`196181 +dSparseUnivariatePolynomial`1`n`(Ring)->Join(UnivariatePolynomialCategory(R),etc)`(R)`SUP`196645 +dSparseUnivariatePolynomialExpressions`1`x`(Ring)->Join(UnivariatePolynomialCategory(R),etc)`(R)`SUPEXPR`197114 +dSparseUnivariatePuiseuxSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,SparseUnivariateLaurentSeries(Coef,var,cen)),etc)`(Coef,var,cen)`SUPXS`197151 +dSparseUnivariateSkewPolynomial`3`n`(R:Ring,Automorphism(R),(R)->R)->Join(UnivariateSkewPolynomialCategory(R),etc)`(R,sigma,delta)`ORESUP`197626 +dSparseUnivariateTaylorSeries`3`n`(Coef:Ring,var:Symbol,Coef)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef,var,cen)`SUTS`197788 +dSplitHomogeneousDirectProduct`3`n`(NonNegativeInteger,NonNegativeInteger,S:OrderedAbelianMonoidSup)->DirectProductCategory(dimtot,S)`(dimtot,dim1,S)`SHDP`198269 +dSplittingNode`2`n`(Join(SetCategory,etc),C:Join(SetCategory,etc))->Join(SetCategory,etc)`(V,C)`SPLNODE`198729 +dSplittingTree`2`n`(Join(SetCategory,etc),C:Join(SetCategory,etc))->Join(RecursiveAggregate(SplittingNode(V,C)),etc)`(V,C)`SPLTREE`199352 +dSquareFreeRegularTriangularSet`4`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(SquareFreeRegularTriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`SREGSET`200394 +dSquareMatrix`2`n`(NonNegativeInteger,R:Ring)->Join(SquareMatrixCategory(ndim,R,DirectProduct(ndim,R),DirectProduct(ndim,R)),etc)`(ndim,R)`SQMATRIX`200608 +dStack`1`x`(SetCategory)->Join(StackAggregate(S),etc)`(S)`STACK`200754 +dStream`1`x`(Type)->Join(LazyStreamAggregate(S),etc)`(S)`STREAM`200798 +dString`0`x`()->StringCategory``STRING`200968 +dStringTable`1`n`(SetCategory)->Join(TableAggregate(String,Entry),etc)`(Entry)`STRTBL`201036 +dSubSpace`2`n`(PositiveInteger,R:Ring)->Join(SetCategory,etc)`(n,R)`SUBSPACE`201147 +dSubSpaceComponentProperty`0`n`()->Join(SetCategory,etc)``COMPPROP`201183 +dSuchThat`2`n`(SetCategory,S2:SetCategory)->Join(SetCategory,etc)`(S1,S2)`SUCH`201249 +dSwitch`0`x`()->Join(CoercibleTo(OutputForm),etc)``SWITCH`201296 +dSymbol`0`x`()->Join(OrderedSet,etc)``SYMBOL`201409 +dSymbolTable`0`x`()->Join(CoercibleTo(OutputForm),etc)``SYMTAB`201443 +dSymmetricPolynomial`1`n`(Ring)->Join(FiniteAbelianMonoidRing(R,Partition),etc)`(R)`SYMPOLY`201513 +dTable`2`n`(SetCategory,Entry:SetCategory)->Join(TableAggregate(Key,Entry),etc)`(Key,Entry)`TABLE`201563 +dTableau`1`x`(SetCategory)->etc`(S)`TABLEAU`201787 +dTaylorSeries`1`x`(Ring)->Join(MultivariateTaylorSeriesCategory(Coef,Symbol),etc)`(Coef)`TS`201916 +dTexFormat`0`x`()->Join(SetCategory,etc)``TEX`202047 +dTextFile`0`x`()->Join(FileCategory(FileName,String),etc)``TEXTFILE`202799 +dTheSymbolTable`0`x`()->Join(CoercibleTo(OutputForm),etc)``SYMS`202937 +dThreeDimensionalMatrix`1`x`(SetCategory)->Join(HomogeneousAggregate(R),etc)`(R)`M3D`203087 +dThreeDimensionalViewport`0`x`()->Join(SetCategory,etc)``VIEW3D`203170 +dThreeSpace`1`x`(Ring)->ThreeSpaceCategory(R)`(R)`SPACE3`203237 +dTree`1`x`(SetCategory)->Join(RecursiveAggregate(S),etc)`(S)`TREE`203419 +dTubePlot`1`n`(PlottableSpaceCurveCategory)->etc`(Curve)`TUBE`203575 +dTuple`1`n`(Type)->Join(CoercibleTo(PrimitiveArray(S)),etc)`(S)`TUPLE`203708 +dTwoDimensionalArray`1`n`(Type)->Join(TwoDimensionalArrayCategory(R,OneDimensionalArray(R),OneDimensionalArray(R)),etc)`(R)`ARRAY2`203824 +dTwoDimensionalViewport`0`n`()->Join(SetCategory,etc)``VIEW2D`203928 +dUnion`1`x`special`(A,B,...,C)`UNION`203994 +dUnivariateFormalPowerSeries`1`x`(Ring)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef)`UFPS`204142 +dUnivariateLaurentSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariateLaurentSeriesConstructorCategory(Coef,UnivariateTaylorSeries(Coef,var,cen)),etc)`(Coef,var,cen)`ULS`204179 +dUnivariateLaurentSeriesConstructor`2`n`(Coef:Ring,UTS:UnivariateTaylorSeriesCategory(Coef))->UnivariateLaurentSeriesConstructorCategory(Coef,UTS)`(Coef,UTS)`ULSCONS`204630 +dUnivariatePolynomial`2`x`(Symbol,R:Ring)->Join(UnivariatePolynomialCategory(R),etc)`(x,R)`UP`204957 +dUnivariatePuiseuxSeries`3`n`(Coef:Ring,var:Symbol,cen:Coef)->Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,UnivariateLaurentSeries(Coef,var,cen)),etc)`(Coef,var,cen)`UPXS`205263 +dUnivariatePuiseuxSeriesConstructor`2`n`(Coef:Ring,ULS:UnivariateLaurentSeriesCategory(Coef))->UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)`(Coef,ULS)`UPXSCONS`205725 +dUnivariatePuiseuxSeriesWithExponentialSingularity`4`n`(R:Join(OrderedSet,etc),FE:Join(AlgebraicallyClosedField,etc),var:Symbol,cen:FE)->Join(FiniteAbelianMonoidRing(UnivariatePuiseuxSeries(FE,var,cen),ExponentialOfUnivariatePuiseuxSeries(FE,var,cen)),etc)`(R,FE,var,cen)`UPXSSING`206055 +dUnivariateSkewPolynomial`4`n`(Symbol,R:Ring,Automorphism(R),(R)->R)->Join(UnivariateSkewPolynomialCategory(R),etc)`(x,R,sigma,delta)`OREUP`206584 +dUnivariateTaylorSeries`3`n`(Coef:Ring,var:Symbol,Coef)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef,var,cen)`UTS`206759 +dUnivariateTaylorSeriesCZero`2`x`(Ring,var:Symbol)->Join(UnivariateTaylorSeriesCategory(Coef),etc)`(Coef,var)`UTSZ`207227 +dUniversalSegment`1`x`(Type)->Join(SegmentCategory(S),etc)`(S)`UNISEG`207304 +dVariable`1`n`(Symbol)->Join(SetCategory,etc)`(sym)`VARIABLE`207421 +dVector`1`x`(Type)->Join(VectorCategory(R),etc)`(R)`VECTOR`207460 +dVoid`0`x`()->etc``VOID`207587 +dWeightedPolynomials`7`n`(R:Ring,VarSet:OrderedSet,E:OrderedAbelianMonoidSup,P:PolynomialCategory(R,E,VarSet),List(VarSet),List(NonNegativeInteger),NonNegativeInteger)->Join(Ring,etc)`(R,VarSet,E,P,vl,wl,wtlevel)`WP`207811 +dWuWenTsunTriangularSet`4`x`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->Join(TriangularSetCategory(R,E,V,P),etc)`(R,E,V,P)`WUTSET`208073 +dXDistributedPolynomial`2`n`(OrderedSet,R:Ring)->Join(FreeModuleCat(R,OrderedFreeMonoid(vl)),etc)`(vl,R)`XDPOLY`208737 +dXPBWPolynomial`2`n`(OrderedSet,R:CommutativeRing)->Join(XPolynomialsCat(VarSet,R),etc)`(VarSet,R)`XPBWPOLY`208927 +dXPolynomial`1`n`(Ring)->Join(XPolynomialsCat(Symbol,R),etc)`(R)`XPOLY`209153 +dXPolynomialRing`2`n`(Ring,E:OrderedMonoid)->Join(Ring,etc)`(R,E)`XPR`209406 +dXRecursivePolynomial`2`n`(OrderedSet,R:Ring)->Join(XPolynomialsCat(VarSet,R),etc)`(VarSet,R)`XRPOLY`209707 +o0`0`n`()->_$`dInputForm``0 +o0`0`n`()->_$`dPattern(R)``0 +o0`0`n`()->S`xGradedAlgebra&(S,R,E)``0 +o0`0`x`()->_$`cAbelianMonoid``0 +o0`0`x`()->_$`cGradedModule(R,E)``0 +o1`0`n`()->_$`dInputForm``0 +o1`0`n`()->_$`dPattern(R)``0 +o1`0`n`()->_$`dPoincareBirkhoffWittLyndonBasis(VarSet)``0 +o1`0`n`()->S`xGradedAlgebra&(S,R,E)``0 +o1`0`x`()->_$`cGradedAlgebra(R,E)``0 +o1`0`x`()->_$`cMonadWithUnit``0 +o1`0`x`()->_$`cMonoid``0 o#`1`n`(A)->NonNegativeInteger`xBinaryRecursiveAggregate&(A,S)``0 o#`1`n`(A)->NonNegativeInteger`xBinaryTreeCategory&(A,S)``0 o#`1`n`(A)->NonNegativeInteger`xCollection&(A,S)``0 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-oD`2`n`(A,S)->A`xPartialDifferentialRing&(A,S)``0 -oD`2`n`(S,(R)->R)->S`xDifferentialExtension&(S,R)``0 -oD`2`n`(S,List(Symbol))->S`xDifferentialExtension&(S,R)``0 -oD`2`n`(S,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 -oD`2`n`(S,NonNegativeInteger)->S`xDifferentialRing&(S)``0 -oD`2`n`(S,Symbol)->S`xDifferentialExtension&(S,R)``0 -oD`2`x`(_$,(R)->R)->_$`cDifferentialExtension(R)``163549 -oD`2`x`(_$,List(S))->_$`cPartialDifferentialRing(S)``163644 -oD`2`x`(_$,NonNegativeInteger)->_$`cDifferentialRing``163772 -oD`2`x`(_$,NonNegativeInteger)->_$`dFullPartialFractionExpansion(F,UP)``163843 -oD`2`x`(_$,S)->_$`cPartialDifferentialRing(S)``163914 -oD`3`n`(A,List(S),List(NonNegativeInteger))->A`xPartialDifferentialRing&(A,S)``0 -oD`3`n`(A,S,NonNegativeInteger)->A`xPartialDifferentialRing&(A,S)``0 -oD`3`n`(S,(R)->R,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 -oD`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xDifferentialExtension&(S,R)``0 -oD`3`n`(S,Symbol,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 -oD`3`x`(_$,(R)->R,NonNegativeInteger)->_$`cDifferentialExtension(R)``164006 -oD`3`x`(_$,List(S),List(NonNegativeInteger))->_$`cPartialDifferentialRing(S)``164135 -oD`3`x`(_$,S,NonNegativeInteger)->_$`cPartialDifferentialRing(S)``164296 -oEQ`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``164444 -oEi`1`n`(F)->F`pLiouvillianFunction(R,F)``164536 -oEi`1`x`(_$)->_$`cLiouvillianFunctionCategory``164595 -oF2FG`1`n`(F)->FG`pInnerTrigonometricManipulations(R,F,FG)``164723 -oFG2F`1`n`(FG)->F`pInnerTrigonometricManipulations(R,F,FG)``164781 -oF`2`n`(NonNegativeInteger,NonNegativeInteger)->()->Float`pRandomFloatDistributions``164839 -oFormatArabic`1`n`(PositiveInteger)->String`pNumberFormats``164875 -oFormatRoman`1`n`(PositiveInteger)->String`pNumberFormats``164961 -oFrobenius`1`n`(ExtP)->ExtP`pNormRetractPackage(F,ExtF,SUEx,ExtP,n)``165044 -oFrobenius`1`n`(S)->S`xExtensionField&(S,F)``0 -oFrobenius`1`x`(_$)->_$`cExtensionField(F)`has(F,Finite)`165084 -oFrobenius`2`n`(S,NonNegativeInteger)->S`xExtensionField&(S,F)``0 -oFrobenius`2`x`(_$,NonNegativeInteger)->_$`cExtensionField(F)`has(F,Finite)`165172 -oGE`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``165267 -oGF2FG`1`n`(Complex(F))->FG`pInnerTrigonometricManipulations(R,F,FG)``165358 -oGT`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``165489 -oGamma`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``165579 -oGamma`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``165655 -oGamma`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``165817 -oGamma`1`x`(_$)->_$`cSpecialFunctionCategory``165979 -oGamma`1`x`(_$)->_$`dDoubleFloat``166030 -oGamma`2`n`(F,F)->F`pFunctionalSpecialFunction(R,F)``166081 -oGamma`2`x`(_$,_$)->_$`cSpecialFunctionCategory``166171 -oGospersMethod`3`n`(Q,V,()->V)->Union(Q,"failed")`pGosperSummationMethod(E,V,R,P,Q)``166231 -oHausdorff`3`n`(XPOLY,XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``166797 -oHenselLift`4`n`(TP,List(TP),RP,PositiveInteger)->Record(plist:List(TP),modulo:RP)`pGeneralHenselPackage(RP,TP)``166917 -oHermiteIntegrate`2`n`(Fraction(UP),(UP)->UP)->Record(answer:Fraction(UP),logpart:Fraction(UP),specpart:Fraction(UP),polypart:UP)`pTranscendentalHermiteIntegration(F,UP)``167128 -oHermiteIntegrate`2`n`(R,(UP)->UP)->Record(answer:R,logpart:R)`pAlgebraicHermiteIntegration(F,UP,UPUP,R)``167560 -oIs`2`x`(List(Subject),Pat)->PatternMatchListResult(Base,Subject,List(Subject))`pPatternMatch(Base,Subject,Pat)``167701 -oIs`2`x`(Subject,Pat)->List(Equation(Polynomial(Subject)))`pPatternMatch(Base,Subject,Pat)`AND(has(Subject,Ring),not(has(Subject,RetractableTo(Symbol))))`167839 -oIs`2`x`(Subject,Pat)->List(Equation(Subject))`pPatternMatch(Base,Subject,Pat)`has(Subject,RetractableTo(Symbol))`168092 -oIs`2`x`(Subject,Pat)->PatternMatchResult(Base,Subject)`pPatternMatch(Base,Subject,Pat)`AND(not(has(Subject,RetractableTo(Symbol))),not(has(Subject,Ring)))`168345 -oKrullNumber`2`x`(List(P),List(TS))->NonNegativeInteger`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oKrullNumber`2`x`(List(P),List(TS))->NonNegativeInteger`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oLE`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``168625 -oLODO2FUN`1`n`(L)->(List(UTS))->UTS`pUTSodetools(F,UP,L,UTS)``168716 -oLT`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``168831 -oLagrangeInterpolation`2`n`(List(F),List(F))->P`pPolynomialInterpolationAlgorithms(F,P)``168921 -oLazard2`4`n`(polR,R,R,NonNegativeInteger)->polR`pPseudoRemainderSequence(R,polR)``168979 -oLazardQuotient2`4`x`(_$,_$,_$,NonNegativeInteger)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`169109 -oLazardQuotient`3`x`(_$,_$,NonNegativeInteger)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`169299 -oLazard`3`n`(R,R,NonNegativeInteger)->R`pPseudoRemainderSequence(R,polR)``169446 -oLiePolyIfCan`1`n`(XDistributedPolynomial(VarSet,R))->Union(_$,"failed")`dLiePolynomial(VarSet,R)``169539 -oLiePolyIfCan`1`n`(_$)->Union(LiePolynomial(VarSet,R),"failed")`dXPBWPolynomial(VarSet,R)``169700 -oLiePoly`1`x`(LyndonWord(VarSet))->_$`cFreeLieAlgebra(VarSet,R)``169802 -oListOfTerms`1`n`(_$)->List(LyndonWord(VarSet))`dPoincareBirkhoffWittLyndonBasis(VarSet)``169902 -oListOfTerms`1`n`(_$)->List(Record(k:PoincareBirkhoffWittLyndonBasis(VarSet),c:R))`dLieExponentials(VarSet,R,Order)``170000 -oListOfTerms`1`x`(_$)->List(Record(k:Basis,c:R))`cFreeModuleCat(R,Basis)``170093 -oLowTriBddDenomInv`2`n`(M,R)->M`pTriangularMatrixOperations(R,Row,Col,M)``170279 -oLyndonBasis`1`n`(List(VarSet))->List(LiePolynomial(VarSet,R))`dLieExponentials(VarSet,R,Order)``170490 -oLyndonCoordinates`1`n`(_$)->List(Record(k:LyndonWord(VarSet),c:R))`dLieExponentials(VarSet,R,Order)``170587 -oLyndonWordsList1`2`n`(List(VarSet),PositiveInteger)->OneDimensionalArray(List(_$))`dLyndonWord(VarSet)``170686 -oLyndonWordsList`2`n`(List(VarSet),PositiveInteger)->List(_$)`dLyndonWord(VarSet)``170858 -oNOT`1`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``171013 -oNOT`1`x`(_$)->_$`dSwitch``171101 -oNot`1`n`(_$)->_$`dIndexedBits(mn)``171189 -oNot`1`x`(_$)->_$`dSingleInteger``171263 -oNul`1`n`(NonNegativeInteger)->_$`dExtAlgBasis``171356 -oODESolve`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Result`cOrdinaryDifferentialEquationsSolverCategory``171451 -oOMParseError?`1`x`(_$)->Boolean`dOpenMathErrorKind``171581 -oOMReadError?`1`x`(_$)->Boolean`dOpenMathErrorKind``171664 -oOMUnknownCD?`1`x`(_$)->Boolean`dOpenMathErrorKind``171743 -oOMUnknownSymbol?`1`x`(_$)->Boolean`dOpenMathErrorKind``171835 -oOMbindTCP`2`x`(_$,SingleInteger)->Boolean`dOpenMathConnection``171928 -oOMcloseConn`1`x`(_$)->Void`dOpenMathConnection``171951 -oOMclose`1`x`(_$)->Void`dOpenMathDevice``171976 -oOMconnInDevice`1`x`(_$)->OpenMathDevice`dOpenMathConnection``172061 -oOMconnOutDevice`1`x`(_$)->OpenMathDevice`dOpenMathConnection``172090 -oOMconnectTCP`3`x`(_$,String,SingleInteger)->Boolean`dOpenMathConnection``172120 -oOMencodingBinary`0`x`()->_$`dOpenMathEncoding``172146 -oOMencodingSGML`0`x`()->_$`dOpenMathEncoding``172228 -oOMencodingUnknown`0`x`()->_$`dOpenMathEncoding``172317 -oOMencodingXML`0`x`()->_$`dOpenMathEncoding``172512 -oOMgetApp`1`x`(_$)->Void`dOpenMathDevice``172595 -oOMgetAtp`1`x`(_$)->Void`dOpenMathDevice``172679 -oOMgetAttr`1`x`(_$)->Void`dOpenMathDevice``172766 -oOMgetBVar`1`x`(_$)->Void`dOpenMathDevice``172849 -oOMgetBind`1`x`(_$)->Void`dOpenMathDevice``172942 -oOMgetEndApp`1`x`(_$)->Void`dOpenMathDevice``173022 -oOMgetEndAtp`1`x`(_$)->Void`dOpenMathDevice``173108 -oOMgetEndAttr`1`x`(_$)->Void`dOpenMathDevice``173197 -oOMgetEndBVar`1`x`(_$)->Void`dOpenMathDevice``173282 -oOMgetEndBind`1`x`(_$)->Void`dOpenMathDevice``173377 -oOMgetEndError`1`x`(_$)->Void`dOpenMathDevice``173459 -oOMgetEndObject`1`x`(_$)->Void`dOpenMathDevice``173541 -oOMgetError`1`x`(_$)->Void`dOpenMathDevice``173625 -oOMgetFloat`1`x`(_$)->DoubleFloat`dOpenMathDevice``173705 -oOMgetInteger`1`x`(_$)->Integer`dOpenMathDevice``173773 -oOMgetObject`1`x`(_$)->Void`dOpenMathDevice``173846 -oOMgetString`1`x`(_$)->String`dOpenMathDevice``173928 -oOMgetSymbol`1`x`(_$)->Record(cd:String,name:String)`dOpenMathDevice``173998 -oOMgetType`1`x`(_$)->Symbol`dOpenMathDevice``174068 -oOMgetVariable`1`x`(_$)->Symbol`dOpenMathDevice``174155 -oOMlistCDs`0`x`()->List(String)`pOpenMathPackage``174229 -oOMlistSymbols`1`x`(String)->List(String)`pOpenMathPackage``174299 -oOMmakeConn`1`x`(SingleInteger)->_$`dOpenMathConnection``174374 -oOMopenFile`3`x`(String,String,OpenMathEncoding)->_$`dOpenMathDevice``174398 -oOMopenString`2`x`(String,OpenMathEncoding)->_$`dOpenMathDevice``174667 -oOMputApp`1`x`(_$)->Void`dOpenMathDevice``174802 -oOMputAtp`1`x`(_$)->Void`dOpenMathDevice``174885 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-oOMreadFile`1`x`(String)->Any`pOpenMathPackage``176482 -oOMreadStr`1`x`(String)->Any`pOpenMathPackage``176580 -oOMread`1`x`(OpenMathDevice)->Any`pOpenMathPackage``176677 -oOMreceive`1`x`(OpenMathConnection)->Any`pOpenMathServerPackage``176775 -oOMsend`2`x`(OpenMathConnection,Any)->Void`pOpenMathServerPackage``176901 -oOMserve`2`x`(SingleInteger,SingleInteger)->Void`pOpenMathServerPackage``176997 -oOMsetEncoding`2`x`(_$,OpenMathEncoding)->Void`dOpenMathDevice``177197 -oOMsupportsCD?`1`x`(String)->Boolean`pOpenMathPackage``177351 -oOMsupportsSymbol?`2`x`(String,String)->Boolean`pOpenMathPackage``177465 -oOMunhandledSymbol`2`x`(String,String)->Exit`pOpenMathPackage``177626 -oOMwrite`1`x`(Expression(R))->String`pExpressionToOpenMath(R)``0 -oOMwrite`1`x`(_$)->String`cOpenMath``177790 -oOMwrite`2`x`(Expression(R),Boolean)->String`pExpressionToOpenMath(R)``0 -oOMwrite`2`x`(OpenMathDevice,Expression(R))->Void`pExpressionToOpenMath(R)``0 -oOMwrite`2`x`(OpenMathDevice,_$)->Void`cOpenMath``177906 -oOMwrite`2`x`(_$,Boolean)->String`cOpenMath``178055 -oOMwrite`3`x`(OpenMathDevice,Expression(R),Boolean)->Void`pExpressionToOpenMath(R)``0 -oOMwrite`3`x`(OpenMathDevice,_$,Boolean)->Void`cOpenMath``178299 -oOR`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``178547 -oOr`2`n`(_$,_$)->_$`dIndexedBits(mn)``178640 -oOr`2`x`(_$,_$)->_$`dSingleInteger``178729 -oPDESolve`1`x`(Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat))->Result`cPartialDifferentialEquationsSolverCategory``178838 -oParCondList`2`n`(Matrix(GR),NonNegativeInteger)->List(Record(rank:NonNegativeInteger,eqns:List(Record(det:GR,rows:List(Integer),cols:List(Integer))),fgb:List(GR)))`pParametricLinearEquations(R,Var,Expon,GR)``178968 -oParCond`2`n`(Matrix(GR),NonNegativeInteger)->List(Record(det:GR,rows:List(Integer),cols:List(Integer)))`pParametricLinearEquations(R,Var,Expon,GR)``179147 -oPollardSmallFactor`1`n`(I)->Union(I,"failed")`pIntegerFactorizationPackage(I)``179259 -oRF2UTS`1`n`(Fraction(UP))->UTS`pUTSodetools(F,UP,L,UTS)`has(F,IntegralDomain)`179354 -oReduceOrder`2`n`(L,F)->L`pReductionOfOrder(F,L)``179415 -oReduceOrder`2`n`(L,List(F))->Record(eq:L,op:List(F))`pReductionOfOrder(F,L)``179620 -oRemainderList`1`n`(_$)->List(Record(k:Symbol,c:_$))`dXPolynomial(R)``0 -oRemainderList`1`n`(_$)->List(Record(k:VarSet,c:_$))`dXRecursivePolynomial(VarSet,R)``179916 -oRittWuCompare`2`n`(S,S)->Union(Boolean,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 -oRittWuCompare`2`x`(_$,_$)->Union(Boolean,"failed")`cRecursivePolynomialCategory(R,E,V)``180003 -oSEGMENT`1`n`(_$)->_$`dOutputForm``180263 -oSEGMENT`1`x`(S)->_$`dUniversalSegment(S)``180324 -oSEGMENT`2`n`(_$,_$)->_$`dOutputForm``180409 -oSEGMENT`2`x`(S,S)->_$`cSegmentCategory(S)``180474 -oSFunction`1`x`(List(Integer))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``180555 -oScanArabic`1`n`(String)->PositiveInteger`pNumberFormats``180715 -oScanFloatIgnoreSpacesIfCan`1`n`(String)->Union(Float,"failed")`pNumberFormats``180799 -oScanFloatIgnoreSpaces`1`n`(String)->Float`pNumberFormats``180926 -oScanRoman`1`n`(String)->PositiveInteger`pNumberFormats``181119 -oSi`1`n`(F)->F`pLiouvillianFunction(R,F)``181200 -oSi`1`x`(_$)->_$`cLiouvillianFunctionCategory``181252 -oSturmHabichtCoefficients`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->List(R)`pSturmHabichtPackage(R,x)``181375 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-oacot`1`n`(F)->F`pElementaryFunction(R,F)``186278 +oacosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``233683 +oacosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``233774 +oacosh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``233865 +oacosh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``233953 +oacosh`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``234043 +oacoshIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``234112 +oacosIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``234202 +oacot`1`n`(F)->F`pElementaryFunction(R,F)``234290 oacot`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oacot`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oacot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``186350 -oacot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``186423 -oacot`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``186496 -oacot`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``186571 -oacot`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``186648 -oacothIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``186708 -oacoth`1`n`(F)->F`pElementaryFunction(R,F)``186798 +oacot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``234362 +oacot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``234435 +oacot`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``234508 +oacot`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``234583 +oacot`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``234660 +oacoth`1`n`(F)->F`pElementaryFunction(R,F)``234720 oacoth`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oacoth`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oacoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``186882 -oacoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``186976 -oacoth`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``187070 -oacoth`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``187161 -oacoth`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``187254 -oacscIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``187326 -oacsc`1`n`(F)->F`pElementaryFunction(R,F)``187414 +oacoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``234804 +oacoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``234898 +oacoth`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``234992 +oacoth`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``235083 +oacoth`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``235176 +oacothIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``235248 +oacotIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``235338 +oacsc`1`n`(F)->F`pElementaryFunction(R,F)``235426 oacsc`1`n`(S)->S`xArcTrigonometricFunctionCategory&(S)``0 oacsc`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oacsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``187485 -oacsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``187557 -oacsc`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``187629 -oacsc`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``187703 -oacsc`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``187779 -oacschIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``187838 -oacsch`1`n`(F)->F`pElementaryFunction(R,F)``187928 +oacsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``235497 +oacsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``235569 +oacsc`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``235641 +oacsc`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``235715 +oacsc`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``235791 +oacsch`1`n`(F)->F`pElementaryFunction(R,F)``235850 oacsch`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oacsch`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oacsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``188011 -oacsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``188104 -oacsch`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``188197 -oacsch`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``188287 -oacsch`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``188379 -oadaptive3D?`0`n`()->Boolean`dPlot3D``188450 -oadaptive?`0`n`()->Boolean`dPlot``188525 -oadaptive`0`x`()->Boolean`pGraphicsDefaults``188597 -oadaptive`1`x`(Boolean)->Boolean`pGraphicsDefaults``188674 -oadaptive`1`x`(Boolean)->_$`dDrawOption``188782 -oadaptive`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``188962 -oaddBadValue`2`n`(Pattern(R),D)->Pattern(R)`pPatternFunctions1(R,D)``189171 -oaddBadValue`2`n`(_$,Any)->_$`dPattern(R)``189318 -oaddMatchRestricted`4`n`(Pattern(R),S,_$,S)->_$`dPatternMatchResult(R,S)``189471 -oaddMatch`3`n`(Pattern(R),S,_$)->_$`dPatternMatchResult(R,S)``189850 -oaddPoint2`2`n`(_$,Point(R))->_$`dSubSpace(n,R)``190092 -oaddPointLast`4`n`(_$,_$,Point(R),NonNegativeInteger)->_$`dSubSpace(n,R)``190271 -oaddPoint`2`n`(_$,Point(R))->NonNegativeInteger`dSubSpace(n,R)``190572 -oaddPoint`3`n`(_$,List(NonNegativeInteger),NonNegativeInteger)->_$`dSubSpace(n,R)``190733 -oaddPoint`3`n`(_$,List(NonNegativeInteger),Point(R))->_$`dSubSpace(n,R)``191524 -oaddiag`1`n`(Stream(Stream(A)))->Stream(A)`pStreamTaylorSeriesOperations(A)``192283 -oaddmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``192551 -oadjoint`1`n`(S)->S`xLinearOrdinaryDifferentialOperatorCategory&(S,A)``0 +oacsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``235933 +oacsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``236026 +oacsch`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``236119 +oacsch`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``236209 +oacsch`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``236301 +oacschIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``236372 +oacscIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``236462 +oactualExtensionV`1`x`(_$)->K`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +oaCubic`4`n`(F,F,F,F)->F`pPolynomialSolveByFormulas(UP,F)``236550 +oadaptive?`0`n`()->Boolean`dPlot``236599 +oadaptive`0`x`()->Boolean`pGraphicsDefaults``236671 +oadaptive`1`x`(Boolean)->Boolean`pGraphicsDefaults``236748 +oadaptive`1`x`(Boolean)->_$`dDrawOption``236856 +oadaptive`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``237036 +oadaptive3D?`0`n`()->Boolean`dPlot3D``237245 +oaddBadValue`2`n`(_$,Any)->_$`dPattern(R)``237320 +oaddBadValue`2`n`(Pattern(R),D)->Pattern(R)`pPatternFunctions1(R,D)``237473 +oaddiag`1`n`(Stream(Stream(A)))->Stream(A)`pStreamTaylorSeriesOperations(A)``237620 +oaddMatch`3`n`(Pattern(R),S,_$)->_$`dPatternMatchResult(R,S)``237887 +oaddMatchRestricted`4`n`(Pattern(R),S,_$,S)->_$`dPatternMatchResult(R,S)``238128 +oaddmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``238506 +oaddPoint2`2`n`(_$,Point(R))->_$`dSubSpace(n,R)``238587 +oaddPoint`2`n`(_$,Point(R))->NonNegativeInteger`dSubSpace(n,R)``238765 +oaddPoint`3`n`(_$,List(NonNegativeInteger),NonNegativeInteger)->_$`dSubSpace(n,R)``238925 +oaddPoint`3`n`(_$,List(NonNegativeInteger),Point(R))->_$`dSubSpace(n,R)``239714 +oaddPointLast`4`n`(_$,_$,Point(R),NonNegativeInteger)->_$`dSubSpace(n,R)``240471 oadjoint`1`n`(_$)->_$`dOperator(R)`has(R,CommutativeRing)`0 -oadjoint`1`x`(M)->Record(adjMat:M,detMat:R)`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`192633 -oadjoint`1`x`(_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)``192816 -oadjoint`1`x`(_$)->_$`dModuleOperator(R,M)`has(R,CommutativeRing)`192876 +oadjoint`1`n`(S)->S`xLinearOrdinaryDifferentialOperatorCategory&(S,A)``0 +oadjoint`1`x`(_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)``240771 +oadjoint`1`x`(_$)->_$`dModuleOperator(R,M)`has(R,CommutativeRing)`240830 +oadjoint`1`x`(M)->Record(adjMat:M,detMat:R)`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`240902 oadjoint`2`n`(_$,_$)->_$`dOperator(R)`has(R,CommutativeRing)`0 -oadjoint`2`x`(_$,_$)->_$`dModuleOperator(R,M)`has(R,CommutativeRing)`192949 -oairyAi`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``193068 -oairyAi`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``193140 -oairyAi`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``193317 -oairyAi`1`x`(_$)->_$`cSpecialFunctionCategory``193494 -oairyBi`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``193560 -oairyBi`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``193632 -oairyBi`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``193809 -oairyBi`1`x`(_$)->_$`cSpecialFunctionCategory``193986 -oalgDsolve`2`n`(LinearOrdinaryDifferentialOperator1(R),R)->Record(particular:Union(R,"failed"),basis:List(R))`pPureAlgebraicLODE(F,UP,UPUP,R)``194052 -oalgSplitSimple`2`n`(S,(UP)->UP)->Record(num:S,den:UP,derivden:UP,gd:UP)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -oalgSplitSimple`2`x`(_$,(UP)->UP)->Record(num:_$,den:UP,derivden:UP,gd:UP)`cFunctionFieldCategory(F,UP,UPUP)``194374 +oadjoint`2`x`(_$,_$)->_$`dModuleOperator(R,M)`has(R,CommutativeRing)`241084 +oadjunctionDivisor`0`x`()->DIVISOR`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``241202 +oadjunctionDivisor`0`x`()->Divisor(Places(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``241320 +oadjunctionDivisor`0`x`()->Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``241458 +oadjunctionDivisor`1`x`(DesTree)->DIVISOR`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``241585 +oaffineAlgSet`1`x`(List(PolyRing))->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithGroebnerBasis(K,symb,PolyRing,E,ProjPt)``0 +oaffineAlgSet`1`x`(List(PolyRing))->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +oaffineAlgSetLocal`1`x`(List(SparseUnivariatePolynomial(SparseUnivariatePolynomial(K))))->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +oaffinePoint`1`x`(List(K))->_$`cAffineSpaceCategory(K)``241716 +oaffineRationalPoints`2`x`(PolyRing,PositiveInteger)->List(ProjPt)`pAffineAlgebraicSetComputeWithGroebnerBasis(K,symb,PolyRing,E,ProjPt)``241776 +oaffineRationalPoints`2`x`(PolyRing,PositiveInteger)->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +oaffineSingularPoints`1`x`(PolyRing)->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithGroebnerBasis(K,symb,PolyRing,E,ProjPt)``0 +oaffineSingularPoints`1`x`(PolyRing)->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +oaffineSingularPoints`1`x`(SparseUnivariatePolynomial(SparseUnivariatePolynomial(K)))->Union(List(ProjPt),"failed","Infinite",Integer)`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +oairyAi`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``242050 +oairyAi`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``242121 +oairyAi`1`x`(_$)->_$`cSpecialFunctionCategory``242297 +oairyAi`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``242362 +oairyBi`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``242538 +oairyBi`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``242609 +oairyBi`1`x`(_$)->_$`cSpecialFunctionCategory``242785 +oairyBi`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``242850 +oAleph`1`x`(NonNegativeInteger)->_$`dCardinalNumber``243026 +oalgDsolve`2`n`(LinearOrdinaryDifferentialOperator1(R),R)->Record(particular:Union(R,"failed"),basis:List(R))`pPureAlgebraicLODE(F,UP,UPUP,R)``243141 oalgebraic?`1`n`(S)->Boolean`xExtensionField&(S,F)``0 oalgebraic?`1`n`(S)->Boolean`xFiniteAlgebraicExtensionField&(S,F)``0 -oalgebraic?`1`x`(_$)->Boolean`cExtensionField(F)``194696 +oalgebraic?`1`x`(_$)->Boolean`cExtensionField(F)``243462 oalgebraic?`2`n`(V,S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -oalgebraic?`2`x`(V,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``194814 +oalgebraic?`2`x`(V,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``243579 oalgebraicCoefficients?`2`n`(P,S)->Boolean`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -oalgebraicCoefficients?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``194965 +oalgebraicCoefficients?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``243729 oalgebraicDecompose`2`x`(P,TS)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 oalgebraicDecompose`3`x`(P,TS,Boolean)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oalgebraicOf`2`x`(RightOpenIntervalRootCharacterization(_$,SparseUnivariatePolynomial(_$)),OutputForm)->_$`dRealClosure(TheField)``195151 -oalgebraicSort`1`x`(List(TS))->List(TS)`pQuasiComponentPackage(R,E,V,P,TS)``195207 -oalgebraicSort`1`x`(List(TS))->List(TS)`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``195356 +oalgebraicOf`2`x`(RightOpenIntervalRootCharacterization(_$,SparseUnivariatePolynomial(_$)),OutputForm)->_$`dRealClosure(TheField)``243914 +oalgebraicSet`1`x`(List(PolyRing))->List(ProjPt)`pProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt)``243969 +oalgebraicSort`1`x`(List(TS))->List(TS)`pQuasiComponentPackage(R,E,V,P,TS)``244046 +oalgebraicSort`1`x`(List(TS))->List(TS)`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``244156 oalgebraicVariables`1`n`(S)->List(V)`xTriangularSetCategory&(S,R,E,V,P)``0 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+oallDegrees`1`x`(Boolean)->_$`dGuessOption``245078 +oallDegrees`1`x`(List(GuessOption))->Boolean`dGuessOptionFunctions0``245329 +oallPairsAmong`1`x`(List(SparseUnivariatePolynomial(SparseUnivariatePolynomial(K))))->List(List(SparseUnivariatePolynomial(SparseUnivariatePolynomial(K))))`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 oallRootsOf`1`n`(Polynomial(Fraction(Integer)))->List(S)`xRealClosedField&(S)``0 oallRootsOf`1`n`(Polynomial(Integer))->List(S)`xRealClosedField&(S)``0 oallRootsOf`1`n`(Polynomial(S))->List(S)`xRealClosedField&(S)``0 oallRootsOf`1`n`(SparseUnivariatePolynomial(Fraction(Integer)))->List(S)`xRealClosedField&(S)``0 oallRootsOf`1`n`(SparseUnivariatePolynomial(Integer))->List(S)`xRealClosedField&(S)``0 oallRootsOf`1`n`(SparseUnivariatePolynomial(S))->List(S)`xRealClosedField&(S)``0 -oallRootsOf`1`x`(Polynomial(Fraction(Integer)))->List(_$)`cRealClosedField``195929 -oallRootsOf`1`x`(Polynomial(Integer))->List(_$)`cRealClosedField``196018 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oany?`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->Boolean`xTableAggregate&(S,Key,Entry)``0 @@ -1454,430 +1343,435 @@ oany?`2`n`((S)->Boolean,A)->Boolean`xCollection&(A,S)``0 oany?`2`n`((S)->Boolean,A)->Boolean`xHomogeneousAggregate&(A,S)``0 oany?`2`n`((S)->Boolean,A)->Boolean`xLazyStreamAggregate&(A,S)``0 oany?`2`n`((S)->Boolean,A)->Boolean`xOneDimensionalArrayAggregate&(A,S)``0 -oany?`2`x`((S)->Boolean,_$)->Boolean`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`201387 -oany`2`x`(SExpression,None)->_$`dAny``201631 -oappendPoint`2`n`(_$,Point(DoubleFloat))->Void`dGraphImage``201823 -oappend`2`x`(_$,_$)->_$`dList(S)``202019 +oany?`2`x`((S)->Boolean,_$)->Boolean`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`251654 +oany?`2`x`((S)->Boolean,_$)->Boolean`dArrayStack(S)`has(_$,ATTRIBUTE(finiteAggregate))`251902 +oany?`2`x`((S)->Boolean,_$)->Boolean`dDequeue(S)`has(_$,ATTRIBUTE(finiteAggregate))`252022 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-oasech`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``209344 -oasech`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``209433 -oasech`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``209524 -oasimpson`8`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``209594 -oasinIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``210394 -oasin`1`n`(F)->F`pElementaryFunction(R,F)``210483 +oasech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``260635 +oasech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``260727 +oasech`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``260819 +oasech`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``260908 +oasech`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``260999 +oasechIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``261069 +oasecIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``261160 +oasimpson`8`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``261249 +oasin`1`n`(F)->F`pElementaryFunction(R,F)``262049 oasin`1`n`(S)->S`xComplexCategory&(S,R)``0 oasin`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oasin`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oasin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``210551 -oasin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``210620 -oasin`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``210689 -oasin`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``210760 -oasin`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``210833 -oasin`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``210889 -oasinhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``210958 -oasinh`1`n`(F)->F`pElementaryFunction(R,F)``211049 +oasin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``262117 +oasin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``262186 +oasin`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``262255 +oasin`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``262326 +oasin`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``262399 +oasin`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``262455 +oasinh`1`n`(F)->F`pElementaryFunction(R,F)``262524 oasinh`1`n`(S)->S`xComplexCategory&(S,R)``0 oasinh`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oasinh`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oasinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``211129 -oasinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``211219 -oasinh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``211309 -oasinh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``211396 -oasinh`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``211485 -oaspFilename`1`x`(String)->String`pNAGLinkSupportPackage``211553 -oassert`2`x`(F,String)->F`pFunctionSpaceAssertions(R,F)``211706 -oassert`2`x`(Symbol,String)->Expression(Integer)`pPatternMatchAssertions``211816 -oassert`2`x`(_$,String)->_$`dBasicOperator``211890 -oassign`2`n`(_$,_$)->_$`dOutputForm``212041 -oassign`2`x`(Symbol,Expression(Complex(Float)))->_$`dFortranCode``212118 -oassign`2`x`(Symbol,Expression(Float))->_$`dFortranCode``212202 -oassign`2`x`(Symbol,Expression(Integer))->_$`dFortranCode``212286 -oassign`2`x`(Symbol,Expression(MachineComplex))->_$`dFortranCode``212370 -oassign`2`x`(Symbol,Expression(MachineFloat))->_$`dFortranCode``212454 -oassign`2`x`(Symbol,Expression(MachineInteger))->_$`dFortranCode``212538 -oassign`2`x`(Symbol,Matrix(Expression(Complex(Float))))->_$`dFortranCode``212622 -oassign`2`x`(Symbol,Matrix(Expression(Float)))->_$`dFortranCode``212706 -oassign`2`x`(Symbol,Matrix(Expression(Integer)))->_$`dFortranCode``212790 -oassign`2`x`(Symbol,Matrix(Expression(MachineComplex)))->_$`dFortranCode``212874 -oassign`2`x`(Symbol,Matrix(Expression(MachineFloat)))->_$`dFortranCode``212958 -oassign`2`x`(Symbol,Matrix(Expression(MachineInteger)))->_$`dFortranCode``213042 -oassign`2`x`(Symbol,Matrix(MachineComplex))->_$`dFortranCode``213126 -oassign`2`x`(Symbol,Matrix(MachineFloat))->_$`dFortranCode``213210 -oassign`2`x`(Symbol,Matrix(MachineInteger))->_$`dFortranCode``213294 -oassign`2`x`(Symbol,String)->_$`dFortranCode``213378 -oassign`2`x`(Symbol,Vector(Expression(Complex(Float))))->_$`dFortranCode``213462 -oassign`2`x`(Symbol,Vector(Expression(Float)))->_$`dFortranCode``213546 -oassign`2`x`(Symbol,Vector(Expression(Integer)))->_$`dFortranCode``213630 -oassign`2`x`(Symbol,Vector(Expression(MachineComplex)))->_$`dFortranCode``213714 -oassign`2`x`(Symbol,Vector(Expression(MachineFloat)))->_$`dFortranCode``213798 -oassign`2`x`(Symbol,Vector(Expression(MachineInteger)))->_$`dFortranCode``213882 -oassign`2`x`(Symbol,Vector(MachineComplex))->_$`dFortranCode``213966 -oassign`2`x`(Symbol,Vector(MachineFloat))->_$`dFortranCode``214050 -oassign`2`x`(Symbol,Vector(MachineInteger))->_$`dFortranCode``214134 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Complex(Float)))->_$`dFortranCode``214218 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Float))->_$`dFortranCode``214390 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Integer))->_$`dFortranCode``214562 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineComplex))->_$`dFortranCode``214734 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineFloat))->_$`dFortranCode``214906 -oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineInteger))->_$`dFortranCode``215078 -oassoc`2`x`(Key,_$)->Union(Record(key:Key,entry:Entry),"failed")`cAssociationListAggregate(Key,Entry)``215250 -oassociatedEquations`2`n`(L,PositiveInteger)->Record(minor:List(PositiveInteger),eq:L,minors:List(List(PositiveInteger)),ops:List(L))`pAssociatedEquations(R,L)`has(R,Field)`215408 -oassociatedSystem`2`n`(L,PositiveInteger)->Record(mat:Matrix(R),vec:Vector(List(PositiveInteger)))`pAssociatedEquations(R,L)``215606 +oasinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``262604 +oasinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``262694 +oasinh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``262784 +oasinh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``262871 +oasinh`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``262960 +oasinhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``263028 +oasinIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``263119 +oaspFilename`1`x`(String)->String`pNAGLinkSupportPackage``263208 +oassert`2`x`(F,String)->F`pFunctionSpaceAssertions(R,F)``263361 +oassert`2`x`(_$,String)->_$`dBasicOperator``263471 +oassert`2`x`(Symbol,String)->Expression(Integer)`pPatternMatchAssertions``263622 +oassign`2`n`(_$,_$)->_$`dOutputForm``263696 +oassign`2`x`(Symbol,Expression(Complex(Float)))->_$`dFortranCode``263773 +oassign`2`x`(Symbol,Expression(Float))->_$`dFortranCode``263857 +oassign`2`x`(Symbol,Expression(Integer))->_$`dFortranCode``263941 +oassign`2`x`(Symbol,Expression(MachineComplex))->_$`dFortranCode``264025 +oassign`2`x`(Symbol,Expression(MachineFloat))->_$`dFortranCode``264109 +oassign`2`x`(Symbol,Expression(MachineInteger))->_$`dFortranCode``264193 +oassign`2`x`(Symbol,Matrix(Expression(Complex(Float))))->_$`dFortranCode``264277 +oassign`2`x`(Symbol,Matrix(Expression(Float)))->_$`dFortranCode``264361 +oassign`2`x`(Symbol,Matrix(Expression(Integer)))->_$`dFortranCode``264445 +oassign`2`x`(Symbol,Matrix(Expression(MachineComplex)))->_$`dFortranCode``264529 +oassign`2`x`(Symbol,Matrix(Expression(MachineFloat)))->_$`dFortranCode``264613 +oassign`2`x`(Symbol,Matrix(Expression(MachineInteger)))->_$`dFortranCode``264697 +oassign`2`x`(Symbol,Matrix(MachineComplex))->_$`dFortranCode``264781 +oassign`2`x`(Symbol,Matrix(MachineFloat))->_$`dFortranCode``264865 +oassign`2`x`(Symbol,Matrix(MachineInteger))->_$`dFortranCode``264949 +oassign`2`x`(Symbol,String)->_$`dFortranCode``265033 +oassign`2`x`(Symbol,Vector(Expression(Complex(Float))))->_$`dFortranCode``265117 +oassign`2`x`(Symbol,Vector(Expression(Float)))->_$`dFortranCode``265201 +oassign`2`x`(Symbol,Vector(Expression(Integer)))->_$`dFortranCode``265285 +oassign`2`x`(Symbol,Vector(Expression(MachineComplex)))->_$`dFortranCode``265369 +oassign`2`x`(Symbol,Vector(Expression(MachineFloat)))->_$`dFortranCode``265453 +oassign`2`x`(Symbol,Vector(Expression(MachineInteger)))->_$`dFortranCode``265537 +oassign`2`x`(Symbol,Vector(MachineComplex))->_$`dFortranCode``265621 +oassign`2`x`(Symbol,Vector(MachineFloat))->_$`dFortranCode``265705 +oassign`2`x`(Symbol,Vector(MachineInteger))->_$`dFortranCode``265789 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Complex(Float)))->_$`dFortranCode``265873 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Float))->_$`dFortranCode``266045 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(Integer))->_$`dFortranCode``266217 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineComplex))->_$`dFortranCode``266389 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineFloat))->_$`dFortranCode``266561 +oassign`3`x`(Symbol,List(Polynomial(Integer)),Expression(MachineInteger))->_$`dFortranCode``266733 +oassoc`2`x`(Key,_$)->Union(Record(key:Key,entry:Entry),"failed")`cAssociationListAggregate(Key,Entry)``266905 +oassociatedEquations`2`n`(L,PositiveInteger)->Record(minor:List(PositiveInteger),eq:L,minors:List(List(PositiveInteger)),ops:List(L))`pAssociatedEquations(R,L)`has(R,Field)`267063 +oassociatedSystem`2`n`(L,PositiveInteger)->Record(mat:Matrix(R),vec:Vector(List(PositiveInteger)))`pAssociatedEquations(R,L)``267261 oassociates?`2`n`(S,S)->Boolean`xField&(S)``0 oassociates?`2`n`(S,S)->Boolean`xIntegralDomain&(S)``0 -oassociates?`2`x`(_$,_$)->Boolean`cIntegralDomain``215754 -oassociative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``215884 -oassociative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``215964 -oassociatorDependence`0`n`()->List(Vector(R))`xFiniteRankNonAssociativeAlgebra&(S,R)``216044 -oassociatorDependence`0`x`()->List(Vector(R))`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`216389 +oassociates?`2`x`(_$,_$)->Boolean`cIntegralDomain``267409 +oassociative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``267539 +oassociative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``267619 oassociator`3`n`(S,S,S)->S`xNonAssociativeRng&(S)``0 -oassociator`3`x`(_$,_$,_$)->_$`cNonAssociativeRng``216734 -oatanIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``216802 -oatan`1`n`(F)->F`pElementaryFunction(R,F)``216891 +oassociator`3`x`(_$,_$,_$)->_$`cNonAssociativeRng``267699 +oassociatorDependence`0`n`()->List(Vector(R))`xFiniteRankNonAssociativeAlgebra&(S,R)``267767 +oassociatorDependence`0`x`()->List(Vector(R))`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`268112 +oatan`1`n`(F)->F`pElementaryFunction(R,F)``268457 oatan`1`n`(S)->S`xComplexCategory&(S,R)``0 oatan`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oatan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``216962 -oatan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``217034 -oatan`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``217106 -oatan`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``217180 -oatan`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``217256 -oatan`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``217315 -oatan`2`x`(_$,_$)->_$`dDoubleFloat``217384 -oatan`2`x`(_$,_$)->_$`dFloat``217470 -oatanhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``217556 -oatanh`1`n`(F)->F`pElementaryFunction(R,F)``217647 +oatan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``268528 +oatan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``268600 +oatan`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``268672 +oatan`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``268746 +oatan`1`x`(_$)->_$`cArcTrigonometricFunctionCategory``268822 +oatan`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``268881 +oatan`2`x`(_$,_$)->_$`dDoubleFloat``268950 +oatan`2`x`(_$,_$)->_$`dFloat``269036 +oatanh`1`n`(F)->F`pElementaryFunction(R,F)``269122 oatanh`1`n`(S)->S`xComplexCategory&(S,R)``0 oatanh`1`n`(S)->S`xTranscendentalFunctionCategory&(S)``0 oatanh`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -oatanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``217730 -oatanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``217823 -oatanh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``217916 -oatanh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``218006 -oatanh`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``218098 -oatom?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``218169 -oatoms`1`n`(_$)->PatternMatchResult(R,S)`dPatternMatchListResult(R,S,L)``218235 -oatrapezoidal`8`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``218328 -oatt2Result`1`x`(Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The botto--m of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")))->Result`pExpertSystemToolsPackage``219136 +oatanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``269205 +oatanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``269298 +oatanh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``269391 +oatanh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``269481 +oatanh`1`x`(_$)->_$`cArcHyperbolicFunctionCategory``269573 +oatanhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``269644 +oatanIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``269735 +oatom?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``269824 +oatoms`1`n`(_$)->PatternMatchResult(R,S)`dPatternMatchListResult(R,S,L)``269890 +oatrapezoidal`8`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``269983 +oatt2Result`1`x`(Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The botto--m of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")))->Result`pExpertSystemToolsPackage``270791 oaugment`2`n`(List(P),List(S))->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 oaugment`2`n`(List(P),S)->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 oaugment`2`n`(P,List(S))->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 oaugment`2`n`(P,S)->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -oaugment`2`x`(List(P),List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``219219 -oaugment`2`x`(List(P),_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``219319 -oaugment`2`x`(P,List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``219497 -oaugment`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``219595 +oaugment`2`x`(List(P),_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``270874 +oaugment`2`x`(List(P),List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``271052 +oaugment`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``271152 +oaugment`2`x`(P,List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``271583 oautoReduced?`2`n`(S,(P,List(P))->Boolean)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -oautoReduced?`2`x`(_$,(P,List(P))->Boolean)->Boolean`cTriangularSetCategory(R,E,V,P)``220026 -oaxesColorDefault`0`x`()->Palette`pViewDefaultsPackage``220217 -oaxesColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``220306 -oaxes`2`x`(_$,String)->Void`dThreeDimensionalViewport``220417 -oaxes`3`n`(_$,PositiveInteger,Palette)->Void`dTwoDimensionalViewport``220648 -oaxes`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``220897 -obackOldPos`1`x`(Record(mval:Matrix(F),invmval:Matrix(F),genIdeal:_$))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``221159 -oback`1`x`(_$)->S`cQueueAggregate(S)``221401 -obadNum`1`n`(UP)->Record(den:Integer,gcdnum:Integer)`pPointsOfFiniteOrderTools(UP,UPUP)``221549 -obadNum`1`n`(UPUP)->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``221587 -obadValues`1`n`(Pattern(R))->List(D)`pPatternFunctions1(R,D)``221625 +oautoReduced?`2`x`(_$,(P,List(P))->Boolean)->Boolean`cTriangularSetCategory(R,E,V,P)``271681 +oaxes`2`x`(_$,String)->Void`dThreeDimensionalViewport``271872 +oaxes`3`n`(_$,PositiveInteger,Palette)->Void`dTwoDimensionalViewport``272103 +oaxes`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``272352 +oaxesColorDefault`0`x`()->Palette`pViewDefaultsPackage``272614 +oaxesColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``272703 +oaxServer`2`x`(Integer,(SExpression)->Void)->Void`pAxiomServer``0 +oB1solve`1`n`(Record(mat:Matrix(Fraction(Polynomial(R))),vec:List(Fraction(Polynomial(R))),rank:NonNegativeInteger,rows:List(Integer),cols:List(Integer)))->Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))`pParametricLinearEquations(R,Var,Expon,GR)``272814 +oback`1`x`(_$)->S`cQueueAggregate(S)``273416 +oback`1`x`(_$)->S`dDequeue(S)``273564 +oback`1`x`(_$)->S`dQueue(S)``273651 +obackOldPos`1`x`(Record(mval:Matrix(F),invmval:Matrix(F),genIdeal:_$))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``273734 +obadNum`1`n`(UP)->Record(den:Integer,gcdnum:Integer)`pPointsOfFiniteOrderTools(UP,UPUP)``273966 +obadNum`1`n`(UPUP)->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``274004 +obadValues`1`n`(Pattern(R))->List(D)`pPatternFunctions1(R,D)``274042 obag`1`n`(List(S))->A`xBagAggregate&(A,S)``0 -obag`1`x`(List(S))->_$`cBagAggregate(S)``221757 -obalancedBinaryTree`2`x`(NonNegativeInteger,S)->_$`dBalancedBinaryTree(S)``221860 -obalancedFactorisation`2`n`(UP,List(UP))->Factored(UP)`pBalancedFactorisation(R,UP)``221978 -obalancedFactorisation`2`n`(UP,UP)->Factored(UP)`pBalancedFactorisation(R,UP)``222164 -obandedHessian`3`x`(F,FLAS,NonNegativeInteger)->Matrix(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``222329 -obandedJacobian`4`x`(FLAF,FLAS,NonNegativeInteger,NonNegativeInteger)->Matrix(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``222910 -obaseRDE`2`n`(Fraction(UP),Fraction(UP))->Record(ans:Fraction(UP),nosol:Boolean)`pTranscendentalRischDE(F,UP)``223651 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-ocenter`2`n`(_$,Integer)->_$`dOutputForm``249590 -ocenter`3`x`(List(String),Integer,String)->List(String)`pDisplayPackage``249672 -ocenter`3`x`(String,Integer,String)->String`pDisplayPackage``249956 -ocentral?`3`x`(DoubleFloat,DoubleFloat,List(Expression(DoubleFloat)))->Boolean`pd03AgentsPackage``250273 -ocertainlySubVariety?`2`n`(List(P),List(P))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``250323 -ocfirst`1`n`(NonNegativeInteger)->(Stream(Polynomial(R)))->Stream(Polynomial(R))`pWeierstrassPreparation(R)``250562 -ochainSubResultants`2`n`(polR,polR)->List(polR)`pPseudoRemainderSequence(R,polR)``250605 -ochangeBase`3`x`(Integer,Integer,PositiveInteger)->_$`dMachineFloat``250747 -ochangeBase`4`n`(Matrix(K),Matrix(K),Automorphism(K),(K)->K)->Matrix(K)`pPseudoLinearNormalForm(K)``250806 -ochangeMeasure`3`x`(_$,Symbol,Float)->_$`dRoutinesTable``250963 -ochangeNameToObjf`2`x`(Symbol,Result)->Result`pe04AgentsPackage``251075 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+ocentral?`3`x`(DoubleFloat,DoubleFloat,List(Expression(DoubleFloat)))->Boolean`pd03AgentsPackage``304354 +ocertainlySubVariety?`2`n`(List(P),List(P))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``304404 +ocExp`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`304643 +ocfirst`1`n`(NonNegativeInteger)->(Stream(Polynomial(R)))->Stream(Polynomial(R))`pWeierstrassPreparation(R)``304770 +ochainSubResultants`2`n`(polR,polR)->List(polR)`pPseudoRemainderSequence(R,polR)``304813 +ochangeBase`3`x`(Integer,Integer,PositiveInteger)->_$`dMachineFloat``304955 +ochangeBase`4`n`(Matrix(K),Matrix(K),Automorphism(K),(K)->K)->Matrix(K)`pPseudoLinearNormalForm(K)``305016 +ochangeMeasure`3`x`(_$,Symbol,Float)->_$`dRoutinesTable``305173 +ochangeName`3`x`(Symbol,Symbol,Result)->Result`pd01AgentsPackage``305285 +ochangeNameToObjf`2`x`(Symbol,Result)->Result`pe04AgentsPackage``305404 +ochangeThreshhold`3`x`(_$,Symbol,Float)->_$`dRoutinesTable``305513 +ochangeVar`2`n`(L,Fraction(UP))->L`pPrimitiveRatRicDE(F,UP,L,LQ)``305703 +ochangeVar`2`n`(L,UP)->L`pPrimitiveRatRicDE(F,UP,L,LQ)``305809 +ochangeWeightLevel`1`n`(NonNegativeInteger)->Void`dOrdinaryWeightedPolynomials(R,vl,wl,wtlevel)``305915 +ochangeWeightLevel`1`n`(NonNegativeInteger)->Void`dWeightedPolynomials(R,VarSet,E,P,vl,wl,wtlevel)``306060 +ochar`1`x`(Integer)->_$`dCharacter``306200 +ochar`1`x`(String)->_$`dCharacter``306445 +ocharacter?`1`x`(_$)->Boolean`dFortranScalarType``306643 ocharacteristic`0`n`()->NonNegativeInteger`xComplexCategory&(S,R)``0 ocharacteristic`0`n`()->NonNegativeInteger`xDirectProductCategory&(S,dim,R)``0 ocharacteristic`0`n`()->NonNegativeInteger`xFunctionSpace&(S,R)``0 @@ -1887,123 +1781,145 @@ ocharacteristic`0`n`()->NonNegativeInteger`xQuaternionCategory&(S,R)``0 ocharacteristic`0`n`()->NonNegativeInteger`xQuotientFieldCategory&(A,S)``0 ocharacteristic`0`n`()->NonNegativeInteger`xRealClosedField&(S)``0 ocharacteristic`0`n`()->NonNegativeInteger`xRealNumberSystem&(S)``0 -ocharacteristic`0`x`()->NonNegativeInteger`cNonAssociativeRing``255640 -ocharacteristic`0`x`()->NonNegativeInteger`cRing``255711 -ocharpol`1`n`(Matrix(K))->SparseUnivariatePolynomial(K)`pInnerNumericEigenPackage(K,F,Par)``255919 +ocharacteristic`0`x`()->NonNegativeInteger`cNonAssociativeRing``306739 +ocharacteristic`0`x`()->NonNegativeInteger`cRing``306810 +ocharacteristicPolynomial`1`n`(E)->PolR`pCharacteristicPolynomialInMonogenicalAlgebra(R,PolR,E)``307018 +ocharacteristicPolynomial`1`n`(S)->SparseUnivariatePolynomial(R)`xComplexCategory&(S,R)``0 +ocharacteristicPolynomial`1`n`(S)->UP`xFramedAlgebra&(S,R,UP)``0 +ocharacteristicPolynomial`1`n`(S)->UP`xMonogenicAlgebra&(S,R,UP)``0 +ocharacteristicPolynomial`1`x`(Matrix(Complex(Fraction(Integer))))->Polynomial(Complex(Fraction(Integer)))`pNumericComplexEigenPackage(Par)``307127 +ocharacteristicPolynomial`1`x`(Matrix(Fraction(Integer)))->Polynomial(Fraction(Integer))`pNumericRealEigenPackage(Par)``307308 +ocharacteristicPolynomial`1`x`(Matrix(Fraction(Polynomial(R))))->Polynomial(R)`pEigenPackage(R)``307481 +ocharacteristicPolynomial`1`x`(_$)->UP`cFiniteRankAlgebra(R,UP)``307641 +ocharacteristicPolynomial`2`x`(Matrix(Complex(Fraction(Integer))),Symbol)->Polynomial(Complex(Fraction(Integer)))`pNumericComplexEigenPackage(Par)``307790 +ocharacteristicPolynomial`2`x`(Matrix(Fraction(Integer)),Symbol)->Polynomial(Fraction(Integer))`pNumericRealEigenPackage(Par)``307968 +ocharacteristicPolynomial`2`x`(Matrix(Fraction(Polynomial(R))),Symbol)->Polynomial(R)`pEigenPackage(R)``308167 +ocharacteristicPolynomial`2`x`(Matrix(R),R)->R`pCharacteristicPolynomialPackage(R)``308325 +ocharacteristicSerie`1`x`(List(P))->List(_$)`dWuWenTsunTriangularSet(R,E,V,P)``308612 +ocharacteristicSerie`3`x`(List(P),(P,P)->Boolean,(P,P)->P)->List(_$)`dWuWenTsunTriangularSet(R,E,V,P)``308756 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-ocheckRur`2`n`(TS,List(TS))->Boolean`pInternalRationalUnivariateRepresentationPackage(R,E,V,P,TS)``258082 -ocheck`1`x`(_$)->_$`cThreeSpaceCategory(R)``258203 -ocheck`2`n`(List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)),List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)))->Boolean`pMultivariateSquareFree(E,OV,R,P)``258329 -ochiSquare1`1`n`(NonNegativeInteger)->Float`pRandomFloatDistributions``258365 -ochiSquare`1`n`(NonNegativeInteger)->()->Float`pRandomFloatDistributions``258407 +ocharthRoot`1`x`(_$)->_$`cFiniteFieldCategory``310598 +ocharthRoot`1`x`(_$)->Union(_$,"failed")`cCharacteristicNonZero``310722 +ocharthRoot`1`x`(_$)->Union(_$,"failed")`cPolynomialFactorizationExplicit`has(_$,CharacteristicNonZero)`310840 +ochartV`1`x`(_$)->BLMET`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``310961 +ochebyshevT`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pPolynomialNumberTheoryFunctions``311303 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-ochineseRemainder`3`n`(List(UP),List(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))),NonNegativeInteger)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pChineseRemainderToolsForIntegralBases(K,R,UP)``259238 -ochineseRemainder`4`x`(Integer,Integer,Integer,Integer)->Integer`pIntegerNumberTheoryFunctions``259296 -ochoosemon`2`n`(DistributedMultivariatePolynomial(lv,F),List(DistributedMultivariatePolynomial(lv,F)))->DistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``259497 -ochvar`2`n`(UPUP,UPUP)->Record(func:UPUP,poly:UPUP,c1:Fraction(UP),c2:Fraction(UP),deg:NonNegativeInteger)`pChangeOfVariable(F,UP,UPUP)``259535 -oclearCache`0`n`()->Void`pSortedCache(S)``259924 -oclearDenominator`1`n`(B)->A`pInnerCommonDenominator(R,Q,A,B)``259970 -oclearDenominator`1`x`(A)->A`pCommonDenominator(R,Q,A)``260150 -oclearDenominator`1`x`(Matrix(Q))->Matrix(R)`pMatrixCommonDenominator(R,Q)``260330 -oclearDenominator`1`x`(UP)->UP`pUnivariatePolynomialCommonDenominator(R,Q,UP)``260475 -oclearFortranOutputStack`0`x`()->Stack(String)`pFortranOutputStackPackage``260624 -oclearTable!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``260696 -oclearTheFTable`0`x`()->Void`dIntegrationFunctionsTable``260791 -oclearTheIFTable`0`x`()->Void`dODEIntensityFunctionsTable``260861 -oclearTheSymbolTable`0`x`()->Void`dTheSymbolTable``260942 -oclearTheSymbolTable`1`x`(Symbol)->Void`dTheSymbolTable``261011 -oclikeUniv`1`n`(Symbol)->(Polynomial(R))->SparseUnivariatePolynomial(Polynomial(R))`pWeierstrassPreparation(R)``261091 -oclipBoolean`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``261138 -oclipParametric`1`n`(Plot)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``261354 -oclipParametric`3`n`(Plot,Fraction(Integer),Fraction(Integer))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``261723 -oclipPointsDefault`0`x`()->Boolean`pGraphicsDefaults``262124 -oclipPointsDefault`1`x`(Boolean)->Boolean`pGraphicsDefaults``262218 -oclipSurface`2`x`(_$,String)->Void`dThreeDimensionalViewport``262383 -oclipWithRanges`5`n`(List(List(Point(DoubleFloat))),DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``262688 -oclip`1`n`(List(List(Point(DoubleFloat))))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``263042 -oclip`1`n`(List(Point(DoubleFloat)))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``263317 -oclip`1`n`(Plot)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``263598 -oclip`1`x`(Boolean)->_$`dDrawOption``263882 -oclip`1`x`(List(Segment(Float)))->_$`dDrawOption``264046 -oclip`3`n`(Plot,Fraction(Integer),Fraction(Integer))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``264204 -oclose!`1`x`(_$)->_$`cFileCategory(Name,S)``264517 -ocloseComponent`3`n`(_$,List(NonNegativeInteger),Boolean)->_$`dSubSpace(n,R)``264595 -oclose`1`n`(_$)->Void`dTwoDimensionalViewport``265071 -oclose`1`x`(_$)->Void`dThreeDimensionalViewport``265275 -oclose`2`n`(_$,Boolean)->Boolean`dSubSpaceComponentProperty``265483 -oclosed?`1`n`(_$)->Boolean`dSubSpaceComponentProperty``265524 -oclosed?`1`n`(_$)->Boolean`dTubePlot(Curve)``265563 -oclosedCurve?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``265642 -oclosedCurve`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``265878 -oclosedCurve`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``266141 -oclosedCurve`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``266486 -oclosedCurve`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``267029 -ocn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``267304 -ocoHeight`1`n`(S)->NonNegativeInteger`xTriangularSetCategory&(S,R,E,V,P)``0 -ocoHeight`1`x`(_$)->NonNegativeInteger`cTriangularSetCategory(R,E,V,P)`has(V,Finite)`267402 -ocode`1`x`(_$)->Union(nullBranch:"null",assignmentBranch:Record(var:Symbol,arrayIndex:List(Polynomial(Integer)),rand:Record(ints2Floats?:Boolean,expr:OutputForm)),arrayAssignmentBranch:Record(var:Symbol,rand:OutputForm,ints2Floats?:Boolean),conditionalBranch:Record(switch:Switch,thenClause:_$,elseClause:_$),returnBranch:Record(empty?:Boolean,value:Record(ints2Floats?:Boolean,expr:OutputForm)),blockBranch:List(_$),commentBranch:List(String),callBranch:String,forBranch:Record(range:SegmentBinding(--Polynomial(Integer)),span:Polynomial(Integer),body:_$),labelBranch:SingleInteger,loopBranch:Record(switch:Switch,body:_$),commonBranch:Record(name:Symbol,contents:List(Symbol)),printBranch:List(OutputForm))`dFortranCode``267511 -ocoefChoose`2`n`(Integer,Factored(P))->P`pMultivariateSquareFree(E,OV,R,P)``267608 -ocoef`2`n`(_$,E)->R`dXPolynomialRing(R,E)``267649 -ocoef`2`x`(XRecursivePolynomial(VarSet,R),_$)->R`cFreeLieAlgebra(VarSet,R)``267767 -ocoef`2`x`(_$,OrderedFreeMonoid(vl))->R`cXFreeAlgebra(vl,R)``267934 -ocoef`2`x`(_$,_$)->R`cXFreeAlgebra(vl,R)``268018 +ochildren`1`n`(_$)->List(_$)`dSubSpace(n,R)``313337 +ochildren`1`x`(_$)->List(_$)`cRecursiveAggregate(S)``313381 +ochineseRemainder`2`x`(List(List(R)),List(R))->List(R)`pCRApackage(R)``313461 +ochineseRemainder`2`x`(List(R),List(R))->R`pCRApackage(R)``313720 +ochineseRemainder`3`n`(List(UP),List(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))),NonNegativeInteger)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pChineseRemainderToolsForIntegralBases(K,R,UP)``314010 +ochineseRemainder`4`x`(Integer,Integer,Integer,Integer)->Integer`pIntegerNumberTheoryFunctions``314068 +ochiSquare1`1`n`(NonNegativeInteger)->Float`pRandomFloatDistributions``314273 +ochiSquare`1`n`(NonNegativeInteger)->()->Float`pRandomFloatDistributions``314315 +ochoosemon`2`n`(DistributedMultivariatePolynomial(lv,F),List(DistributedMultivariatePolynomial(lv,F)))->DistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``314356 +ochvar`2`n`(UPUP,UPUP)->Record(func:UPUP,poly:UPUP,c1:Fraction(UP),c2:Fraction(UP),deg:NonNegativeInteger)`pChangeOfVariable(F,UP,UPUP)``314394 +oCi`1`n`(F)->F`pLiouvillianFunction(R,F)``314783 +oCi`1`x`(_$)->_$`cLiouvillianFunctionCategory``314838 +oclassNumber`0`x`()->Integer`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)`has(K,Finite)`314964 +oclassNumber`0`x`()->Integer`pPackageForAlgebraicFunctionField(K,symb,BLMET)`has(K,Finite)`315010 +oclassNumber`0`x`()->Integer`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)`has(PseudoAlgebraicClosureOfFiniteField(K),Finite)`315056 +oclearCache`0`n`()->Void`pSortedCache(S)``315102 +oclearDenominator`1`n`(B)->A`pInnerCommonDenominator(R,Q,A,B)``315148 +oclearDenominator`1`x`(A)->A`pCommonDenominator(R,Q,A)``315328 +oclearDenominator`1`x`(Matrix(Q))->Matrix(R)`pMatrixCommonDenominator(R,Q)``315508 +oclearDenominator`1`x`(UP)->UP`pUnivariatePolynomialCommonDenominator(R,Q,UP)``315653 +oclearFortranOutputStack`0`x`()->Stack(String)`pFortranOutputStackPackage``315802 +oclearTable!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``315874 +oclearTheFTable`0`x`()->Void`dIntegrationFunctionsTable``315969 +oclearTheIFTable`0`x`()->Void`dODEIntensityFunctionsTable``316039 +oclearTheSymbolTable`0`x`()->Void`dTheSymbolTable``316120 +oclearTheSymbolTable`1`x`(Symbol)->Void`dTheSymbolTable``316189 +oclikeUniv`1`n`(Symbol)->(Polynomial(R))->SparseUnivariatePolynomial(Polynomial(R))`pWeierstrassPreparation(R)``316269 +oclip`1`n`(List(List(Point(DoubleFloat))))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``316316 +oclip`1`n`(List(Point(DoubleFloat)))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``316591 +oclip`1`n`(Plot)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``316872 +oclip`1`x`(Boolean)->_$`dDrawOption``317156 +oclip`1`x`(List(Segment(Float)))->_$`dDrawOption``317320 +oclip`3`n`(Plot,Fraction(Integer),Fraction(Integer))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``317478 +oclipBoolean`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``317791 +oclipParametric`1`n`(Plot)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``318007 +oclipParametric`3`n`(Plot,Fraction(Integer),Fraction(Integer))->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``318376 +oclipPointsDefault`0`x`()->Boolean`pGraphicsDefaults``318777 +oclipPointsDefault`1`x`(Boolean)->Boolean`pGraphicsDefaults``318871 +oclipSurface`2`x`(_$,String)->Void`dThreeDimensionalViewport``319036 +oclipWithRanges`5`n`(List(List(Point(DoubleFloat))),DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat)->Record(brans:List(List(Point(DoubleFloat))),xValues:Segment(DoubleFloat),yValues:Segment(DoubleFloat))`pTwoDimensionalPlotClipping``319341 +ocLog`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`319695 +oclose`1`n`(_$)->Void`dTwoDimensionalViewport``319820 +oclose!`1`x`(_$)->_$`cFileCategory(Name,S)``320024 +oclose!`1`x`(_$)->_$`dLibrary``320102 +oclose`1`x`(_$)->Void`dThreeDimensionalViewport``320183 +oclose`2`n`(_$,Boolean)->Boolean`dSubSpaceComponentProperty``320391 +ocloseComponent`3`n`(_$,List(NonNegativeInteger),Boolean)->_$`dSubSpace(n,R)``320436 +oclosed?`1`n`(_$)->Boolean`dSubSpaceComponentProperty``320912 +oclosed?`1`n`(_$)->Boolean`dTubePlot(Curve)``320955 +oclosedCurve?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``321034 +oclosedCurve`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``321270 +oclosedCurve`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``321533 +oclosedCurve`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``321878 +oclosedCurve`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``322421 +ocn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``322696 +ocode`1`x`(_$)->Union(nullBranch:"null",assignmentBranch:Record(var:Symbol,arrayIndex:List(Polynomial(Integer)),rand:Record(ints2Floats?:Boolean,expr:OutputForm)),arrayAssignmentBranch:Record(var:Symbol,rand:OutputForm,ints2Floats?:Boolean),conditionalBranch:Record(switch:Switch,thenClause:_$,elseClause:_$),returnBranch:Record(empty?:Boolean,value:Record(ints2Floats?:Boolean,expr:OutputForm)),blockBranch:List(_$),commentBranch:List(String),callBranch:String,forBranch:Record(range:SegmentBinding(--Polynomial(Integer)),span:Polynomial(Integer),body:_$),labelBranch:SingleInteger,loopBranch:Record(switch:Switch,body:_$),commonBranch:Record(name:Symbol,contents:List(Symbol)),printBranch:List(OutputForm))`dFortranCode``322794 +ocoef`2`n`(_$,E)->R`dXPolynomialRing(R,E)``322891 +ocoef`2`x`(_$,OrderedFreeMonoid(vl))->R`cXFreeAlgebra(vl,R)``323009 +ocoef`2`x`(_$,_$)->R`cXFreeAlgebra(vl,R)``323093 +ocoef`2`x`(XRecursivePolynomial(VarSet,R),_$)->R`cFreeLieAlgebra(VarSet,R)``323225 +ocoefChoose`2`n`(Integer,Factored(P))->P`pMultivariateSquareFree(E,OV,R,P)``323392 +ocoefficient`2`n`(_$,_$)->Expression(CoefRing)`dDeRhamComplex(CoefRing,listIndVar)``323433 +ocoefficient`2`n`(_$,Integer)->R`dLaurentPolynomial(R,UP)``323626 +ocoefficient`2`n`(_$,M)->R`dMonoidRing(R,M)``323677 +ocoefficient`2`n`(_$,NonNegativeInteger)->SMP`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``323805 +ocoefficient`2`n`(_$,_$)->R`dAntiSymm(R,lVar)``324018 ocoefficient`2`n`(S,E)->R`xPolynomialCategory&(S,R,E,VarSet)``0 -ocoefficient`2`n`(_$,Integer)->R`dLaurentPolynomial(R,UP)``268150 -ocoefficient`2`n`(_$,M)->R`dMonoidRing(R,M)``268197 -ocoefficient`2`n`(_$,NonNegativeInteger)->SMP`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``268325 -ocoefficient`2`n`(_$,_$)->Expression(CoefRing)`dDeRhamComplex(CoefRing,listIndVar)``268401 -ocoefficient`2`n`(_$,_$)->R`dAntiSymm(R,lVar)``268594 -ocoefficient`2`x`(S,_$)->E`cFreeAbelianMonoidCategory(S,E)``268815 -ocoefficient`2`x`(_$,Basis)->R`cFreeModuleCat(R,Basis)``268974 -ocoefficient`2`x`(_$,E)->R`cAbelianMonoidRing(R,E)``269056 -ocoefficient`2`x`(_$,List(PositiveInteger))->K`dCliffordAlgebra(n,K,Q)``269225 -ocoefficient`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`dTaylorSeries(Coef)``269347 -ocoefficient`2`x`(_$,NonNegativeInteger)->R`cMonogenicLinearOperator(R)``269423 -ocoefficient`2`x`(_$,NonNegativeInteger)->R`cUnivariateSkewPolynomialCategory(R)``269536 +ocoefficient`2`x`(_$,Basis)->R`cFreeModuleCat(R,Basis)``324239 +ocoefficient`2`x`(_$,E)->R`cAbelianMonoidRing(R,E)``324321 +ocoefficient`2`x`(_$,List(PositiveInteger))->K`dCliffordAlgebra(n,K,Q)``324490 +ocoefficient`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`dTaylorSeries(Coef)``324612 +ocoefficient`2`x`(_$,NonNegativeInteger)->R`cMonogenicLinearOperator(R)``324688 +ocoefficient`2`x`(_$,NonNegativeInteger)->R`cUnivariateSkewPolynomialCategory(R)``324801 +ocoefficient`2`x`(S,_$)->E`cFreeAbelianMonoidCategory(S,E)``324914 ocoefficient`3`n`(S,List(VarSet),List(NonNegativeInteger))->S`xPolynomialCategory&(S,R,E,VarSet)``0 ocoefficient`3`n`(S,VarSet,NonNegativeInteger)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -ocoefficient`3`x`(_$,List(Var),List(NonNegativeInteger))->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``269649 -ocoefficient`3`x`(_$,List(VarSet),List(NonNegativeInteger))->_$`cPolynomialCategory(R,E,VarSet)``269791 -ocoefficient`3`x`(_$,Var,NonNegativeInteger)->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``270010 -ocoefficient`3`x`(_$,VarSet,NonNegativeInteger)->_$`cPolynomialCategory(R,E,VarSet)``270098 +ocoefficient`3`x`(_$,List(Var),List(NonNegativeInteger))->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``325073 +ocoefficient`3`x`(_$,List(VarSet),List(NonNegativeInteger))->_$`cPolynomialCategory(R,E,VarSet)``325215 +ocoefficient`3`x`(_$,Var,NonNegativeInteger)->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``325434 +ocoefficient`3`x`(_$,VarSet,NonNegativeInteger)->_$`cPolynomialCategory(R,E,VarSet)``325522 +ocoefficients`1`n`(_$)->List(R)`dMonoidRing(R,M)``325681 ocoefficients`1`n`(S)->List(R)`xFiniteAbelianMonoidRing&(S,R,E)``0 ocoefficients`1`n`(S)->List(R)`xUnivariateSkewPolynomialCategory&(S,R)``0 -ocoefficients`1`n`(_$)->List(R)`dMonoidRing(R,M)``270257 -ocoefficients`1`n`(_$)->Stream(Coef)`dInnerTaylorSeries(Coef)``270320 -ocoefficients`1`x`(_$)->List(R)`cFiniteAbelianMonoidRing(R,E)``270661 -ocoefficients`1`x`(_$)->List(R)`cFreeModuleCat(R,Basis)``270755 -ocoefficients`1`x`(_$)->List(R)`cUnivariateSkewPolynomialCategory(R)``270831 -ocoefficients`1`x`(_$)->Stream(Coef)`cUnivariateTaylorSeriesCategory(Coef)``270923 -ocoerceImages`1`x`(List(S))->_$`dPermutation(S)`AND(has(S,Finite),not(has(S,IntegerNumberSystem)))`271079 -ocoerceImages`1`x`(List(S))->_$`dPermutation(S)`has(S,IntegerNumberSystem)`271328 -ocoerceListOfPairs`1`x`(List(List(S)))->_$`dPermutation(S)``271577 -ocoerceP`1`n`(Vector(Matrix(R)))->Vector(Matrix(Polynomial(R)))`pCoerceVectorMatrixPackage(R)``271871 -ocoercePreimagesImages`1`x`(List(List(S)))->_$`dPermutation(S)``272004 +ocoefficients`1`n`(_$)->Stream(Coef)`dInnerTaylorSeries(Coef)``325744 +ocoefficients`1`x`(_$)->List(R)`cFiniteAbelianMonoidRing(R,E)``326085 +ocoefficients`1`x`(_$)->List(R)`cFreeModuleCat(R,Basis)``326179 +ocoefficients`1`x`(_$)->List(R)`cUnivariateSkewPolynomialCategory(R)``326254 +ocoefficients`1`x`(_$)->Stream(Coef)`cUnivariateTaylorSeriesCategory(Coef)``326346 +ocoefOfFirstNonZeroTerm`1`x`(_$)->K`cLocalPowerSeriesCategory(K)``326502 ocoerce`1`n`(A)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 ocoerce`1`n`(A)->A`xQuotientFieldCategory&(A,S)``0 ocoerce`1`n`(A)->OutputForm`xBinaryRecursiveAggregate&(A,S)``0 @@ -2014,12 +1930,12 @@ ocoerce`1`n`(A)->OutputForm`xFiniteSetAggregate&(A,S)``0 ocoerce`1`n`(A)->OutputForm`xHomogeneousAggregate&(A,S)``0 ocoerce`1`n`(A)->OutputForm`xOneDimensionalArrayAggregate&(A,S)``0 ocoerce`1`n`(A)->OutputForm`xQuotientFieldCategory&(A,S)``0 -ocoerce`1`n`(A)->Stream(A)`pStreamTaylorSeriesOperations(A)``272151 +ocoerce`1`n`(A)->Stream(A)`pStreamTaylorSeriesOperations(A)``326596 ocoerce`1`n`(Character)->S`xStringAggregate&(S)``0 ocoerce`1`n`(Coef)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 ocoerce`1`n`(Col)->S`xMatrixCategory&(S,R,Row,Col)``0 -ocoerce`1`n`(E)->_$`dXPolynomialRing(R,E)``272238 -ocoerce`1`n`(FPol)->_$`dResidueRing(F,Expon,VarSet,FPol,LFPol)``272281 +ocoerce`1`n`(E)->_$`dXPolynomialRing(R,E)``326683 +ocoerce`1`n`(FPol)->_$`dResidueRing(F,Expon,VarSet,FPol,LFPol)``326726 ocoerce`1`n`(Fraction(Integer))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 ocoerce`1`n`(Fraction(Integer))->A`xFullyRetractableTo&(A,S)``0 ocoerce`1`n`(Fraction(Integer))->A`xQuotientFieldCategory&(A,S)``0 @@ -2038,7 +1954,7 @@ ocoerce`1`n`(Fraction(Integer))->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 ocoerce`1`n`(Fraction(Polynomial(Fraction(R))))->S`xFunctionSpace&(S,R)``0 ocoerce`1`n`(Fraction(Polynomial(R)))->S`xFunctionSpace&(S,R)``0 ocoerce`1`n`(Fraction(R))->S`xFunctionSpace&(S,R)``0 -ocoerce`1`n`(GraphImage)->TwoDimensionalViewport`pViewportPackage``272368 +ocoerce`1`n`(GraphImage)->TwoDimensionalViewport`pViewportPackage``326813 ocoerce`1`n`(Integer)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 ocoerce`1`n`(Integer)->A`xFullyRetractableTo&(A,S)``0 ocoerce`1`n`(Integer)->A`xQuotientFieldCategory&(A,S)``0 @@ -2059,16 +1975,33 @@ ocoerce`1`n`(Integer)->S`xUnivariatePolynomialCategory&(S,R)``0 ocoerce`1`n`(Integer)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 ocoerce`1`n`(Integer)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 ocoerce`1`n`(Kernel(S))->S`xFunctionSpace&(S,R)``0 -ocoerce`1`n`(LiePolynomial(VarSet,R))->_$`dXPBWPolynomial(VarSet,R)``272510 -ocoerce`1`n`(List(Integer))->_$`dExtAlgBasis``272568 -ocoerce`1`n`(List(List(Point(DoubleFloat))))->_$`dGraphImage``272839 -ocoerce`1`n`(List(Record(coef:R,monom:M)))->_$`dMonoidRing(R,M)``273350 -ocoerce`1`n`(P)->_$`dWeightedPolynomials(R,VarSet,E,P,vl,wl,wtlevel)``273444 +ocoerce`1`n`(LiePolynomial(VarSet,R))->_$`dXPBWPolynomial(VarSet,R)``326955 +ocoerce`1`n`(List(Integer))->_$`dExtAlgBasis``327013 +ocoerce`1`n`(_$)->List(Integer)`dPartition``327284 +ocoerce`1`n`(List(List(Point(DoubleFloat))))->_$`dGraphImage``327352 +ocoerce`1`n`(List(Record(coef:R,monom:M)))->_$`dMonoidRing(R,M)``327863 +ocoerce`1`n`(_$)->Magma(VarSet)`dLyndonWord(VarSet)``327957 +ocoerce`1`n`(_$)->Matrix(R)`dRectangularMatrix(m,n,R)``328073 +ocoerce`1`n`(_$)->Matrix(R)`dSquareMatrix(ndim,R)``328187 +ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dLyndonWord(VarSet)``328300 +ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dMagma(VarSet)``328428 +ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dPoincareBirkhoffWittLyndonBasis(VarSet)``328608 +ocoerce`1`n`(_$)->OutputForm`dGraphImage``328759 +ocoerce`1`n`(_$)->OutputForm`dTwoDimensionalViewport``328921 +ocoerce`1`n`(_$)->P`dWeightedPolynomials(R,VarSet,E,P,vl,wl,wtlevel)``329103 +ocoerce`1`n`(P)->_$`dWeightedPolynomials(R,VarSet,E,P,vl,wl,wtlevel)``329161 ocoerce`1`n`(Polynomial(Fraction(R)))->S`xFunctionSpace&(S,R)``0 +ocoerce`1`n`(Polynomial(R))->_$`dOrdinaryWeightedPolynomials(R,vl,wl,wtlevel)``329260 +ocoerce`1`n`(_$)->Polynomial(R)`dOrdinaryWeightedPolynomials(R,vl,wl,wtlevel)``329373 ocoerce`1`n`(Polynomial(R))->S`xFunctionSpace&(S,R)``0 -ocoerce`1`n`(Polynomial(R))->_$`dOrdinaryWeightedPolynomials(R,vl,wl,wtlevel)``273543 -ocoerce`1`n`(PrimitiveArray(S))->_$`dTuple(S)``273656 +ocoerce`1`n`(PrimitiveArray(S))->_$`dTuple(S)``329459 ocoerce`1`n`(R)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 +ocoerce`1`n`(_$)->R`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``329663 +ocoerce`1`n`(_$)->R`dModularField(R,Mod,reduction,merge,exactQuo)``329705 +ocoerce`1`n`(_$)->R`dModularRing(R,Mod,reduction,merge,exactQuo)``329747 +ocoerce`1`n`(_$)->Record(index:IS,exponent:E)`dModuleMonomial(IS,E,ff)``329789 +ocoerce`1`n`(Record(index:IS,exponent:E))->_$`dModuleMonomial(IS,E,ff)``329831 +ocoerce`1`n`(Rep)->_$`dModMonic(R,Rep)``329873 ocoerce`1`n`(R)->S`xAlgebra&(S,R)``0 ocoerce`1`n`(R)->S`xComplexCategory&(S,R)``0 ocoerce`1`n`(R)->S`xDirectProductCategory&(S,dim,R)``0 @@ -2080,13 +2013,14 @@ ocoerce`1`n`(R)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 ocoerce`1`n`(R)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 ocoerce`1`n`(R)->S`xUnivariatePolynomialCategory&(S,R)``0 ocoerce`1`n`(R)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 -ocoerce`1`n`(Record(index:IS,exponent:E))->_$`dModuleMonomial(IS,E,ff)``273717 -ocoerce`1`n`(Rep)->_$`dModMonic(R,Rep)``273755 ocoerce`1`n`(S)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 ocoerce`1`n`(S)->A`xDifferentialVariableCategory&(A,S)``0 ocoerce`1`n`(S)->A`xFullyRetractableTo&(A,S)``0 ocoerce`1`n`(S)->A`xQuotientFieldCategory&(A,S)``0 +ocoerce`1`n`(S)->_$`dMakeCachableSet(S)``329915 +ocoerce`1`n`(SingletonAsOrderedSet)->S`xUnivariatePolynomialCategory&(S,R)``0 ocoerce`1`n`(S)->List(P)`xTriangularSetCategory&(S,R,E,V,P)``0 +ocoerce`1`n`(SMP)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``329984 ocoerce`1`n`(S)->OutputForm`xAlgebra&(S,R)``0 ocoerce`1`n`(S)->OutputForm`xComplexCategory&(S,R)``0 ocoerce`1`n`(S)->OutputForm`xDirectProductCategory&(S,dim,R)``0 @@ -2107,6 +2041,8 @@ ocoerce`1`n`(S)->OutputForm`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 ocoerce`1`n`(S)->OutputForm`xUnivariatePolynomialCategory&(S,R)``0 ocoerce`1`n`(S)->OutputForm`xUnivariateSkewPolynomialCategory&(S,R)``0 ocoerce`1`n`(S)->OutputForm`xUnivariateTaylorSeriesCategory&(S,Coef)``0 +ocoerce`1`n`(SparseMultivariatePolynomial(Integer,Kernel(_$)))->_$`dInnerAlgebraicNumber``330066 +ocoerce`1`n`(SparseMultivariatePolynomial(R,Kernel(S)))->S`xFunctionSpace&(S,R)``0 ocoerce`1`n`(S)->Polynomial(R)`xRecursivePolynomialCategory&(S,R,E,V)``0 ocoerce`1`n`(S)->S`xComplexCategory&(S,R)``0 ocoerce`1`n`(S)->S`xFunctionSpace&(S,R)``0 @@ -2115,503 +2051,523 @@ ocoerce`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 ocoerce`1`n`(S)->S`xUnivariatePolynomialCategory&(S,R)``0 ocoerce`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 ocoerce`1`n`(S)->Vector(R)`xDirectProductCategory&(S,dim,R)``0 -ocoerce`1`n`(S)->_$`dMakeCachableSet(S)``273793 -ocoerce`1`n`(SMP)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``273862 -ocoerce`1`n`(SingletonAsOrderedSet)->S`xUnivariatePolynomialCategory&(S,R)``0 -ocoerce`1`n`(SparseMultivariatePolynomial(Integer,Kernel(_$)))->_$`dInnerAlgebraicNumber``273944 -ocoerce`1`n`(SparseMultivariatePolynomial(R,Kernel(S)))->S`xFunctionSpace&(S,R)``0 ocoerce`1`n`(Symbol)->A`xQuotientFieldCategory&(A,S)``0 +ocoerce`1`n`(_$)->Symbol`dVariable(sym)``330138 ocoerce`1`n`(Symbol)->S`xFunctionSpace&(S,R)``0 -ocoerce`1`n`(UnivariatePolynomial(var,Coef))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``274016 -ocoerce`1`n`(UnivariatePolynomial(var,Coef))->_$`dUnivariateTaylorSeries(Coef,var,cen)``274154 -ocoerce`1`n`(UnivariatePuiseuxSeries(FE,var,cen))->_$`dExponentialExpansion(R,FE,var,cen)``274292 +ocoerce`1`n`(UnivariatePolynomial(var,Coef))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``330181 +ocoerce`1`n`(UnivariatePolynomial(var,Coef))->_$`dUnivariateTaylorSeries(Coef,var,cen)``330319 +ocoerce`1`n`(UnivariatePuiseuxSeries(FE,var,cen))->_$`dExponentialExpansion(R,FE,var,cen)``330457 +ocoerce`1`n`(Var)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``330566 +ocoerce`1`n`(Variable(var))->_$`dSparseUnivariateLaurentSeries(Coef,var,cen)``330631 +ocoerce`1`n`(Variable(var))->_$`dSparseUnivariatePuiseuxSeries(Coef,var,cen)``330720 +ocoerce`1`n`(Variable(var))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``330809 +ocoerce`1`n`(Variable(var))->_$`dUnivariateLaurentSeries(Coef,var,cen)``330911 +ocoerce`1`n`(Variable(var))->_$`dUnivariatePuiseuxSeries(Coef,var,cen)``331000 +ocoerce`1`n`(Variable(var))->_$`dUnivariateTaylorSeries(Coef,var,cen)``331089 +ocoerce`1`n`(Variable(x))->_$`dUnivariateSkewPolynomial(x,R,sigma,delta)``331191 +ocoerce`1`n`(VarSet)->_$`dPoincareBirkhoffWittLyndonBasis(VarSet)``331254 ocoerce`1`n`(V)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 +ocoerce`1`n`(Vector(Fraction(Polynomial(R))))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``331294 +ocoerce`1`n`(Vector(Matrix(R)))->Vector(Matrix(Fraction(Polynomial(R))))`pCoerceVectorMatrixPackage(R)``331468 ocoerce`1`n`(V)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -ocoerce`1`n`(Var)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``274401 -ocoerce`1`n`(VarSet)->_$`dPoincareBirkhoffWittLyndonBasis(VarSet)``274466 -ocoerce`1`n`(Variable(var))->_$`dSparseUnivariateLaurentSeries(Coef,var,cen)``274506 -ocoerce`1`n`(Variable(var))->_$`dSparseUnivariatePuiseuxSeries(Coef,var,cen)``274595 -ocoerce`1`n`(Variable(var))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``274684 -ocoerce`1`n`(Variable(var))->_$`dUnivariateLaurentSeries(Coef,var,cen)``274786 -ocoerce`1`n`(Variable(var))->_$`dUnivariatePuiseuxSeries(Coef,var,cen)``274875 -ocoerce`1`n`(Variable(var))->_$`dUnivariateTaylorSeries(Coef,var,cen)``274964 -ocoerce`1`n`(Variable(x))->_$`dUnivariateSkewPolynomial(x,R,sigma,delta)``275066 -ocoerce`1`n`(Vector(Fraction(Polynomial(R))))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``275129 -ocoerce`1`n`(Vector(Matrix(R)))->Vector(Matrix(Fraction(Polynomial(R))))`pCoerceVectorMatrixPackage(R)``275303 -ocoerce`1`n`(_$)->List(Integer)`dPartition``275444 -ocoerce`1`n`(_$)->Magma(VarSet)`dLyndonWord(VarSet)``275512 -ocoerce`1`n`(_$)->Matrix(R)`dRectangularMatrix(m,n,R)``275628 -ocoerce`1`n`(_$)->Matrix(R)`dSquareMatrix(ndim,R)``275742 -ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dLyndonWord(VarSet)``275855 -ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dMagma(VarSet)``275983 -ocoerce`1`n`(_$)->OrderedFreeMonoid(VarSet)`dPoincareBirkhoffWittLyndonBasis(VarSet)``276135 -ocoerce`1`n`(_$)->OutputForm`dGraphImage``276286 -ocoerce`1`n`(_$)->OutputForm`dTwoDimensionalViewport``276448 -ocoerce`1`n`(_$)->P`dWeightedPolynomials(R,VarSet,E,P,vl,wl,wtlevel)``276630 -ocoerce`1`n`(_$)->Polynomial(R)`dOrdinaryWeightedPolynomials(R,vl,wl,wtlevel)``276688 -ocoerce`1`n`(_$)->R`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``276774 -ocoerce`1`n`(_$)->R`dModularField(R,Mod,reduction,merge,exactQuo)``276812 -ocoerce`1`n`(_$)->R`dModularRing(R,Mod,reduction,merge,exactQuo)``276850 -ocoerce`1`n`(_$)->Record(index:IS,exponent:E)`dModuleMonomial(IS,E,ff)``276888 -ocoerce`1`n`(_$)->Symbol`dVariable(sym)``276926 -ocoerce`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``276969 -ocoerce`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dXPBWPolynomial(VarSet,R)``277058 -ocoerce`1`n`(_$)->XPBWPolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``277144 -ocoerce`1`n`(_$)->XRecursivePolynomial(VarSet,R)`dXPBWPolynomial(VarSet,R)``277233 -ocoerce`1`x`(A)->()->A`pMappingPackage1(A)``277317 -ocoerce`1`x`(A)->_$`dAssociatedJordanAlgebra(R,A)``277400 -ocoerce`1`x`(A)->_$`dAssociatedLieAlgebra(R,A)``277563 -ocoerce`1`x`(Character)->_$`cStringAggregate``277720 -ocoerce`1`x`(Col)->_$`cMatrixCategory(R,Row,Col)``277811 -ocoerce`1`x`(Color)->_$`dPalette``277888 -ocoerce`1`x`(Complex(Float))->_$`dMachineComplex``277992 -ocoerce`1`x`(Complex(Integer))->_$`dMachineComplex``278058 -ocoerce`1`x`(Complex(MachineFloat))->_$`dMachineComplex``278124 -ocoerce`1`x`(Complex(MachineInteger))->_$`dMachineComplex``278190 -ocoerce`1`x`(DirectProduct(dim,R))->_$`dCartesianTensor(minix,dim,R)``278256 -ocoerce`1`x`(Equation(Expression(Complex(Float))))->_$`dFortranProgram(name,returnType,arguments,symbols)``278315 -ocoerce`1`x`(Equation(Expression(Float)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278356 -ocoerce`1`x`(Equation(Expression(Integer)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278397 -ocoerce`1`x`(Equation(Expression(MachineComplex)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278438 -ocoerce`1`x`(Equation(Expression(MachineFloat)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278479 -ocoerce`1`x`(Equation(Expression(MachineInteger)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278520 -ocoerce`1`x`(Exit)->S`pResolveLatticeCompletion(S)``278561 -ocoerce`1`x`(Expression(Complex(Float)))->_$`dFortranProgram(name,returnType,arguments,symbols)``278718 -ocoerce`1`x`(Expression(Float))->_$`dFortranProgram(name,returnType,arguments,symbols)``278758 -ocoerce`1`x`(Expression(Integer))->Expression(_$)`dMachineInteger``278798 -ocoerce`1`x`(Expression(Integer))->_$`dFortranProgram(name,returnType,arguments,symbols)``278871 -ocoerce`1`x`(Expression(MachineComplex))->_$`dFortranProgram(name,returnType,arguments,symbols)``278911 -ocoerce`1`x`(Expression(MachineFloat))->_$`dFortranProgram(name,returnType,arguments,symbols)``278951 -ocoerce`1`x`(Expression(MachineInteger))->_$`dFortranProgram(name,returnType,arguments,symbols)``278991 -ocoerce`1`x`(F1)->F2`pFiniteFieldHomomorphisms(F1,GF,F2)``279031 -ocoerce`1`x`(F2)->F1`pFiniteFieldHomomorphisms(F1,GF,F2)``279492 -ocoerce`1`x`(FortranCode)->_$`cFortranFunctionCategory``279956 -ocoerce`1`x`(FortranCode)->_$`cFortranMatrixCategory``280073 -ocoerce`1`x`(FortranCode)->_$`cFortranMatrixFunctionCategory``280190 -ocoerce`1`x`(FortranCode)->_$`cFortranVectorCategory``280307 -ocoerce`1`x`(FortranCode)->_$`cFortranVectorFunctionCategory``280424 -ocoerce`1`x`(FortranCode)->_$`dFortranProgram(name,returnType,arguments,symbols)``280541 -ocoerce`1`x`(FortranExpression(construct('X),construct('Y),MachineFloat))->_$`dAsp9(name)``280582 -ocoerce`1`x`(FortranExpression(construct('X),construct,MachineFloat))->_$`dAsp1(name)``280715 -ocoerce`1`x`(FortranExpression(construct,construct('X),MachineFloat))->_$`dAsp4(name)``280848 -ocoerce`1`x`(FortranExpression(construct,construct('X),MachineFloat))->_$`dAsp49(name)``280981 -ocoerce`1`x`(FortranExpression(construct,construct('XC),MachineFloat))->_$`dAsp24(name)``281114 -ocoerce`1`x`(FortranScalarType)->_$`dFortranType``281247 -ocoerce`1`x`(FourierComponent(E))->_$`dFourierSeries(R,E)``281309 -ocoerce`1`x`(Fraction(Factored(R)))->_$`dPartialFraction(R)``281376 -ocoerce`1`x`(Fraction(Polynomial(AlgebraicNumber)))->Expression(Integer)`pPolynomialAN2Expression``281668 -ocoerce`1`x`(Fraction(Polynomial(Fraction(R))))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`281818 -ocoerce`1`x`(Fraction(R))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`281880 -ocoerce`1`x`(Integer)->_$`cNonAssociativeRing``281942 -ocoerce`1`x`(Integer)->_$`cRing``282022 -ocoerce`1`x`(Integer)->_$`dOrdSetInts``282109 -ocoerce`1`x`(List(DPoly))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``282179 -ocoerce`1`x`(List(FortranCode))->_$`cFortranFunctionCategory``282272 -ocoerce`1`x`(List(FortranCode))->_$`cFortranMatrixCategory``282394 -ocoerce`1`x`(List(FortranCode))->_$`cFortranMatrixFunctionCategory``282516 -ocoerce`1`x`(List(FortranCode))->_$`cFortranVectorCategory``282638 -ocoerce`1`x`(List(FortranCode))->_$`cFortranVectorFunctionCategory``282760 -ocoerce`1`x`(List(FortranCode))->_$`dFortranProgram(name,returnType,arguments,symbols)``282882 -ocoerce`1`x`(List(List(S)))->_$`dPermutation(S)``282924 -ocoerce`1`x`(List(Permutation(S)))->_$`dPermutationGroup(S)``283249 -ocoerce`1`x`(List(R))->_$`dCartesianTensor(minix,dim,R)``283351 -ocoerce`1`x`(List(S))->_$`dDataList(S)``283439 -ocoerce`1`x`(List(S))->_$`dDatabase(S)``283496 -ocoerce`1`x`(List(S))->_$`dPermutation(S)``283551 -ocoerce`1`x`(List(S))->_$`dStream(S)``283779 -ocoerce`1`x`(List(_$))->_$`dCartesianTensor(minix,dim,R)``283841 -ocoerce`1`x`(MachineInteger)->_$`dMachineFloat``283929 -ocoerce`1`x`(Matrix(FortranExpression(construct('X),construct,MachineFloat)))->_$`dAsp77(name)``284001 -ocoerce`1`x`(Matrix(FortranExpression(construct('X,'Y),construct,MachineFloat)))->_$`dAsp74(name)``284134 -ocoerce`1`x`(Matrix(FortranExpression(construct('XL,'XR,'ELAM),construct,MachineFloat)))->_$`dAsp80(name)``284267 -ocoerce`1`x`(Matrix(FortranExpression(construct,construct('X,'HESS),MachineFloat)))->_$`dAsp20(name)``284400 -ocoerce`1`x`(Matrix(MachineFloat))->_$`cFortranMatrixCategory``284533 -ocoerce`1`x`(OutputForm)->_$`dScriptFormulaFormat``284610 -ocoerce`1`x`(OutputForm)->_$`dTexFormat``284707 -ocoerce`1`x`(Pi)->Expression(R)`pPiCoercions(R)``284793 -ocoerce`1`x`(Polynomial(AlgebraicNumber))->Expression(Integer)`pPolynomialAN2Expression``284862 -ocoerce`1`x`(Polynomial(Coef))->_$`dTaylorSeries(Coef)``284988 -ocoerce`1`x`(Polynomial(Fraction(R)))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`285089 -ocoerce`1`x`(PrimitiveArray(PrimitiveArray(PrimitiveArray(R))))->_$`dThreeDimensionalMatrix(R)``285151 -ocoerce`1`x`(R)->Fraction(Polynomial(R))`pRationalFunction(R)``285280 -ocoerce`1`x`(R)->_$`cAlgebra(R)``285366 -ocoerce`1`x`(R)->_$`cLeftAlgebra(R)``285449 -ocoerce`1`x`(R)->_$`cXAlgebra(R)``285539 -ocoerce`1`x`(R)->_$`dFourierSeries(R,E)``285582 -ocoerce`1`x`(R)->_$`dOrdinaryDifferentialRing(Kernels,R,var)``285648 -ocoerce`1`x`(Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))))->_$`dNumericalOptimizationProblem``285733 -ocoerce`1`x`(Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalIntegrationProblem``285773 -ocoerce`1`x`(Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))->_$`dNumericalOptimizationProblem``285813 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranFunctionCategory``285853 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranMatrixCategory``286045 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranMatrixFunctionCategory``286237 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranVectorCategory``286429 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranVectorFunctionCategory``286621 -ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`dFortranProgram(name,returnType,arguments,symbols)``286813 -ocoerce`1`x`(Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat))->_$`dNumericalPDEProblem``286853 -ocoerce`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalIntegrationProblem``286893 -ocoerce`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalODEProblem``286933 -ocoerce`1`x`(S)->Any`pAnyFunctions1(S)``286973 -ocoerce`1`x`(S)->None`pNoneFunctions1(S)``287076 -ocoerce`1`x`(S)->ScriptFormulaFormat`pScriptFormulaFormat1(S)``287157 -ocoerce`1`x`(S)->TexFormat`pTexFormat1(S)``287430 -ocoerce`1`x`(S)->Void`pResolveLatticeCompletion(S)``287657 -ocoerce`1`x`(S)->_$`cDifferentialVariableCategory(S)``287992 -ocoerce`1`x`(S)->_$`cRetractableTo(S)``288088 -ocoerce`1`x`(Segment(S))->_$`dUniversalSegment(S)``288148 -ocoerce`1`x`(SegmentBinding(Expression(R)))->SegmentBinding(Float)`pDrawNumericHack(R)``288223 -ocoerce`1`x`(SparseMultivariatePolynomial(Integer,Kernel(_$)))->_$`dAlgebraicNumber``288357 -ocoerce`1`x`(SparseMultivariatePolynomial(R,Kernel(_$)))->_$`cFunctionSpace(R)`has(R,Ring)`288429 -ocoerce`1`x`(SquareMatrix(dim,R))->_$`dCartesianTensor(minix,dim,R)``288491 -ocoerce`1`x`(String)->_$`cFileNameCategory``288550 -ocoerce`1`x`(String)->_$`dFortranScalarType``288660 -ocoerce`1`x`(String)->_$`dIndexCard``288949 -ocoerce`1`x`(String)->_$`dSymbol``289122 -ocoerce`1`x`(Symbol)->_$`dFortranScalarType``289188 -ocoerce`1`x`(Symbol)->_$`dOpenMathErrorKind``289452 -ocoerce`1`x`(Symbol)->_$`dSwitch``289696 -ocoerce`1`x`(Symbol)->_$`dTaylorSeries(Coef)``289736 -ocoerce`1`x`(ULS)->_$`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``289799 -ocoerce`1`x`(UTS)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``289887 -ocoerce`1`x`(Union(nia:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),mdnia:Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat)))->_$`dNumericalIntegrationProblem``289974 -ocoerce`1`x`(Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat))))->_$`dNumericalOptimizationProblem``290014 -ocoerce`1`x`(UnivariatePuiseuxSeries(Coef,var,cen))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``290054 -ocoerce`1`x`(VarSet)->_$`cFreeLieAlgebra(VarSet,R)``290131 -ocoerce`1`x`(Variable(var))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``290209 -ocoerce`1`x`(Variable(x))->_$`dUnivariatePolynomial(x,R)``290298 -ocoerce`1`x`(Vector(FortranExpression(construct('EPS),construct('YA,'YB),MachineFloat)))->_$`dAsp42(nameOne,nameTwo,nameThree)``290381 -ocoerce`1`x`(Vector(FortranExpression(construct('JINT,'X,'ELAM),construct,MachineFloat)))->_$`dAsp10(name)``290514 -ocoerce`1`x`(Vector(FortranExpression(construct('X),construct('Y),MachineFloat)))->_$`dAsp31(name)``290647 -ocoerce`1`x`(Vector(FortranExpression(construct('X),construct('Y),MachineFloat)))->_$`dAsp7(name)``290780 -ocoerce`1`x`(Vector(FortranExpression(construct('X),construct,MachineFloat)))->_$`dAsp78(name)``290913 -ocoerce`1`x`(Vector(FortranExpression(construct('X,'EPS),construct('Y),MachineFloat)))->_$`dAsp41(nameOne,nameTwo,nameThree)``291046 -ocoerce`1`x`(Vector(FortranExpression(construct('X,'Y),construct,MachineFloat)))->_$`dAsp73(name)``291179 -ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp35(name)``291312 -ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp55(name)``291445 -ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp6(name)``291578 -ocoerce`1`x`(Vector(FortranExpression(construct,construct('XC),MachineFloat)))->_$`dAsp19(name)``291711 -ocoerce`1`x`(Vector(FortranExpression(construct,construct('XC),MachineFloat)))->_$`dAsp50(name)``291844 -ocoerce`1`x`(Vector(MachineFloat))->_$`cFortranVectorCategory``291977 -ocoerce`1`x`(Vector(R))->_$`dAlgebraGivenByStructuralConstants(R,n,ls,gamma)``292054 -ocoerce`1`x`(_$)->Complex(Float)`dMachineComplex``292261 -ocoerce`1`x`(_$)->Expression(R)`dFortranExpression(basicSymbols,subscriptedSymbols,R)``292326 -ocoerce`1`x`(_$)->Float`dMachineFloat``292366 -ocoerce`1`x`(_$)->Fraction(Integer)`dBinaryExpansion``292436 -ocoerce`1`x`(_$)->Fraction(Integer)`dDecimalExpansion``292510 -ocoerce`1`x`(_$)->Fraction(Integer)`dHexadecimalExpansion``292585 -ocoerce`1`x`(_$)->Fraction(Integer)`dRadixExpansion(bb)``292664 -ocoerce`1`x`(_$)->Fraction(R)`dPartialFraction(R)``292738 -ocoerce`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``292840 -ocoerce`1`x`(_$)->List(S)`dDataList(S)``292911 -ocoerce`1`x`(_$)->OutputForm`cThreeSpaceCategory(R)``292976 -ocoerce`1`x`(_$)->OutputForm`dFortranCode``293061 -ocoerce`1`x`(_$)->OutputForm`dFortranType``293123 -ocoerce`1`x`(_$)->OutputForm`dNumericalIntegrationProblem``293186 -ocoerce`1`x`(_$)->OutputForm`dNumericalODEProblem``293226 -ocoerce`1`x`(_$)->OutputForm`dNumericalOptimizationProblem``293266 -ocoerce`1`x`(_$)->OutputForm`dNumericalPDEProblem``293306 -ocoerce`1`x`(_$)->OutputForm`dTableau(S)``293346 -ocoerce`1`x`(_$)->OutputForm`dVoid``293417 -ocoerce`1`x`(_$)->PrimitiveArray(PrimitiveArray(PrimitiveArray(R)))`dThreeDimensionalMatrix(R)``293476 -ocoerce`1`x`(_$)->R`dOrdinaryDifferentialRing(Kernels,R,var)``293549 -ocoerce`1`x`(_$)->RadixExpansion(10)`dDecimalExpansion``293633 -ocoerce`1`x`(_$)->RadixExpansion(16)`dHexadecimalExpansion``293721 -ocoerce`1`x`(_$)->RadixExpansion(2)`dBinaryExpansion``293813 -ocoerce`1`x`(_$)->SExpression`dFortranScalarType``293899 -ocoerce`1`x`(_$)->S`cCoercibleTo(S)``293980 -ocoerce`1`x`(_$)->String`cFileNameCategory``294046 -ocoerce`1`x`(_$)->Symbol`dFortranScalarType``294158 -ocoerce`1`x`(_$)->Table(Symbol,FortranType)`dSymbolTable``294226 -ocoerce`1`x`(_$)->Tree(S)`dPendantTree(S)``294283 -ocoerce`1`x`(_$)->XDistributedPolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``294321 -ocoerce`1`x`(_$)->XRecursivePolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``294405 -ocoerce`1`x`(vl)->_$`cXFreeAlgebra(vl,R)``294489 -ocoleman`3`x`(List(Integer),List(Integer),List(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``294531 +ocoerce`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``331609 +ocoerce`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dXPBWPolynomial(VarSet,R)``331698 +ocoerce`1`n`(_$)->XPBWPolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``331784 +ocoerce`1`n`(_$)->XRecursivePolynomial(VarSet,R)`dXPBWPolynomial(VarSet,R)``331873 +ocoerce`1`x`(A)->()->A`pMappingPackage1(A)``331957 +ocoerce`1`x`(A)->_$`dAssociatedJordanAlgebra(R,A)``332040 +ocoerce`1`x`(A)->_$`dAssociatedLieAlgebra(R,A)``332203 +ocoerce`1`x`(Character)->_$`cStringAggregate``332360 +ocoerce`1`x`(Col)->_$`cMatrixCategory(R,Row,Col)``332451 +ocoerce`1`x`(Color)->_$`dPalette``332587 +ocoerce`1`x`(_$)->Complex(Float)`dMachineComplex``332691 +ocoerce`1`x`(Complex(Float))->_$`dMachineComplex``332756 +ocoerce`1`x`(Complex(Integer))->_$`dMachineComplex``332822 +ocoerce`1`x`(Complex(MachineFloat))->_$`dMachineComplex``332888 +ocoerce`1`x`(Complex(MachineInteger))->_$`dMachineComplex``332954 +ocoerce`1`x`(DirectProduct(dim,R))->_$`dCartesianTensor(minix,dim,R)``333020 +ocoerce`1`x`(Equation(Expression(Complex(Float))))->_$`dFortranProgram(name,returnType,arguments,symbols)``333220 +ocoerce`1`x`(Equation(Expression(Float)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333263 +ocoerce`1`x`(Equation(Expression(Integer)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333306 +ocoerce`1`x`(Equation(Expression(MachineComplex)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333349 +ocoerce`1`x`(Equation(Expression(MachineFloat)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333392 +ocoerce`1`x`(Equation(Expression(MachineInteger)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333435 +ocoerce`1`x`(Exit)->S`pResolveLatticeCompletion(S)``333478 +ocoerce`1`x`(Expression(Complex(Float)))->_$`dFortranProgram(name,returnType,arguments,symbols)``333635 +ocoerce`1`x`(Expression(Float))->_$`dFortranProgram(name,returnType,arguments,symbols)``333677 +ocoerce`1`x`(Expression(Integer))->_$`dFortranProgram(name,returnType,arguments,symbols)``333719 +ocoerce`1`x`(Expression(Integer))->Expression(_$)`dMachineInteger``333761 +ocoerce`1`x`(Expression(MachineComplex))->_$`dFortranProgram(name,returnType,arguments,symbols)``333834 +ocoerce`1`x`(Expression(MachineFloat))->_$`dFortranProgram(name,returnType,arguments,symbols)``333876 +ocoerce`1`x`(Expression(MachineInteger))->_$`dFortranProgram(name,returnType,arguments,symbols)``333918 +ocoerce`1`x`(_$)->Expression(R)`dFortranExpression(basicSymbols,subscriptedSymbols,R)``333960 +ocoerce`1`x`(F1)->F2`pFiniteFieldHomomorphisms(F1,GF,F2)``334002 +ocoerce`1`x`(F2)->F1`pFiniteFieldHomomorphisms(F1,GF,F2)``334464 +ocoerce`1`x`(_$)->Float`dMachineFloat``334929 +ocoerce`1`x`(FortranCode)->_$`cFortranFunctionCategory``334999 +ocoerce`1`x`(FortranCode)->_$`cFortranMatrixCategory``335116 +ocoerce`1`x`(FortranCode)->_$`cFortranMatrixFunctionCategory``335233 +ocoerce`1`x`(FortranCode)->_$`cFortranVectorCategory``335350 +ocoerce`1`x`(FortranCode)->_$`cFortranVectorFunctionCategory``335467 +ocoerce`1`x`(FortranCode)->_$`dFortranProgram(name,returnType,arguments,symbols)``335584 +ocoerce`1`x`(FortranExpression(construct,construct('XC),MachineFloat))->_$`dAsp24(name)``335627 +ocoerce`1`x`(FortranExpression(construct,construct('X),MachineFloat))->_$`dAsp49(name)``335760 +ocoerce`1`x`(FortranExpression(construct,construct('X),MachineFloat))->_$`dAsp4(name)``335893 +ocoerce`1`x`(FortranExpression(construct('X),construct,MachineFloat))->_$`dAsp1(name)``336026 +ocoerce`1`x`(FortranExpression(construct('X),construct('Y),MachineFloat))->_$`dAsp9(name)``336159 +ocoerce`1`x`(FortranScalarType)->_$`dFortranType``336292 +ocoerce`1`x`(FourierComponent(E))->_$`dFourierSeries(R,E)``336354 +ocoerce`1`x`(Fraction(Factored(R)))->_$`dPartialFraction(R)``336421 +ocoerce`1`x`(_$)->Fraction(Integer)`dBinaryExpansion``336829 +ocoerce`1`x`(_$)->Fraction(Integer)`dDecimalExpansion``336903 +ocoerce`1`x`(_$)->Fraction(Integer)`dHexadecimalExpansion``336978 +ocoerce`1`x`(_$)->Fraction(Integer)`dRadixExpansion(bb)``337057 +ocoerce`1`x`(Fraction(MyUnivariatePolynomial(q,R)))->_$`dMyExpression(q,R)``0 +ocoerce`1`x`(Fraction(Polynomial(AlgebraicNumber)))->Expression(Integer)`pPolynomialAN2Expression``337131 +ocoerce`1`x`(Fraction(Polynomial(Fraction(R))))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`337281 +ocoerce`1`x`(Fraction(R))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`337343 +ocoerce`1`x`(_$)->Fraction(R)`dPartialFraction(R)``337405 +ocoerce`1`x`(Integer)->_$`cNonAssociativeRing``337598 +ocoerce`1`x`(Integer)->_$`cRing``337678 +ocoerce`1`x`(Integer)->_$`dOrdSetInts``337765 +ocoerce`1`x`(List(_$))->_$`dCartesianTensor(minix,dim,R)``337835 +ocoerce`1`x`(List(DPoly))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``338121 +ocoerce`1`x`(List(FortranCode))->_$`cFortranFunctionCategory``338214 +ocoerce`1`x`(List(FortranCode))->_$`cFortranMatrixCategory``338336 +ocoerce`1`x`(List(FortranCode))->_$`cFortranMatrixFunctionCategory``338458 +ocoerce`1`x`(List(FortranCode))->_$`cFortranVectorCategory``338580 +ocoerce`1`x`(List(FortranCode))->_$`cFortranVectorFunctionCategory``338702 +ocoerce`1`x`(List(FortranCode))->_$`dFortranProgram(name,returnType,arguments,symbols)``338824 +ocoerce`1`x`(List(Integer))->_$`cBlowUpMethodCategory``0 +ocoerce`1`x`(_$)->List(K)`cAffineSpaceCategory(K)``0 +ocoerce`1`x`(List(K))->_$`cAffineSpaceCategory(K)``338868 +ocoerce`1`x`(_$)->List(K)`cProjectiveSpaceCategory(K)``338927 +ocoerce`1`x`(List(K))->_$`cProjectiveSpaceCategory(K)``338986 +ocoerce`1`x`(List(List(S)))->_$`dPermutation(S)``339049 +ocoerce`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``339390 +ocoerce`1`x`(List(Permutation(S)))->_$`dPermutationGroup(S)``339462 +ocoerce`1`x`(List(R))->_$`dCartesianTensor(minix,dim,R)``339565 +ocoerce`1`x`(List(S))->_$`dDatabase(S)``339774 +ocoerce`1`x`(List(S))->_$`dDataList(S)``339829 +ocoerce`1`x`(_$)->List(S)`dDataList(S)``339886 +ocoerce`1`x`(List(S))->_$`dPermutation(S)``339951 +ocoerce`1`x`(List(S))->_$`dStream(S)``340196 +ocoerce`1`x`(MachineInteger)->_$`dMachineFloat``340423 +ocoerce`1`x`(Matrix(FortranExpression(construct,construct('X,'HESS),MachineFloat)))->_$`dAsp20(name)``340495 +ocoerce`1`x`(Matrix(FortranExpression(construct('X),construct,MachineFloat)))->_$`dAsp77(name)``340628 +ocoerce`1`x`(Matrix(FortranExpression(construct('XL,'XR,'ELAM),construct,MachineFloat)))->_$`dAsp80(name)``340761 +ocoerce`1`x`(Matrix(FortranExpression(construct('X,'Y),construct,MachineFloat)))->_$`dAsp74(name)``340894 +ocoerce`1`x`(Matrix(MachineFloat))->_$`cFortranMatrixCategory``341027 +ocoerce`1`x`(_$)->OutputForm`cThreeSpaceCategory(R)``341104 +ocoerce`1`x`(_$)->OutputForm`dArrayStack(S)`has(S,SetCategory)`341189 +ocoerce`1`x`(_$)->OutputForm`dDequeue(S)`has(S,SetCategory)`341284 +ocoerce`1`x`(_$)->OutputForm`dFortranCode``341373 +ocoerce`1`x`(_$)->OutputForm`dFortranType``341435 +ocoerce`1`x`(_$)->OutputForm`dHeap(S)`has(S,SetCategory)`341498 +ocoerce`1`x`(_$)->OutputForm`dNumericalIntegrationProblem``341581 +ocoerce`1`x`(_$)->OutputForm`dNumericalODEProblem``341623 +ocoerce`1`x`(_$)->OutputForm`dNumericalOptimizationProblem``341665 +ocoerce`1`x`(_$)->OutputForm`dNumericalPDEProblem``341707 +ocoerce`1`x`(_$)->OutputForm`dQueue(S)`has(S,SetCategory)`341749 +ocoerce`1`x`(OutputForm)->_$`dScriptFormulaFormat``341834 +ocoerce`1`x`(_$)->OutputForm`dStack(S)`has(S,SetCategory)`341931 +ocoerce`1`x`(_$)->OutputForm`dTableau(S)``342016 +ocoerce`1`x`(OutputForm)->_$`dTexFormat``342087 +ocoerce`1`x`(_$)->OutputForm`dVoid``342173 +ocoerce`1`x`(OutputForm)->String`dMathMLFormat``342232 +ocoerce`1`x`(Pi)->Expression(R)`pPiCoercions(R)``342322 +ocoerce`1`x`(Polynomial(AlgebraicNumber))->Expression(Integer)`pPolynomialAN2Expression``342391 +ocoerce`1`x`(Polynomial(Coef))->_$`dTaylorSeries(Coef)``342517 +ocoerce`1`x`(Polynomial(Fraction(R)))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`342618 +ocoerce`1`x`(Polynomial(R))->_$`dMyUnivariatePolynomial(x,R)``0 +ocoerce`1`x`(PrimitiveArray(PrimitiveArray(PrimitiveArray(R))))->_$`dThreeDimensionalMatrix(R)``342680 +ocoerce`1`x`(_$)->PrimitiveArray(PrimitiveArray(PrimitiveArray(R)))`dThreeDimensionalMatrix(R)``342809 +ocoerce`1`x`(_$)->RadixExpansion(10)`dDecimalExpansion``342882 +ocoerce`1`x`(_$)->RadixExpansion(16)`dHexadecimalExpansion``342970 +ocoerce`1`x`(_$)->RadixExpansion(2)`dBinaryExpansion``343062 +ocoerce`1`x`(R)->_$`cAlgebra(R)``343148 +ocoerce`1`x`(R)->_$`cLeftAlgebra(R)``343231 +ocoerce`1`x`(R)->_$`cXAlgebra(R)``343321 +ocoerce`1`x`(R)->_$`dFourierSeries(R,E)``343364 +ocoerce`1`x`(R)->_$`dMyUnivariatePolynomial(x,R)`has(R,SIGNATURE(univariate,SparseUnivariatePolynomial(R)(R,Symbol)))`0 +ocoerce`1`x`(_$)->R`dOrdinaryDifferentialRing(Kernels,R,var)``343430 +ocoerce`1`x`(R)->_$`dOrdinaryDifferentialRing(Kernels,R,var)``343514 +ocoerce`1`x`(Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))))->_$`dNumericalOptimizationProblem``343599 +ocoerce`1`x`(Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalIntegrationProblem``343641 +ocoerce`1`x`(Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))->_$`dNumericalOptimizationProblem``343683 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranFunctionCategory``343725 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranMatrixCategory``343917 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranMatrixFunctionCategory``344109 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranVectorCategory``344301 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`cFortranVectorFunctionCategory``344493 +ocoerce`1`x`(Record(localSymbols:SymbolTable,code:List(FortranCode)))->_$`dFortranProgram(name,returnType,arguments,symbols)``344685 +ocoerce`1`x`(Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat))->_$`dNumericalPDEProblem``344727 +ocoerce`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalIntegrationProblem``344769 +ocoerce`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->_$`dNumericalODEProblem``344811 +ocoerce`1`x`(R)->Fraction(Polynomial(R))`pRationalFunction(R)``344853 +ocoerce`1`x`(S)->Any`pAnyFunctions1(S)``344939 +ocoerce`1`x`(_$)->S`cCoercibleTo(S)``345042 +ocoerce`1`x`(S)->_$`cDifferentialVariableCategory(S)``345108 +ocoerce`1`x`(S)->_$`cRetractableTo(S)``345204 +ocoerce`1`x`(SegmentBinding(Expression(R)))->SegmentBinding(Float)`pDrawNumericHack(R)``345264 +ocoerce`1`x`(Segment(S))->_$`dUniversalSegment(S)``345398 +ocoerce`1`x`(_$)->SExpression`dFortranScalarType``345473 +ocoerce`1`x`(S)->None`pNoneFunctions1(S)``345554 +ocoerce`1`x`(SparseMultivariatePolynomial(Integer,Kernel(_$)))->_$`dAlgebraicNumber``345635 +ocoerce`1`x`(SparseMultivariatePolynomial(R,Kernel(_$)))->_$`cFunctionSpace(R)`has(R,Ring)`345707 +ocoerce`1`x`(SquareMatrix(dim,R))->_$`dCartesianTensor(minix,dim,R)``345769 +ocoerce`1`x`(S)->ScriptFormulaFormat`pScriptFormulaFormat1(S)``345973 +ocoerce`1`x`(S)->TexFormat`pTexFormat1(S)``346246 +ocoerce`1`x`(_$)->Stream(Record(k:Integer,c:K))`cLocalPowerSeriesCategory(K)``0 +ocoerce`1`x`(Stream(Record(k:Integer,c:K)))->_$`cLocalPowerSeriesCategory(K)``0 +ocoerce`1`x`(_$)->String`cFileNameCategory``346473 +ocoerce`1`x`(String)->_$`cFileNameCategory``346585 +ocoerce`1`x`(String)->_$`dFortranScalarType``346695 +ocoerce`1`x`(String)->_$`dIndexCard``346984 +ocoerce`1`x`(String)->_$`dSymbol``347142 +ocoerce`1`x`(S)->Void`pResolveLatticeCompletion(S)``347208 +ocoerce`1`x`(Symbol)->_$`dFortranScalarType``347543 +ocoerce`1`x`(_$)->Symbol`dFortranScalarType``347807 +ocoerce`1`x`(Symbol)->_$`dOpenMathErrorKind``347875 +ocoerce`1`x`(Symbol)->_$`dSwitch``348119 +ocoerce`1`x`(Symbol)->_$`dTaylorSeries(Coef)``348161 +ocoerce`1`x`(_$)->Table(Symbol,FortranType)`dSymbolTable``348224 +ocoerce`1`x`(_$)->Tree(S)`dPendantTree(S)``348281 +ocoerce`1`x`(ULS)->_$`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``348470 +ocoerce`1`x`(Union(nia:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),mdnia:Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat)))->_$`dNumericalIntegrationProblem``348558 +ocoerce`1`x`(Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat))))->_$`dNumericalOptimizationProblem``348600 +ocoerce`1`x`(UnivariatePolynomial(var,Coef))->_$`dUnivariateTaylorSeriesCZero(Coef,var)``348642 +ocoerce`1`x`(UnivariatePolynomial('x,Coef))->_$`dUnivariateFormalPowerSeries(Coef)``0 +ocoerce`1`x`(UnivariatePuiseuxSeries(Coef,var,cen))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``348780 +ocoerce`1`x`(UTS)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``348857 +ocoerce`1`x`(Variable(var))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``348944 +ocoerce`1`x`(Variable(var))->_$`dUnivariateTaylorSeriesCZero(Coef,var)``349033 +ocoerce`1`x`(Variable(x))->_$`dMyUnivariatePolynomial(x,R)``349135 +ocoerce`1`x`(Variable('x))->_$`dUnivariateFormalPowerSeries(Coef)``0 +ocoerce`1`x`(Variable(x))->_$`dUnivariatePolynomial(x,R)``349218 +ocoerce`1`x`(VarSet)->_$`cFreeLieAlgebra(VarSet,R)``349301 +ocoerce`1`x`(Vector(FortranExpression(construct,construct('XC),MachineFloat)))->_$`dAsp19(name)``349379 +ocoerce`1`x`(Vector(FortranExpression(construct,construct('XC),MachineFloat)))->_$`dAsp50(name)``349512 +ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp35(name)``349645 +ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp55(name)``349778 +ocoerce`1`x`(Vector(FortranExpression(construct,construct('X),MachineFloat)))->_$`dAsp6(name)``349911 +ocoerce`1`x`(Vector(FortranExpression(construct('EPS),construct('YA,'YB),MachineFloat)))->_$`dAsp42(nameOne,nameTwo,nameThree)``350044 +ocoerce`1`x`(Vector(FortranExpression(construct('JINT,'X,'ELAM),construct,MachineFloat)))->_$`dAsp10(name)``350177 +ocoerce`1`x`(Vector(FortranExpression(construct('X),construct,MachineFloat)))->_$`dAsp78(name)``350310 +ocoerce`1`x`(Vector(FortranExpression(construct('X),construct('Y),MachineFloat)))->_$`dAsp31(name)``350443 +ocoerce`1`x`(Vector(FortranExpression(construct('X),construct('Y),MachineFloat)))->_$`dAsp7(name)``350576 +ocoerce`1`x`(Vector(FortranExpression(construct('X,'EPS),construct('Y),MachineFloat)))->_$`dAsp41(nameOne,nameTwo,nameThree)``350709 +ocoerce`1`x`(Vector(FortranExpression(construct('X,'Y),construct,MachineFloat)))->_$`dAsp73(name)``350842 +ocoerce`1`x`(Vector(MachineFloat))->_$`cFortranVectorCategory``350975 +ocoerce`1`x`(Vector(R))->_$`dAlgebraGivenByStructuralConstants(R,n,ls,gamma)``351052 +ocoerce`1`x`(vl)->_$`cXFreeAlgebra(vl,R)``351259 +ocoerce`1`x`(_$)->XDistributedPolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``351301 +ocoerce`1`x`(_$)->XRecursivePolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``351385 +ocoerceImages`1`x`(List(S))->_$`dPermutation(S)`AND(has(S,Finite),not(has(S,IntegerNumberSystem)))`351469 +ocoerceImages`1`x`(List(S))->_$`dPermutation(S)`has(S,IntegerNumberSystem)`351788 +ocoerceL`1`x`(OutputForm)->String`dMathMLFormat``352107 +ocoerceListOfPairs`1`x`(List(List(S)))->_$`dPermutation(S)``352236 +ocoerceP`1`n`(Vector(Matrix(R)))->Vector(Matrix(Polynomial(R)))`pCoerceVectorMatrixPackage(R)``352531 +ocoercePreimagesImages`1`x`(List(List(S)))->_$`dPermutation(S)``352664 +ocoerceS`1`x`(OutputForm)->String`dMathMLFormat``353121 +ocoHeight`1`n`(S)->NonNegativeInteger`xTriangularSetCategory&(S,R,E,V,P)``0 +ocoHeight`1`x`(_$)->NonNegativeInteger`cTriangularSetCategory(R,E,V,P)`has(V,Finite)`353241 +ocoleman`3`x`(List(Integer),List(Integer),List(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``353350 +ocollect`1`x`(_$)->_$`cDivisorCategory(S)``354145 +ocollect`2`n`(S,VarSet)->S`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 +ocollect`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``354215 ocollectQuasiMonic`1`n`(S)->S`xTriangularSetCategory&(S,R,E,V,P)``0 -ocollectQuasiMonic`1`x`(_$)->_$`cTriangularSetCategory(R,E,V,P)``295341 -ocollectUnder`2`n`(S,V)->S`xTriangularSetCategory&(S,R,E,V,P)``0 +ocollectQuasiMonic`1`x`(_$)->_$`cTriangularSetCategory(R,E,V,P)``354367 ocollectUnder`2`n`(S,VarSet)->S`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -ocollectUnder`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``295489 -ocollectUpper`2`n`(S,V)->S`xTriangularSetCategory&(S,R,E,V,P)``0 +ocollectUnder`2`n`(S,V)->S`xTriangularSetCategory&(S,R,E,V,P)``0 +ocollectUnder`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``354515 ocollectUpper`2`n`(S,VarSet)->S`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -ocollectUpper`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``295653 -ocollect`2`n`(S,VarSet)->S`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -ocollect`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``295820 -ocolorDef`3`x`(_$,Color,Color)->Void`dThreeDimensionalViewport``295972 -ocolorFunction`1`x`((DoubleFloat)->DoubleFloat)->_$`dDrawOption``296285 -ocolorFunction`1`x`((DoubleFloat,DoubleFloat)->DoubleFloat)->_$`dDrawOption``296468 -ocolorFunction`1`x`((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->_$`dDrawOption``296680 -ocolor`1`n`(Point(R))->R`pPointPackage(R)``296912 -ocolor`1`x`(Integer)->_$`dColor``297225 +ocollectUpper`2`n`(S,V)->S`xTriangularSetCategory&(S,R,E,V,P)``0 +ocollectUpper`2`x`(_$,VarSet)->_$`cPolynomialSetCategory(R,E,VarSet,P)``354679 +ocolor`1`n`(Point(R))->R`pPointPackage(R)``354846 +ocolor`1`x`(Integer)->_$`dColor``355159 +ocolorDef`3`x`(_$,Color,Color)->Void`dThreeDimensionalViewport``355229 +ocolorFunction`1`x`((DoubleFloat)->DoubleFloat)->_$`dDrawOption``355542 +ocolorFunction`1`x`((DoubleFloat,DoubleFloat)->DoubleFloat)->_$`dDrawOption``355725 +ocolorFunction`1`x`((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->_$`dDrawOption``355937 ocolumn`2`n`(S,Integer)->Col`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -ocolumn`2`x`(_$,Integer)->Col`cRectangularMatrixCategory(m,n,R,Row,Col)``297295 -ocolumn`2`x`(_$,Integer)->Col`cTwoDimensionalArrayCategory(R,Row,Col)``297423 -ocombineFeatureCompatibility`2`x`(Float,Float)->Float`pd02AgentsPackage``297547 -ocombineFeatureCompatibility`2`x`(Float,List(Float))->Float`pd02AgentsPackage``297628 -ocommaSeparate`1`n`(List(_$))->_$`dOutputForm``297708 -ocommaSeparate`1`x`(List(String))->String`pd01AgentsPackage``297803 -ocomment`1`x`(List(String))->_$`dFortranCode``297892 -ocomment`1`x`(String)->_$`dFortranCode``297999 -ocommonDenominator`1`n`(B)->R`pInnerCommonDenominator(R,Q,A,B)``298101 -ocommonDenominator`1`x`(A)->R`pCommonDenominator(R,Q,A)``298221 -ocommonDenominator`1`x`(Matrix(Q))->R`pMatrixCommonDenominator(R,Q)``298341 -ocommonDenominator`1`x`(UP)->R`pUnivariatePolynomialCommonDenominator(R,Q,UP)``298444 -ocommon`2`x`(Symbol,List(Symbol))->_$`dFortranCode``298551 -ocommutative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``298636 -ocommutative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``298720 -ocommutativeEquality`2`n`(_$,_$)->Boolean`dListMonoidOps(S,E,un)``298804 +ocolumn`2`x`(_$,Integer)->Col`cRectangularMatrixCategory(m,n,R,Row,Col)``356169 +ocolumn`2`x`(_$,Integer)->Col`cTwoDimensionalArrayCategory(R,Row,Col)``356297 +ocolumnSpace`1`n`(S)->List(Col)`xMatrixCategory&(S,R,Row,Col)``0 +ocolumnSpace`1`x`(_$)->List(Col)`cMatrixCategory(R,Row,Col)`has(R,EuclideanDomain)`356551 +ocombineFeatureCompatibility`2`x`(Float,Float)->Float`pd02AgentsPackage``356791 +ocombineFeatureCompatibility`2`x`(Float,List(Float))->Float`pd02AgentsPackage``356872 +ocommaSeparate`1`n`(List(_$))->_$`dOutputForm``356952 +ocommaSeparate`1`x`(List(String))->String`pd01AgentsPackage``357047 +ocomment`1`x`(List(String))->_$`dFortranCode``357136 +ocomment`1`x`(String)->_$`dFortranCode``357243 +ocommon`2`x`(Symbol,List(Symbol))->_$`dFortranCode``357345 +ocommonDenominator`1`n`(B)->R`pInnerCommonDenominator(R,Q,A,B)``357430 +ocommonDenominator`1`x`(A)->R`pCommonDenominator(R,Q,A)``357550 +ocommonDenominator`1`x`(Matrix(Q))->R`pMatrixCommonDenominator(R,Q)``357670 +ocommonDenominator`1`x`(UP)->R`pUnivariatePolynomialCommonDenominator(R,Q,UP)``357773 +ocommutative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``357880 +ocommutative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``357964 +ocommutativeEquality`2`n`(_$,_$)->Boolean`dListMonoidOps(S,E,un)``358048 ocommutator`2`n`(S,S)->S`xGroup&(S)``0 ocommutator`2`n`(S,S)->S`xNonAssociativeRng&(S)``0 -ocommutator`2`x`(_$,_$)->_$`cGroup``298923 -ocommutator`2`x`(_$,_$)->_$`cNonAssociativeRng``298996 -ocompBound`2`n`(BP,List(BP))->NonNegativeInteger`pGenExEuclid(R,BP)``299052 -ocomp`3`n`((B)->C,(A)->B,A)->C`pMappingPackageInternalHacks3(A,B,C)``299296 -ocompactFraction`1`x`(_$)->_$`dPartialFraction(R)``299344 -ocompanionBlocks`2`n`(Matrix(K),Vector(K))->List(Record(C:Matrix(K),g:Vector(K)))`pPseudoLinearNormalForm(K)``299545 -ocomparison`2`x`(_$,(_$,_$)->Boolean)->_$`dBasicOperator``299723 -ocompdegd`1`n`(List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)))->Integer`pMultivariateSquareFree(E,OV,R,P)``299990 -ocompile`2`n`(Symbol,List(_$))->Symbol`dInputForm``300029 -ocompiledFunction`2`n`(S,Symbol)->(D)->I`pMakeUnaryCompiledFunction(S,D,I)``300362 -ocompiledFunction`3`n`(S,Symbol,Symbol)->(D1,D2)->I`pMakeBinaryCompiledFunction(S,D1,D2,I)``300555 +ocommutator`2`x`(_$,_$)->_$`cGroup``358167 +ocommutator`2`x`(_$,_$)->_$`cNonAssociativeRng``358240 +ocomp`3`n`((B)->C,(A)->B,A)->C`pMappingPackageInternalHacks3(A,B,C)``358296 +ocompactFraction`1`x`(_$)->_$`dPartialFraction(R)``358344 +ocompanionBlocks`2`n`(Matrix(K),Vector(K))->List(Record(C:Matrix(K),g:Vector(K)))`pPseudoLinearNormalForm(K)``358722 +ocomparison`2`x`(_$,(_$,_$)->Boolean)->_$`dBasicOperator``358900 +ocompBound`2`n`(BP,List(BP))->NonNegativeInteger`pGenExEuclid(R,BP)``359167 +ocompdegd`1`n`(List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)))->Integer`pMultivariateSquareFree(E,OV,R,P)``359411 +ocompile`2`n`(Symbol,List(_$))->Symbol`dInputForm``359450 +ocompiledFunction`2`n`(S,Symbol)->(D)->I`pMakeUnaryCompiledFunction(S,D,I)``359783 +ocompiledFunction`3`n`(S,Symbol,Symbol)->(D1,D2)->I`pMakeBinaryCompiledFunction(S,D1,D2,I)``359976 ocomplement`1`n`(A)->A`xFiniteSetAggregate&(A,S)``0 -ocomplement`1`x`(_$)->_$`cFiniteSetAggregate(S)`has(S,Finite)`300773 +ocomplement`1`x`(_$)->_$`cFiniteSetAggregate(S)`has(S,Finite)`360194 ocomplementaryBasis`1`n`(Vector(S))->Vector(S)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -ocomplementaryBasis`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``300904 -ocompleteEchelonBasis`1`x`(Vector(Vector(R)))->Matrix(R)`pRepresentationPackage2(R)``301036 -ocompleteEval`3`n`(SparseUnivariatePolynomial(P),List(OV),List(R))->SparseUnivariatePolynomial(R)`pFactoringUtilities(E,OV,R,P)``301431 -ocompleteHensel`4`n`(TP,List(TP),RP,PositiveInteger)->List(TP)`pGeneralHenselPackage(RP,TP)``301704 -ocompleteHermite`1`x`(M)->Record(Hermite:M,eqMat:M)`pSmithNormalForm(R,Row,Col,M)``301912 -ocompleteSmith`1`x`(M)->Record(Smith:M,leftEqMat:M,rightEqMat:M)`pSmithNormalForm(R,Row,Col,M)``302081 +ocomplementaryBasis`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``360325 ocomplete`1`n`(A)->A`xLazyStreamAggregate&(A,S)``0 -ocomplete`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``302278 -ocomplete`1`x`(_$)->_$`cLazyStreamAggregate(S)``302517 -ocomplete`1`x`(_$)->_$`cPAdicIntegerCategory(p)``302664 -ocomplete`1`x`(_$)->_$`cPowerSeriesCategory(Coef,Expon,Var)``302728 -ocomplete`1`x`(_$)->_$`dContinuedFraction(R)``302877 -ocomplex?`1`x`(_$)->Boolean`dFortranScalarType``303130 -ocomplexEigenvalues`2`x`(Matrix(Complex(Fraction(Integer))),Par)->List(Complex(Par))`pNumericComplexEigenPackage(Par)``303222 -ocomplexEigenvectors`2`x`(Matrix(Complex(Fraction(Integer))),Par)->List(Record(outval:Complex(Par),outmult:Integer,outvect:List(Matrix(Complex(Par)))))`pNumericComplexEigenPackage(Par)``303470 -ocomplexElementary`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``303838 -ocomplexElementary`1`x`(F)->F`pTrigonometricManipulations(R,F)``303985 -ocomplexElementary`2`x`(F,Symbol)->F`pComplexTrigonometricManipulations(R,F)``304132 -ocomplexElementary`2`x`(F,Symbol)->F`pTrigonometricManipulations(R,F)``304318 -ocomplexExpand`1`x`(IntegrationResult(F))->F`pIntegrationResultToFunction(R,F)``304504 -ocomplexExpand`1`x`(IntegrationResult(Fraction(Polynomial(R))))->Expression(R)`pIntegrationResultRFToFunction(R)``304600 -ocomplexForm`1`x`(F)->Complex(Expression(R))`pComplexTrigonometricManipulations(R,F)``304696 -ocomplexForm`1`x`(F)->Complex(F)`pTrigonometricManipulations(R,F)``304760 -ocomplexIntegrate`2`x`(F,Symbol)->F`pFunctionSpaceComplexIntegration(R,F)``304824 -ocomplexIntegrate`2`x`(Fraction(Polynomial(R)),Symbol)->Expression(R)`pIntegrationResultRFToFunction(R)`has(R,CharacteristicZero)`304949 -ocomplexLimit`2`x`(FE,Equation(OnePointCompletion(FE)))->Union(OnePointCompletion(FE),"failed")`pPowerSeriesLimitPackage(R,FE)``305074 -ocomplexLimit`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->OnePointCompletion(Fraction(Polynomial(R)))`pRationalFunctionLimitPackage(R)``305169 -ocomplexLimit`2`x`(Fraction(Polynomial(R)),Equation(OnePointCompletion(Polynomial(R))))->OnePointCompletion(Fraction(Polynomial(R)))`pRationalFunctionLimitPackage(R)``305295 -ocomplexNormalize`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``305421 -ocomplexNormalize`1`x`(F)->F`pTrigonometricManipulations(R,F)``305537 -ocomplexNormalize`2`x`(F,Symbol)->F`pComplexTrigonometricManipulations(R,F)``305653 -ocomplexNormalize`2`x`(F,Symbol)->F`pTrigonometricManipulations(R,F)``305793 -ocomplexNumericIfCan`1`x`(Expression(Complex(S)))->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`305933 -ocomplexNumericIfCan`1`x`(Expression(S))->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`306068 -ocomplexNumericIfCan`1`x`(Fraction(Polynomial(Complex(S))))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`306203 -ocomplexNumericIfCan`1`x`(Fraction(Polynomial(S)))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`306338 -ocomplexNumericIfCan`1`x`(Polynomial(Complex(S)))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,CommutativeRing)`306473 -ocomplexNumericIfCan`1`x`(Polynomial(S))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,Ring)`306606 -ocomplexNumericIfCan`2`x`(Expression(Complex(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`306741 -ocomplexNumericIfCan`2`x`(Expression(S),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`306911 -ocomplexNumericIfCan`2`x`(Fraction(Polynomial(Complex(S))),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`307081 -ocomplexNumericIfCan`2`x`(Fraction(Polynomial(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`307251 -ocomplexNumericIfCan`2`x`(Polynomial(Complex(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,CommutativeRing)`307391 -ocomplexNumericIfCan`2`x`(Polynomial(S),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,Ring)`307561 -ocomplexNumeric`1`x`(Complex(S))->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`307731 -ocomplexNumeric`1`x`(Expression(Complex(S)))->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`307808 -ocomplexNumeric`1`x`(Expression(S))->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`307885 -ocomplexNumeric`1`x`(Fraction(Polynomial(Complex(S))))->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`307962 -ocomplexNumeric`1`x`(Fraction(Polynomial(S)))->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`308039 -ocomplexNumeric`1`x`(Polynomial(Complex(S)))->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`308116 -ocomplexNumeric`1`x`(Polynomial(S))->Complex(Float)`pNumeric(S)`has(S,Ring)`308193 -ocomplexNumeric`1`x`(S)->Complex(Float)`pNumeric(S)``308270 -ocomplexNumeric`2`x`(Complex(S),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`308347 -ocomplexNumeric`2`x`(Expression(Complex(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`308459 -ocomplexNumeric`2`x`(Expression(S),PositiveInteger)->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`308571 -ocomplexNumeric`2`x`(Fraction(Polynomial(Complex(S))),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`308683 -ocomplexNumeric`2`x`(Fraction(Polynomial(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`308795 -ocomplexNumeric`2`x`(Polynomial(Complex(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`308876 -ocomplexNumeric`2`x`(Polynomial(S),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,Ring)`308988 -ocomplexNumeric`2`x`(S,PositiveInteger)->Complex(Float)`pNumeric(S)``309100 -ocomplexRoots`2`x`(Fraction(Polynomial(Complex(Integer))),Par)->List(Complex(Par))`pFloatingComplexPackage(Par)``309212 -ocomplexRoots`3`x`(List(Fraction(Polynomial(Complex(Integer)))),List(Symbol),Par)->List(List(Complex(Par)))`pFloatingComplexPackage(Par)``309396 -ocomplexSolve`2`x`(Equation(Fraction(Polynomial(Complex(Integer)))),Par)->List(Equation(Polynomial(Complex(Par))))`pFloatingComplexPackage(Par)``309712 -ocomplexSolve`2`x`(Fraction(Polynomial(Complex(Integer))),Par)->List(Equation(Polynomial(Complex(Par))))`pFloatingComplexPackage(Par)``309952 -ocomplexSolve`2`x`(List(Equation(Fraction(Polynomial(Complex(Integer))))),Par)->List(List(Equation(Polynomial(Complex(Par)))))`pFloatingComplexPackage(Par)``310174 -ocomplexSolve`2`x`(List(Fraction(Polynomial(Complex(Integer)))),Par)->List(List(Equation(Polynomial(Complex(Par)))))`pFloatingComplexPackage(Par)``310409 -ocomplexZeros`1`n`(UP)->List(Complex(R))`pComplexRootFindingPackage(R,UP)``310633 -ocomplexZeros`2`n`(UP,R)->List(Complex(R))`pComplexRootFindingPackage(R,UP)``310832 -ocomplexZeros`2`x`(UP,Par)->List(Complex(Par))`pComplexRootPackage(UP,Par)``310967 -ocomplex`2`x`(R,R)->_$`cComplexCategory(R)``311174 -ocomponent`2`n`(_$,Point(DoubleFloat))->Void`dGraphImage``311232 -ocomponent`5`n`(_$,List(Point(DoubleFloat)),Palette,Palette,PositiveInteger)->Void`dGraphImage``311568 -ocomponent`5`n`(_$,Point(DoubleFloat),Palette,Palette,PositiveInteger)->Void`dGraphImage``312072 -ocomponents`1`x`(_$)->List(_$)`cThreeSpaceCategory(R)``312419 -ocompose`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``312660 -ocompose`2`x`(UP,UP)->UP`pPolynomialComposition(UP,R)``312756 -ocomposite`1`x`(List(_$))->_$`cThreeSpaceCategory(R)``312799 +ocomplete`1`x`(_$)->_$`cLazyStreamAggregate(S)``360457 +ocomplete`1`x`(_$)->_$`cPAdicIntegerCategory(p)``360864 +ocomplete`1`x`(_$)->_$`cPowerSeriesCategory(Coef,Expon,Var)``360928 +ocomplete`1`x`(_$)->_$`dContinuedFraction(R)``361081 +ocomplete`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``361334 +ocompleteEchelonBasis`1`x`(Vector(Vector(R)))->Matrix(R)`pRepresentationPackage2(R)``361573 +ocompleteEval`3`n`(SparseUnivariatePolynomial(P),List(OV),List(R))->SparseUnivariatePolynomial(R)`pFactoringUtilities(E,OV,R,P)``361961 +ocompleteHensel`4`n`(TP,List(TP),RP,PositiveInteger)->List(TP)`pGeneralHenselPackage(RP,TP)``362234 +ocompleteHermite`1`x`(M)->Record(Hermite:M,eqMat:M)`pSmithNormalForm(R,Row,Col,M)``362442 +ocompleteSmith`1`x`(M)->Record(Smith:M,leftEqMat:M,rightEqMat:M)`pSmithNormalForm(R,Row,Col,M)``362611 +ocomplex?`1`x`(_$)->Boolean`dFortranScalarType``362808 +ocomplex`2`x`(R,R)->_$`cComplexCategory(R)``362900 +ocomplexEigenvalues`2`x`(Matrix(Complex(Fraction(Integer))),Par)->List(Complex(Par))`pNumericComplexEigenPackage(Par)``362958 +ocomplexEigenvectors`2`x`(Matrix(Complex(Fraction(Integer))),Par)->List(Record(outval:Complex(Par),outmult:Integer,outvect:List(Matrix(Complex(Par)))))`pNumericComplexEigenPackage(Par)``363206 +ocomplexElementary`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``363574 +ocomplexElementary`1`x`(F)->F`pTrigonometricManipulations(R,F)``363721 +ocomplexElementary`2`x`(F,Symbol)->F`pComplexTrigonometricManipulations(R,F)``363868 +ocomplexElementary`2`x`(F,Symbol)->F`pTrigonometricManipulations(R,F)``364054 +ocomplexExpand`1`x`(IntegrationResult(F))->F`pIntegrationResultToFunction(R,F)``364240 +ocomplexExpand`1`x`(IntegrationResult(Fraction(Polynomial(R))))->Expression(R)`pIntegrationResultRFToFunction(R)``364336 +ocomplexForm`1`x`(F)->Complex(Expression(R))`pComplexTrigonometricManipulations(R,F)``364432 +ocomplexForm`1`x`(F)->Complex(F)`pTrigonometricManipulations(R,F)``364496 +ocomplexIntegrate`2`x`(Fraction(Polynomial(R)),Symbol)->Expression(R)`pIntegrationResultRFToFunction(R)`has(R,CharacteristicZero)`364560 +ocomplexIntegrate`2`x`(F,Symbol)->F`pFunctionSpaceComplexIntegration(R,F)``364685 +ocomplexLimit`2`x`(FE,Equation(OnePointCompletion(FE)))->Union(OnePointCompletion(FE),"failed")`pPowerSeriesLimitPackage(R,FE)``364810 +ocomplexLimit`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->OnePointCompletion(Fraction(Polynomial(R)))`pRationalFunctionLimitPackage(R)``364905 +ocomplexLimit`2`x`(Fraction(Polynomial(R)),Equation(OnePointCompletion(Polynomial(R))))->OnePointCompletion(Fraction(Polynomial(R)))`pRationalFunctionLimitPackage(R)``365031 +ocomplexNormalize`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``365157 +ocomplexNormalize`1`x`(F)->F`pTrigonometricManipulations(R,F)``365273 +ocomplexNormalize`2`x`(F,Symbol)->F`pComplexTrigonometricManipulations(R,F)``365389 +ocomplexNormalize`2`x`(F,Symbol)->F`pTrigonometricManipulations(R,F)``365529 +ocomplexNumeric`1`x`(Complex(S))->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`365669 +ocomplexNumeric`1`x`(Expression(Complex(S)))->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`365746 +ocomplexNumeric`1`x`(Expression(S))->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`365823 +ocomplexNumeric`1`x`(Fraction(Polynomial(Complex(S))))->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`365900 +ocomplexNumeric`1`x`(Fraction(Polynomial(S)))->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`365977 +ocomplexNumeric`1`x`(Polynomial(Complex(S)))->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`366054 +ocomplexNumeric`1`x`(Polynomial(S))->Complex(Float)`pNumeric(S)`has(S,Ring)`366131 +ocomplexNumeric`1`x`(S)->Complex(Float)`pNumeric(S)``366208 +ocomplexNumeric`2`x`(Complex(S),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`366285 +ocomplexNumeric`2`x`(Expression(Complex(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`366397 +ocomplexNumeric`2`x`(Expression(S),PositiveInteger)->Complex(Float)`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`366509 +ocomplexNumeric`2`x`(Fraction(Polynomial(Complex(S))),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`366621 +ocomplexNumeric`2`x`(Fraction(Polynomial(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,IntegralDomain)`366733 +ocomplexNumeric`2`x`(Polynomial(Complex(S)),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,CommutativeRing)`366814 +ocomplexNumeric`2`x`(Polynomial(S),PositiveInteger)->Complex(Float)`pNumeric(S)`has(S,Ring)`366926 +ocomplexNumeric`2`x`(S,PositiveInteger)->Complex(Float)`pNumeric(S)``367038 +ocomplexNumericIfCan`1`x`(Expression(Complex(S)))->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`367150 +ocomplexNumericIfCan`1`x`(Expression(S))->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`367285 +ocomplexNumericIfCan`1`x`(Fraction(Polynomial(Complex(S))))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`367420 +ocomplexNumericIfCan`1`x`(Fraction(Polynomial(S)))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`367555 +ocomplexNumericIfCan`1`x`(Polynomial(Complex(S)))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,CommutativeRing)`367690 +ocomplexNumericIfCan`1`x`(Polynomial(S))->Union(Complex(Float),"failed")`pNumeric(S)`has(S,Ring)`367823 +ocomplexNumericIfCan`2`x`(Expression(Complex(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`367958 +ocomplexNumericIfCan`2`x`(Expression(S),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`AND(has(S,IntegralDomain),has(S,OrderedSet))`368128 +ocomplexNumericIfCan`2`x`(Fraction(Polynomial(Complex(S))),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`368298 +ocomplexNumericIfCan`2`x`(Fraction(Polynomial(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,IntegralDomain)`368468 +ocomplexNumericIfCan`2`x`(Polynomial(Complex(S)),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,CommutativeRing)`368608 +ocomplexNumericIfCan`2`x`(Polynomial(S),PositiveInteger)->Union(Complex(Float),"failed")`pNumeric(S)`has(S,Ring)`368778 +ocomplexRoots`2`x`(Fraction(Polynomial(Complex(Integer))),Par)->List(Complex(Par))`pFloatingComplexPackage(Par)``368948 +ocomplexRoots`3`x`(List(Fraction(Polynomial(Complex(Integer)))),List(Symbol),Par)->List(List(Complex(Par)))`pFloatingComplexPackage(Par)``369132 +ocomplexSolve`2`x`(Equation(Fraction(Polynomial(Complex(Integer)))),Par)->List(Equation(Polynomial(Complex(Par))))`pFloatingComplexPackage(Par)``369448 +ocomplexSolve`2`x`(Fraction(Polynomial(Complex(Integer))),Par)->List(Equation(Polynomial(Complex(Par))))`pFloatingComplexPackage(Par)``369688 +ocomplexSolve`2`x`(List(Equation(Fraction(Polynomial(Complex(Integer))))),Par)->List(List(Equation(Polynomial(Complex(Par)))))`pFloatingComplexPackage(Par)``369910 +ocomplexSolve`2`x`(List(Fraction(Polynomial(Complex(Integer)))),Par)->List(List(Equation(Polynomial(Complex(Par)))))`pFloatingComplexPackage(Par)``370145 +ocomplexZeros`1`n`(UP)->List(Complex(R))`pComplexRootFindingPackage(R,UP)``370369 +ocomplexZeros`2`n`(UP,R)->List(Complex(R))`pComplexRootFindingPackage(R,UP)``370556 +ocomplexZeros`2`x`(UP,Par)->List(Complex(Par))`pComplexRootPackage(UP,Par)``370685 +ocomponent`2`n`(_$,Point(DoubleFloat))->Void`dGraphImage``370892 +ocomponent`5`n`(_$,List(Point(DoubleFloat)),Palette,Palette,PositiveInteger)->Void`dGraphImage``371228 +ocomponent`5`n`(_$,Point(DoubleFloat),Palette,Palette,PositiveInteger)->Void`dGraphImage``371732 +ocomponents`1`x`(_$)->List(_$)`cThreeSpaceCategory(R)``372079 +ocompose`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``372320 +ocompose`2`x`(UP,UP)->UP`pPolynomialComposition(UP,R)``372416 +ocomposite`1`x`(List(_$))->_$`cThreeSpaceCategory(R)``372459 ocomposite`2`n`(Fraction(S),S)->Union(Fraction(S),"failed")`xUnivariatePolynomialCategory&(S,R)``0 ocomposite`2`n`(S,S)->Union(S,"failed")`xUnivariatePolynomialCategory&(S,R)``0 -ocomposite`2`x`(Fraction(_$),_$)->Union(Fraction(_$),"failed")`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`313004 -ocomposite`2`x`(_$,_$)->Union(_$,"failed")`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`313130 -ocomposites`1`x`(_$)->List(_$)`cThreeSpaceCategory(R)``313239 -ocomputeBasis`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(HomogeneousDistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``313588 -ocomputeCycleEntry`2`n`(ST,ST)->ST`pCyclicStreamTools(S,ST)``313629 -ocomputeCycleLength`1`n`(ST)->NonNegativeInteger`pCyclicStreamTools(S,ST)``313820 -ocomputeInt`5`n`(Kernel(F),F,OrderedCompletion(F),OrderedCompletion(F),Boolean)->Union(OrderedCompletion(F),"failed")`pDefiniteIntegrationTools(R,F)``313989 -ocomputePowers`0`n`()->PrimitiveArray(_$)`dModMonic(R,Rep)``314409 -oconcat!`2`n`(A,A)->A`xExtensibleLinearAggregate&(A,S)``0 -oconcat!`2`n`(A,A)->A`xStreamAggregate&(A,S)``0 -oconcat!`2`n`(A,S)->A`xExtensibleLinearAggregate&(A,S)``0 -oconcat!`2`n`(A,S)->A`xStreamAggregate&(A,S)``0 -oconcat!`2`x`(_$,S)->_$`cExtensibleLinearAggregate(S)``314453 -oconcat!`2`x`(_$,S)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`314542 -oconcat!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`314695 -oconcat!`2`x`(_$,_$)->_$`cExtensibleLinearAggregate(S)``314832 -oconcat!`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`314938 +ocomposite`2`x`(Fraction(_$),_$)->Union(Fraction(_$),"failed")`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`372664 +ocomposite`2`x`(_$,_$)->Union(_$,"failed")`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`372790 +ocomposites`1`x`(_$)->List(_$)`cThreeSpaceCategory(R)``372899 +ocomputeBasis`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(HomogeneousDistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``373248 +ocomputeCycleEntry`2`n`(ST,ST)->ST`pCyclicStreamTools(S,ST)``373289 +ocomputeCycleLength`1`n`(ST)->NonNegativeInteger`pCyclicStreamTools(S,ST)``373650 +ocomputeInt`5`n`(Kernel(F),F,OrderedCompletion(F),OrderedCompletion(F),Boolean)->Union(OrderedCompletion(F),"failed")`pDefiniteIntegrationTools(R,F)``373986 +ocomputePowers`0`n`()->PrimitiveArray(_$)`dModMonic(R,Rep)``374406 oconcat`1`n`(List(A))->A`xExtensibleLinearAggregate&(A,S)``0 oconcat`1`n`(List(A))->A`xLinearAggregate&(A,S)``0 oconcat`1`n`(List(A))->A`xOneDimensionalArrayAggregate&(A,S)``0 oconcat`1`n`(List(A))->A`xStreamAggregate&(A,S)``0 -oconcat`1`x`(List(Result))->Result`pExpertSystemToolsPackage``315104 -oconcat`1`x`(List(_$))->_$`cLinearAggregate(S)``315189 -oconcat`1`x`(Stream(Stream(S)))->Stream(S)`pStreamFunctions1(S)``315539 +oconcat`1`x`(List(_$))->_$`cLinearAggregate(S)``374454 +oconcat`1`x`(List(Result))->Result`pExpertSystemToolsPackage``374808 +oconcat`1`x`(Stream(Stream(S)))->Stream(S)`pStreamFunctions1(S)``374893 oconcat`2`n`(A,A)->A`xExtensibleLinearAggregate&(A,S)``0 +oconcat!`2`n`(A,A)->A`xExtensibleLinearAggregate&(A,S)``0 oconcat`2`n`(A,A)->A`xLinearAggregate&(A,S)``0 oconcat`2`n`(A,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 oconcat`2`n`(A,A)->A`xStreamAggregate&(A,S)``0 +oconcat!`2`n`(A,A)->A`xStreamAggregate&(A,S)``0 oconcat`2`n`(A,A)->A`xUnaryRecursiveAggregate&(A,S)``0 oconcat`2`n`(A,S)->A`xExtensibleLinearAggregate&(A,S)``0 +oconcat!`2`n`(A,S)->A`xExtensibleLinearAggregate&(A,S)``0 oconcat`2`n`(A,S)->A`xLinearAggregate&(A,S)``0 oconcat`2`n`(A,S)->A`xOneDimensionalArrayAggregate&(A,S)``0 oconcat`2`n`(A,S)->A`xStreamAggregate&(A,S)``0 +oconcat!`2`n`(A,S)->A`xStreamAggregate&(A,S)``0 oconcat`2`n`(S,A)->A`xExtensibleLinearAggregate&(A,S)``0 oconcat`2`n`(S,A)->A`xLinearAggregate&(A,S)``0 oconcat`2`n`(S,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 oconcat`2`n`(S,A)->A`xStreamAggregate&(A,S)``0 oconcat`2`n`(S,A)->A`xUnaryRecursiveAggregate&(A,S)``0 -oconcat`2`x`(Result,Result)->Result`pExpertSystemToolsPackage``315677 -oconcat`2`x`(S,_$)->_$`cLinearAggregate(S)``315753 -oconcat`2`x`(S,_$)->_$`cUnaryRecursiveAggregate(S)``315940 -oconcat`2`x`(_$,S)->_$`cLinearAggregate(S)``316180 -oconcat`2`x`(_$,_$)->_$`cLinearAggregate(S)``316375 -oconcat`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)``316747 -oconcat`2`x`(_$,_$)->_$`dRoutinesTable``316929 -ocond`2`x`(Switch,_$)->_$`dFortranCode``316997 -ocond`3`x`(Switch,_$,_$)->_$`dFortranCode``317103 +oconcat`2`x`(_$,_$)->_$`cDivisorCategory(S)``375293 +oconcat!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`375399 +oconcat!`2`x`(_$,_$)->_$`cExtensibleLinearAggregate(S)``375536 +oconcat`2`x`(_$,_$)->_$`cLinearAggregate(S)``375642 +oconcat!`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`376018 +oconcat`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)``376188 +oconcat`2`x`(_$,_$)->_$`dRoutinesTable``376374 +oconcat`2`x`(Result,Result)->Result`pExpertSystemToolsPackage``376442 +oconcat!`2`x`(_$,S)->_$`cExtensibleLinearAggregate(S)``376518 +oconcat`2`x`(_$,S)->_$`cLinearAggregate(S)``376607 +oconcat`2`x`(S,_$)->_$`cLinearAggregate(S)``376806 +oconcat!`2`x`(_$,S)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`376997 +oconcat`2`x`(S,_$)->_$`cUnaryRecursiveAggregate(S)``377154 +ocond`2`x`(Switch,_$)->_$`dFortranCode``377398 +ocond`3`x`(Switch,_$,_$)->_$`dFortranCode``377504 +ocondition`1`n`(_$)->C`dSplittingNode(V,C)``377628 oconditionP`1`n`(Matrix(S))->Union(Vector(S),"failed")`xFiniteFieldCategory&(S)``0 oconditionP`1`n`(Matrix(S))->Union(Vector(S),"failed")`xPolynomialCategory&(S,R,E,VarSet)``0 -oconditionP`1`x`(Matrix(_$))->Union(Vector(_$),"failed")`cFiniteFieldCategory``317227 -oconditionP`1`x`(Matrix(_$))->Union(Vector(_$),"failed")`cPolynomialFactorizationExplicit`has(_$,CharacteristicNonZero)`317440 -ocondition`1`n`(_$)->C`dSplittingNode(V,C)``317709 -oconditionsForIdempotents`0`n`()->List(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`317788 -oconditionsForIdempotents`0`n`()->List(Polynomial(R))`xFramedNonAssociativeAlgebra&(S,R)``317964 -oconditionsForIdempotents`0`x`()->List(Polynomial(R))`cFramedNonAssociativeAlgebra(R)``318141 +oconditionP`1`x`(Matrix(_$))->Union(Vector(_$),"failed")`cFiniteFieldCategory``377707 +oconditionP`1`x`(Matrix(_$))->Union(Vector(_$),"failed")`cPolynomialFactorizationExplicit`has(_$,CharacteristicNonZero)`377920 +oconditions`1`n`(_$)->List(C)`dSplittingTree(V,C)``378189 +oconditionsForIdempotents`0`n`()->List(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`378272 +oconditionsForIdempotents`0`n`()->List(Polynomial(R))`xFramedNonAssociativeAlgebra&(S,R)``378448 +oconditionsForIdempotents`0`x`()->List(Polynomial(R))`cFramedNonAssociativeAlgebra(R)``378625 +oconditionsForIdempotents`1`n`(Vector(_$))->List(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`378802 oconditionsForIdempotents`1`n`(Vector(S))->List(Polynomial(R))`xFramedNonAssociativeAlgebra&(S,R)``0 -oconditionsForIdempotents`1`n`(Vector(_$))->List(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`318318 -oconditionsForIdempotents`1`x`(Vector(_$))->List(Polynomial(R))`cFiniteRankNonAssociativeAlgebra(R)``318531 -oconditions`1`n`(_$)->List(C)`dSplittingTree(V,C)``318745 -oconical`2`x`(R,R)->(Point(R))->Point(R)`pCoordinateSystems(R)``318828 +oconditionsForIdempotents`1`x`(Vector(_$))->List(Polynomial(R))`cFiniteRankNonAssociativeAlgebra(R)``379015 +oconical`2`x`(R,R)->(Point(R))->Point(R)`pCoordinateSystems(R)``379229 oconjug`1`n`(R)->R`dOperator(R)`has(R,CommutativeRing)`0 -oconjug`1`x`(R)->R`dModuleOperator(R,M)`has(R,CommutativeRing)`319174 +oconjug`1`x`(R)->R`dModuleOperator(R,M)`has(R,CommutativeRing)`379575 +oconjugate`1`n`(_$)->_$`dPartition``379630 oconjugate`1`n`(S)->S`xComplexCategory&(S,R)``0 oconjugate`1`n`(S)->S`xOctonionCategory&(S,R)``0 oconjugate`1`n`(S)->S`xQuaternionCategory&(S,R)``0 -oconjugate`1`n`(_$)->_$`dPartition``319229 -oconjugate`1`x`(List(Integer))->List(Integer)`pPartitionsAndPermutations``319312 -oconjugate`1`x`(_$)->_$`cComplexCategory(R)``319385 -oconjugate`1`x`(_$)->_$`cOctonionCategory(R)``319460 -oconjugate`1`x`(_$)->_$`cQuaternionCategory(R)``319612 +oconjugate`1`x`(_$)->_$`cAffineSpaceCategory(K)``379713 +oconjugate`1`x`(_$)->_$`cComplexCategory(R)``379837 +oconjugate`1`x`(_$)->_$`cOctonionCategory(R)``379912 +oconjugate`1`x`(_$)->_$`cProjectiveSpaceCategory(K)``380064 +oconjugate`1`x`(_$)->_$`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +oconjugate`1`x`(_$)->_$`cQuaternionCategory(R)``380188 +oconjugate`1`x`(List(Integer))->List(Integer)`pPartitionsAndPermutations``380267 oconjugate`2`n`(S,S)->S`xGroup&(S)``0 -oconjugate`2`x`(_$,_$)->_$`cGroup``319691 -oconjugates`1`x`(Stream(List(Integer)))->Stream(List(Integer))`pPartitionsAndPermutations``319793 -oconnect`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``319901 -ocons`2`x`(S,_$)->_$`dList(S)``320183 -ocons`2`x`(S,_$)->_$`dStream(S)``320353 -oconsnewpol`3`n`(SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),Integer)->Record(pol:SparseUnivariatePolynomial(P),polval:SparseUnivariatePolynomial(R))`pMultivariateSquareFree(E,OV,R,P)``320504 -oconstDsolve`3`n`(L,F,Symbol)->Record(particular:F,basis:List(F))`pConstantLODE(R,F,L)``320545 -oconst`1`x`(C)->(A)->C`pMappingPackage2(A,C)``320783 -oconstant?`1`n`(_$)->Boolean`dPattern(R)``320887 -oconstant?`1`n`(_$)->Boolean`dXPolynomialRing(R,E)``320964 -oconstant?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``321062 -oconstantCoefficientRicDE`2`n`(L,(UP)->List(F))->List(Record(constant:F,eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``321134 -oconstantIfCan`1`x`(Kernel(S))->Union(R,"failed")`pKernelFunctions2(R,S)``321600 -oconstantKernel`1`x`(R)->Kernel(S)`pKernelFunctions2(R,S)``321645 -oconstantLeft`1`x`((B)->C)->(A,B)->C`pMappingPackage3(A,B,C)``321691 -oconstantOpIfCan`1`x`(BasicOperator)->Union(A,"failed")`pBasicOperatorFunctions1(A)`has(A,OrderedSet)`321793 -oconstantOperator`1`x`(A)->BasicOperator`pBasicOperatorFunctions1(A)`has(A,OrderedSet)`321939 -oconstantRight`1`x`((A)->C)->(A,B)->C`pMappingPackage3(A,B,C)``322054 -oconstantToUnaryFunction`1`n`(DoubleFloat)->(DoubleFloat)->DoubleFloat`pExpressionTubePlot``322157 -oconstant`1`n`(_$)->R`dXPolynomialRing(R,E)``322383 -oconstant`1`x`(()->C)->(A)->C`pMappingPackage2(A,C)``322447 -oconstant`1`x`(F)->F`pFunctionSpaceAssertions(R,F)``322534 -oconstant`1`x`(Symbol)->Expression(Integer)`pPatternMatchAssertions``322698 -oconstant`1`x`(_$)->R`cXFreeAlgebra(vl,R)``322826 +oconjugate`2`x`(_$,_$)->_$`cGroup``380340 +oconjugate`2`x`(_$,NonNegativeInteger)->_$`cAffineSpaceCategory(K)``380442 +oconjugate`2`x`(_$,NonNegativeInteger)->_$`cProjectiveSpaceCategory(K)``380554 +oconjugates`1`x`(Stream(List(Integer)))->Stream(List(Integer))`pPartitionsAndPermutations``380666 +oconnect`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``380774 +ocons`2`x`(S,_$)->_$`dList(S)``381056 +ocons`2`x`(S,_$)->_$`dStream(S)``381226 +oconsnewpol`3`n`(SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),Integer)->Record(pol:SparseUnivariatePolynomial(P),polval:SparseUnivariatePolynomial(R))`pMultivariateSquareFree(E,OV,R,P)``381521 +oconst`1`x`(C)->(A)->C`pMappingPackage2(A,C)``381562 +oconstant?`1`n`(_$)->Boolean`dPattern(R)``381666 +oconstant?`1`n`(_$)->Boolean`dXPolynomialRing(R,E)``381743 +oconstant`1`n`(_$)->R`dXPolynomialRing(R,E)``381841 +oconstant?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``381905 +oconstant`1`x`(()->C)->(A)->C`pMappingPackage2(A,C)``381977 +oconstant`1`x`(F)->F`pFunctionSpaceAssertions(R,F)``382064 +oconstant`1`x`(PolyRing)->R`pPackageForPoly(R,PolyRing,E,dim)``382228 +oconstant`1`x`(_$)->R`cXFreeAlgebra(vl,R)``382301 +oconstant`1`x`(Symbol)->Expression(Integer)`pPatternMatchAssertions``382366 +oconstantCoefficientRicDE`2`n`(L,(UP)->List(F))->List(Record(constant:F,eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``382494 +oconstantIfCan`1`x`(Kernel(S))->Union(R,"failed")`pKernelFunctions2(R,S)``382960 +oconstantKernel`1`x`(R)->Kernel(S)`pKernelFunctions2(R,S)``383005 +oconstantLeft`1`x`((B)->C)->(A,B)->C`pMappingPackage3(A,B,C)``383051 +oconstantOperator`1`x`(A)->BasicOperator`pBasicOperatorFunctions1(A)`has(A,OrderedSet)`383153 +oconstantOpIfCan`1`x`(BasicOperator)->Union(A,"failed")`pBasicOperatorFunctions1(A)`has(A,OrderedSet)`383268 +oconstantRight`1`x`((A)->C)->(A,B)->C`pMappingPackage3(A,B,C)``383414 +oconstantToUnaryFunction`1`n`(DoubleFloat)->(DoubleFloat)->DoubleFloat`pExpressionTubePlot``383517 +oconstDsolve`3`n`(L,F,Symbol)->Record(particular:F,basis:List(F))`pConstantLODE(R,F,L)``383743 oconstruct`1`n`(List(P))->S`xTriangularSetCategory&(S,R,E,V,P)``0 -oconstruct`1`n`(List(Record(key:Symbol,entry:S)))->_$`dPatternMatchResult(R,S)``322891 -oconstruct`1`n`(List(Record(val:V,tower:C)))->List(_$)`dSplittingNode(V,C)``323042 +oconstruct`1`n`(List(Record(key:Symbol,entry:S)))->_$`dPatternMatchResult(R,S)``383981 +oconstruct`1`n`(List(Record(val:V,tower:C)))->List(_$)`dSplittingNode(V,C)``384132 oconstruct`1`n`(List(S))->A`xDictionaryOperations&(A,S)``0 oconstruct`1`n`(List(S))->A`xFiniteSetAggregate&(A,S)``0 oconstruct`1`n`(List(S))->A`xLazyStreamAggregate&(A,S)``0 oconstruct`1`n`(List(S))->A`xOneDimensionalArrayAggregate&(A,S)``0 -oconstruct`1`n`(Record(val:V,tower:C))->_$`dSplittingNode(V,C)``323180 -oconstruct`1`n`(SplittingNode(V,C))->_$`dSplittingTree(V,C)``323287 -oconstruct`1`x`(List(List(List(R))))->_$`dThreeDimensionalMatrix(R)``323635 -oconstruct`1`x`(List(Record(exponent:NonNegativeInteger,center:UP,num:UP)))->_$`dFullPartialFractionExpansion(F,UP)``323734 -oconstruct`1`x`(List(S))->_$`cCollection(S)``323789 -oconstruct`1`x`(_$)->Stream(S)`dInfiniteTuple(S)``324112 -oconstruct`2`n`(IS,E)->_$`dModuleMonomial(IS,E,ff)``324179 -oconstruct`2`n`(LyndonWord(VarSet),LyndonWord(VarSet))->_$`dLiePolynomial(VarSet,R)``324224 -oconstruct`2`n`(LyndonWord(VarSet),_$)->_$`dLiePolynomial(VarSet,R)``324325 -oconstruct`2`n`(S1,S2)->_$`dSuchThat(S1,S2)``324426 -oconstruct`2`n`(V,C)->_$`dSplittingNode(V,C)``324481 -oconstruct`2`n`(V,List(C))->List(_$)`dSplittingNode(V,C)``324601 -oconstruct`2`n`(_$,LyndonWord(VarSet))->_$`dLiePolynomial(VarSet,R)``324735 -oconstruct`2`x`(_$,_$)->_$`cLieAlgebra(R)``324836 -oconstruct`3`n`(V,C,Boolean)->_$`dSplittingNode(V,C)``324948 -oconstruct`3`n`(V,C,List(SplittingNode(V,C)))->_$`dSplittingTree(V,C)``325092 -oconstruct`3`n`(V,C,List(_$))->_$`dSplittingTree(V,C)``325351 -oconstruct`3`x`(Union(fst:FortranScalarType,void:"void"),List(Polynomial(Integer)),Boolean)->_$`dFortranType``325557 -oconstruct`3`x`(Union(fst:FortranScalarType,void:"void"),List(Symbol),Boolean)->_$`dFortranType``325628 -oconstruct`4`n`(V,C,V,List(C))->_$`dSplittingTree(V,C)``325699 -ocontains?`2`x`(_$,R)->Boolean`cIntervalCategory(R)``325994 -ocontent`1`n`(List(BP))->List(Integer)`pHeuGcd(BP)``326142 +oconstruct`1`n`(Record(val:V,tower:C))->_$`dSplittingNode(V,C)``384270 +oconstruct`1`n`(SplittingNode(V,C))->_$`dSplittingTree(V,C)``384377 +oconstruct`1`x`(List(List(List(R))))->_$`dThreeDimensionalMatrix(R)``384725 +oconstruct`1`x`(List(Record(exponent:NonNegativeInteger,center:UP,num:UP)))->_$`dFullPartialFractionExpansion(F,UP)``384824 +oconstruct`1`x`(List(S))->_$`cCollection(S)``384879 +oconstruct`1`x`(_$)->Stream(S)`dInfiniteTuple(S)``385202 +oconstruct`2`n`(IS,E)->_$`dModuleMonomial(IS,E,ff)``385269 +oconstruct`2`n`(_$,LyndonWord(VarSet))->_$`dLiePolynomial(VarSet,R)``385318 +oconstruct`2`n`(LyndonWord(VarSet),_$)->_$`dLiePolynomial(VarSet,R)``385419 +oconstruct`2`n`(LyndonWord(VarSet),LyndonWord(VarSet))->_$`dLiePolynomial(VarSet,R)``385520 +oconstruct`2`n`(S1,S2)->_$`dSuchThat(S1,S2)``385621 +oconstruct`2`n`(V,C)->_$`dSplittingNode(V,C)``385676 +oconstruct`2`n`(V,List(C))->List(_$)`dSplittingNode(V,C)``385796 +oconstruct`2`x`(_$,_$)->_$`cLieAlgebra(R)``385930 +oconstruct`3`n`(V,C,Boolean)->_$`dSplittingNode(V,C)``386042 +oconstruct`3`n`(V,C,List(_$))->_$`dSplittingTree(V,C)``386186 +oconstruct`3`n`(V,C,List(SplittingNode(V,C)))->_$`dSplittingTree(V,C)``386392 +oconstruct`3`x`(Union(fst:FortranScalarType,void:"void"),List(Polynomial(Integer)),Boolean)->_$`dFortranType``386651 +oconstruct`3`x`(Union(fst:FortranScalarType,void:"void"),List(Symbol),Boolean)->_$`dFortranType``386722 +oconstruct`4`n`(V,C,V,List(C))->_$`dSplittingTree(V,C)``386793 +ocontains?`2`x`(_$,R)->Boolean`cIntervalCategory(R)``387088 +ocontent`1`n`(List(BP))->List(Integer)`pHeuGcd(BP)``387236 ocontent`1`n`(S)->R`xFiniteAbelianMonoidRing&(S,R,E)``0 ocontent`1`n`(S)->R`xPolynomialCategory&(S,R,E,VarSet)``0 ocontent`1`n`(S)->R`xUnivariatePolynomialCategory&(S,R)``0 ocontent`1`n`(S)->R`xUnivariateSkewPolynomialCategory&(S,R)``0 -ocontent`1`x`(_$)->R`cFiniteAbelianMonoidRing(R,E)`has(R,GcdDomain)`326226 -ocontent`1`x`(_$)->R`cUnivariateSkewPolynomialCategory(R)`has(R,GcdDomain)`326316 +ocontent`1`x`(_$)->R`cFiniteAbelianMonoidRing(R,E)`has(R,GcdDomain)`387320 +ocontent`1`x`(_$)->R`cUnivariateSkewPolynomialCategory(R)`has(R,GcdDomain)`387410 ocontent`2`n`(S,SingletonAsOrderedSet)->S`xUnivariatePolynomialCategory&(S,R)``0 ocontent`2`n`(S,VarSet)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -ocontent`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`326401 -ocontinue`1`x`(SingleInteger)->_$`dFortranCode``326700 +ocontent`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`387495 +ocontinue`1`x`(SingleInteger)->_$`dFortranCode``387794 ocontinuedFraction`1`n`(_$)->ContinuedFraction(Fraction(Integer))`dBalancedPAdicRational(p)``0 +ocontinuedFraction`1`n`(_$)->ContinuedFraction(Fraction(Integer))`dPAdicRationalConstructor(p,PADIC)``387890 ocontinuedFraction`1`n`(_$)->ContinuedFraction(Fraction(Integer))`dPAdicRational(p)``0 -ocontinuedFraction`1`n`(_$)->ContinuedFraction(Fraction(Integer))`dPAdicRationalConstructor(p,PADIC)``326796 -ocontinuedFraction`1`x`(F)->ContinuedFraction(Integer)`pNumericContinuedFraction(F)``326908 -ocontinuedFraction`1`x`(Fraction(R))->_$`dContinuedFraction(R)``327020 -ocontinuedFraction`3`x`(R,Stream(R),Stream(R))->_$`dContinuedFraction(R)``327168 -ocontractSolve`2`x`(Equation(Fraction(Polynomial(R))),Symbol)->SuchThat(List(Expression(R)),List(Equation(Expression(R))))`pRadicalSolvePackage(R)``327406 -ocontractSolve`2`x`(Fraction(Polynomial(R)),Symbol)->SuchThat(List(Expression(R)),List(Equation(Expression(R))))`pRadicalSolvePackage(R)``327679 -ocontract`2`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))),List(OrderedVariableList(vl)))->PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pIdealDecompositionPackage(vl,nv)``327976 -ocontract`3`x`(_$,Integer,Integer)->_$`dCartesianTensor(minix,dim,R)``328077 -ocontract`4`x`(_$,Integer,_$,Integer)->_$`dCartesianTensor(minix,dim,R)``328429 -ocontrolPanel`2`n`(_$,String)->Void`dTwoDimensionalViewport``328896 -ocontrolPanel`2`x`(_$,String)->Void`dThreeDimensionalViewport``329138 -oconvergents`1`x`(_$)->Stream(Fraction(R))`dContinuedFraction(R)``329384 +ocontinuedFraction`1`x`(F)->ContinuedFraction(Integer)`pNumericContinuedFraction(F)``388002 +ocontinuedFraction`1`x`(Fraction(R))->_$`dContinuedFraction(R)``388114 +ocontinuedFraction`3`x`(R,Stream(R),Stream(R))->_$`dContinuedFraction(R)``388262 +ocontract`2`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))),List(OrderedVariableList(vl)))->PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pIdealDecompositionPackage(vl,nv)``388500 +ocontract`3`x`(_$,Integer,Integer)->_$`dCartesianTensor(minix,dim,R)``388601 +ocontract`4`x`(_$,Integer,_$,Integer)->_$`dCartesianTensor(minix,dim,R)``389344 +ocontractSolve`2`x`(Equation(Fraction(Polynomial(R))),Symbol)->SuchThat(List(Expression(R)),List(Equation(Expression(R))))`pRadicalSolvePackage(R)``390225 +ocontractSolve`2`x`(Fraction(Polynomial(R)),Symbol)->SuchThat(List(Expression(R)),List(Equation(Expression(R))))`pRadicalSolvePackage(R)``390706 +ocontrolPanel`2`n`(_$,String)->Void`dTwoDimensionalViewport``391223 +ocontrolPanel`2`x`(_$,String)->Void`dThreeDimensionalViewport``391465 +oconvergents`1`x`(_$)->Stream(Fraction(R))`dContinuedFraction(R)``391711 oconvert`1`n`(A)->DoubleFloat`xQuotientFieldCategory&(A,S)``0 oconvert`1`n`(A)->Float`xQuotientFieldCategory&(A,S)``0 oconvert`1`n`(A)->InputForm`xQuotientFieldCategory&(A,S)``0 oconvert`1`n`(A)->Pattern(Float)`xQuotientFieldCategory&(A,S)``0 oconvert`1`n`(A)->Pattern(Integer)`xQuotientFieldCategory&(A,S)``0 -oconvert`1`n`(CS)->Pattern(R)`pComplexPattern(R,S,CS)``329568 +oconvert`1`n`(CS)->Pattern(R)`pComplexPattern(R,S,CS)``391895 oconvert`1`n`(Factored(S))->S`xFunctionSpace&(S,R)``0 -oconvert`1`n`(List(P))->_$`dGeneralPolynomialSet(R,E,VarSet,P)``329649 -oconvert`1`n`(List(_$))->_$`dPattern(R)``329766 +oconvert`1`n`(List(_$))->_$`dPattern(R)``391976 +oconvert`1`n`(List(P))->_$`dGeneralPolynomialSet(R,E,VarSet,P)``392059 oconvert`1`n`(Polynomial(Fraction(Integer)))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 oconvert`1`n`(Polynomial(Integer))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 oconvert`1`n`(Polynomial(R))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 @@ -2619,6 +2575,7 @@ oconvert`1`n`(S)->Complex(DoubleFloat)`xComplexCategory&(S,R)``0 oconvert`1`n`(S)->Complex(Float)`xComplexCategory&(S,R)``0 oconvert`1`n`(S)->DoubleFloat`xIntegerNumberSystem&(S)``0 oconvert`1`n`(S)->DoubleFloat`xRealNumberSystem&(S)``0 +oconvert`1`n`(SExpression)->_$`dInputForm``392176 oconvert`1`n`(S)->Float`xIntegerNumberSystem&(S)``0 oconvert`1`n`(S)->Float`xRealNumberSystem&(S)``0 oconvert`1`n`(S)->InputForm`xComplexCategory&(S,R)``0 @@ -2629,6 +2586,7 @@ oconvert`1`n`(S)->InputForm`xPolynomialCategory&(S,R,E,VarSet)``0 oconvert`1`n`(S)->InputForm`xQuaternionCategory&(S,R)``0 oconvert`1`n`(S)->InputForm`xRecursivePolynomialCategory&(S,R,E,V)``0 oconvert`1`n`(S)->Integer`xIntegerNumberSystem&(S)``0 +oconvert`1`n`(SparseUnivariatePolynomial(R))->S`xComplexCategory&(S,R)``0 oconvert`1`n`(S)->Pattern(Float)`xComplexCategory&(S,R)``0 oconvert`1`n`(S)->Pattern(Float)`xFunctionSpace&(S,R)``0 oconvert`1`n`(S)->Pattern(Float)`xPolynomialCategory&(S,R,E,VarSet)``0 @@ -2647,52 +2605,50 @@ oconvert`1`n`(S)->Vector(R)`xComplexCategory&(S,R)``0 oconvert`1`n`(S)->Vector(R)`xFramedAlgebra&(S,R,UP)``0 oconvert`1`n`(S)->Vector(R)`xFramedNonAssociativeAlgebra&(S,R)``0 oconvert`1`n`(S)->Vector(R)`xMonogenicAlgebra&(S,R,UP)``0 -oconvert`1`n`(SExpression)->_$`dInputForm``329849 -oconvert`1`n`(SparseUnivariatePolynomial(R))->S`xComplexCategory&(S,R)``0 +oconvert`1`n`(_$)->Symbol`dSingletonAsOrderedSet``0 oconvert`1`n`(UP)->S`xMonogenicAlgebra&(S,R,UP)``0 oconvert`1`n`(Vector(R))->S`xComplexCategory&(S,R)``0 oconvert`1`n`(Vector(R))->S`xFramedAlgebra&(S,R,UP)``0 oconvert`1`n`(Vector(R))->S`xFramedNonAssociativeAlgebra&(S,R)``0 oconvert`1`n`(Vector(R))->S`xMonogenicAlgebra&(S,R,UP)``0 -oconvert`1`n`(_$)->Symbol`dSingletonAsOrderedSet``0 -oconvert`1`x`(DoubleFloat)->_$`dFloat``329909 -oconvert`1`x`(Expr)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``330000 -oconvert`1`x`(Factored(_$))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`330057 -oconvert`1`x`(Flt)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``330233 -oconvert`1`x`(Int)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``330290 -oconvert`1`x`(List(R))->_$`cPointCategory(R)``330347 -oconvert`1`x`(List(Segment(OrderedCompletion(Float))))->List(Segment(OrderedCompletion(DoubleFloat)))`pExpertSystemToolsPackage``330473 -oconvert`1`x`(List(_$))->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``330624 -oconvert`1`x`(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))->NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))`pZeroDimensionalSolvePackage(R,ls,ls2)``330719 -oconvert`1`x`(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)))->Polynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``330763 -oconvert`1`x`(Polynomial(Fraction(Integer)))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`330807 -oconvert`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`330887 -oconvert`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`330967 -oconvert`1`x`(Polynomial(R))->Polynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``331047 -oconvert`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`has(V,ConvertibleTo(Symbol))`331091 +oconvert`1`x`(DoubleFloat)->_$`dFloat``392236 +oconvert`1`x`(Expr)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``392327 +oconvert`1`x`(Factored(_$))->_$`cFunctionSpace(R)`has(R,IntegralDomain)`392384 +oconvert`1`x`(Flt)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``392560 +oconvert`1`x`(Int)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``392617 +oconvert`1`x`(List(_$))->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``392674 +oconvert`1`x`(List(R))->_$`cPointCategory(R)``392768 +oconvert`1`x`(List(Segment(OrderedCompletion(Float))))->List(Segment(OrderedCompletion(DoubleFloat)))`pExpertSystemToolsPackage``392894 +oconvert`1`x`(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)))->Polynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``393045 +oconvert`1`x`(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))->NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))`pZeroDimensionalSolvePackage(R,ls,ls2)``393089 +oconvert`1`x`(Polynomial(Fraction(Integer)))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`393133 +oconvert`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`393213 +oconvert`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`393293 +oconvert`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`has(V,ConvertibleTo(Symbol))`393373 +oconvert`1`x`(Polynomial(R))->Polynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``393550 oconvert`1`x`(Record(val:List(P),tower:TS))->String`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 oconvert`1`x`(Record(val:List(P),tower:TS))->String`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oconvert`1`x`(S)->_$`cSegmentCategory(S)``331268 -oconvert`1`x`(SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``331326 -oconvert`1`x`(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))))->List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)))`pZeroDimensionalSolvePackage(R,ls,ls2)``331370 -oconvert`1`x`(Str)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``331430 -oconvert`1`x`(Sym)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``331487 -oconvert`1`x`(Symbol)->_$`dRomanNumeral``331544 -oconvert`1`x`(UP)->_$`cMonogenicAlgebra(R,UP)``331614 -oconvert`1`x`(Vector(R))->_$`cFramedAlgebra(R,UP)``331768 -oconvert`1`x`(Vector(R))->_$`cFramedNonAssociativeAlgebra(R)``331917 -oconvert`1`x`(_$)->S`cConvertibleTo(S)``332083 -oconvert`1`x`(_$)->Vector(R)`cFramedAlgebra(R,UP)``332150 -oconvert`1`x`(_$)->Vector(R)`cFramedNonAssociativeAlgebra(R)``332260 -oconvert`2`x`(OutputForm,Integer)->_$`dScriptFormulaFormat``332370 -oconvert`2`x`(OutputForm,Integer)->_$`dTexFormat``332660 -oconvert`3`x`(OutputForm,Integer,OutputForm)->_$`dTexFormat``332939 -ocoord`1`x`((Point(DoubleFloat))->Point(DoubleFloat))->_$`dDrawOption``333241 -ocoord`2`n`(HomogeneousDistributedMultivariatePolynomial(lv,F),List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->Vector(F)`pLinGroebnerPackage(lv,F)``333373 -ocoord`2`n`(List(DrawOption),(Point(DoubleFloat))->Point(DoubleFloat))->(Point(DoubleFloat))->Point(DoubleFloat)`pDrawOptionFunctions0``333407 -ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricPlaneCurve(ComponentFunction)``333611 -ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricSpaceCurve(ComponentFunction)``333826 -ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricSurface(ComponentFunction)``334046 +oconvert`1`x`(_$)->S`cConvertibleTo(S)``393594 +oconvert`1`x`(S)->_$`cSegmentCategory(S)``393661 +oconvert`1`x`(SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(RealClosure(Fraction(R)))`pZeroDimensionalSolvePackage(R,ls,ls2)``393719 +oconvert`1`x`(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))))->List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2)))`pZeroDimensionalSolvePackage(R,ls,ls2)``393763 +oconvert`1`x`(Str)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``393823 +oconvert`1`x`(Symbol)->_$`dRomanNumeral``393880 +oconvert`1`x`(Sym)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``393950 +oconvert`1`x`(UP)->_$`cMonogenicAlgebra(R,UP)``394007 +oconvert`1`x`(Vector(R))->_$`cFramedAlgebra(R,UP)``394161 +oconvert`1`x`(_$)->Vector(R)`cFramedAlgebra(R,UP)``394310 +oconvert`1`x`(Vector(R))->_$`cFramedNonAssociativeAlgebra(R)``394420 +oconvert`1`x`(_$)->Vector(R)`cFramedNonAssociativeAlgebra(R)``394586 +oconvert`2`x`(OutputForm,Integer)->_$`dScriptFormulaFormat``394696 +oconvert`2`x`(OutputForm,Integer)->_$`dTexFormat``394986 +oconvert`3`x`(OutputForm,Integer,OutputForm)->_$`dTexFormat``395265 +ocoord`1`x`((Point(DoubleFloat))->Point(DoubleFloat))->_$`dDrawOption``395567 +ocoord`2`n`(HomogeneousDistributedMultivariatePolynomial(lv,F),List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->Vector(F)`pLinGroebnerPackage(lv,F)``395699 +ocoord`2`n`(List(DrawOption),(Point(DoubleFloat))->Point(DoubleFloat))->(Point(DoubleFloat))->Point(DoubleFloat)`pDrawOptionFunctions0``395733 +ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricPlaneCurve(ComponentFunction)``395937 +ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricSpaceCurve(ComponentFunction)``396152 +ocoordinate`2`x`(_$,NonNegativeInteger)->ComponentFunction`dParametricSurface(ComponentFunction)``396372 ocoordinates`1`n`(S)->Vector(F)`xFiniteAlgebraicExtensionField&(S,F)``0 ocoordinates`1`n`(S)->Vector(R)`xComplexCategory&(S,R)``0 ocoordinates`1`n`(S)->Vector(R)`xFramedAlgebra&(S,R,UP)``0 @@ -2701,13 +2657,13 @@ ocoordinates`1`n`(Vector(S))->Matrix(F)`xFiniteAlgebraicExtensionField&(S,F)``0 ocoordinates`1`n`(Vector(S))->Matrix(R)`xComplexCategory&(S,R)``0 ocoordinates`1`n`(Vector(S))->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 ocoordinates`1`n`(Vector(S))->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``0 -ocoordinates`1`x`((Point(DoubleFloat))->Point(DoubleFloat))->_$`dDrawOption``334262 -ocoordinates`1`x`(Vector(_$))->Matrix(F)`cFiniteAlgebraicExtensionField(F)``334413 -ocoordinates`1`x`(Vector(_$))->Matrix(R)`cFramedAlgebra(R,UP)``334637 -ocoordinates`1`x`(Vector(_$))->Matrix(R)`cFramedNonAssociativeAlgebra(R)``334861 -ocoordinates`1`x`(_$)->Vector(F)`cFiniteAlgebraicExtensionField(F)``335041 -ocoordinates`1`x`(_$)->Vector(R)`cFramedAlgebra(R,UP)``335160 -ocoordinates`1`x`(_$)->Vector(R)`cFramedNonAssociativeAlgebra(R)``335274 +ocoordinates`1`x`((Point(DoubleFloat))->Point(DoubleFloat))->_$`dDrawOption``396588 +ocoordinates`1`x`(_$)->Vector(F)`cFiniteAlgebraicExtensionField(F)``396739 +ocoordinates`1`x`(Vector(_$))->Matrix(F)`cFiniteAlgebraicExtensionField(F)``396858 +ocoordinates`1`x`(Vector(_$))->Matrix(R)`cFramedAlgebra(R,UP)``397082 +ocoordinates`1`x`(Vector(_$))->Matrix(R)`cFramedNonAssociativeAlgebra(R)``397306 +ocoordinates`1`x`(_$)->Vector(R)`cFramedAlgebra(R,UP)``397486 +ocoordinates`1`x`(_$)->Vector(R)`cFramedNonAssociativeAlgebra(R)``397600 ocoordinates`2`n`(S,Vector(S))->Vector(R)`xComplexCategory&(S,R)``0 ocoordinates`2`n`(S,Vector(S))->Vector(R)`xFiniteRankAlgebra&(S,R,UP)``0 ocoordinates`2`n`(S,Vector(S))->Vector(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 @@ -2718,396 +2674,486 @@ ocoordinates`2`n`(Vector(S),Vector(S))->Matrix(R)`xFiniteRankAlgebra&(S,R,UP)``0 ocoordinates`2`n`(Vector(S),Vector(S))->Matrix(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 ocoordinates`2`n`(Vector(S),Vector(S))->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 ocoordinates`2`n`(Vector(S),Vector(S))->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``0 -ocoordinates`2`x`(Matrix(R),List(Matrix(R)))->Vector(R)`pStructuralConstantsPackage(R)``335388 -ocoordinates`2`x`(Vector(_$),Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``335542 -ocoordinates`2`x`(Vector(_$),Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``335782 -ocoordinates`2`x`(_$,Vector(_$))->Vector(R)`cFiniteRankAlgebra(R,UP)``336002 -ocoordinates`2`x`(_$,Vector(_$))->Vector(R)`cFiniteRankNonAssociativeAlgebra(R)``336122 -ocopies`2`x`(Integer,String)->String`pDisplayPackage``336276 -ocopy!`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``336397 -ocopyInto!`3`n`(A,A,Integer)->A`xListAggregate&(A,S)``0 -ocopyInto!`3`n`(A,A,Integer)->A`xOneDimensionalArrayAggregate&(A,S)``0 -ocopyInto!`3`x`(_$,_$,Integer)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`336542 +ocoordinates`2`x`(Matrix(R),List(Matrix(R)))->Vector(R)`pStructuralConstantsPackage(R)``397714 +ocoordinates`2`x`(Vector(_$),Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``397868 +ocoordinates`2`x`(Vector(_$),Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``398108 +ocoordinates`2`x`(_$,Vector(_$))->Vector(R)`cFiniteRankAlgebra(R,UP)``398328 +ocoordinates`2`x`(_$,Vector(_$))->Vector(R)`cFiniteRankNonAssociativeAlgebra(R)``398448 +ocopies`2`x`(Integer,String)->String`pDisplayPackage``398602 ocopy`1`n`(A)->A`xBinaryTreeCategory&(A,S)``0 ocopy`1`n`(A)->A`xDictionaryOperations&(A,S)``0 ocopy`1`n`(A)->A`xListAggregate&(A,S)``0 ocopy`1`n`(A)->A`xOneDimensionalArrayAggregate&(A,S)``0 +ocopy`1`n`(_$)->_$`dPattern(R)``398723 +ocopy`1`n`(_$)->_$`dSplittingNode(V,C)``398783 +ocopy`1`n`(_$)->_$`dSubSpaceComponentProperty``398841 ocopy`1`n`(S)->S`xIntegerNumberSystem&(S)``0 ocopy`1`n`(S)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -ocopy`1`n`(_$)->_$`dPattern(R)``336664 -ocopy`1`n`(_$)->_$`dSplittingNode(V,C)``336724 -ocopy`1`n`(_$)->_$`dSubSpaceComponentProperty``336782 -ocopy`1`x`(_$)->_$`cAggregate``336818 -ocopy`1`x`(_$)->_$`cIntegerNumberSystem``336989 -ocopy`1`x`(_$)->_$`cThreeSpaceCategory(R)``337037 -ocopy`1`x`(_$)->_$`dBasicOperator``337130 -ocorrPoly`7`n`(SparseUnivariatePolynomial(P),List(OV),List(R),List(NonNegativeInteger),List(SparseUnivariatePolynomial(P)),Vector(List(SparseUnivariatePolynomial(R))),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``337182 -ocos2sec`1`x`(F)->F`pTranscendentalManipulations(R,F)``337250 -ocosIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``337348 -ocosSinInfo`1`n`(Integer)->List(List(DoubleFloat))`pTubePlotTools``337435 -ocos`1`n`(E)->_$`dFourierComponent(E)``337679 -ocos`1`n`(F)->F`pElementaryFunction(R,F)``337745 +ocopy`1`x`(_$)->_$`cAggregate``398881 +ocopy`1`x`(_$)->_$`cIntegerNumberSystem``399056 +ocopy`1`x`(_$)->_$`cThreeSpaceCategory(R)``399104 +ocopy`1`x`(_$)->_$`dArrayStack(S)``399197 +ocopy`1`x`(_$)->_$`dBasicOperator``399290 +ocopy`1`x`(_$)->_$`dDequeue(S)``399342 +ocopy`1`x`(_$)->_$`dHeap(S)``399429 +ocopy`1`x`(_$)->_$`dQueue(S)``399510 +ocopy`1`x`(_$)->_$`dStack(S)``399593 +ocopy!`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``399676 +ocopyInto!`3`n`(A,A,Integer)->A`xListAggregate&(A,S)``0 +ocopyInto!`3`n`(A,A,Integer)->A`xOneDimensionalArrayAggregate&(A,S)``0 +ocopyInto!`3`x`(_$,_$,Integer)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`399821 +ocorrPoly`7`n`(SparseUnivariatePolynomial(P),List(OV),List(R),List(NonNegativeInteger),List(SparseUnivariatePolynomial(P)),Vector(List(SparseUnivariatePolynomial(R))),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``399943 +ocos`1`n`(E)->_$`dFourierComponent(E)``400011 +ocos`1`n`(F)->F`pElementaryFunction(R,F)``400077 ocos`1`n`(S)->S`xComplexCategory&(S,R)``0 ocos`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocos`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``337806 -ocos`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``337873 -ocos`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``337940 -ocos`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``338008 -ocos`1`x`(_$)->_$`cTrigonometricFunctionCategory``338078 -ocos`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``338131 -ocosh2sech`1`x`(F)->F`pTranscendentalManipulations(R,F)``338198 -ocoshIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``338300 -ocosh`1`n`(F)->F`pElementaryFunction(R,F)``338389 +ocos`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``400138 +ocos`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``400205 +ocos`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``400272 +ocos`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``400340 +ocos`1`x`(_$)->_$`cTrigonometricFunctionCategory``400410 +ocos`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``400463 +ocos2sec`1`x`(F)->F`pTranscendentalManipulations(R,F)``400530 +ocosh`1`n`(F)->F`pElementaryFunction(R,F)``400628 ocosh`1`n`(S)->S`xComplexCategory&(S,R)``0 ocosh`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 ocosh`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``338462 -ocosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``338545 -ocosh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``338628 -ocosh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``338708 -ocosh`1`x`(_$)->_$`cHyperbolicFunctionCategory``338790 -ocosh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``338855 -ocot2tan`1`x`(F)->F`pTranscendentalManipulations(R,F)``338924 -ocot2trig`1`x`(F)->F`pTranscendentalManipulations(R,F)``339022 -ocotIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``339126 -ocot`1`n`(F)->F`pElementaryFunction(R,F)``339213 +ocosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``400701 +ocosh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``400784 +ocosh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``400867 +ocosh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``400947 +ocosh`1`x`(_$)->_$`cHyperbolicFunctionCategory``401029 +ocosh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``401094 +ocosh2sech`1`x`(F)->F`pTranscendentalManipulations(R,F)``401163 +ocoshIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``401265 +ocosIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``401354 +ocosSinInfo`1`n`(Integer)->List(List(DoubleFloat))`pTubePlotTools``401441 +ocot`1`n`(F)->F`pElementaryFunction(R,F)``401684 ocot`1`n`(S)->S`xTrigonometricFunctionCategory&(S)``0 ocot`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``339277 -ocot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``339347 -ocot`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``339417 -ocot`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``339488 -ocot`1`x`(_$)->_$`cTrigonometricFunctionCategory``339561 -ocoth2tanh`1`x`(F)->F`pTranscendentalManipulations(R,F)``339617 -ocoth2trigh`1`x`(F)->F`pTranscendentalManipulations(R,F)``339719 -ocothIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``339828 -ocoth`1`n`(F)->F`pElementaryFunction(R,F)``339917 +ocot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``401748 +ocot`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``401818 +ocot`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``401888 +ocot`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``401959 +ocot`1`x`(_$)->_$`cTrigonometricFunctionCategory``402032 +ocot2tan`1`x`(F)->F`pTranscendentalManipulations(R,F)``402088 +ocot2trig`1`x`(F)->F`pTranscendentalManipulations(R,F)``402186 +ocoth`1`n`(F)->F`pElementaryFunction(R,F)``402290 ocoth`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 ocoth`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``339993 -ocoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``340079 -ocoth`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``340165 -ocoth`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``340248 -ocoth`1`x`(_$)->_$`cHyperbolicFunctionCategory``340333 -ocountRealRootsMultiple`1`x`(UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)`has(R,GcdDomain)`340401 -ocountRealRoots`1`x`(UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)``340508 +ocoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``402366 +ocoth`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``402452 +ocoth`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``402538 +ocoth`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``402621 +ocoth`1`x`(_$)->_$`cHyperbolicFunctionCategory``402706 +ocoth2tanh`1`x`(F)->F`pTranscendentalManipulations(R,F)``402774 +ocoth2trigh`1`x`(F)->F`pTranscendentalManipulations(R,F)``402876 +ocothIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``402985 +ocotIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``403074 ocount`2`n`((Entry)->Boolean,S)->NonNegativeInteger`xTableAggregate&(S,Key,Entry)``0 +ocount`2`n`(Entry,S)->NonNegativeInteger`xTableAggregate&(S,Key,Entry)``0 ocount`2`n`((R)->Boolean,S)->NonNegativeInteger`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 ocount`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->NonNegativeInteger`xTableAggregate&(S,Key,Entry)``0 -ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xCollection&(A,S)``0 -ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xFiniteSetAggregate&(A,S)``0 -ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xHomogeneousAggregate&(A,S)``0 -ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xOneDimensionalArrayAggregate&(A,S)``0 -ocount`2`n`(Entry,S)->NonNegativeInteger`xTableAggregate&(S,Key,Entry)``0 -ocount`2`n`(R,S)->NonNegativeInteger`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 ocount`2`n`(Record(key:Key,entry:Entry),S)->NonNegativeInteger`xTableAggregate&(S,Key,Entry)``0 +ocount`2`n`(R,S)->NonNegativeInteger`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 ocount`2`n`(S,A)->NonNegativeInteger`xCollection&(A,S)``0 ocount`2`n`(S,A)->NonNegativeInteger`xFiniteSetAggregate&(A,S)``0 ocount`2`n`(S,A)->NonNegativeInteger`xHomogeneousAggregate&(A,S)``0 ocount`2`n`(S,A)->NonNegativeInteger`xOneDimensionalArrayAggregate&(A,S)``0 -ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`340578 -ocount`2`x`(S,_$)->NonNegativeInteger`cHomogeneousAggregate(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`340833 -ocountable?`1`x`(_$)->Boolean`dCardinalNumber``341023 -ocreate3Space`0`x`()->_$`cThreeSpaceCategory(R)``341161 -ocreate3Space`1`x`(SubSpace(3,R))->_$`cThreeSpaceCategory(R)``341303 -ocreateGenericMatrix`1`x`(NonNegativeInteger)->Matrix(Polynomial(R))`pRepresentationPackage1(R)``341445 -ocreateIrreduciblePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``341644 -ocreateLowComplexityNormalBasis`1`n`(PositiveInteger)->Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value:GF,index:SingleInteger))))`pFiniteFieldFunctions(GF)``341805 -ocreateLowComplexityTable`1`n`(PositiveInteger)->Union(Vector(List(Record(value:GF,index:SingleInteger))),"failed")`pFiniteFieldFunctions(GF)``342159 -ocreateMultiplicationMatrix`1`n`(Vector(List(Record(value:GF,index:SingleInteger))))->Matrix(GF)`pFiniteFieldFunctions(GF)``342367 -ocreateMultiplicationTable`1`n`(SparseUnivariatePolynomial(GF))->Vector(List(Record(value:GF,index:SingleInteger)))`pFiniteFieldFunctions(GF)``342487 +ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xCollection&(A,S)``0 +ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xFiniteSetAggregate&(A,S)``0 +ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xHomogeneousAggregate&(A,S)``0 +ocount`2`n`((S)->Boolean,A)->NonNegativeInteger`xOneDimensionalArrayAggregate&(A,S)``0 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`403161 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`dArrayStack(S)`has(_$,ATTRIBUTE(finiteAggregate))`403416 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`dDequeue(S)`has(_$,ATTRIBUTE(finiteAggregate))`403537 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`dHeap(S)`has(_$,ATTRIBUTE(finiteAggregate))`403652 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`dQueue(S)`has(_$,ATTRIBUTE(finiteAggregate))`403761 +ocount`2`x`((S)->Boolean,_$)->NonNegativeInteger`dStack(S)`has(_$,ATTRIBUTE(finiteAggregate))`403872 +ocount`2`x`(S,_$)->NonNegativeInteger`cHomogeneousAggregate(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`403983 +ocount`2`x`(S,_$)->NonNegativeInteger`dArrayStack(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`404173 +ocount`2`x`(S,_$)->NonNegativeInteger`dDequeue(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`404272 +ocount`2`x`(S,_$)->NonNegativeInteger`dHeap(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`404365 +ocount`2`x`(S,_$)->NonNegativeInteger`dQueue(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`404452 +ocount`2`x`(S,_$)->NonNegativeInteger`dStack(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`404541 +ocountable?`1`x`(_$)->Boolean`dCardinalNumber``404630 +ocountRealRoots`1`x`(UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)``404977 +ocountRealRootsMultiple`1`x`(UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)`has(R,GcdDomain)`405047 +ocPower`2`n`(_$,Coef)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`405154 +ocRationalPower`2`n`(_$,Fraction(Integer))->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`405298 +ocreate`0`n`()->_$`dSingletonAsOrderedSet``0 +ocreate`1`x`(List(K))->_$`cPlacesCategory(K,PCS)``0 +ocreate`1`x`(Symbol)->_$`cPlacesCategory(K,PCS)``0 +ocreate`2`x`(ProjPt,PolyRing)->_$`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +ocreate3Space`0`x`()->_$`cThreeSpaceCategory(R)``405405 +ocreate3Space`1`x`(SubSpace(3,R))->_$`cThreeSpaceCategory(R)``405547 +ocreate`9`x`(ProjPt,DistributedMultivariatePolynomial(construct('X,'Y),K),AffinePlane(K),NonNegativeInteger,BLMET,NonNegativeInteger,DIVISOR,K,Symbol)->_$`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``405689 +ocreateGenericMatrix`1`x`(NonNegativeInteger)->Matrix(Polynomial(R))`pRepresentationPackage1(R)``405735 +ocreateHN`7`x`(Integer,Integer,Integer,Integer,Integer,Boolean,Union("left","center","right","vertical","horizontal"))->_$`cBlowUpMethodCategory``0 +ocreateIrreduciblePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``405949 +ocreateLowComplexityNormalBasis`1`n`(PositiveInteger)->Union(SparseUnivariatePolynomial(GF),Vector(List(Record(value:GF,index:SingleInteger))))`pFiniteFieldFunctions(GF)``406111 +ocreateLowComplexityTable`1`n`(PositiveInteger)->Union(Vector(List(Record(value:GF,index:SingleInteger))),"failed")`pFiniteFieldFunctions(GF)``406469 +ocreateMultiplicationMatrix`1`n`(Vector(List(Record(value:GF,index:SingleInteger))))->Matrix(GF)`pFiniteFieldFunctions(GF)``406679 +ocreateMultiplicationTable`1`n`(SparseUnivariatePolynomial(GF))->Vector(List(Record(value:GF,index:SingleInteger)))`pFiniteFieldFunctions(GF)``406800 ocreateNormalElement`0`n`()->S`xFiniteAlgebraicExtensionField&(S,F)``0 -ocreateNormalElement`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`342780 -ocreateNormalPoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``343053 -ocreateNormalPrimitivePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``343187 +ocreateNormalElement`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`407094 +ocreateNormalPoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``407367 +ocreateNormalPrimitivePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``407502 ocreatePrimitiveElement`0`n`()->S`xFiniteFieldCategory&(S)``0 -ocreatePrimitiveElement`0`x`()->_$`cFiniteFieldCategory``343410 -ocreatePrimitiveNormalPoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``343521 -ocreatePrimitivePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``343726 -ocreateRandomElement`2`x`(List(Matrix(R)),Matrix(R))->Matrix(R)`pRepresentationPackage2(R)``343866 -ocreateThreeSpace`0`x`()->ThreeSpace(DoubleFloat)`pTopLevelThreeSpace``343977 -ocreateZechTable`1`n`(SparseUnivariatePolynomial(GF))->PrimitiveArray(SingleInteger)`pFiniteFieldFunctions(GF)``344136 -ocreate`0`n`()->_$`dSingletonAsOrderedSet``0 -ocredPol`2`n`(Dpol,List(Dpol))->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344572 -ocrest`1`n`(NonNegativeInteger)->(Stream(Polynomial(R)))->Stream(Polynomial(R))`pWeierstrassPreparation(R)``344608 -ocritB`4`n`(Expon,Expon,Expon,Expon)->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344650 -ocritBonD`2`n`(Dpol,List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344684 -ocritMTonD1`1`n`(List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344721 -ocritM`2`n`(Expon,Expon)->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344760 -ocritMonD1`2`n`(Expon,List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344794 -ocritT`1`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344832 -ocritpOrder`2`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol),Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``344866 -ocross`2`n`(Point(DoubleFloat),Point(DoubleFloat))->Point(DoubleFloat)`pTubePlotTools``344905 +ocreatePrimitiveElement`0`x`()->_$`cFiniteFieldCategory``407730 +ocreatePrimitiveNormalPoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``407841 +ocreatePrimitivePoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``408048 +ocreateRandomElement`2`x`(List(Matrix(R)),Matrix(R))->Matrix(R)`pRepresentationPackage2(R)``408189 +ocreateThreeSpace`0`x`()->ThreeSpace(DoubleFloat)`pTopLevelThreeSpace``408301 +ocreateZechTable`1`n`(SparseUnivariatePolynomial(GF))->PrimitiveArray(SingleInteger)`pFiniteFieldFunctions(GF)``408460 +ocredits`0`x`()->Void`pApplicationProgramInterface``408905 +ocredPol`2`n`(Dpol,List(Dpol))->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409015 +ocrest`1`n`(NonNegativeInteger)->(Stream(Polynomial(R)))->Stream(Polynomial(R))`pWeierstrassPreparation(R)``409051 +ocritB`4`n`(Expon,Expon,Expon,Expon)->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409093 +ocritBonD`2`n`(Dpol,List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409127 +ocritM`2`n`(Expon,Expon)->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409164 +ocritMonD1`2`n`(Expon,List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409198 +ocritMTonD1`1`n`(List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409236 +ocritpOrder`2`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol),Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409275 +ocritT`1`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))->Boolean`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``409314 +ocross`2`n`(Point(DoubleFloat),Point(DoubleFloat))->Point(DoubleFloat)`pTubePlotTools``409348 ocross`2`n`(S,S)->S`xVectorCategory&(S,R)``0 -ocross`2`x`(_$,_$)->_$`cPointCategory(R)``345127 -ocross`2`x`(_$,_$)->_$`cVectorCategory(R)`has(R,Ring)`345279 -ocrushedSet`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``345429 -ocsc2sin`1`x`(F)->F`pTranscendentalManipulations(R,F)``345678 -ocscIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``345776 -ocsc`1`n`(F)->F`pElementaryFunction(R,F)``345870 +ocross`2`x`(_$,_$)->_$`cPointCategory(R)``409570 +ocross`2`x`(_$,_$)->_$`cVectorCategory(R)`has(R,Ring)`409722 +ocrushedSet`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``409872 +ocsc`1`n`(F)->F`pElementaryFunction(R,F)``410121 ocsc`1`n`(S)->S`xTrigonometricFunctionCategory&(S)``0 ocsc`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``345933 -ocsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``346002 -ocsc`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``346071 -ocsc`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``346141 -ocsc`1`x`(_$)->_$`cTrigonometricFunctionCategory``346213 -ocsch2sinh`1`x`(F)->F`pTranscendentalManipulations(R,F)``346268 -ocschIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``346370 -ocsch`1`n`(F)->F`pElementaryFunction(R,F)``346459 +ocsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``410184 +ocsc`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``410253 +ocsc`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``410322 +ocsc`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``410392 +ocsc`1`x`(_$)->_$`cTrigonometricFunctionCategory``410464 +ocsc2sin`1`x`(F)->F`pTranscendentalManipulations(R,F)``410519 +ocsch`1`n`(F)->F`pElementaryFunction(R,F)``410617 ocsch`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 ocsch`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ocsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``346534 -ocsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``346619 -ocsch`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``346704 -ocsch`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``346786 -ocsch`1`x`(_$)->_$`cHyperbolicFunctionCategory``346870 -ocsubst`2`n`(List(Var),List(Stream(SMP)))->(SMP)->Stream(SMP)`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``346937 -ocubic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``346990 -ocubic`4`n`(F,F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``347027 -ocup`2`x`(SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial(Fraction(Integer)))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``347076 -ocurrentSubProgram`0`x`()->Symbol`dTheSymbolTable``347269 -ocurryLeft`2`x`((A,B)->C,A)->(B)->C`pMappingPackage3(A,B,C)``347362 -ocurryRight`2`x`((A,B)->C,B)->(A)->C`pMappingPackage3(A,B,C)``347465 -ocurry`2`x`((A)->C,A)->()->C`pMappingPackage2(A,C)``347569 -ocurve?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``347660 -ocurveColorPalette`2`n`(List(DrawOption),Palette)->Palette`pDrawOptionFunctions0``347885 -ocurveColor`1`x`(Float)->_$`dDrawOption``348113 -ocurveColor`1`x`(Palette)->_$`dDrawOption``348256 -ocurve`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``348426 -ocurve`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``348624 -ocurve`2`x`(ComponentFunction,ComponentFunction)->_$`dParametricPlaneCurve(ComponentFunction)``348863 -ocurve`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``348966 -ocurve`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``349331 -ocurve`3`x`(ComponentFunction,ComponentFunction,ComponentFunction)->_$`dParametricSpaceCurve(ComponentFunction)``349504 -ocycleElt`1`n`(ST)->Union(ST,"failed")`pCyclicStreamTools(S,ST)``349628 +ocsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``410692 +ocsch`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``410777 +ocsch`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``410862 +ocsch`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``410944 +ocsch`1`x`(_$)->_$`cHyperbolicFunctionCategory``411028 +ocsch2sinh`1`x`(F)->F`pTranscendentalManipulations(R,F)``411095 +ocschIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``411197 +ocscIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``411286 +ocSec`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`411380 +ocSech`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`411502 +ocSin`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`411636 +ocSinh`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`411756 +ocsubst`2`n`(List(Var),List(Stream(SMP)))->(SMP)->Stream(SMP)`dSparseMultivariateTaylorSeries(Coef,Var,SMP)``411888 +ocTan`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`411941 +ocTanh`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`412064 +ocubic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``412199 +ocubic`4`n`(F,F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``412236 +ocubicBezier`4`x`(List(R),List(R),List(R),List(R))->(R)->List(R)`pBezier(R)``412285 +ocup`2`x`(SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial(Fraction(Integer)))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``413220 +ocurrentSubProgram`0`x`()->Symbol`dTheSymbolTable``413413 +ocurry`2`x`((A)->C,A)->()->C`pMappingPackage2(A,C)``413506 +ocurryLeft`2`x`((A,B)->C,A)->(B)->C`pMappingPackage3(A,B,C)``413597 +ocurryRight`2`x`((A,B)->C,B)->(A)->C`pMappingPackage3(A,B,C)``413700 +ocurve?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``413804 +ocurve`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``414029 +ocurve`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``414227 +ocurve`2`x`(ComponentFunction,ComponentFunction)->_$`dParametricPlaneCurve(ComponentFunction)``414466 +ocurve`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``414569 +ocurve`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``414934 +ocurve`3`x`(ComponentFunction,ComponentFunction,ComponentFunction)->_$`dParametricSpaceCurve(ComponentFunction)``415107 +ocurveColor`1`x`(Float)->_$`dDrawOption``415231 +ocurveColor`1`x`(Palette)->_$`dDrawOption``415374 +ocurveColorPalette`2`n`(List(DrawOption),Palette)->Palette`pDrawOptionFunctions0``415544 +ocurveV`1`x`(_$)->DistributedMultivariatePolynomial(construct('X,'Y),K)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``415772 +ocycle`1`x`(List(S))->_$`cPermutationCategory(S)``415907 +ocycleElt`1`n`(ST)->Union(ST,"failed")`pCyclicStreamTools(S,ST)``416151 ocycleEntry`1`n`(A)->A`xLazyStreamAggregate&(A,S)``0 ocycleEntry`1`n`(A)->A`xUnaryRecursiveAggregate&(A,S)``0 -ocycleEntry`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``349775 +ocycleEntry`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``416505 ocycleLength`1`n`(A)->NonNegativeInteger`xLazyStreamAggregate&(A,S)``0 ocycleLength`1`n`(A)->NonNegativeInteger`xUnaryRecursiveAggregate&(A,S)``0 -ocycleLength`1`x`(_$)->NonNegativeInteger`cUnaryRecursiveAggregate(S)``349911 -ocyclePartition`1`x`(_$)->Partition`dPermutation(S)``350051 -ocycleRagits`1`x`(_$)->List(Integer)`dRadixExpansion(bb)``350194 +ocycleLength`1`x`(_$)->NonNegativeInteger`cUnaryRecursiveAggregate(S)``416641 +ocyclePartition`1`x`(_$)->Partition`dPermutation(S)``416781 +ocycleRagits`1`x`(_$)->List(Integer)`dRadixExpansion(bb)``416924 +ocycles`1`x`(List(List(S)))->_$`cPermutationCategory(S)``417153 ocycleSplit!`1`n`(A)->A`xUnaryRecursiveAggregate&(A,S)``0 -ocycleSplit!`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`350423 +ocycleSplit!`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`417500 ocycleTail`1`n`(A)->A`xLazyStreamAggregate&(A,S)``0 ocycleTail`1`n`(A)->A`xUnaryRecursiveAggregate&(A,S)``0 -ocycleTail`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``350829 -ocycle`1`x`(List(S))->_$`cPermutationCategory(S)``350919 -ocycles`1`x`(List(List(S)))->_$`cPermutationCategory(S)``351146 +ocycleTail`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``417906 ocyclic?`1`n`(A)->Boolean`xBinaryRecursiveAggregate&(A,S)``0 ocyclic?`1`n`(A)->Boolean`xLazyStreamAggregate&(A,S)``0 ocyclic?`1`n`(A)->Boolean`xUnaryRecursiveAggregate&(A,S)``0 -ocyclic?`1`x`(_$)->Boolean`cRecursiveAggregate(S)``351476 -ocyclic?`1`x`(_$)->Boolean`dTree(S)``351532 -ocyclicCopy`1`x`(_$)->_$`dTree(S)``351593 -ocyclicEntries`1`x`(_$)->List(_$)`dTree(S)``351672 -ocyclicEqual?`2`x`(_$,_$)->Boolean`dTree(S)``351756 -ocyclicGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``351844 -ocyclicGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``352029 -ocyclicParents`1`x`(_$)->List(_$)`dTree(S)``352147 -ocyclicSubmodule`2`x`(List(Matrix(R)),Vector(R))->Vector(Vector(R))`pRepresentationPackage2(R)`has(R,EuclideanDomain)`352233 -ocyclic`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``352872 -ocyclotomicDecomposition`1`n`(Integer)->List(SparseUnivariatePolynomial(Integer))`pCyclotomicPolynomialPackage``352968 -ocyclotomicFactorization`1`n`(Integer)->Factored(SparseUnivariatePolynomial(Integer))`pCyclotomicPolynomialPackage``353025 -ocyclotomic`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pCyclotomicPolynomialPackage``353082 -ocyclotomic`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pPolynomialNumberTheoryFunctions``353126 -ocyclotomic`2`x`(NonNegativeInteger,R)->R`pNumberTheoreticPolynomialFunctions(R)``353330 -ocylindrical`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``353376 -od01ajf`8`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``353611 -od01akf`8`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``353879 -od01alf`10`x`(DoubleFloat,DoubleFloat,Integer,Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``354207 -od01amf`8`x`(DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``354491 -od01anf`10`x`(DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``354747 -od01apf`11`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``354983 -od01aqf`9`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``355283 -od01asf`9`x`(DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``355508 -od01bbf`6`x`(DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer)->Result`pNagIntegrationPackage``355737 -od01fcf`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp4(FUNCTN)))->Result`pNagIntegrationPackage``355992 -od01gaf`4`x`(Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer)->Result`pNagIntegrationPackage``356308 -od01gbf`10`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp4(FUNCTN)))->Result`pNagIntegrationPackage``356628 -od02bbf`10`x`(DoubleFloat,Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``357000 -od02bhf`10`x`(DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)))->Result`pNagOrdinaryDifferentialEquationsPackage``357351 -od02cjf`11`x`(DoubleFloat,Integer,Integer,DoubleFloat,String,DoubleFloat,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``357699 -od02ejf`13`x`(DoubleFloat,Integer,Integer,String,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp31(PEDERV)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``358157 -od02gaf`13`x`(Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp7(FCN)))->Result`pNagOrdinaryDifferentialEquationsPackage``358700 -od02gbf`15`x`(DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp77(FCNF)),Union(fn:FileName,fp:Asp78(FCNG)))->Result`pNagOrdinaryDifferentialEquationsPackage``359028 -od02kef`13`x`(Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp10(COEFFN)),Union(fn:FileName,fp:Asp80(BDYVAL)))->Result`pNagOrdinaryDifferentialEquationsPackage``359327 -od02kef`15`x`(Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp10(COEFFN)),Union(fn:FileName,fp:Asp80(BDYVAL)),FileName,FileName)->Result`pNagOrdinaryDifferentialEquationsPackage``359990 -od02raf`17`x`(Integer,Integer,Integer,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp41(FCN,JACOBF,JACEPS)),Union(fn:FileName,fp:Asp42(G,JACOBG,JACGEP)))->Result`pNagOrdinaryDifferentialEquationsPackage``360664 -od03edf`10`x`(Integer,Integer,Integer,Integer,DoubleFloat,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagPartialDifferentialEquationsPackage``361037 -od03eef`11`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,String,Integer,Union(fn:FileName,fp:Asp73(PDEF)),Union(fn:FileName,fp:Asp74(BNDY)))->Result`pNagPartialDifferentialEquationsPackage``361361 -od03faf`24`x`(DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,ThreeDimensionalMatrix(DoubleFloat),Integer)->Result`pNagPartialDifferentialEquationsPackage``361600 -odAndcExp`3`n`(Vector(GF),NonNegativeInteger,SingleInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``362046 -odark`1`x`(Color)->_$`dPalette``362484 -odatalist`1`x`(List(S))->_$`dDataList(S)``362583 -oddFact`2`x`(U,Integer)->List(Record(factor:U,degree:Integer))`pModularDistinctDegreeFactorizer(U)``362642 -odebug3D`1`n`(Boolean)->Boolean`dPlot3D``362933 -odebug`1`n`(Boolean)->Boolean`dPlot``363026 -odec`1`x`(_$)->_$`cIntegerNumberSystem``363113 -odecimal`1`x`(Fraction(Integer))->_$`dDecimalExpansion``363156 -odeclare!`2`x`(Symbol,FortranType)->FortranType`dTheSymbolTable``363232 -odeclare!`3`x`(List(Symbol),FortranType,_$)->FortranType`dSymbolTable``363358 -odeclare!`3`x`(Symbol,FortranType,Symbol)->FortranType`dTheSymbolTable``363480 -odeclare!`3`x`(Symbol,FortranType,_$)->FortranType`dSymbolTable``363585 -odeclare!`4`x`(List(Symbol),FortranType,Symbol,_$)->FortranType`dTheSymbolTable``363700 -odeclare!`4`x`(Symbol,FortranType,Symbol,_$)->FortranType`dTheSymbolTable``363850 -odeclare`1`n`(List(_$))->Symbol`dInputForm``363999 -odecomposeFunc`3`n`(Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R))))->Fraction(SparseUnivariatePolynomial(Expression(R)))`pTransSolvePackageService(R)``364348 -odecompose`1`x`(UP)->List(UP)`pPolynomialDecomposition(UP,F)``364587 -odecompose`1`x`(_$)->Record(id:FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart:R)`cFiniteDivisorCategory(F,UP,UPUP,R)``364629 -odecompose`2`n`(Fraction(UP),(UP)->UP)->Record(poly:UP,normal:Fraction(UP),special:Fraction(UP))`pMonomialExtensionTools(F,UP)``364713 -odecompose`3`x`(UP,NonNegativeInteger,NonNegativeInteger)->Union(Record(left:UP,right:UP),"failed")`pPolynomialDecomposition(UP,F)``365071 +ocyclic?`1`x`(_$)->Boolean`cRecursiveAggregate(S)``417996 +ocyclic?`1`x`(_$)->Boolean`dTree(S)``418052 +ocyclic`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``418199 +ocyclicCopy`1`x`(_$)->_$`dTree(S)``418295 +ocyclicEntries`1`x`(_$)->List(_$)`dTree(S)``418463 +ocyclicEqual?`2`x`(_$,_$)->Boolean`dTree(S)``418639 +ocyclicGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``418886 +ocyclicGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``419070 +ocyclicParents`1`x`(_$)->List(_$)`dTree(S)``419188 +ocyclicSubmodule`2`x`(List(Matrix(R)),Vector(R))->Vector(Vector(R))`pRepresentationPackage2(R)`has(R,EuclideanDomain)`419366 +ocyclotomic`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pCyclotomicPolynomialPackage``420005 +ocyclotomic`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pPolynomialNumberTheoryFunctions``420049 +ocyclotomic`2`x`(NonNegativeInteger,R)->R`pNumberTheoreticPolynomialFunctions(R)``420257 +ocyclotomicDecomposition`1`n`(Integer)->List(SparseUnivariatePolynomial(Integer))`pCyclotomicPolynomialPackage``420303 +ocyclotomicFactorization`1`n`(Integer)->Factored(SparseUnivariatePolynomial(Integer))`pCyclotomicPolynomialPackage``420360 +ocylindrical`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``420417 +od01ajf`8`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``420652 +od01akf`8`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``420920 +od01alf`10`x`(DoubleFloat,DoubleFloat,Integer,Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``421248 +od01amf`8`x`(DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(F)))->Result`pNagIntegrationPackage``421532 +od01anf`10`x`(DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``421788 +od01apf`11`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``422024 +od01aqf`9`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``422324 +od01asf`9`x`(DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Union(fn:FileName,fp:Asp1(G)))->Result`pNagIntegrationPackage``422549 +od01bbf`6`x`(DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer)->Result`pNagIntegrationPackage``422778 +od01fcf`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Integer,Union(fn:FileName,fp:Asp4(FUNCTN)))->Result`pNagIntegrationPackage``423033 +od01gaf`4`x`(Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer)->Result`pNagIntegrationPackage``423349 +od01gbf`10`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp4(FUNCTN)))->Result`pNagIntegrationPackage``423669 +od02bbf`10`x`(DoubleFloat,Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``424041 +od02bhf`10`x`(DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)))->Result`pNagOrdinaryDifferentialEquationsPackage``424392 +od02cjf`11`x`(DoubleFloat,Integer,Integer,DoubleFloat,String,DoubleFloat,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``424740 +od02ejf`13`x`(DoubleFloat,Integer,Integer,String,Integer,DoubleFloat,Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp9(G)),Union(fn:FileName,fp:Asp7(FCN)),Union(fn:FileName,fp:Asp31(PEDERV)),Union(fn:FileName,fp:Asp8(OUTPUT)))->Result`pNagOrdinaryDifferentialEquationsPackage``425198 +od02gaf`13`x`(Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp7(FCN)))->Result`pNagOrdinaryDifferentialEquationsPackage``425741 +od02gbf`15`x`(DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp77(FCNF)),Union(fn:FileName,fp:Asp78(FCNG)))->Result`pNagOrdinaryDifferentialEquationsPackage``426069 +od02kef`13`x`(Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp10(COEFFN)),Union(fn:FileName,fp:Asp80(BDYVAL)))->Result`pNagOrdinaryDifferentialEquationsPackage``426368 +od02kef`15`x`(Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Union(fn:FileName,fp:Asp10(COEFFN)),Union(fn:FileName,fp:Asp80(BDYVAL)),FileName,FileName)->Result`pNagOrdinaryDifferentialEquationsPackage``427053 +od02raf`17`x`(Integer,Integer,Integer,Integer,DoubleFloat,Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Union(fn:FileName,fp:Asp41(FCN,JACOBF,JACEPS)),Union(fn:FileName,fp:Asp42(G,JACOBG,JACGEP)))->Result`pNagOrdinaryDifferentialEquationsPackage``427749 +od03edf`10`x`(Integer,Integer,Integer,Integer,DoubleFloat,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagPartialDifferentialEquationsPackage``428179 +od03eef`11`x`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,String,Integer,Union(fn:FileName,fp:Asp73(PDEF)),Union(fn:FileName,fp:Asp74(BNDY)))->Result`pNagPartialDifferentialEquationsPackage``428503 +od03faf`24`x`(DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,ThreeDimensionalMatrix(DoubleFloat),Integer)->Result`pNagPartialDifferentialEquationsPackage``428742 +oD`0`n`()->S`xLinearOrdinaryDifferentialOperatorCategory&(S,A)``0 +oD`0`x`()->_$`cLinearOrdinaryDifferentialOperatorCategory(A)``429266 +oD`1`n`(S)->S`xDifferentialExtension&(S,R)``0 +oD`1`n`(S)->S`xDifferentialRing&(S)``0 +oD`1`x`(_$)->_$`cDifferentialRing``429358 +oD`1`x`(_$)->_$`dFullPartialFractionExpansion(F,UP)``429502 +oD`2`n`(A,List(S))->A`xPartialDifferentialRing&(A,S)``0 +oD`2`n`(A,S)->A`xPartialDifferentialRing&(A,S)``0 +oD`2`n`(S,List(Symbol))->S`xDifferentialExtension&(S,R)``0 +oD`2`n`(S,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 +oD`2`n`(S,NonNegativeInteger)->S`xDifferentialRing&(S)``0 +oD`2`n`(S,(R)->R)->S`xDifferentialExtension&(S,R)``0 +oD`2`n`(S,Symbol)->S`xDifferentialExtension&(S,R)``0 +oD`2`x`(_$,List(S))->_$`cPartialDifferentialRing(S)``429557 +oD`2`x`(_$,NonNegativeInteger)->_$`cDifferentialRing``429686 +oD`2`x`(_$,NonNegativeInteger)->_$`dFullPartialFractionExpansion(F,UP)``429758 +oD`2`x`(_$,(R)->R)->_$`cDifferentialExtension(R)``429830 +oD`2`x`(_$,S)->_$`cPartialDifferentialRing(S)``429926 +oD`3`n`(A,List(S),List(NonNegativeInteger))->A`xPartialDifferentialRing&(A,S)``0 +oD`3`n`(A,S,NonNegativeInteger)->A`xPartialDifferentialRing&(A,S)``0 +oD`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xDifferentialExtension&(S,R)``0 +oD`3`n`(S,(R)->R,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 +oD`3`n`(S,Symbol,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 +oD`3`x`(_$,List(S),List(NonNegativeInteger))->_$`cPartialDifferentialRing(S)``430019 +oD`3`x`(_$,(R)->R,NonNegativeInteger)->_$`cDifferentialExtension(R)``430181 +oD`3`x`(_$,S,NonNegativeInteger)->_$`cPartialDifferentialRing(S)``430311 +odAndcExp`3`n`(Vector(GF),NonNegativeInteger,SingleInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``430460 +odark`1`x`(Color)->_$`dPalette``430898 +odasum`3`x`(SingleInteger,PrimitiveArray(DoubleFloat),SingleInteger)->DoubleFloat`pBlasLevelOne``430997 +odatalist`1`x`(List(S))->_$`dDataList(S)``431286 +odaxpy`6`x`(SingleInteger,DoubleFloat,PrimitiveArray(DoubleFloat),SingleInteger,PrimitiveArray(DoubleFloat),SingleInteger)->PrimitiveArray(DoubleFloat)`pBlasLevelOne``431345 +odcabs1`1`x`(Complex(DoubleFloat))->DoubleFloat`pBlasLevelOne``432106 +odcopy`5`x`(SingleInteger,PrimitiveArray(DoubleFloat),SingleInteger,PrimitiveArray(DoubleFloat),SingleInteger)->PrimitiveArray(DoubleFloat)`pBlasLevelOne``432312 +oddFact`2`x`(U,Integer)->List(Record(factor:U,degree:Integer))`pModularDistinctDegreeFactorizer(U)``432999 +odebug`1`n`(Boolean)->Boolean`dPlot``433290 +odebug`1`x`(Boolean)->_$`dGuessOption``433377 +odebug`1`x`(List(GuessOption))->Boolean`dGuessOptionFunctions0``433517 +odebug3D`1`n`(Boolean)->Boolean`dPlot3D``433625 +odec`1`x`(_$)->_$`cIntegerNumberSystem``433718 +odecimal`1`x`(Fraction(Integer))->_$`dDecimalExpansion``433761 +odeclare`1`n`(List(_$))->Symbol`dInputForm``433837 +odeclare!`2`x`(Symbol,FortranType)->FortranType`dTheSymbolTable``434186 +odeclare!`3`x`(List(Symbol),FortranType,_$)->FortranType`dSymbolTable``434312 +odeclare!`3`x`(Symbol,FortranType,_$)->FortranType`dSymbolTable``434434 +odeclare!`3`x`(Symbol,FortranType,Symbol)->FortranType`dTheSymbolTable``434549 +odeclare!`4`x`(List(Symbol),FortranType,Symbol,_$)->FortranType`dTheSymbolTable``434654 +odeclare!`4`x`(Symbol,FortranType,Symbol,_$)->FortranType`dTheSymbolTable``434804 +odecompose`1`x`(_$)->Record(id:FractionalIdeal(UP,Fraction(UP),UPUP,R),principalPart:R)`cFiniteDivisorCategory(F,UP,UPUP,R)``434953 +odecompose`1`x`(UP)->List(UP)`pPolynomialDecomposition(UP,F)``435037 +odecompose`2`n`(Fraction(UP),(UP)->UP)->Record(poly:UP,normal:Fraction(UP),special:Fraction(UP))`pMonomialExtensionTools(F,UP)``435079 +odecompose`3`x`(UP,NonNegativeInteger,NonNegativeInteger)->Union(Record(left:UP,right:UP),"failed")`pPolynomialDecomposition(UP,F)``435437 odecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(TS)`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 odecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(TS)`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 odecompose`7`x`(List(P),List(TS),Boolean,Boolean,Boolean,Boolean,Boolean)->List(TS)`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 odecompose`7`x`(List(P),List(TS),Boolean,Boolean,Boolean,Boolean,Boolean)->List(TS)`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -odecreasePrecision`1`x`(Integer)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`365121 -odecrease`1`x`(String)->Float`dAttributeButtons``365261 -odecrease`2`x`(String,String)->Float`dAttributeButtons``365534 -odeepCopy`1`n`(_$)->_$`dSubSpace(n,R)``365836 -odeepExpand`1`x`(_$)->OutputForm`dFreeNilpotentLie(n,class,R)``365876 +odecomposeFunc`3`n`(Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R))),Fraction(SparseUnivariatePolynomial(Expression(R))))->Fraction(SparseUnivariatePolynomial(Expression(R)))`pTransSolvePackageService(R)``435487 +odecrease`1`x`(String)->Float`dAttributeButtons``435726 +odecrease`2`x`(String,String)->Float`dAttributeButtons``435999 +odecreasePrecision`1`x`(Integer)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`436301 +odeepCopy`1`n`(_$)->_$`dSubSpace(n,R)``436441 odeepestInitial`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -odeepestInitial`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``365920 +odeepestInitial`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``436485 odeepestTail`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -odeepestTail`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``366099 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odegree`1`n`(S)->Expon`xUnivariatePowerSeriesCategory&(S,Coef,Expon)``0 odegree`1`n`(S)->NonNegativeInteger`xTriangularSetCategory&(S,R,E,V,P)``0 odegree`1`n`(S)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 odegree`1`n`(S)->OnePointCompletion(PositiveInteger)`xFiniteAlgebraicExtensionField&(S,F)``0 odegree`1`n`(S)->PositiveInteger`xFiniteAlgebraicExtensionField&(S,F)``0 -odegree`1`n`(_$)->Integer`dDeRhamComplex(CoefRing,listIndVar)``368486 -odegree`1`n`(_$)->Integer`dLaurentPolynomial(R,UP)``368574 -odegree`1`n`(_$)->NonNegativeInteger`dAntiSymm(R,lVar)``368612 -odegree`1`n`(_$)->NonNegativeInteger`dExtAlgBasis``368680 -odegree`1`x`(_$)->E`cAbelianMonoidRing(R,E)``368849 -odegree`1`x`(_$)->E`cGradedModule(R,E)``368936 -odegree`1`x`(_$)->Expon`cPowerSeriesCategory(Coef,Expon,Var)``369057 -odegree`1`x`(_$)->Fraction(Integer)`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``369140 -odegree`1`x`(_$)->Integer`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``369281 -odegree`1`x`(_$)->NonNegativeInteger`cFreeLieAlgebra(VarSet,R)``369408 -odegree`1`x`(_$)->NonNegativeInteger`cMonogenicLinearOperator(R)``369514 -odegree`1`x`(_$)->NonNegativeInteger`cTriangularSetCategory(R,E,V,P)``369615 -odegree`1`x`(_$)->NonNegativeInteger`cUnivariateSkewPolynomialCategory(R)``369721 -odegree`1`x`(_$)->NonNegativeInteger`cXPolynomialsCat(vl,R)``369822 -odegree`1`x`(_$)->NonNegativeInteger`dPermutation(S)``369938 -odegree`1`x`(_$)->NonNegativeInteger`dPermutationGroup(S)``370025 -odegree`1`x`(_$)->OnePointCompletion(PositiveInteger)`cExtensionField(F)``370128 -odegree`1`x`(_$)->PositiveInteger`cFiniteAlgebraicExtensionField(F)``370317 +odegree`1`x`(_$)->E`cAbelianMonoidRing(R,E)``438812 +odegree`1`x`(_$)->E`cGradedModule(R,E)``438899 +odegree`1`x`(_$)->Expon`cPowerSeriesCategory(Coef,Expon,Var)``439020 +odegree`1`x`(_$)->Fraction(Integer)`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``439103 +odegree`1`x`(_$)->Integer`cDivisorCategory(S)``439244 +odegree`1`x`(_$)->Integer`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``439311 +odegree`1`x`(_$)->NonNegativeInteger`cFreeLieAlgebra(VarSet,R)``439438 +odegree`1`x`(_$)->NonNegativeInteger`cMonogenicLinearOperator(R)``439544 +odegree`1`x`(_$)->NonNegativeInteger`cTriangularSetCategory(R,E,V,P)``439645 +odegree`1`x`(_$)->NonNegativeInteger`cUnivariateSkewPolynomialCategory(R)``439751 +odegree`1`x`(_$)->NonNegativeInteger`cXPolynomialsCat(vl,R)``439852 +odegree`1`x`(_$)->NonNegativeInteger`dPermutationGroup(S)``439968 +odegree`1`x`(_$)->NonNegativeInteger`dPermutation(S)``440072 +odegree`1`x`(_$)->OnePointCompletion(PositiveInteger)`cExtensionField(F)``440159 +odegree`1`x`(_$)->PositiveInteger`cFiniteAlgebraicExtensionField(F)``440348 +odegree`1`x`(_$)->PositiveInteger`cSetCategoryWithDegree``0 odegree`2`n`(A,List(V))->List(NonNegativeInteger)`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odegree`2`n`(A,S)->NonNegativeInteger`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odegree`2`n`(A,V)->NonNegativeInteger`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odegree`2`n`(S,List(SingletonAsOrderedSet))->List(NonNegativeInteger)`xUnivariatePolynomialCategory&(S,R)``0 +odegree`2`n`(SparseUnivariatePolynomial(P),List(OV))->List(NonNegativeInteger)`pFactoringUtilities(E,OV,R,P)``440472 odegree`2`n`(S,SingletonAsOrderedSet)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 -odegree`2`n`(SparseUnivariatePolynomial(P),List(OV))->List(NonNegativeInteger)`pFactoringUtilities(E,OV,R,P)``370441 -odegree`2`x`(_$,List(VarSet))->List(NonNegativeInteger)`cPolynomialCategory(R,E,VarSet)``370549 -odegree`2`x`(_$,S)->NonNegativeInteger`cDifferentialPolynomialCategory(R,S,V,E)``370688 -odegree`2`x`(_$,VarSet)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``370870 -odelay`1`x`(()->_$)->_$`dStream(S)``370977 -odelete!`2`n`(A,Integer)->A`xListAggregate&(A,S)``0 -odelete!`2`n`(A,UniversalSegment(Integer))->A`xListAggregate&(A,S)``0 -odelete!`2`x`(_$,Integer)->_$`cExtensibleLinearAggregate(S)``371130 -odelete!`2`x`(_$,UniversalSegment(Integer))->_$`cExtensibleLinearAggregate(S)``371225 -odeleteProperty!`2`x`(_$,String)->_$`dBasicOperator``371333 -odeleteRoutine!`2`x`(_$,Symbol)->_$`dRoutinesTable``371497 +odegree`2`x`(_$,List(VarSet))->List(NonNegativeInteger)`cPolynomialCategory(R,E,VarSet)``440580 +odegree`2`x`(PolyRing,Integer)->NonNegativeInteger`pPackageForPoly(R,PolyRing,E,dim)``0 +odegree`2`x`(_$,S)->NonNegativeInteger`cDifferentialPolynomialCategory(R,S,V,E)``440719 +odegree`2`x`(_$,VarSet)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``440901 +odegreeOfMinimalForm`1`x`(PolyRing)->NonNegativeInteger`pPackageForPoly(R,PolyRing,E,dim)``441008 +odegreePartition`1`n`(Factored(UP))->Multiset(NonNegativeInteger)`pGaloisGroupPolynomialUtilities(R,UP)``441060 +odegreePartition`1`n`(List(Record(factor:UP,degree:Integer)))->Multiset(NonNegativeInteger)`pGaloisGroupFactorizer(UP)``441225 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+odesingTreeAtPoint`2`x`(ProjPt,PolyRing)->DesTree`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``448193 +odesingTreeWoFullParam`0`x`()->List(DesingTree(InfClsPt(K,symb,BLMET)))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``448374 +odesingTreeWoFullParam`0`x`()->List(DesingTree(InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(K,symb,BLMET)))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``448575 +odesingTreeWoFullParam`0`x`()->List(DesTree)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``448776 +odestruct`1`n`(_$)->List(Record(key:Symbol,entry:S))`dPatternMatchResult(R,S)``448977 +odestruct`1`x`(_$)->List(_$)`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``449096 +odeterminant`1`n`(M)->R`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``449177 +odeterminant`1`x`(M)->R`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``449312 +odeterminant`1`x`(_$)->R`cMatrixCategory(R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`449447 +odeterminant`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`449678 +odf2ef`1`x`(DoubleFloat)->Expression(Float)`pExpertSystemToolsPackage``449755 +odf2fi`1`x`(DoubleFloat)->Fraction(Integer)`pExpertSystemToolsPackage``449844 +odf2mf`1`x`(DoubleFloat)->MachineFloat`pExpertSystemToolsPackage``449952 +odf2st`1`x`(DoubleFloat)->String`pd01AgentsPackage``450037 +odf2st`1`x`(DoubleFloat)->String`pExpertSystemContinuityPackage``450116 +odf2st`1`x`(DoubleFloat)->String`pExpertSystemToolsPackage``450195 +odflist`1`x`(List(Record(left:Fraction(Integer),right:Fraction(Integer))))->List(DoubleFloat)`pExpertSystemToolsPackage``450274 +odfRange`1`x`(Segment(OrderedCompletion(DoubleFloat)))->Segment(OrderedCompletion(DoubleFloat))`pExpertSystemToolsPackage``450369 +odiag`1`x`((A,A)->C)->(A)->C`pMappingPackage2(A,C)``450510 odiagonal?`1`n`(S)->Boolean`xMatrixCategory&(S,R,Row,Col)``0 odiagonal?`1`n`(S)->Boolean`xRectangularMatrixCategory&(S,m,n,R,Row,Col)``0 -odiagonal?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``377272 -odiagonal?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``377466 +odiagonal`1`n`(S)->Row`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +odiagonal?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``450604 +odiagonal?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``450928 +odiagonal`1`x`(_$)->Row`cSquareMatrixCategory(ndim,R,Row,Col)``451122 odiagonalMatrix`1`n`(List(R))->S`xMatrixCategory&(S,R,Row,Col)``0 odiagonalMatrix`1`n`(List(S))->S`xMatrixCategory&(S,R,Row,Col)``0 -odiagonalMatrix`1`x`(List(R))->_$`cMatrixCategory(R,Row,Col)``377660 -odiagonalMatrix`1`x`(List(R))->_$`cSquareMatrixCategory(ndim,R,Row,Col)``377765 -odiagonalMatrix`1`x`(List(_$))->_$`cMatrixCategory(R,Row,Col)``377870 -odiagonalMatrix`1`x`(Vector(R))->_$`dMatrix(R)``378427 -odiagonalProduct`1`n`(Matrix(R))->R`pIntegralBasisTools(R,UP,F)``378540 +odiagonalMatrix`1`x`(List(_$))->_$`cMatrixCategory(R,Row,Col)``451229 +odiagonalMatrix`1`x`(List(R))->_$`cMatrixCategory(R,Row,Col)``452024 +odiagonalMatrix`1`x`(List(R))->_$`cSquareMatrixCategory(ndim,R,Row,Col)``452204 +odiagonalMatrix`1`x`(Vector(R))->_$`dMatrix(R)``452309 +odiagonalProduct`1`n`(Matrix(R))->R`pIntegralBasisTools(R,UP,F)``452422 odiagonalProduct`1`n`(S)->R`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -odiagonalProduct`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)``378648 -odiagonal`1`n`(S)->Row`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -odiagonal`1`x`(_$)->Row`cSquareMatrixCategory(ndim,R,Row,Col)``378757 -odiagonals`2`x`(_$,String)->Void`dThreeDimensionalViewport``378864 +odiagonalProduct`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)``452530 +odiagonals`2`x`(_$,String)->Void`dThreeDimensionalViewport``452639 odictionary`0`n`()->A`xDictionary&(A,S)``0 odictionary`0`n`()->A`xDictionaryOperations&(A,S)``0 -odictionary`0`x`()->_$`cDictionaryOperations(S)``379207 +odictionary`0`x`()->_$`cDictionaryOperations(S)``452982 odictionary`1`n`(List(S))->A`xDictionary&(A,S)``0 odictionary`1`n`(List(S))->A`xDictionaryOperations&(A,S)``0 -odictionary`1`x`(List(S))->_$`cDictionaryOperations(S)``379290 -odiff`1`n`(Symbol)->(F)->F`pODEIntegration(R,F)``379423 +odictionary`1`x`(List(S))->_$`cDictionaryOperations(S)``453065 +odiff`1`n`(Symbol)->(F)->F`pODEIntegration(R,F)``453198 +oDiffAction`3`x`(NonNegativeInteger,NonNegativeInteger,V)->D`pFractionFreeFastGaussian(D,V)``453269 +oDiffC`1`x`(NonNegativeInteger)->List(D)`pFractionFreeFastGaussian(D,V)``453493 odifference`2`n`(A,A)->A`xFiniteSetAggregate&(A,S)``0 odifference`2`n`(A,A)->A`xSetAggregate&(A,S)``0 odifference`2`n`(A,S)->A`xFiniteSetAggregate&(A,S)``0 odifference`2`n`(A,S)->A`xSetAggregate&(A,S)``0 -odifference`2`x`(_$,S)->_$`cSetAggregate(S)``379494 -odifference`2`x`(_$,_$)->_$`cSetAggregate(S)``379750 +odifference`2`x`(_$,_$)->_$`cSetAggregate(S)``453803 +odifference`2`x`(_$,S)->_$`cSetAggregate(S)``454220 odifferentialVariables`1`n`(A)->List(S)`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -odifferentialVariables`1`x`(_$)->List(S)`cDifferentialPolynomialCategory(R,S,V,E)``380163 +odifferentialVariables`1`x`(_$)->List(S)`cDifferentialPolynomialCategory(R,S,V,E)``454480 odifferentiate`1`n`(A)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`1`n`(A)->A`xDifferentialVariableCategory&(A,S)``0 odifferentiate`1`n`(A)->A`xQuotientFieldCategory&(A,S)``0 @@ -3122,11 +3168,9 @@ odifferentiate`1`n`(S)->S`xMonogenicAlgebra&(S,R,UP)``0 odifferentiate`1`n`(S)->S`xQuaternionCategory&(S,R)``0 odifferentiate`1`n`(S)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 odifferentiate`1`n`(S)->S`xUnivariatePolynomialCategory&(S,R)``0 -odifferentiate`1`x`(_$)->_$`cDifferentialRing``380297 -odifferentiate`1`x`(_$)->_$`cDifferentialVariableCategory(S)``380453 -odifferentiate`1`x`(_$)->_$`dFullPartialFractionExpansion(F,UP)``380520 -odifferentiate`2`n`(A,(R)->R)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -odifferentiate`2`n`(A,(S)->S)->A`xQuotientFieldCategory&(A,S)``0 +odifferentiate`1`x`(_$)->_$`cDifferentialRing``454614 +odifferentiate`1`x`(_$)->_$`cDifferentialVariableCategory(S)``454770 +odifferentiate`1`x`(_$)->_$`dFullPartialFractionExpansion(F,UP)``454837 odifferentiate`2`n`(A,List(S))->A`xPartialDifferentialRing&(A,S)``0 odifferentiate`2`n`(A,List(Symbol))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`2`n`(A,List(Symbol))->A`xQuotientFieldCategory&(A,S)``0 @@ -3134,19 +3178,15 @@ odifferentiate`2`n`(A,List(V))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`2`n`(A,NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`2`n`(A,NonNegativeInteger)->A`xDifferentialVariableCategory&(A,S)``0 odifferentiate`2`n`(A,NonNegativeInteger)->A`xQuotientFieldCategory&(A,S)``0 +odifferentiate`2`n`(A,(R)->R)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`2`n`(A,S)->A`xPartialDifferentialRing&(A,S)``0 +odifferentiate`2`n`(A,(S)->S)->A`xQuotientFieldCategory&(A,S)``0 odifferentiate`2`n`(A,Symbol)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`2`n`(A,Symbol)->A`xQuotientFieldCategory&(A,S)``0 odifferentiate`2`n`(A,V)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 +odifferentiate`2`n`(_$,(F)->F)->F`dIntegrationResult(F)``454904 +odifferentiate`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``455006 odifferentiate`2`n`(S,(Fraction(UP))->Fraction(UP))->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -odifferentiate`2`n`(S,(R)->R)->S`xComplexCategory&(S,R)``0 -odifferentiate`2`n`(S,(R)->R)->S`xDifferentialExtension&(S,R)``0 -odifferentiate`2`n`(S,(R)->R)->S`xDirectProductCategory&(S,dim,R)``0 -odifferentiate`2`n`(S,(R)->R)->S`xMonogenicAlgebra&(S,R,UP)``0 -odifferentiate`2`n`(S,(R)->R)->S`xQuaternionCategory&(S,R)``0 -odifferentiate`2`n`(S,(R)->R)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -odifferentiate`2`n`(S,(R)->R)->S`xUnivariatePolynomialCategory&(S,R)``0 -odifferentiate`2`n`(S,(UP)->UP)->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 odifferentiate`2`n`(S,List(SingletonAsOrderedSet))->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`2`n`(S,List(Symbol))->S`xComplexCategory&(S,R)``0 odifferentiate`2`n`(S,List(Symbol))->S`xDifferentialExtension&(S,R)``0 @@ -3168,6 +3208,13 @@ odifferentiate`2`n`(S,NonNegativeInteger)->S`xMonogenicAlgebra&(S,R,UP)``0 odifferentiate`2`n`(S,NonNegativeInteger)->S`xQuaternionCategory&(S,R)``0 odifferentiate`2`n`(S,NonNegativeInteger)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 odifferentiate`2`n`(S,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 +odifferentiate`2`n`(S,(R)->R)->S`xComplexCategory&(S,R)``0 +odifferentiate`2`n`(S,(R)->R)->S`xDifferentialExtension&(S,R)``0 +odifferentiate`2`n`(S,(R)->R)->S`xDirectProductCategory&(S,dim,R)``0 +odifferentiate`2`n`(S,(R)->R)->S`xMonogenicAlgebra&(S,R,UP)``0 +odifferentiate`2`n`(S,(R)->R)->S`xQuaternionCategory&(S,R)``0 +odifferentiate`2`n`(S,(R)->R)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +odifferentiate`2`n`(S,(R)->R)->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`2`n`(S,SingletonAsOrderedSet)->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`2`n`(S,Symbol)->S`xComplexCategory&(S,R)``0 odifferentiate`2`n`(S,Symbol)->S`xDifferentialExtension&(S,R)``0 @@ -3178,42 +3225,35 @@ odifferentiate`2`n`(S,Symbol)->S`xMonogenicAlgebra&(S,R,UP)``0 odifferentiate`2`n`(S,Symbol)->S`xQuaternionCategory&(S,R)``0 odifferentiate`2`n`(S,Symbol)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 odifferentiate`2`n`(S,Symbol)->S`xUnivariatePolynomialCategory&(S,R)``0 -odifferentiate`2`n`(_$,(F)->F)->F`dIntegrationResult(F)``380587 -odifferentiate`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``380689 -odifferentiate`2`n`(_$,Symbol)->F`dIntegrationResult(F)`has(F,PartialDifferentialRing(Symbol))`380872 -odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariateLaurentSeries(Coef,var,cen)``380958 -odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariatePuiseuxSeries(Coef,var,cen)``381060 -odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``381162 -odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariateLaurentSeries(Coef,var,cen)``381265 -odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariatePuiseuxSeries(Coef,var,cen)``381367 -odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariateTaylorSeries(Coef,var,cen)``381469 -odifferentiate`2`x`(_$,(R)->R)->_$`cDifferentialExtension(R)``381572 -odifferentiate`2`x`(_$,(UP)->UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``381680 -odifferentiate`2`x`(_$,List(S))->_$`cPartialDifferentialRing(S)``381790 -odifferentiate`2`x`(_$,NonNegativeInteger)->_$`cDifferentialRing``381955 -odifferentiate`2`x`(_$,NonNegativeInteger)->_$`cDifferentialVariableCategory(S)``382039 -odifferentiate`2`x`(_$,NonNegativeInteger)->_$`dFullPartialFractionExpansion(F,UP)``382123 -odifferentiate`2`x`(_$,S)->_$`cPartialDifferentialRing(S)``382207 -odifferentiate`2`x`(_$,Variable(var))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``382312 -odifferentiate`3`n`(A,(R)->R,NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -odifferentiate`3`n`(A,(S)->S,NonNegativeInteger)->A`xQuotientFieldCategory&(A,S)``0 +odifferentiate`2`n`(S,(UP)->UP)->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 +odifferentiate`2`n`(_$,Symbol)->F`dIntegrationResult(F)`has(F,PartialDifferentialRing(Symbol))`455189 +odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariateLaurentSeries(Coef,var,cen)``455275 +odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariatePuiseuxSeries(Coef,var,cen)``455377 +odifferentiate`2`n`(_$,Variable(var))->_$`dSparseUnivariateTaylorSeries(Coef,var,cen)``455479 +odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariateLaurentSeries(Coef,var,cen)``455582 +odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariatePuiseuxSeries(Coef,var,cen)``455684 +odifferentiate`2`n`(_$,Variable(var))->_$`dUnivariateTaylorSeries(Coef,var,cen)``455786 +odifferentiate`2`x`(_$,List(S))->_$`cPartialDifferentialRing(S)``455889 +odifferentiate`2`x`(_$,NonNegativeInteger)->_$`cDifferentialRing``456054 +odifferentiate`2`x`(_$,NonNegativeInteger)->_$`cDifferentialVariableCategory(S)``456138 +odifferentiate`2`x`(_$,NonNegativeInteger)->_$`dFullPartialFractionExpansion(F,UP)``456222 +odifferentiate`2`x`(_$,(R)->R)->_$`cDifferentialExtension(R)``456306 +odifferentiate`2`x`(_$,S)->_$`cPartialDifferentialRing(S)``456414 +odifferentiate`2`x`(_$,(UP)->UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``456519 +odifferentiate`2`x`(_$,Variable(var))->_$`dGeneralUnivariatePowerSeries(Coef,var,cen)``456629 +odifferentiate`2`x`(_$,Variable(var))->_$`dUnivariateTaylorSeriesCZero(Coef,var)``456731 +odifferentiate`2`x`(_$,Variable('x))->_$`dUnivariateFormalPowerSeries(Coef)``0 odifferentiate`3`n`(A,List(S),List(NonNegativeInteger))->A`xPartialDifferentialRing&(A,S)``0 odifferentiate`3`n`(A,List(Symbol),List(NonNegativeInteger))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`3`n`(A,List(Symbol),List(NonNegativeInteger))->A`xQuotientFieldCategory&(A,S)``0 odifferentiate`3`n`(A,List(V),List(NonNegativeInteger))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 +odifferentiate`3`n`(A,(R)->R,NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`3`n`(A,S,NonNegativeInteger)->A`xPartialDifferentialRing&(A,S)``0 +odifferentiate`3`n`(A,(S)->S,NonNegativeInteger)->A`xQuotientFieldCategory&(A,S)``0 odifferentiate`3`n`(A,Symbol,NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`3`n`(A,Symbol,NonNegativeInteger)->A`xQuotientFieldCategory&(A,S)``0 odifferentiate`3`n`(A,V,NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 odifferentiate`3`n`(S,(Fraction(UP))->Fraction(UP),NonNegativeInteger)->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xComplexCategory&(S,R)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xDirectProductCategory&(S,dim,R)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xMonogenicAlgebra&(S,R,UP)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xQuaternionCategory&(S,R)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 -odifferentiate`3`n`(S,(R)->R,S)->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`3`n`(S,List(SingletonAsOrderedSet),List(NonNegativeInteger))->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xComplexCategory&(S,R)``0 odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xDifferentialExtension&(S,R)``0 @@ -3224,6 +3264,14 @@ odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xMonogenicAlgebr odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xQuaternionCategory&(S,R)``0 odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 odifferentiate`3`n`(S,List(Symbol),List(NonNegativeInteger))->S`xUnivariatePolynomialCategory&(S,R)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xComplexCategory&(S,R)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xDirectProductCategory&(S,dim,R)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xMonogenicAlgebra&(S,R,UP)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xQuaternionCategory&(S,R)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +odifferentiate`3`n`(S,(R)->R,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 +odifferentiate`3`n`(S,(R)->R,S)->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`3`n`(S,SingletonAsOrderedSet,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xComplexCategory&(S,R)``0 odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xDifferentialExtension&(S,R)``0 @@ -3234,229 +3282,265 @@ odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xMonogenicAlgebra&(S,R,UP)`` odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xQuaternionCategory&(S,R)``0 odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 odifferentiate`3`n`(S,Symbol,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 -odifferentiate`3`x`(_$,(R)->R,NonNegativeInteger)->_$`cDifferentialExtension(R)``382414 -odifferentiate`3`x`(_$,(R)->R,_$)->_$`cUnivariatePolynomialCategory(R)``382556 -odifferentiate`3`x`(_$,List(S),List(NonNegativeInteger))->_$`cPartialDifferentialRing(S)``382743 -odifferentiate`3`x`(_$,S,NonNegativeInteger)->_$`cPartialDifferentialRing(S)``382871 -odigamma`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``383032 -odigamma`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``383106 -odigamma`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``383228 -odigamma`1`x`(_$)->_$`cSpecialFunctionCategory``383350 -odigit?`1`x`(_$)->Boolean`dCharacter``383473 -odigit`0`x`()->_$`dCharacterClass``383570 -odigits`0`n`()->PositiveInteger`xFloatingPointSystem&(S)``383686 -odigits`0`x`()->PositiveInteger`cFloatingPointSystem``383763 -odigits`1`n`(PositiveInteger)->PositiveInteger`xFloatingPointSystem&(S)``383840 -odigits`1`x`(PositiveInteger)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`383937 -odigits`1`x`(_$)->Stream(Integer)`cPAdicIntegerCategory(p)``384034 -odihedralGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``384112 -odihedralGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``384302 -odihedral`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``384414 -odilog`1`n`(F)->F`pLiouvillianFunction(R,F)``384514 -odilog`1`x`(_$)->_$`cLiouvillianFunctionCategory``384561 -odim`1`x`(Color)->_$`dPalette``384685 -odimensionOfIrreducibleRepresentation`1`x`(List(Integer))->NonNegativeInteger`pIrrRepSymNatPackage``384777 +odifferentiate`3`x`(_$,List(S),List(NonNegativeInteger))->_$`cPartialDifferentialRing(S)``456834 +odifferentiate`3`x`(_$,(R)->R,_$)->_$`cUnivariatePolynomialCategory(R)``456962 +odifferentiate`3`x`(_$,(R)->R,NonNegativeInteger)->_$`cDifferentialExtension(R)``457149 +odifferentiate`3`x`(_$,S,NonNegativeInteger)->_$`cPartialDifferentialRing(S)``457291 +odiffHP`1`x`(List(GuessOption))->HPSPEC`pGuessUnivariatePolynomial(q)``457452 +odiffHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(AlgebraicNumber))->Stream(UnivariateFormalPowerSeries(AlgebraicNumber)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Al--gebraicNumber))->AlgebraicNumber,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->SparseUnivariatePolynomial(AlgebraicNumber),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(AlgebraicNumber))`pGuessAlgebraicNumber``0 +odiffHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Integer)))->Stream(UnivariateFormalPowerSeries(Fraction(Integer))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolyn--omial(Integer))->Integer,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->SparseUnivariatePolynomial(Fraction(Integer)),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Integer))`pGuessInteger``0 +odiffHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))->Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegative--Integer,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer)))->Polynomial(Integer),AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->SparseUnivariatePolynomial(Fraction(Polynomial(Integer))),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Polynomial(Integer)))`pGuessPolynomial``0 +odiffHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F))->F,AF:(NonNegativeInteger,NonNegativeInteger,Univariat--eFormalPowerSeries(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(F))`pGuessFinite(F)``0 +odiffHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(EXPRR,Symbol)->Stream(EXPRR),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S))->S,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUni--variatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,EXPRR)->EXPRR,C:(NonNegativeInteger)->List(S))`pGuess(F,S,EXPRR,R,retract,coerce)``457567 +odiffHP`1`x`(Symbol)->(List(GuessOption))->HPSPEC`pGuessUnivariatePolynomial(q)``457682 +odiffHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(AlgebraicNumber))->Stream(UnivariateFormalPowerSeries(AlgebraicNumber)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePol--ynomial(AlgebraicNumber))->AlgebraicNumber,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->SparseUnivariatePolynomial(AlgebraicNumber),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(AlgebraicNumber))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +odiffHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Integer)))->Stream(UnivariateFormalPowerSeries(Fraction(Integer))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUniva--riatePolynomial(Integer))->Integer,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->SparseUnivariatePolynomial(Fraction(Integer)),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Integer))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +odiffHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))->Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(N--onNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer)))->Polynomial(Integer),AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->SparseUnivariatePolynomial(Fraction(Polynomial(Integer))),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Polynomial(Integer)))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),h--as(Polynomial(Integer),RetractableTo(Symbol)))`0 +odiffHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F))->F,AF:(NonNegativeInteger,NonNegativeInteger--,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(F))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +odiffHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(EXPRR,Symbol)->Stream(EXPRR),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S))->S,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries--(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,EXPRR)->EXPRR,C:(NonNegativeInteger)->List(S))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`457806 +odigamma`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``457930 +odigamma`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``458004 +odigamma`1`x`(_$)->_$`cSpecialFunctionCategory``458126 +odigamma`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``458249 +odigit`0`x`()->_$`dCharacterClass``458371 +odigit?`1`x`(_$)->Boolean`dCharacter``458462 +odigits`0`n`()->PositiveInteger`xFloatingPointSystem&(S)``458752 +odigits`0`x`()->PositiveInteger`cFloatingPointSystem``458829 +odigits`1`n`(PositiveInteger)->PositiveInteger`xFloatingPointSystem&(S)``458906 +odigits`1`x`(PositiveInteger)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`459003 +odigits`1`x`(_$)->Stream(Integer)`cPAdicIntegerCategory(p)``459100 +odihedral`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``459178 +odihedralGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``459278 +odihedralGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``459467 +odilog`1`n`(F)->F`pLiouvillianFunction(R,F)``459579 +odilog`1`x`(_$)->_$`cLiouvillianFunctionCategory``459626 +odim`1`x`(Color)->_$`dPalette``459750 odimension`0`n`()->CardinalNumber`xDirectProductCategory&(S,dim,R)``0 odimension`0`n`()->CardinalNumber`xFiniteAlgebraicExtensionField&(S,F)``0 -odimension`0`x`()->CardinalNumber`cVectorSpace(S)``385005 -odimension`0`x`()->NonNegativeInteger`dFreeNilpotentLie(n,class,R)``385079 -odimension`1`x`(_$)->Integer`dPolynomialIdeals(F,Expon,VarSet,DPoly)``385137 -odimension`1`x`(_$)->PositiveInteger`cPointCategory(R)``385288 -odimension`2`x`(_$,List(VarSet))->Integer`dPolynomialIdeals(F,Expon,VarSet,DPoly)``385369 -odimensionsOf`1`x`(_$)->List(Polynomial(Integer))`dFortranType``385475 -odimensionsOf`2`x`(Symbol,Matrix(DoubleFloat))->SExpression`pNAGLinkSupportPackage``385540 -odimensionsOf`2`x`(Symbol,Matrix(Integer))->SExpression`pNAGLinkSupportPackage``385590 -odimensions`5`n`(_$,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger)->Void`dTwoDimensionalViewport``385640 -odimensions`5`x`(_$,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger)->Void`dThreeDimensionalViewport``386096 -odioSolve`1`x`(Equation(Polynomial(Integer)))->Record(varOrder:List(Symbol),inhom:Union(List(Vector(NonNegativeInteger)),"failed"),hom:List(Vector(NonNegativeInteger)))`pDiophantineSolutionPackage``386556 -odiophantineSystem`2`x`(M,Col)->Record(particular:Union(Col,"failed"),basis:List(Col))`pSmithNormalForm(R,Row,Col,M)``386733 -odirectProduct`1`x`(Vector(R))->_$`cDirectProductCategory(dim,R)``386862 -odirectSum`2`x`(_$,_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`387006 -odirectSum`3`n`(L,L,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``387202 -odirection`1`n`(String)->Integer`pToolsForSign(R)``387437 -odirectory`1`x`(_$)->String`cFileNameCategory``387478 +odimension`0`x`()->CardinalNumber`cVectorSpace(S)``459842 +odimension`0`x`()->NonNegativeInteger`dFreeNilpotentLie(n,class,R)``459916 +odimension`1`x`(_$)->Integer`dPolynomialIdeals(F,Expon,VarSet,DPoly)``459974 +odimension`1`x`(_$)->PositiveInteger`cPointCategory(R)``460125 +odimension`2`x`(_$,List(VarSet))->Integer`dPolynomialIdeals(F,Expon,VarSet,DPoly)``460206 +odimensionOfIrreducibleRepresentation`1`x`(List(Integer))->NonNegativeInteger`pIrrRepSymNatPackage``460312 +odimensions`5`n`(_$,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger)->Void`dTwoDimensionalViewport``460545 +odimensions`5`x`(_$,NonNegativeInteger,NonNegativeInteger,PositiveInteger,PositiveInteger)->Void`dThreeDimensionalViewport``461001 +odimensionsOf`1`x`(_$)->List(Polynomial(Integer))`dFortranType``461461 +odimensionsOf`2`x`(Symbol,Matrix(DoubleFloat))->SExpression`pNAGLinkSupportPackage``461526 +odimensionsOf`2`x`(Symbol,Matrix(Integer))->SExpression`pNAGLinkSupportPackage``461576 +odiophantineSystem`2`x`(M,Col)->Record(particular:Union(Col,"failed"),basis:List(Col))`pSmithNormalForm(R,Row,Col,M)``461626 +odioSolve`1`x`(Equation(Polynomial(Integer)))->Record(varOrder:List(Symbol),inhom:Union(List(Vector(NonNegativeInteger)),"failed"),hom:List(Vector(NonNegativeInteger)))`pDiophantineSolutionPackage``461755 +odirection`1`n`(String)->Integer`pToolsForSign(R)``461932 +odirectory`1`x`(_$)->String`cFileNameCategory``461973 +odirectProduct`1`x`(Vector(R))->_$`cDirectProductCategory(dim,R)``462045 +odirectSum`2`x`(_$,_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`462189 +odirectSum`3`n`(L,L,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``462385 odiscreteLog`1`n`(S)->NonNegativeInteger`xFiniteFieldCategory&(S)``0 -odiscreteLog`1`x`(_$)->NonNegativeInteger`cFiniteFieldCategory``387550 +odiscreteLog`1`x`(_$)->NonNegativeInteger`cFiniteFieldCategory``462620 odiscreteLog`2`n`(S,S)->Union(NonNegativeInteger,"failed")`xFiniteFieldCategory&(S)``0 -odiscreteLog`2`x`(_$,_$)->Union(NonNegativeInteger,"failed")`cFieldOfPrimeCharacteristic``387679 -odiscriminantEuclidean`1`n`(polR)->Record(coef1:polR,coef2:polR,discriminant:R)`pPseudoRemainderSequence(R,polR)``387779 -odiscriminant`0`n`()->Integer`pNumberFieldIntegralBasis(UP,F)``387945 +odiscreteLog`2`x`(_$,_$)->Union(NonNegativeInteger,"failed")`cFieldOfPrimeCharacteristic``462749 +odiscriminant`0`n`()->Integer`pNumberFieldIntegralBasis(UP,F)``462849 odiscriminant`0`n`()->R`xComplexCategory&(S,R)``0 -odiscriminant`0`n`()->R`xFramedAlgebra&(S,R,UP)``388089 -odiscriminant`0`x`()->R`cFramedAlgebra(R,UP)``388148 +odiscriminant`0`n`()->R`xFramedAlgebra&(S,R,UP)``462993 +odiscriminant`0`x`()->R`cFramedAlgebra(R,UP)``463052 +odiscriminant`1`n`(polR)->R`pPseudoRemainderSequence(R,polR)``463111 odiscriminant`1`n`(Vector(S))->R`xComplexCategory&(S,R)``0 odiscriminant`1`n`(Vector(S))->R`xFiniteRankAlgebra&(S,R,UP)``0 odiscriminant`1`n`(Vector(S))->R`xFramedAlgebra&(S,R,UP)``0 -odiscriminant`1`n`(polR)->R`pPseudoRemainderSequence(R,polR)``388207 -odiscriminant`1`x`(Vector(_$))->R`cFiniteRankAlgebra(R,UP)``388324 -odiscriminant`1`x`(_$)->R`cUnivariatePolynomialCategory(R)`has(R,CommutativeRing)`388424 +odiscriminant`1`x`(_$)->R`cUnivariatePolynomialCategory(R)`has(R,CommutativeRing)`463228 +odiscriminant`1`x`(Vector(_$))->R`cFiniteRankAlgebra(R,UP)``463311 odiscriminant`2`n`(S,VarSet)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -odiscriminant`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,CommutativeRing)`388507 -odisplay`1`x`(_$)->Union((List(OutputForm))->OutputForm,"failed")`dBasicOperator``388631 -odisplay`1`x`(_$)->Void`dDatabase(S)``388753 -odisplay`1`x`(_$)->Void`dIndexCard``388838 -odisplay`1`x`(_$)->Void`dScriptFormulaFormat``388932 -odisplay`1`x`(_$)->Void`dTexFormat``389112 -odisplay`2`x`(_$,(List(OutputForm))->OutputForm)->_$`dBasicOperator``389296 -odisplay`2`x`(_$,(OutputForm)->OutputForm)->_$`dBasicOperator``389523 -odisplay`2`x`(_$,Integer)->Void`dScriptFormulaFormat``389760 -odisplay`2`x`(_$,Integer)->Void`dTexFormat``389904 -odistFact`6`n`(Z,List(SparseUnivariatePolynomial(Z)),Record(contp:Z,factors:List(Record(irr:P,pow:Integer))),List(Z),List(OV),List(Z))->Union(Record(polfac:List(P),correct:Z,corrfact:List(SparseUnivariatePolynomial(Z))),"failed")`pLeadingCoefDetermination(OV,E,Z,P)``390052 +odiscriminant`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,CommutativeRing)`463411 +odiscriminantEuclidean`1`n`(polR)->Record(coef1:polR,coef2:polR,discriminant:R)`pPseudoRemainderSequence(R,polR)``463535 +odisplay`1`x`(String)->Void`dMathMLFormat``463701 +odisplay`1`x`(_$)->Union((List(OutputForm))->OutputForm,"failed")`dBasicOperator``463772 +odisplay`1`x`(_$)->Void`dDatabase(S)``463894 +odisplay`1`x`(_$)->Void`dIndexCard``463979 +odisplay`1`x`(_$)->Void`dScriptFormulaFormat``464069 +odisplay`1`x`(_$)->Void`dTexFormat``464249 +odisplay`2`x`(_$,Integer)->Void`dScriptFormulaFormat``464433 +odisplay`2`x`(_$,Integer)->Void`dTexFormat``464577 +odisplay`2`x`(_$,(List(OutputForm))->OutputForm)->_$`dBasicOperator``464725 +odisplay`2`x`(_$,(OutputForm)->OutputForm)->_$`dBasicOperator``464952 +odisplayAsGF`1`x`(Boolean)->_$`dGuessOption``465189 +odisplayAsGF`1`x`(List(GuessOption))->Boolean`dGuessOptionFunctions0``465377 odistance`2`n`(A,A)->Integer`xLazyStreamAggregate&(A,S)``0 -odistance`2`x`(_$,_$)->Integer`cRecursiveAggregate(S)``390585 -odistdfact`2`x`(FP,Boolean)->Record(cont:F,factors:List(Record(irr:FP,pow:Integer)))`pDistinctDegreeFactorize(F,FP)``390684 +odistance`2`x`(_$,_$)->Integer`cRecursiveAggregate(S)``465598 +odistdfact`2`x`(FP,Boolean)->Record(cont:F,factors:List(Record(irr:FP,pow:Integer)))`pDistinctDegreeFactorize(F,FP)``465697 +odistFact`6`n`(Z,List(SparseUnivariatePolynomial(Z)),Record(contp:Z,factors:List(Record(irr:P,pow:Integer))),List(Z),List(OV),List(Z))->Union(Record(polfac:List(P),correct:Z,corrfact:List(SparseUnivariatePolynomial(Z))),"failed")`pLeadingCoefDetermination(OV,E,Z,P)``465921 +odistinguishedCommonRootsOf`2`x`(List(SparseUnivariatePolynomial(K)),K)->Record(zeros:List(K),extDegree:Integer)`pRootsFindingPackage(K)``466454 +odistinguishedRootsOf`2`x`(SparseUnivariatePolynomial(K),K)->Record(zeros:List(K),extDegree:Integer)`pRootsFindingPackage(K)``466759 +odistinguishedRootsOf`2`x`(SparseUnivariatePolynomial(_$),_$)->List(_$)`cPseudoAlgebraicClosureOfPerfectFieldCategory``467183 odistribute`1`n`(S)->S`xExpressionSpace&(S)``0 -odistribute`1`x`(_$)->_$`cExpressionSpace``390908 +odistribute`1`x`(_$)->_$`cExpressionSpace``467362 odistribute`2`n`(S,S)->S`xExpressionSpace&(S)``0 -odistribute`2`x`(_$,_$)->_$`cExpressionSpace``391091 -odiv`2`n`(_$,_$)->Union(Record(lm:_$,rm:_$),"failed")`dOrderedFreeMonoid(S)``391326 -odiv`2`n`(_$,_$)->_$`dOutputForm``391545 -odivergence`2`x`(FLAF,FLAS)->F`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``391602 -odivideExponents`2`x`(_$,NonNegativeInteger)->Union(_$,"failed")`cUnivariatePolynomialCategory(R)``391765 -odivideIfCan!`4`n`(Matrix(R),Matrix(R),R,Integer)->R`pIntegralBasisTools(R,UP,F)``391999 -odivideIfCan`2`n`(UP,UP)->Union(Record(quotient:UP,remainder:UP),"failed")`pUnivariatePolynomialDivisionPackage(R,UP)``392338 +odistribute`2`x`(_$,_$)->_$`cExpressionSpace``467545 +odiv`2`n`(_$,_$)->_$`dOutputForm``467780 +odivergence`2`x`(FLAF,FLAS)->F`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``467837 +odivide`2`n`(polR,polR)->Record(quotient:polR,remainder:polR)`pPseudoRemainderSequence(R,polR)``468000 odivide`2`n`(S,S)->Record(quotient:S,remainder:S)`xComplexCategory&(S,R)``0 odivide`2`n`(S,S)->Record(quotient:S,remainder:S)`xField&(S)``0 odivide`2`n`(S,S)->Record(quotient:S,remainder:S)`xUnivariatePolynomialCategory&(S,R)``0 -odivide`2`n`(_$,_$)->Union(Record(lm:_$,rm:_$),"failed")`dFreeMonoid(S)``392479 -odivide`2`n`(polR,polR)->Record(quotient:polR,remainder:polR)`pPseudoRemainderSequence(R,polR)``392704 -odivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cEuclideanDomain``392847 -odivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`dNonNegativeInteger``393081 -odivisorCascade`2`n`(UP,UP)->List(Record(factors:List(UP),error:R))`pComplexRootFindingPackage(R,UP)``393166 -odivisorCascade`3`n`(UP,UP,Boolean)->List(Record(factors:List(UP),error:R))`pComplexRootFindingPackage(R,UP)``393536 -odivisor`1`x`(FractionalIdeal(UP,Fraction(UP),UPUP,R))->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``393986 -odivisor`1`x`(R)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``394060 -odivisor`2`x`(F,F)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``394131 -odivisor`3`x`(F,F,Integer)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``394246 -odivisor`5`x`(R,UP,UP,UP,F)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``394424 -odivisors`1`x`(Integer)->List(Integer)`pIntegerNumberTheoryFunctions``394745 -odmp2rfi`1`n`(GR)->Fraction(Polynomial(R))`pParametricLinearEquations(R,Var,Expon,GR)``394815 -odmp2rfi`1`n`(List(GR))->List(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``394875 -odmp2rfi`1`n`(Matrix(GR))->Matrix(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``394935 -odmpToHdmp`1`n`(DistributedMultivariatePolynomial(lv,R))->HomogeneousDistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``394995 -odmpToP`1`n`(DistributedMultivariatePolynomial(lv,R))->Polynomial(R)`pPolToPol(lv,R)``395084 -odn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``395170 -odom`1`x`(_$)->SExpression`dAny``395268 -odomainOf`1`x`(_$)->OutputForm`dAny``395394 -odominantTerm`1`n`(_$)->Union(Record(%term:Record(%coef:UnivariatePuiseuxSeries(FE,var,cen),%expon:ExponentialOfUnivariatePuiseuxSeries(FE,var,cen),%expTerms:List(Record(k:Fraction(Integer),c:FE))),%type:String),"failed")`dUnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)``395518 -odot`1`n`(_$)->_$`dOutputForm``395927 -odot`2`n`(Point(DoubleFloat),Point(DoubleFloat))->DoubleFloat`pTubePlotTools``395990 +odivide`2`n`(_$,_$)->Union(Record(lm:_$,rm:_$),"failed")`dFreeMonoid(S)``468143 +odivide`2`n`(_$,_$)->Union(Record(lm:Union(_$,"failed"),rm:Union(_$,"failed")),"failed")`dOrderedFreeMonoid(S)``468368 +odivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cEuclideanDomain``468758 +odivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`dNonNegativeInteger``468992 +odivideExponents`2`x`(_$,NonNegativeInteger)->Union(_$,"failed")`cUnivariatePolynomialCategory(R)``469077 +odivideIfCan`2`n`(UP,UP)->Union(Record(quotient:UP,remainder:UP),"failed")`pUnivariatePolynomialDivisionPackage(R,UP)``469311 +odivideIfCan!`4`n`(Matrix(R),Matrix(R),R,Integer)->R`pIntegralBasisTools(R,UP,F)``469452 +odivisor`1`x`(FractionalIdeal(UP,Fraction(UP),UPUP,R))->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``469791 +odivisor`1`x`(R)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``469865 +odivisor`2`x`(F,F)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``469936 +odivisor`3`x`(F,F,Integer)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``470051 +odivisor`5`x`(R,UP,UP,UP,F)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``470229 +odivisorAtDesingTree`2`x`(PolyRing,DesTree)->DIVISOR`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``470550 +odivisorCascade`2`n`(UP,UP)->List(Record(factors:List(UP),error:R))`pComplexRootFindingPackage(R,UP)``470690 +odivisorCascade`3`n`(UP,UP,Boolean)->List(Record(factors:List(UP),error:R))`pComplexRootFindingPackage(R,UP)``471061 +odivisors`1`x`(Integer)->List(Integer)`pIntegerNumberTheoryFunctions``471507 +odivOfPole`1`x`(_$)->_$`cDivisorCategory(S)``471577 +odivOfZero`1`x`(_$)->_$`cDivisorCategory(S)``471643 +odmp2rfi`1`n`(GR)->Fraction(Polynomial(R))`pParametricLinearEquations(R,Var,Expon,GR)``471709 +odmp2rfi`1`n`(List(GR))->List(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``471769 +odmp2rfi`1`n`(Matrix(GR))->Matrix(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``471829 +odmpToHdmp`1`n`(DistributedMultivariatePolynomial(lv,R))->HomogeneousDistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``471889 +odmpToP`1`n`(DistributedMultivariatePolynomial(lv,R))->Polynomial(R)`pPolToPol(lv,R)``471978 +odn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``472064 +odom`1`x`(_$)->SExpression`dAny``472162 +odomainOf`1`x`(_$)->OutputForm`dAny``472288 +odominantTerm`1`n`(_$)->Union(Record(%term:Record(%coef:UnivariatePuiseuxSeries(FE,var,cen),%expon:ExponentialOfUnivariatePuiseuxSeries(FE,var,cen),%expTerms:List(Record(k:Fraction(Integer),c:FE))),%type:String),"failed")`dUnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)``472412 +odot`1`n`(_$)->_$`dOutputForm``472821 +odot`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``472884 +odot`2`n`(Point(DoubleFloat),Point(DoubleFloat))->DoubleFloat`pTubePlotTools``472964 odot`2`n`(S,S)->R`xVectorCategory&(S,R)``0 -odot`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``396172 -odot`2`x`(_$,_$)->R`cDirectProductCategory(dim,R)`has(R,Ring)`396252 -odot`2`x`(_$,_$)->R`cVectorCategory(R)`has(R,Ring)`396342 -odouble?`1`x`(_$)->Boolean`dFortranScalarType``396496 -odoubleComplex?`1`x`(_$)->Boolean`dFortranScalarType``396595 -odoubleDisc`1`n`(UPUP)->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``396715 -odoubleRank`1`x`(A)->NonNegativeInteger`pAlgebraPackage(R,A)``396757 -odoubleResultant`2`n`(R,(UP)->UP)->UP`pDoubleResultantPackage(F,UP,UPUP,R)``396921 -odouble`2`n`(PositiveInteger,S)->S`pRepeatedDoubling(S)``397111 -odoublyTransitive?`1`x`(UP)->Boolean`pAlgFactor(UP)``397197 -odrawComplexVectorField`3`x`((Complex(DoubleFloat))->Complex(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->ThreeDimensionalViewport`pDrawComplex``397420 -odrawComplex`4`x`((Complex(DoubleFloat))->Complex(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Boolean)->ThreeDimensionalViewport`pDrawComplex``398166 -odrawCurves`2`n`(List(List(Point(DoubleFloat))),List(DrawOption))->TwoDimensionalViewport`pViewportPackage``399041 -odrawCurves`5`n`(List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption))->TwoDimensionalViewport`pViewportPackage``399274 -odrawStyle`2`x`(_$,String)->Void`dThreeDimensionalViewport``399699 -odrawToScale`0`x`()->Boolean`pGraphicsDefaults``400096 -odrawToScale`1`x`(Boolean)->Boolean`pGraphicsDefaults``400182 -odraw`1`x`(List(Point(DoubleFloat)))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``400379 -odraw`2`x`((DoubleFloat)->DoubleFloat,Segment(Float))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``400465 -odraw`2`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``400593 -odraw`2`x`(Ex,SegmentBinding(Float))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``400739 -odraw`2`x`(List(DoubleFloat),List(DoubleFloat))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``400912 -odraw`2`x`(List(Point(DoubleFloat)),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``401053 -odraw`2`x`(ParametricPlaneCurve((DoubleFloat)->DoubleFloat),Segment(Float))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``401231 -odraw`2`x`(ParametricPlaneCurve(Ex),SegmentBinding(Float))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``401403 -odraw`2`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``401632 -odraw`2`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``401824 -odraw`3`x`((DoubleFloat)->DoubleFloat,Segment(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``402073 -odraw`3`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``402293 -odraw`3`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``402527 -odraw`3`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``402730 -odraw`3`x`(Ex,SegmentBinding(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``403039 -odraw`3`x`(Ex,SegmentBinding(Float),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``403306 -odraw`3`x`(List(DoubleFloat),List(DoubleFloat),List(DoubleFloat))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForPoints``403566 -odraw`3`x`(List(DoubleFloat),List(DoubleFloat),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``403762 -odraw`3`x`(ParametricPlaneCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``403995 -odraw`3`x`(ParametricPlaneCurve(Ex),SegmentBinding(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``404259 -odraw`3`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``404582 -odraw`3`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``404862 -odraw`3`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``405209 -odraw`3`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``405498 -odraw`4`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``405850 -odraw`4`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``406149 -odraw`4`x`(Equation(Ex),Symbol,Symbol,List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForAlgebraicCurves(R,Ex)``406459 -odraw`4`x`(Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``406657 -odraw`4`x`(List(DoubleFloat),List(DoubleFloat),List(DoubleFloat),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForPoints``407011 -odraw`4`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``407261 -odraw`4`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``407648 -odroot`1`n`(List(F))->OutputForm`pAlgebraicFunction(R,F)``408108 -oduplicates?`1`n`(_$)->Boolean`dListMultiDictionary(S)``408166 -oduplicates`1`x`(_$)->List(Record(entry:S,count:NonNegativeInteger))`cMultiDictionary(S)``408247 -oe01baf`6`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagInterpolationPackage``408334 -oe01bef`4`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``408482 -oe01bff`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``408663 -oe01bgf`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``408829 -oe01bhf`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``409020 -oe01daf`6`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``409224 -oe01saf`5`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``409459 -oe01sbf`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``409669 -oe01sef`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``409873 -oe01sff`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``410101 -oe02adf`7`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``410305 -oe02aef`4`x`(Integer,Matrix(DoubleFloat),DoubleFloat,Integer)->Result`pNagFittingPackage``410505 -oe02agf`16`x`(Integer,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(Integer),Integer,Integer,Integer)->Result`pNagFittingPackage``410663 -oe02ahf`9`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Integer,Integer,Integer)->Result`pNagFittingPackage``411071 -oe02ajf`10`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,Integer)->Result`pNagFittingPackage``411329 -oe02akf`8`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer)->Result`pNagFittingPackage``411604 -oe02baf`7`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``411862 -oe02bbf`5`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer)->Result`pNagFittingPackage``412131 -oe02bcf`6`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer)->Result`pNagFittingPackage``412269 -oe02bdf`4`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``412471 -oe02bef`13`x`(String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(Integer))->Result`pNagFittingPackage``412636 -oe02daf`15`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``413012 -oe02dcf`18`x`(String,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Integer)->Result`pNagFittingPackage``413294 -oe02ddf`17`x`(String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``413772 -oe02def`9`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``414157 -oe02dff`12`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagFittingPackage``414323 -oe02gaf`7`x`(Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``414571 -oe02zaf`10`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagFittingPackage``414777 -oe04dgf`15`x`(Integer,DoubleFloat,DoubleFloat,Integer,DoubleFloat,Boolean,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp49(OBJFUN)))->Result`pNagOptimisationPackage``414955 -oe04fdf`7`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp50(LSFUN1)))->Result`pNagOptimisationPackage``415353 -oe04gcf`7`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp19(LSFUN2)))->Result`pNagOptimisationPackage``415634 -oe04jaf`9`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp24(FUNCT1)))->Result`pNagOptimisationPackage``415911 -oe04mbf`15`x`(Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Boolean,Integer,Integer,Matrix(DoubleFloat),Integer)->Result`pNagOptimisationPackage``416399 -oe04naf`24`x`(Integer,Integer,Integer,Integer,Integer,Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Boolean,Boolean,Boolean,Integer,Integer,Matrix(DoubleFloat),Matrix(Integer),Integer,Union(fn:FileName,fp:Asp20(QPHESS)))->Result`pNagOptimisationPackage``416745 -oe04ucf`43`x`(Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Boolean,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Boolean,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Boolean,Integer,Integer,Integer,Integer,Integer,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(Integer),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp55--(CONFUN)),Union(fn:FileName,fp:Asp49(OBJFUN)))->Result`pNagOptimisationPackage``417130 -oe04ycf`8`x`(Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagOptimisationPackage``418017 -oe`1`x`(PositiveInteger)->_$`dCliffordAlgebra(n,K,Q)``418355 -oedf2df`1`x`(Expression(DoubleFloat))->DoubleFloat`pExpertSystemToolsPackage``418413 -oedf2ef`1`x`(Expression(DoubleFloat))->Expression(Float)`pExpertSystemToolsPackage``418563 -oedf2efi`1`x`(Expression(DoubleFloat))->Expression(Fraction(Integer))`pExpertSystemToolsPackage``418659 -oedf2fi`1`x`(Expression(DoubleFloat))->Fraction(Integer)`pExpertSystemToolsPackage``418772 -oef2edf`1`x`(Expression(Float))->Expression(DoubleFloat)`pExpertSystemToolsPackage``418932 -oeigenMatrix`1`x`(Matrix(Fraction(Polynomial(Integer))))->Union(Matrix(Expression(Integer)),"failed")`pRadicalEigenPackage``419054 -oeigenvalues`1`x`(Matrix(Fraction(Polynomial(R))))->List(Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))))`pEigenPackage(R)``419199 -oeigenvector`2`x`(Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),Matrix(Fraction(Polynomial(R))))->List(Matrix(Fraction(Polynomial(R))))`pEigenPackage(R)``419346 -oeigenvectors`1`x`(Matrix(Fraction(Polynomial(R))))->List(Record(eigval:Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),eigmult:NonNegativeInteger,eigvec:List(Matrix(Fraction(Polynomial(R))))))`pEigenPackage(R)``419476 -oeisensteinIrreducible?`1`n`(UP)->Boolean`pGaloisGroupFactorizer(UP)``419837 -oelColumn2!`4`x`(M,R,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``420006 -oelRow1!`3`x`(M,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``420161 -oelRow2!`4`x`(M,R,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``420283 -oelem?`1`n`(_$)->Boolean`dIntegrationResult(F)``420429 -oelement?`2`x`(DPoly,_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``420513 -oelementary`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``420612 -oelements`1`n`(_$)->List(PositiveInteger)`dSetOfMIntegersInOneToN(m,n)``420736 -oelliptic?`1`x`(Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat))->Boolean`pd03AgentsPackage``420828 -oellipticCylindrical`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``420871 -oelliptic`0`n`()->Union(UP,"failed")`xFunctionFieldCategory&(S,F,UP,UPUP)``421146 -oelliptic`0`x`()->Union(UP,"failed")`cFunctionFieldCategory(F,UP,UPUP)``421273 -oelliptic`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``421400 -oelt`1`n`(_$)->S`dReference(S)``421625 -oelt`1`x`(_$)->R`dCartesianTensor(minix,dim,R)``421675 +odot`2`x`(_$,_$)->R`cDirectProductCategory(dim,R)`has(R,Ring)`473146 +odot`2`x`(_$,_$)->R`cVectorCategory(R)`has(R,Ring)`473236 +odouble?`1`x`(_$)->Boolean`dFortranScalarType``473390 +odouble`2`n`(PositiveInteger,S)->S`pRepeatedDoubling(S)``473489 +odoubleComplex?`1`x`(_$)->Boolean`dFortranScalarType``473575 +odoubleDisc`1`n`(UPUP)->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``473695 +odoubleFloatFormat`1`x`(String)->String`dDoubleFloat``473737 +odoubleRank`1`x`(A)->NonNegativeInteger`pAlgebraPackage(R,A)``473812 +odoubleResultant`2`n`(R,(UP)->UP)->UP`pDoubleResultantPackage(F,UP,UPUP,R)``473976 +odoublyTransitive?`1`x`(UP)->Boolean`pAlgFactor(UP)``474166 +odraw`1`x`(List(Point(DoubleFloat)))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``474389 +odraw`2`x`((DoubleFloat)->DoubleFloat,Segment(Float))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``474475 +odraw`2`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``474603 +odraw`2`x`(Ex,SegmentBinding(Float))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``474749 +odraw`2`x`(List(DoubleFloat),List(DoubleFloat))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``474922 +odraw`2`x`(List(Point(DoubleFloat)),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``475063 +odraw`2`x`(ParametricPlaneCurve((DoubleFloat)->DoubleFloat),Segment(Float))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``475241 +odraw`2`x`(ParametricPlaneCurve(Ex),SegmentBinding(Float))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``475413 +odraw`2`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``475642 +odraw`2`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``475834 +odraw`3`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``476083 +odraw`3`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``476286 +odraw`3`x`((DoubleFloat)->DoubleFloat,Segment(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``476595 +odraw`3`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``476815 +odraw`3`x`(Ex,SegmentBinding(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``477049 +odraw`3`x`(Ex,SegmentBinding(Float),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``477316 +odraw`3`x`(List(DoubleFloat),List(DoubleFloat),List(DoubleFloat))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForPoints``477576 +odraw`3`x`(List(DoubleFloat),List(DoubleFloat),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForPoints``477772 +odraw`3`x`(ParametricPlaneCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``478005 +odraw`3`x`(ParametricPlaneCurve(Ex),SegmentBinding(Float),List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctions(Ex)``478269 +odraw`3`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``478592 +odraw`3`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``478872 +odraw`3`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``479219 +odraw`3`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``479508 +odraw`4`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``479860 +odraw`4`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``480159 +odraw`4`x`(Equation(Ex),Symbol,Symbol,List(DrawOption))->TwoDimensionalViewport`pTopLevelDrawFunctionsForAlgebraicCurves(R,Ex)``480469 +odraw`4`x`(Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``480667 +odraw`4`x`(List(DoubleFloat),List(DoubleFloat),List(DoubleFloat),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForPoints``481021 +odraw`4`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctionsForCompiledFunctions``481271 +odraw`4`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeDimensionalViewport`pTopLevelDrawFunctions(Ex)``481658 +odrawComplex`4`x`((Complex(DoubleFloat))->Complex(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Boolean)->ThreeDimensionalViewport`pDrawComplex``482118 +odrawComplexVectorField`3`x`((Complex(DoubleFloat))->Complex(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->ThreeDimensionalViewport`pDrawComplex``482975 +odrawCurves`2`n`(List(List(Point(DoubleFloat))),List(DrawOption))->TwoDimensionalViewport`pViewportPackage``483713 +odrawCurves`5`n`(List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption))->TwoDimensionalViewport`pViewportPackage``483946 +odrawStyle`2`x`(_$,String)->Void`dThreeDimensionalViewport``484371 +odrawToScale`0`x`()->Boolean`pGraphicsDefaults``484768 +odrawToScale`1`x`(Boolean)->Boolean`pGraphicsDefaults``484854 +odroot`1`n`(List(F))->OutputForm`pAlgebraicFunction(R,F)``485051 +oduplicates?`1`n`(_$)->Boolean`dListMultiDictionary(S)``485109 +oduplicates`1`x`(_$)->List(Record(entry:S,count:NonNegativeInteger))`cMultiDictionary(S)``485190 +oe01baf`6`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagInterpolationPackage``485277 +oe01bef`4`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``485425 +oe01bff`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``485606 +oe01bgf`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``485772 +oe01bhf`7`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``485963 +oe01daf`6`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``486167 +oe01saf`5`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagInterpolationPackage``486402 +oe01sbf`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``486612 +oe01sef`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``486816 +oe01sff`9`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer)->Result`pNagInterpolationPackage``487044 +oe02adf`7`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``487248 +oe02aef`4`x`(Integer,Matrix(DoubleFloat),DoubleFloat,Integer)->Result`pNagFittingPackage``487448 +oe02agf`16`x`(Integer,Integer,Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(Integer),Integer,Integer,Integer)->Result`pNagFittingPackage``487606 +oe02ahf`9`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,Integer,Integer,Integer)->Result`pNagFittingPackage``488014 +oe02ajf`10`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer,Integer)->Result`pNagFittingPackage``488272 +oe02akf`8`x`(Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer)->Result`pNagFittingPackage``488547 +oe02baf`7`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``488805 +oe02bbf`5`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer)->Result`pNagFittingPackage``489074 +oe02bcf`6`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer)->Result`pNagFittingPackage``489212 +oe02bdf`4`x`(Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``489414 +oe02bef`13`x`(String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(Integer))->Result`pNagFittingPackage``489579 +oe02daf`15`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``489955 +oe02dcf`18`x`(String,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(Integer),Integer)->Result`pNagFittingPackage``490237 +oe02ddf`17`x`(String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``490719 +oe02def`9`x`(Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``491108 +oe02dff`12`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagFittingPackage``491274 +oe02gaf`7`x`(Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer)->Result`pNagFittingPackage``491522 +oe02zaf`10`x`(Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer)->Result`pNagFittingPackage``491711 +oe04dgf`15`x`(Integer,DoubleFloat,DoubleFloat,Integer,DoubleFloat,Boolean,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp49(OBJFUN)))->Result`pNagOptimisationPackage``491889 +oe04fdf`7`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp50(LSFUN1)))->Result`pNagOptimisationPackage``492287 +oe04gcf`7`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp19(LSFUN2)))->Result`pNagOptimisationPackage``492568 +oe04jaf`9`x`(Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp24(FUNCT1)))->Result`pNagOptimisationPackage``492845 +oe04mbf`15`x`(Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Boolean,Integer,Integer,Matrix(DoubleFloat),Integer)->Result`pNagOptimisationPackage``493333 +oe04naf`24`x`(Integer,Integer,Integer,Integer,Integer,Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Boolean,Boolean,Boolean,Integer,Integer,Matrix(DoubleFloat),Matrix(Integer),Integer,Union(fn:FileName,fp:Asp20(QPHESS)))->Result`pNagOptimisationPackage``493708 +oe04ucf`43`x`(Integer,Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Boolean,DoubleFloat,Integer,DoubleFloat,DoubleFloat,Boolean,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Boolean,Integer,Integer,Integer,Integer,Integer,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix(Integer),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn:FileName,fp:Asp55--(CONFUN)),Union(fn:FileName,fp:Asp49(OBJFUN)))->Result`pNagOptimisationPackage``494115 +oe04ycf`8`x`(Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer)->Result`pNagOptimisationPackage``495078 +oE1`1`x`(DoubleFloat)->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``495416 +oe`1`x`(PositiveInteger)->_$`dCliffordAlgebra(n,K,Q)``495601 +oedf2df`1`x`(Expression(DoubleFloat))->DoubleFloat`pExpertSystemToolsPackage``495659 +oedf2ef`1`x`(Expression(DoubleFloat))->Expression(Float)`pExpertSystemToolsPackage``495809 +oedf2efi`1`x`(Expression(DoubleFloat))->Expression(Fraction(Integer))`pExpertSystemToolsPackage``495905 +oedf2fi`1`x`(Expression(DoubleFloat))->Fraction(Integer)`pExpertSystemToolsPackage``496018 +oef2edf`1`x`(Expression(Float))->Expression(DoubleFloat)`pExpertSystemToolsPackage``496178 +oeffective?`1`x`(_$)->Boolean`cDivisorCategory(S)``496300 +oEi1`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``496373 +oEi`1`n`(F)->F`pLiouvillianFunction(R,F)``496528 +oEi`1`x`(_$)->_$`cLiouvillianFunctionCategory``496588 +oEi`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``496717 +oEi2`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``496931 +oEi3`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``497086 +oEi4`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``497257 +oEi5`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``497396 +oEi6`1`x`(OnePointCompletion(DoubleFloat))->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``497536 +oeigenMatrix`1`x`(Matrix(Fraction(Polynomial(Integer))))->Union(Matrix(Expression(Integer)),"failed")`pRadicalEigenPackage``497682 +oeigenvalues`1`x`(Matrix(Fraction(Polynomial(R))))->List(Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))))`pEigenPackage(R)``497827 +oeigenvector`2`x`(Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),Matrix(Fraction(Polynomial(R))))->List(Matrix(Fraction(Polynomial(R))))`pEigenPackage(R)``497974 +oeigenvectors`1`x`(Matrix(Fraction(Polynomial(R))))->List(Record(eigval:Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),eigmult:NonNegativeInteger,eigvec:List(Matrix(Fraction(Polynomial(R))))))`pEigenPackage(R)``498104 +oeisensteinIrreducible?`1`n`(UP)->Boolean`pGaloisGroupFactorizer(UP)``498465 +oelColumn2!`4`x`(M,R,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``498634 +oelem?`1`n`(_$)->Boolean`dIntegrationResult(F)``498789 +oelement?`2`x`(DPoly,_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``498873 +oelementary`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``498972 +oelements`1`n`(_$)->List(PositiveInteger)`dSetOfMIntegersInOneToN(m,n)``499096 +oelliptic`0`n`()->Union(UP,"failed")`xFunctionFieldCategory&(S,F,UP,UPUP)``499188 +oelliptic`0`x`()->Union(UP,"failed")`cFunctionFieldCategory(F,UP,UPUP)``499315 +oelliptic?`1`x`(Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat))->Boolean`pd03AgentsPackage``499442 +oelliptic`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``499485 +oellipticCylindrical`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``499710 +oelRow1!`3`x`(M,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``499985 +oelRow2!`4`x`(M,R,Integer,Integer)->M`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``500107 +oelt`1`n`(_$)->S`dReference(S)``500253 +oelt`1`x`(_$)->R`dCartesianTensor(minix,dim,R)``500303 oelt`2`n`(A,"first")->S`xLazyStreamAggregate&(A,S)``0 oelt`2`n`(A,"first")->S`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"first")->S`xUnaryRecursiveAggregate&(A,S)``0 +oelt`2`n`(A,Integer)->S`xLazyStreamAggregate&(A,S)``0 +oelt`2`n`(A,Integer)->S`xOneDimensionalArrayAggregate&(A,S)``0 +oelt`2`n`(A,Integer)->S`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"last")->S`xLazyStreamAggregate&(A,S)``0 oelt`2`n`(A,"last")->S`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"last")->S`xUnaryRecursiveAggregate&(A,S)``0 @@ -3465,24 +3549,23 @@ oelt`2`n`(A,"rest")->A`xLazyStreamAggregate&(A,S)``0 oelt`2`n`(A,"rest")->A`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"rest")->A`xUnaryRecursiveAggregate&(A,S)``0 oelt`2`n`(A,"right")->A`xBinaryRecursiveAggregate&(A,S)``0 +oelt`2`n`(A,UniversalSegment(Integer))->A`xLazyStreamAggregate&(A,S)``0 +oelt`2`n`(A,UniversalSegment(Integer))->A`xOneDimensionalArrayAggregate&(A,S)``0 +oelt`2`n`(A,UniversalSegment(Integer))->A`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"value")->S`xBinaryRecursiveAggregate&(A,S)``0 oelt`2`n`(A,"value")->S`xLazyStreamAggregate&(A,S)``0 oelt`2`n`(A,"value")->S`xRecursiveAggregate&(A,S)``0 oelt`2`n`(A,"value")->S`xStreamAggregate&(A,S)``0 oelt`2`n`(A,"value")->S`xUnaryRecursiveAggregate&(A,S)``0 -oelt`2`n`(A,Integer)->S`xLazyStreamAggregate&(A,S)``0 -oelt`2`n`(A,Integer)->S`xOneDimensionalArrayAggregate&(A,S)``0 -oelt`2`n`(A,Integer)->S`xStreamAggregate&(A,S)``0 -oelt`2`n`(A,UniversalSegment(Integer))->A`xLazyStreamAggregate&(A,S)``0 -oelt`2`n`(A,UniversalSegment(Integer))->A`xOneDimensionalArrayAggregate&(A,S)``0 -oelt`2`n`(A,UniversalSegment(Integer))->A`xStreamAggregate&(A,S)``0 +oelt`2`n`(BasicOperator,List(_$))->_$`dPattern(R)``500489 oelt`2`n`(BasicOperator,List(S))->S`xExpressionSpace&(S)``0 oelt`2`n`(BasicOperator,List(S))->S`xFunctionSpace&(S,R)``0 -oelt`2`n`(BasicOperator,List(_$))->_$`dPattern(R)``421736 oelt`2`n`(BasicOperator,S)->S`xExpressionSpace&(S)``0 oelt`2`n`(BasicOperator,S)->S`xFunctionSpace&(S,R)``0 oelt`2`n`(Fraction(S),Fraction(S))->Fraction(S)`xUnivariatePolynomialCategory&(S,R)``0 oelt`2`n`(Fraction(S),R)->R`xUnivariatePolynomialCategory&(S,R)``0 +oelt`2`n`(_$,List(_$))->_$`dOutputForm``500564 +oelt`2`n`(_$,R)->R`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``500665 oelt`2`n`(S,Fraction(S))->Fraction(S)`xUnivariatePolynomialCategory&(S,R)``0 oelt`2`n`(S,Index)->Entry`xIndexedAggregate&(S,Index,Entry)``0 oelt`2`n`(S,Integer)->Character`xStringAggregate&(S)``0 @@ -3492,38 +3575,39 @@ oelt`2`n`(S,R)->S`xFullyEvalableOver&(S,R)``0 oelt`2`n`(S,S)->S`xStringAggregate&(S)``0 oelt`2`n`(S,S)->S`xUnivariatePolynomialCategory&(S,R)``0 oelt`2`n`(S,UniversalSegment(Integer))->S`xStringAggregate&(S)``0 -oelt`2`n`(_$,List(_$))->_$`dOutputForm``421811 -oelt`2`n`(_$,R)->R`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``421912 -oelt`2`x`(BasicOperator,List(_$))->_$`cExpressionSpace``421972 -oelt`2`x`(BasicOperator,_$)->_$`cExpressionSpace``422132 -oelt`2`x`(Fraction(_$),Fraction(_$))->Fraction(_$)`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`422231 -oelt`2`x`(Fraction(_$),R)->R`cUnivariatePolynomialCategory(R)`has(R,Field)`422368 -oelt`2`x`(_$,"count")->NonNegativeInteger`dDataList(S)``422518 -oelt`2`x`(_$,"first")->S`cUnaryRecursiveAggregate(S)``422602 -oelt`2`x`(_$,"last")->S`cUnaryRecursiveAggregate(S)``422707 -oelt`2`x`(_$,"left")->_$`cBinaryRecursiveAggregate(S)``422809 -oelt`2`x`(_$,"rest")->_$`cUnaryRecursiveAggregate(S)``422906 -oelt`2`x`(_$,"right")->_$`cBinaryRecursiveAggregate(S)``423015 -oelt`2`x`(_$,"sort")->_$`dDataList(S)``423115 -oelt`2`x`(_$,"unique")->_$`dDataList(S)``423236 -oelt`2`x`(_$,"value")->S`cRecursiveAggregate(S)``423377 -oelt`2`x`(_$,DirectProduct(n,K))->K`dQuadraticForm(n,K)``423476 -oelt`2`x`(_$,Expon)->Coef`cUnivariatePowerSeriesCategory(Coef,Expon)``423587 -oelt`2`x`(_$,Integer)->R`cFramedNonAssociativeAlgebra(R)``423742 -oelt`2`x`(_$,Integer)->R`dCartesianTensor(minix,dim,R)``423864 -oelt`2`x`(_$,Integer)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``423927 -oelt`2`x`(_$,List(Integer))->R`dCartesianTensor(minix,dim,R)``423993 -oelt`2`x`(_$,List(Integer))->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``424077 -oelt`2`x`(_$,List(OutputForm))->_$`dSymbol``424167 -oelt`2`x`(_$,NonNegativeInteger)->Permutation(S)`dPermutationGroup(S)``424298 -oelt`2`x`(_$,QueryEquation)->_$`dDatabase(S)``424381 -oelt`2`x`(_$,S)->Index`cEltable(S,Index)``424481 -oelt`2`x`(_$,S)->S`cPermutationCategory(S)``424643 -oelt`2`x`(_$,Symbol)->Any`dLibrary``424732 -oelt`2`x`(_$,Symbol)->DataList(String)`dDatabase(S)``424864 -oelt`2`x`(_$,Symbol)->String`dIndexCard``424963 -oelt`2`x`(_$,UniversalSegment(Integer))->_$`cLinearAggregate(S)``425163 -oelt`2`x`(_$,_$)->_$`cStringAggregate``425422 +oelt`2`x`(BasicOperator,_$)->_$`cExpressionSpace``500729 +oelt`2`x`(BasicOperator,List(_$))->_$`cExpressionSpace``500828 +oelt`2`x`(_$,"count")->NonNegativeInteger`dDataList(S)``500988 +oelt`2`x`(_$,_$)->_$`cStringAggregate``501072 +oelt`2`x`(_$,DirectProduct(n,K))->K`dQuadraticForm(n,K)``501289 +oelt`2`x`(_$,Expon)->Coef`cUnivariatePowerSeriesCategory(Coef,Expon)``501400 +oelt`2`x`(_$,"first")->S`cUnaryRecursiveAggregate(S)``501555 +oelt`2`x`(Fraction(_$),Fraction(_$))->Fraction(_$)`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`501660 +oelt`2`x`(Fraction(_$),R)->R`cUnivariatePolynomialCategory(R)`has(R,Field)`501797 +oelt`2`x`(_$,Integer)->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``501947 +oelt`2`x`(_$,Integer)->K`cAffineSpaceCategory(K)``502013 +oelt`2`x`(_$,Integer)->K`cPlacesCategory(K,PCS)``502076 +oelt`2`x`(_$,Integer)->K`cProjectiveSpaceCategory(K)``502181 +oelt`2`x`(_$,Integer)->R`cFramedNonAssociativeAlgebra(R)``502244 +oelt`2`x`(_$,Integer)->R`dCartesianTensor(minix,dim,R)``502366 +oelt`2`x`(_$,"last")->S`cUnaryRecursiveAggregate(S)``502593 +oelt`2`x`(_$,"left")->_$`cBinaryRecursiveAggregate(S)``502695 +oelt`2`x`(_$,List(Integer))->_$`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``502792 +oelt`2`x`(_$,List(Integer))->R`dCartesianTensor(minix,dim,R)``502882 +oelt`2`x`(_$,List(OutputForm))->_$`dSymbol``503444 +oelt`2`x`(_$,NonNegativeInteger)->Permutation(S)`dPermutationGroup(S)``503575 +oelt`2`x`(_$,QueryEquation)->_$`dDatabase(S)``503659 +oelt`2`x`(_$,"rest")->_$`cUnaryRecursiveAggregate(S)``503759 +oelt`2`x`(_$,"right")->_$`cBinaryRecursiveAggregate(S)``503868 +oelt`2`x`(_$,S)->Index`cEltable(S,Index)``503968 +oelt`2`x`(_$,"sort")->_$`dDataList(S)``504130 +oelt`2`x`(_$,S)->S`cPermutationCategory(S)``504251 +oelt`2`x`(_$,Symbol)->Any`dLibrary``504334 +oelt`2`x`(_$,Symbol)->DataList(String)`dDatabase(S)``504466 +oelt`2`x`(_$,Symbol)->String`dIndexCard``504565 +oelt`2`x`(_$,"unique")->_$`dDataList(S)``504765 +oelt`2`x`(_$,UniversalSegment(Integer))->_$`cLinearAggregate(S)``504906 +oelt`2`x`(_$,"value")->S`cRecursiveAggregate(S)``505169 oelt`3`n`(A,Integer,S)->S`xLazyStreamAggregate&(A,S)``0 oelt`3`n`(A,Integer,S)->S`xOneDimensionalArrayAggregate&(A,S)``0 oelt`3`n`(A,Integer,S)->S`xStreamAggregate&(A,S)``0 @@ -3536,92 +3620,114 @@ oelt`3`n`(S,Integer,Integer)->R`xMatrixCategory&(S,R,Row,Col)``0 oelt`3`n`(S,Integer,Integer)->R`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 oelt`3`n`(S,Key,Entry)->Entry`xTableAggregate&(S,Key,Entry)``0 oelt`3`n`(S,List(Integer),List(Integer))->S`xMatrixCategory&(S,R,Row,Col)``0 -oelt`3`x`(BasicOperator,_$,_$)->_$`cExpressionSpace``425639 -oelt`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)``425768 -oelt`3`x`(_$,F,F)->F`cFunctionFieldCategory(F,UP,UPUP)``426141 -oelt`3`x`(_$,F,PositiveInteger)->F`dRewriteRule(Base,R,F)``426287 -oelt`3`x`(_$,F,PositiveInteger)->F`dRuleset(Base,R,F)``426412 -oelt`3`x`(_$,Integer,Integer)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``426545 -oelt`3`x`(_$,Integer,Integer)->R`cTwoDimensionalArrayCategory(R,Row,Col)``426711 -oelt`3`x`(_$,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``426883 -oelt`3`x`(_$,List(Integer),List(Integer))->_$`cMatrixCategory(R,Row,Col)``426950 +oelt`3`x`(BasicOperator,_$,_$)->_$`cExpressionSpace``505268 +oelt`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)``505397 +oelt`3`x`(_$,F,F)->F`cFunctionFieldCategory(F,UP,UPUP)``505770 +oelt`3`x`(_$,F,PositiveInteger)->F`dRewriteRule(Base,R,F)``505916 +oelt`3`x`(_$,F,PositiveInteger)->F`dRuleset(Base,R,F)``506041 +oelt`3`x`(_$,Integer,Integer)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``506174 +oelt`3`x`(_$,Integer,Integer)->R`cTwoDimensionalArrayCategory(R,Row,Col)``506340 +oelt`3`x`(_$,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``506664 +oelt`3`x`(_$,List(Integer),List(Integer))->_$`cMatrixCategory(R,Row,Col)``506987 oelt`4`n`(BasicOperator,S,S,S)->S`xExpressionSpace&(S)``0 oelt`4`n`(BasicOperator,S,S,S)->S`xFunctionSpace&(S,R)``0 oelt`4`n`(S,Integer,Integer,R)->R`xMatrixCategory&(S,R,Row,Col)``0 oelt`4`n`(S,Integer,Integer,R)->R`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -oelt`4`x`(BasicOperator,_$,_$,_$)->_$`cExpressionSpace``427316 -oelt`4`x`(_$,Integer,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``427474 -oelt`4`x`(_$,Integer,Integer,R)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``427545 -oelt`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``427761 -oelt`4`x`(_$,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)->R`dThreeDimensionalMatrix(R)``427975 +oelt`4`x`(BasicOperator,_$,_$,_$)->_$`cExpressionSpace``507544 +oelt`4`x`(_$,Integer,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``507702 +oelt`4`x`(_$,Integer,Integer,R)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``508121 +oelt`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``508337 +oelt`4`x`(_$,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)->R`dThreeDimensionalMatrix(R)``508745 oelt`5`n`(BasicOperator,S,S,S,S)->S`xExpressionSpace&(S)``0 oelt`5`n`(BasicOperator,S,S,S,S)->S`xFunctionSpace&(S,R)``0 -oelt`5`x`(BasicOperator,_$,_$,_$,_$)->_$`cExpressionSpace``428052 -oelt`5`x`(_$,Integer,Integer,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``428236 +oelt`5`x`(BasicOperator,_$,_$,_$,_$)->_$`cExpressionSpace``508822 +oelt`5`x`(_$,Integer,Integer,Integer,Integer)->R`dCartesianTensor(minix,dim,R)``509006 +oempty`0`n`()->_$`dOutputForm``509531 +oempty`0`n`()->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``509576 +oempty`0`n`()->_$`dSplittingNode(V,C)``509636 +oempty`0`x`()->_$`cAggregate``509746 +oempty`0`x`()->_$`dArrayStack(S)``509958 +oempty`0`x`()->_$`dDequeue(S)``510014 +oempty`0`x`()->_$`dHeap(S)``510067 +oempty`0`x`()->_$`dQueue(S)``510117 +oempty`0`x`()->_$`dStack(S)``510168 +oempty`0`x`()->_$`dSymbolTable``510219 +oempty`0`x`()->_$`dTheSymbolTable``510277 +oempty?`1`n`(_$)->Boolean`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``510336 +oempty?`1`n`(_$)->Boolean`dSplittingNode(V,C)``510460 oempty?`1`n`(S)->Boolean`xAggregate&(S)``0 -oempty?`1`n`(_$)->Boolean`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``428311 -oempty?`1`n`(_$)->Boolean`dSplittingNode(V,C)``428435 -oempty?`1`x`(_$)->Boolean`cAggregate``428533 -oempty`0`n`()->_$`dOutputForm``428591 -oempty`0`n`()->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``428636 -oempty`0`n`()->_$`dSplittingNode(V,C)``428696 -oempty`0`x`()->_$`cAggregate``428806 -oempty`0`x`()->_$`dSymbolTable``429013 -oempty`0`x`()->_$`dTheSymbolTable``429071 -oendOfFile?`1`x`(_$)->Boolean`dTextFile``429130 -oendSubProgram`0`x`()->Symbol`dTheSymbolTable``429303 -oenqueue!`2`x`(S,_$)->S`cQueueAggregate(S)``429398 -oenterInCache`2`n`(S,(S)->Boolean)->S`pSortedCache(S)``429486 -oenterInCache`2`n`(S,(S,S)->Integer)->S`pSortedCache(S)``429681 -oenterPointData`2`x`(_$,List(Point(R)))->NonNegativeInteger`cThreeSpaceCategory(R)``429937 +oempty?`1`x`(_$)->Boolean`cAggregate``510558 +oempty?`1`x`(_$)->Boolean`dArrayStack(S)``510616 +oempty?`1`x`(_$)->Boolean`dDequeue(S)``510711 +oempty?`1`x`(_$)->Boolean`dHeap(S)``510800 +oempty?`1`x`(_$)->Boolean`dQueue(S)``510883 +oempty?`1`x`(_$)->Boolean`dStack(S)``510968 +oEn`2`x`(Integer,DoubleFloat)->OnePointCompletion(DoubleFloat)`pDoubleFloatSpecialFunctions``511053 +oencode`1`x`(_$)->String`dDesingTree(S)``511125 +oendOfFile?`1`x`(_$)->Boolean`dTextFile``511201 +oendSubProgram`0`x`()->Symbol`dTheSymbolTable``511374 +oenqueue!`2`x`(S,_$)->S`cQueueAggregate(S)``511469 +oenqueue!`2`x`(S,_$)->S`dDequeue(S)``511557 +oenqueue!`2`x`(S,_$)->S`dQueue(S)``511665 +oenterInCache`2`n`(S,(S)->Boolean)->S`pSortedCache(S)``511769 +oenterInCache`2`n`(S,(S,S)->Integer)->S`pSortedCache(S)``511964 +oenterPointData`2`x`(_$,List(Point(R)))->NonNegativeInteger`cThreeSpaceCategory(R)``512220 oentries`1`n`(A)->List(S)`xLazyStreamAggregate&(A,S)``0 oentries`1`n`(S)->List(Entry)`xIndexedAggregate&(S,Index,Entry)``0 oentries`1`n`(S)->List(Entry)`xTableAggregate&(S,Key,Entry)``0 -oentries`1`x`(_$)->List(Entry)`cIndexedAggregate(Index,Entry)``430151 -oentries`1`x`(_$)->List(Record(key:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStrea--m:Union(str:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))))`dIntegrationFunctionsTable``430253 +oentries`1`x`(_$)->List(Entry)`cIndexedAggregate(Index,Entry)``512434 +oentries`1`x`(_$)->List(Record(key:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStrea--m:Union(str:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))))`dIntegrationFunctionsTable``512536 +oentry`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:Stream(DoubleFl--oat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))`dIntegrationFunctionsTable``512579 oentry?`2`n`(Entry,S)->Boolean`xIndexedAggregate&(S,Index,Entry)``0 -oentry?`2`x`(Entry,_$)->Boolean`cIndexedAggregate(Index,Entry)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(Entry,SetCategory))`430294 -oentry`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:Stream(DoubleFl--oat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))`dIntegrationFunctionsTable``430400 -oenumerate`0`n`()->Vector(_$)`dSetOfMIntegersInOneToN(m,n)``430439 -oepilogue`1`x`(_$)->List(String)`dScriptFormulaFormat``430535 -oepilogue`1`x`(_$)->List(String)`dTexFormat``430623 +oentry?`2`x`(Entry,_$)->Boolean`cIndexedAggregate(Index,Entry)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(Entry,SetCategory))`512620 +oenumerate`0`n`()->Vector(_$)`dSetOfMIntegersInOneToN(m,n)``512726 +oepilogue`1`x`(_$)->List(String)`dScriptFormulaFormat``512822 +oepilogue`1`x`(_$)->List(String)`dTexFormat``512910 oeq?`2`n`(S,S)->Boolean`xAggregate&(S)``0 -oeq?`2`x`(_$,_$)->Boolean`cAggregate``430703 -oeq`2`x`(_$,_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``430777 -oequality`2`x`(_$,(_$,_$)->Boolean)->_$`dBasicOperator``430868 -oequation`2`x`(S,S)->_$`dEquation(S)``431172 -oequation`2`x`(Symbol,Segment(S))->_$`dSegmentBinding(S)``431223 -oequation`2`x`(Symbol,String)->_$`dQueryEquation``431397 -oerf`1`n`(F)->F`pLiouvillianFunction(R,F)``431453 -oerf`1`x`(_$)->_$`cLiouvillianFunctionCategory``431501 -oerrorInfo`1`x`(_$)->List(Symbol)`dOpenMathError``431655 -oerrorKind`1`x`(_$)->OpenMathErrorKind`dOpenMathError``431728 -oerror`1`x`(List(String))->Exit`pErrorFunctions``431808 -oerror`1`x`(String)->Exit`pErrorFunctions``431885 -oerror`2`x`(String,List(String))->Exit`pErrorFunctions``431960 -oerror`2`x`(String,String)->Exit`pErrorFunctions``432130 -oescape`0`x`()->_$`dCharacter``432297 -oeuclideanGroebner`1`x`(List(Dpol))->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``432438 -oeuclideanGroebner`2`x`(List(Dpol),String)->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``432595 -oeuclideanGroebner`3`x`(List(Dpol),String,String)->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``432930 -oeuclideanNormalForm`2`x`(Dpol,List(Dpol))->Dpol`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``433237 +oeq?`2`x`(_$,_$)->Boolean`cAggregate``512990 +oeq`2`x`(_$,_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``513064 +oeq?`2`x`(_$,_$)->Boolean`dArrayStack(S)``513155 +oeq?`2`x`(_$,_$)->Boolean`dDequeue(S)``513278 +oeq?`2`x`(_$,_$)->Boolean`dHeap(S)``513395 +oeq?`2`x`(_$,_$)->Boolean`dQueue(S)``513506 +oeq?`2`x`(_$,_$)->Boolean`dStack(S)``513619 +oEQ`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``513732 +oequality`2`x`(_$,(_$,_$)->Boolean)->_$`dBasicOperator``513825 +oequation`2`x`(S,S)->_$`dEquation(S)``514129 +oequation`2`x`(Symbol,Segment(S))->_$`dSegmentBinding(S)``514180 +oequation`2`x`(Symbol,String)->_$`dQueryEquation``514354 +oerf`1`n`(F)->F`pLiouvillianFunction(R,F)``514410 +oerf`1`x`(_$)->_$`cLiouvillianFunctionCategory``514458 +oerror`1`x`(List(String))->Exit`pErrorFunctions``514612 +oerror`1`x`(String)->Exit`pErrorFunctions``514689 +oerror`2`x`(String,List(String))->Exit`pErrorFunctions``514764 +oerror`2`x`(String,String)->Exit`pErrorFunctions``514934 +oerrorInfo`1`x`(_$)->List(Symbol)`dOpenMathError``515101 +oerrorKind`1`x`(_$)->OpenMathErrorKind`dOpenMathError``515174 +oescape`0`x`()->_$`dCharacter``515254 +oeuclideanGroebner`1`x`(List(Dpol))->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``515453 +oeuclideanGroebner`2`x`(List(Dpol),String)->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``516069 +oeuclideanGroebner`3`x`(List(Dpol),String,String)->List(Dpol)`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``517001 +oeuclideanNormalForm`2`x`(Dpol,List(Dpol))->Dpol`pEuclideanGroebnerBasisPackage(Dom,Expon,VarSet,Dpol)``517829 oeuclideanSize`1`n`(S)->NonNegativeInteger`xComplexCategory&(S,R)``0 oeuclideanSize`1`n`(S)->NonNegativeInteger`xField&(S)``0 oeuclideanSize`1`n`(S)->NonNegativeInteger`xIntegerNumberSystem&(S)``0 oeuclideanSize`1`n`(S)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 -oeuclideanSize`1`x`(_$)->NonNegativeInteger`cEuclideanDomain``433421 -oeulerE`2`x`(NonNegativeInteger,R)->R`pNumberTheoreticPolynomialFunctions(R)`has(R,Algebra(Fraction(Integer)))`433532 -oeulerPhi`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``433574 -oeuler`1`n`(Integer)->SparseUnivariatePolynomial(Fraction(Integer))`pPolynomialNumberTheoryFunctions``433791 -oeuler`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``434104 +oeuclideanSize`1`x`(_$)->NonNegativeInteger`cEuclideanDomain``518013 +oeuler`1`n`(Integer)->SparseUnivariatePolynomial(Fraction(Integer))`pPolynomialNumberTheoryFunctions``518124 +oeuler`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``518441 +oeulerE`2`x`(NonNegativeInteger,R)->R`pNumberTheoreticPolynomialFunctions(R)`has(R,Algebra(Fraction(Integer)))`518592 +oeulerPhi`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``518634 oeval`1`n`(S)->S`xFunctionSpace&(S,R)``0 -oeval`1`x`(SymmetricPolynomial(Fraction(Integer)))->Fraction(Integer)`pCycleIndicators``434255 -oeval`1`x`(_$)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`434325 -oeval`2`n`((Integer)->F,SymmetricPolynomial(Fraction(Integer)))->F`pEvaluateCycleIndicators(F)``434394 +oeval`1`x`(_$)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`518851 +oeval`1`x`(SymmetricPolynomial(Fraction(Integer)))->Fraction(Integer)`pCycleIndicators``518920 oeval`2`n`(A,Equation(A))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 oeval`2`n`(A,Equation(S))->A`xHomogeneousAggregate&(A,S)``0 oeval`2`n`(A,List(Equation(A)))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 oeval`2`n`(A,List(Equation(S)))->A`xHomogeneousAggregate&(A,S)``0 +oeval`2`n`(_$,F)->F`dMoebiusTransform(F)``518990 +oeval`2`n`((Integer)->F,SymmetricPolynomial(Fraction(Integer)))->F`pEvaluateCycleIndicators(F)``519128 +oeval`2`n`(_$,OnePointCompletion(F))->OnePointCompletion(F)`dMoebiusTransform(F)``519355 oeval`2`n`(S,Equation(R))->S`xEvalable&(S,R)``0 oeval`2`n`(S,Equation(R))->S`xFullyEvalableOver&(S,R)``0 oeval`2`n`(S,Equation(S))->S`xExpressionSpace&(S)``0 @@ -3636,19 +3742,24 @@ oeval`2`n`(S,List(Equation(S)))->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`2`n`(S,List(Equation(S)))->S`xUnivariatePolynomialCategory&(S,R)``0 oeval`2`n`(S,List(Symbol))->S`xFunctionSpace&(S,R)``0 oeval`2`n`(S,Symbol)->S`xFunctionSpace&(S,R)``0 -oeval`2`n`(Stream(A),A)->Stream(A)`pStreamTaylorSeriesOperations(A)``434621 -oeval`2`n`(_$,F)->F`dMoebiusTransform(F)``434767 -oeval`2`n`(_$,OnePointCompletion(F))->OnePointCompletion(F)`dMoebiusTransform(F)``434915 -oeval`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->Fraction(Polynomial(R))`pRationalFunction(R)``435063 -oeval`2`x`(Fraction(Polynomial(R)),List(Equation(Fraction(Polynomial(R)))))->Fraction(Polynomial(R))`pRationalFunction(R)``435183 -oeval`2`x`(_$,Coef)->Stream(Coef)`cUnivariatePowerSeriesCategory(Coef,Expon)`has(Coef,SIGNATURE(**,Coef(Coef,Expon)))`435444 -oeval`2`x`(_$,Equation(R))->_$`cEvalable(R)``435564 -oeval`2`x`(_$,List(Equation(R)))->_$`cEvalable(R)``435637 -oeval`2`x`(_$,List(Symbol))->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`435733 -oeval`2`x`(_$,List(_$))->_$`dEquation(S)`AND(has(S,Evalable(S)),has(S,SetCategory))`435829 -oeval`2`x`(_$,S)->S`cPermutationCategory(S)``435933 -oeval`2`x`(_$,Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`436023 -oeval`2`x`(_$,_$)->_$`dEquation(S)`AND(has(S,Evalable(S)),has(S,SetCategory))`436095 +oeval`2`n`(Stream(A),A)->Stream(A)`pStreamTaylorSeriesOperations(A)``519493 +oeval`2`x`(_$,Coef)->Stream(Coef)`cUnivariatePowerSeriesCategory(Coef,Expon)`has(Coef,SIGNATURE(**,Coef(Coef,Expon)))`519639 +oeval`2`x`(_$,_$)->_$`dEquation(S)`AND(has(S,Evalable(S)),has(S,SetCategory))`519759 +oeval`2`x`(DistributedMultivariatePolynomial(symb,K),Places(K))->K`pPackageForAlgebraicFunctionField(K,symb,BLMET)``519844 +oeval`2`x`(DistributedMultivariatePolynomial(symb,K),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->K`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``519913 +oeval`2`x`(_$,Equation(R))->_$`cEvalable(R)``519982 +oeval`2`x`(Fraction(DistributedMultivariatePolynomial(symb,K)),Places(K))->K`pPackageForAlgebraicFunctionField(K,symb,BLMET)``520055 +oeval`2`x`(Fraction(DistributedMultivariatePolynomial(symb,K)),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->K`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``520137 +oeval`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->Fraction(Polynomial(R))`pRationalFunction(R)``520219 +oeval`2`x`(Fraction(Polynomial(R)),List(Equation(Fraction(Polynomial(R)))))->Fraction(Polynomial(R))`pRationalFunction(R)``520339 +oeval`2`x`(Fraction(PolyRing),Plc)->K`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``520600 +oeval`2`x`(_$,List(_$))->_$`dEquation(S)`AND(has(S,Evalable(S)),has(S,SetCategory))`520682 +oeval`2`x`(_$,List(Equation(R)))->_$`cEvalable(R)``520786 +oeval`2`x`(_$,List(Symbol))->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`520882 +oeval`2`x`(PolyRing,Plc)->K`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``520978 +oeval`2`x`(PolyRing,ProjPt)->K`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``521047 +oeval`2`x`(_$,S)->S`cPermutationCategory(S)``521100 +oeval`2`x`(_$,Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`521184 oeval`3`n`(A,A,A)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 oeval`3`n`(A,List(A),List(A))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 oeval`3`n`(A,List(S),List(A))->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 @@ -3677,81 +3788,97 @@ oeval`3`n`(S,List(Kernel(S)),List(S))->S`xExpressionSpace&(S)``0 oeval`3`n`(S,List(Kernel(S)),List(S))->S`xFunctionSpace&(S,R)``0 oeval`3`n`(S,List(R),List(R))->S`xEvalable&(S,R)``0 oeval`3`n`(S,List(R),List(R))->S`xFullyEvalableOver&(S,R)``0 +oeval`3`n`(S,List(SingletonAsOrderedSet),List(R))->S`xUnivariatePolynomialCategory&(S,R)``0 +oeval`3`n`(S,List(SingletonAsOrderedSet),List(S))->S`xUnivariatePolynomialCategory&(S,R)``0 oeval`3`n`(S,List(S),List(S))->S`xExpressionSpace&(S)``0 oeval`3`n`(S,List(S),List(S))->S`xFunctionSpace&(S,R)``0 oeval`3`n`(S,List(S),List(S))->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`3`n`(S,List(S),List(S))->S`xUnivariatePolynomialCategory&(S,R)``0 -oeval`3`n`(S,List(SingletonAsOrderedSet),List(R))->S`xUnivariatePolynomialCategory&(S,R)``0 -oeval`3`n`(S,List(SingletonAsOrderedSet),List(S))->S`xUnivariatePolynomialCategory&(S,R)``0 oeval`3`n`(S,List(Symbol),List((List(S))->S))->S`xExpressionSpace&(S)``0 oeval`3`n`(S,List(Symbol),List((List(S))->S))->S`xFunctionSpace&(S,R)``0 +oeval`3`n`(S,List(Symbol),List(R))->S`xFullyEvalableOver&(S,R)``0 oeval`3`n`(S,List(Symbol),List((S)->S))->S`xExpressionSpace&(S)``0 oeval`3`n`(S,List(Symbol),List((S)->S))->S`xFunctionSpace&(S,R)``0 -oeval`3`n`(S,List(Symbol),List(R))->S`xFullyEvalableOver&(S,R)``0 oeval`3`n`(S,List(VarSet),List(R))->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`3`n`(S,List(VarSet),List(S))->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`3`n`(S,R,R)->S`xEvalable&(S,R)``0 oeval`3`n`(S,R,R)->S`xFullyEvalableOver&(S,R)``0 +oeval`3`n`(S,SingletonAsOrderedSet,R)->S`xUnivariatePolynomialCategory&(S,R)``0 +oeval`3`n`(S,SingletonAsOrderedSet,S)->S`xUnivariatePolynomialCategory&(S,R)``0 oeval`3`n`(S,S,S)->S`xExpressionSpace&(S)``0 oeval`3`n`(S,S,S)->S`xFunctionSpace&(S,R)``0 oeval`3`n`(S,S,S)->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`3`n`(S,S,S)->S`xUnivariatePolynomialCategory&(S,R)``0 -oeval`3`n`(S,SingletonAsOrderedSet,R)->S`xUnivariatePolynomialCategory&(S,R)``0 -oeval`3`n`(S,SingletonAsOrderedSet,S)->S`xUnivariatePolynomialCategory&(S,R)``0 oeval`3`n`(S,Symbol,(List(S))->S)->S`xExpressionSpace&(S)``0 oeval`3`n`(S,Symbol,(List(S))->S)->S`xFunctionSpace&(S,R)``0 +oeval`3`n`(S,Symbol,R)->S`xFullyEvalableOver&(S,R)``0 oeval`3`n`(S,Symbol,(S)->S)->S`xExpressionSpace&(S)``0 oeval`3`n`(S,Symbol,(S)->S)->S`xFunctionSpace&(S,R)``0 -oeval`3`n`(S,Symbol,R)->S`xFullyEvalableOver&(S,R)``0 oeval`3`n`(S,VarSet,R)->S`xPolynomialCategory&(S,R,E,VarSet)``0 oeval`3`n`(S,VarSet,S)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -oeval`3`n`(UPUP,Fraction(UP),Fraction(UP))->UPUP`pChangeOfVariable(F,UP,UPUP)``436180 -oeval`3`x`(Fraction(Polynomial(R)),List(Symbol),List(Fraction(Polynomial(R))))->Fraction(Polynomial(R))`pRationalFunction(R)``436261 -oeval`3`x`(Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R)))->Fraction(Polynomial(R))`pRationalFunction(R)``436490 -oeval`3`x`(Matrix(Expression(DoubleFloat)),List(Symbol),Vector(Expression(DoubleFloat)))->Matrix(Expression(DoubleFloat))`pd02AgentsPackage``436575 -oeval`3`x`(_$,A,B)->_$`cInnerEvalable(A,B)``436706 -oeval`3`x`(_$,BasicOperator,(List(_$))->_$)->_$`cExpressionSpace``436781 -oeval`3`x`(_$,BasicOperator,(_$)->_$)->_$`cExpressionSpace``436926 -oeval`3`x`(_$,List(A),List(B))->_$`cInnerEvalable(A,B)``437030 -oeval`3`x`(_$,List(BasicOperator),List((List(_$))->_$))->_$`cExpressionSpace``437135 -oeval`3`x`(_$,List(BasicOperator),List((_$)->_$))->_$`cExpressionSpace``437326 -oeval`3`x`(_$,List(Symbol),List((List(_$))->_$))->_$`cExpressionSpace``437474 -oeval`3`x`(_$,List(Symbol),List((_$)->_$))->_$`cExpressionSpace``437665 -oeval`3`x`(_$,List(VarSet),List(_$))->_$`cFreeLieAlgebra(VarSet,R)``437813 -oeval`3`x`(_$,Symbol,(List(_$))->_$)->_$`cExpressionSpace``437978 -oeval`3`x`(_$,Symbol,(_$)->_$)->_$`cExpressionSpace``438123 -oeval`3`x`(_$,VarSet,_$)->_$`cFreeLieAlgebra(VarSet,R)``438227 +oeval`3`n`(UPUP,Fraction(UP),Fraction(UP))->UPUP`pChangeOfVariable(F,UP,UPUP)``521256 +oeval`3`x`(_$,A,B)->_$`cInnerEvalable(A,B)``521337 +oeval`3`x`(_$,BasicOperator,(_$)->_$)->_$`cExpressionSpace``521412 +oeval`3`x`(_$,BasicOperator,(List(_$))->_$)->_$`cExpressionSpace``521516 +oeval`3`x`(DistributedMultivariatePolynomial(symb,K),DistributedMultivariatePolynomial(symb,K),Places(K))->K`pPackageForAlgebraicFunctionField(K,symb,BLMET)``521661 +oeval`3`x`(DistributedMultivariatePolynomial(symb,K),DistributedMultivariatePolynomial(symb,K),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->K`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``521749 +oeval`3`x`(Fraction(Polynomial(R)),List(Symbol),List(Fraction(Polynomial(R))))->Fraction(Polynomial(R))`pRationalFunction(R)``521837 +oeval`3`x`(Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R)))->Fraction(Polynomial(R))`pRationalFunction(R)``522066 +oeval`3`x`(_$,List(A),List(B))->_$`cInnerEvalable(A,B)``522151 +oeval`3`x`(_$,List(BasicOperator),List((_$)->_$))->_$`cExpressionSpace``522256 +oeval`3`x`(_$,List(BasicOperator),List((List(_$))->_$))->_$`cExpressionSpace``522404 +oeval`3`x`(_$,List(Symbol),List((_$)->_$))->_$`cExpressionSpace``522595 +oeval`3`x`(_$,List(Symbol),List((List(_$))->_$))->_$`cExpressionSpace``522743 +oeval`3`x`(_$,List(VarSet),List(_$))->_$`cFreeLieAlgebra(VarSet,R)``522934 +oeval`3`x`(Matrix(Expression(DoubleFloat)),List(Symbol),Vector(Expression(DoubleFloat)))->Matrix(Expression(DoubleFloat))`pd02AgentsPackage``523099 +oeval`3`x`(PolyRing,PolyRing,Plc)->K`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``523230 +oeval`3`x`(_$,Symbol,(_$)->_$)->_$`cExpressionSpace``523318 +oeval`3`x`(_$,Symbol,(List(_$))->_$)->_$`cExpressionSpace``523422 +oeval`3`x`(_$,VarSet,_$)->_$`cFreeLieAlgebra(VarSet,R)``523567 oeval`4`n`(S,BasicOperator,S,Symbol)->S`xFunctionSpace&(S,R)``0 oeval`4`n`(S,List(BasicOperator),List(S),Symbol)->S`xFunctionSpace&(S,R)``0 oeval`4`n`(S,List(Symbol),List(NonNegativeInteger),List((List(S))->S))->S`xFunctionSpace&(S,R)``0 oeval`4`n`(S,List(Symbol),List(NonNegativeInteger),List((S)->S))->S`xFunctionSpace&(S,R)``0 oeval`4`n`(S,Symbol,NonNegativeInteger,(List(S))->S)->S`xFunctionSpace&(S,R)``0 oeval`4`n`(S,Symbol,NonNegativeInteger,(S)->S)->S`xFunctionSpace&(S,R)``0 -oeval`4`x`(_$,BasicOperator,_$,Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`438348 -oeval`4`x`(_$,List(BasicOperator),List(_$),Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`438492 -oeval`4`x`(_$,List(Symbol),List(NonNegativeInteger),List((List(_$))->_$))->_$`cFunctionSpace(R)`has(R,Ring)`438680 -oeval`4`x`(_$,List(Symbol),List(NonNegativeInteger),List((_$)->_$))->_$`cFunctionSpace(R)`has(R,Ring)`438887 -oeval`4`x`(_$,Symbol,NonNegativeInteger,(List(_$))->_$)->_$`cFunctionSpace(R)`has(R,Ring)`439058 -oeval`4`x`(_$,Symbol,NonNegativeInteger,(_$)->_$)->_$`cFunctionSpace(R)`has(R,Ring)`439206 -oevaluateInverse`2`n`(_$,(R)->R)->_$`dOperator(R)``0 -oevaluateInverse`2`x`(_$,(M)->M)->_$`dModuleOperator(R,M)``439318 -oevaluate`1`x`(BasicOperator)->Union((List(A))->A,"failed")`pBasicOperatorFunctions1(A)``439369 +oeval`4`x`(_$,BasicOperator,_$,Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`523688 +oeval`4`x`(_$,List(BasicOperator),List(_$),Symbol)->_$`cFunctionSpace(R)`has(R,ConvertibleTo(InputForm))`523832 +oeval`4`x`(_$,List(Symbol),List(NonNegativeInteger),List((_$)->_$))->_$`cFunctionSpace(R)`has(R,Ring)`524020 +oeval`4`x`(_$,List(Symbol),List(NonNegativeInteger),List((List(_$))->_$))->_$`cFunctionSpace(R)`has(R,Ring)`524191 +oeval`4`x`(_$,Symbol,NonNegativeInteger,(_$)->_$)->_$`cFunctionSpace(R)`has(R,Ring)`524398 +oeval`4`x`(_$,Symbol,NonNegativeInteger,(List(_$))->_$)->_$`cFunctionSpace(R)`has(R,Ring)`524510 +oevalADE`6`x`(BasicOperator,Symbol,F,F,F,List(F))->F`pRecurrenceOperator(R,F)``524658 +oevalIfCan`2`x`(DistributedMultivariatePolynomial(symb,K),Places(K))->Union(K,"failed")`pPackageForAlgebraicFunctionField(K,symb,BLMET)``525110 +oevalIfCan`2`x`(DistributedMultivariatePolynomial(symb,K),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->Union(K,"failed")`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``525219 +oevalIfCan`2`x`(Fraction(DistributedMultivariatePolynomial(symb,K)),Places(K))->Union(K,"failed")`pPackageForAlgebraicFunctionField(K,symb,BLMET)``525328 +oevalIfCan`2`x`(Fraction(DistributedMultivariatePolynomial(symb,K)),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->Union(K,"failed")`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``525450 +oevalIfCan`2`x`(Fraction(PolyRing),Plc)->Union(K,"failed")`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``525572 +oevalIfCan`2`x`(PolyRing,Plc)->Union(K,"failed")`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``525694 +oevalIfCan`3`x`(DistributedMultivariatePolynomial(symb,K),DistributedMultivariatePolynomial(symb,K),Places(K))->Union(K,"failed")`pPackageForAlgebraicFunctionField(K,symb,BLMET)``525803 +oevalIfCan`3`x`(DistributedMultivariatePolynomial(symb,K),DistributedMultivariatePolynomial(symb,K),PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->Union(K,"failed")`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``525931 +oevalIfCan`3`x`(PolyRing,PolyRing,Plc)->Union(K,"failed")`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``526059 +oevalRec`6`x`(BasicOperator,Symbol,F,F,F,List(F))->F`pRecurrenceOperator(R,F)``526187 +oevaluate`1`x`(BasicOperator)->Union((List(A))->A,"failed")`pBasicOperatorFunctions1(A)``526706 oevaluate`2`n`(_$,(R)->R)->_$`dOperator(R)``0 -oevaluate`2`x`(BasicOperator,(A)->A)->BasicOperator`pBasicOperatorFunctions1(A)``439493 -oevaluate`2`x`(BasicOperator,(List(A))->A)->BasicOperator`pBasicOperatorFunctions1(A)``439727 -oevaluate`2`x`(BasicOperator,List(A))->Union(A,"failed")`pBasicOperatorFunctions1(A)``439960 -oevaluate`2`x`(_$,(M)->M)->_$`dModuleOperator(R,M)``440142 +oevaluate`2`x`(BasicOperator,(A)->A)->BasicOperator`pBasicOperatorFunctions1(A)``526830 +oevaluate`2`x`(BasicOperator,(List(A))->A)->BasicOperator`pBasicOperatorFunctions1(A)``527064 +oevaluate`2`x`(BasicOperator,List(A))->Union(A,"failed")`pBasicOperatorFunctions1(A)``527297 +oevaluate`2`x`(_$,(M)->M)->_$`dModuleOperator(R,M)``527479 +oevaluateInverse`2`n`(_$,(R)->R)->_$`dOperator(R)``0 +oevaluateInverse`2`x`(_$,(M)->M)->_$`dModuleOperator(R,M)``527806 oeven?`1`n`(S)->Boolean`xExpressionSpace&(S)``0 oeven?`1`n`(S)->Boolean`xIntegerNumberSystem&(S)``0 -oeven?`1`x`(_$)->Boolean`cExpressionSpace`has(_$,RetractableTo(Integer))`440469 -oeven?`1`x`(_$)->Boolean`cIntegerNumberSystem``440538 -oeven?`1`x`(_$)->Boolean`dPermutation(S)``440614 -oevenInfiniteProduct`1`n`(Stream(Coef))->Stream(Coef)`pStreamInfiniteProduct(Coef)``440745 -oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductCharacteristicZero(Coef,UTS)``440895 -oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductFiniteField(K,UP,Coef,UTS)``441045 -oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductPrimeField(Coef,UTS)``441195 -oevenlambert`1`n`(Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``441345 -oevenlambert`1`n`(_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``441672 +oeven?`1`x`(_$)->Boolean`cExpressionSpace`has(_$,RetractableTo(Integer))`527861 +oeven?`1`x`(_$)->Boolean`cIntegerNumberSystem``527930 +oeven?`1`x`(_$)->Boolean`dPermutation(S)``528006 +oevenInfiniteProduct`1`n`(Stream(Coef))->Stream(Coef)`pStreamInfiniteProduct(Coef)``528280 +oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductCharacteristicZero(Coef,UTS)``528430 +oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductFiniteField(K,UP,Coef,UTS)``528580 +oevenInfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductPrimeField(Coef,UTS)``528730 +oevenlambert`1`n`(_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``528880 +oevenlambert`1`n`(Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``529260 +oevenlambert`1`x`(_$)->_$`dUnivariateFormalPowerSeries(Coef)``0 +oevenlambert`1`x`(_$)->_$`dUnivariateTaylorSeriesCZero(Coef,var)``529587 oevery?`2`n`((Entry)->Boolean,S)->Boolean`xTableAggregate&(S,Key,Entry)``0 oevery?`2`n`((R)->Boolean,S)->Boolean`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 oevery?`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->Boolean`xTableAggregate&(S,Key,Entry)``0 @@ -3759,84 +3886,90 @@ oevery?`2`n`((S)->Boolean,A)->Boolean`xCollection&(A,S)``0 oevery?`2`n`((S)->Boolean,A)->Boolean`xHomogeneousAggregate&(A,S)``0 oevery?`2`n`((S)->Boolean,A)->Boolean`xLazyStreamAggregate&(A,S)``0 oevery?`2`n`((S)->Boolean,A)->Boolean`xOneDimensionalArrayAggregate&(A,S)``0 -oevery?`2`x`((S)->Boolean,_$)->Boolean`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`442052 -oexQuo`2`n`(_$,_$)->Union(_$,"failed")`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``442294 -oexQuo`2`n`(_$,_$)->Union(_$,"failed")`dModularField(R,Mod,reduction,merge,exactQuo)``442335 -oexQuo`2`n`(_$,_$)->Union(_$,"failed")`dModularRing(R,Mod,reduction,merge,exactQuo)``442376 -oexactQuotient!`2`n`(S,R)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oexactQuotient!`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oexactQuotient!`2`x`(_$,R)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`442417 -oexactQuotient!`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`442541 +oevery?`2`x`((S)->Boolean,_$)->Boolean`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(finiteAggregate))`529965 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-oexp`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``444412 -oexp`2`n`(XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``444479 -oexp`2`n`(_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)`has(R,Module(Fraction(Integer)))`444601 -oexpandLog`1`x`(F)->F`pTranscendentalManipulations(R,F)``444727 -oexpandPower`1`x`(F)->F`pTranscendentalManipulations(R,F)``444894 -oexpandTrigProducts`1`x`(F)->F`pTranscendentalManipulations(R,F)`AND(has(R,ConvertibleTo(Pattern(R))),has(R,PatternMatchable(R)),has(F,ConvertibleTo(Pattern(R))),has(F,PatternMatchable(R)))`445010 +oexp`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``531941 +oexp`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``532017 +oexp`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``532093 +oexp`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``532166 +oexp`1`x`(_$)->_$`cElementaryFunctionCategory``532241 +oexp`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``532304 +oexp`2`n`(_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)`has(R,Module(Fraction(Integer)))`532371 +oexp`2`n`(XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``532497 oexpand`1`n`(_$)->XDistributedPolynomial(Symbol,R)`dXPolynomial(R)``0 -oexpand`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dXRecursivePolynomial(VarSet,R)``445452 -oexpand`1`x`(F)->F`pTranscendentalManipulations(R,F)``445514 -oexpand`1`x`(IntegrationResult(F))->List(F)`pIntegrationResultToFunction(R,F)``445924 -oexpand`1`x`(IntegrationResult(Fraction(Polynomial(R))))->List(Expression(R))`pIntegrationResultRFToFunction(R)``446019 -oexpand`1`x`(List(_$))->L`cSegmentExpansionCategory(S,L)``446114 -oexpand`1`x`(_$)->L`cSegmentExpansionCategory(S,L)``446364 -oexpand`1`x`(_$)->R`dFactored(R)``446551 -oexpand`2`n`(Expression(R2),PositiveInteger)->List(Expression(R2))`pDegreeReductionPackage(R1,R2)``446764 -oexpenseOfEvaluationIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Float`pd02AgentsPackage``446808 -oexpenseOfEvaluation`1`x`(Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))->Float`pe04AgentsPackage``447280 -oexpenseOfEvaluation`1`x`(Vector(Expression(DoubleFloat)))->Float`pExpertSystemToolsPackage``447504 -oexpextendedint`4`n`(Fraction(UP),(UP)->UP,(Integer,F)->Record(ans:F,right:F,sol?:Boolean),Fraction(UP))->Union(Record(answer:Fraction(UP),a0:F),Record(ratpart:Fraction(UP),coeff:Fraction(UP)),"failed")`pTranscendentalIntegration(F,UP)``447871 -oexpint`2`n`(F,Symbol)->F`pODEIntegration(R,F)``448238 -oexpintegrate`3`n`(Fraction(UP),(UP)->UP,(Integer,F)->Record(ans:F,right:F,sol?:Boolean))->Record(answer:IntegrationResult(Fraction(UP)),a0:F)`pTranscendentalIntegration(F,UP)``448330 -oexpintfldpoly`2`n`(LaurentPolynomial(F,UP),(Integer,F)->Record(ans:F,right:F,sol?:Boolean))->Union(LaurentPolynomial(F,UP),"failed")`pTranscendentalIntegration(F,UP)``448551 -oexplicitEntries?`1`x`(_$)->Boolean`cLazyStreamAggregate(S)``448738 -oexplicitlyEmpty?`1`x`(_$)->Boolean`cLazyStreamAggregate(S)``448878 +oexpand`1`n`(_$)->XDistributedPolynomial(VarSet,R)`dXRecursivePolynomial(VarSet,R)``532619 +oexpand`1`x`(F)->F`pTranscendentalManipulations(R,F)``532681 +oexpand`1`x`(IntegrationResult(F))->List(F)`pIntegrationResultToFunction(R,F)``533091 +oexpand`1`x`(IntegrationResult(Fraction(Polynomial(R))))->List(Expression(R))`pIntegrationResultRFToFunction(R)``533186 +oexpand`1`x`(_$)->L`cSegmentExpansionCategory(S,L)``533281 +oexpand`1`x`(List(_$))->L`cSegmentExpansionCategory(S,L)``533468 +oexpand`1`x`(_$)->R`dFactored(R)``533718 +oexpand`2`n`(Expression(R2),PositiveInteger)->List(Expression(R2))`pDegreeReductionPackage(R1,R2)``534069 +oexpandLog`1`x`(F)->F`pTranscendentalManipulations(R,F)``534113 +oexpandPower`1`x`(F)->F`pTranscendentalManipulations(R,F)``534280 +oexpandTrigProducts`1`x`(F)->F`pTranscendentalManipulations(R,F)`AND(has(R,ConvertibleTo(Pattern(R))),has(R,PatternMatchable(R)),has(F,ConvertibleTo(Pattern(R))),has(F,PatternMatchable(R)))`534396 +oexpenseOfEvaluation`1`x`(Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))->Float`pe04AgentsPackage``534838 +oexpenseOfEvaluation`1`x`(Vector(Expression(DoubleFloat)))->Float`pExpertSystemToolsPackage``535062 +oexpenseOfEvaluationIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Float`pd02AgentsPackage``535429 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oexplicitlyFinite?`1`n`(A)->Boolean`xStreamAggregate&(A,S)``0 -oexplicitlyFinite?`1`x`(_$)->Boolean`cStreamAggregate(S)``449043 -oexplimitedint`4`n`(Fraction(UP),(UP)->UP,(Integer,F)->Record(ans:F,right:F,sol?:Boolean),List(Fraction(UP)))->Union(Record(answer:Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),a0:F),"failed")`pTranscendentalIntegration(F,UP)``449260 -oexplogs2trigs`1`n`(FG)->Complex(F)`pInnerTrigonometricManipulations(R,F,FG)``449654 -oexponent`1`n`(_$)->E`dModuleMonomial(IS,E,ff)``449791 -oexponent`1`n`(_$)->UnivariatePuiseuxSeries(FE,var,cen)`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``449831 -oexponent`1`x`(_$)->Integer`cFloatingPointSystem``449885 -oexponent`1`x`(_$)->Integer`dFactored(R)``449985 -oexponent`1`x`(_$)->Integer`dMachineFloat``450130 -oexponential1`0`n`()->Float`pRandomFloatDistributions``450189 -oexponentialOrder`1`n`(_$)->Fraction(Integer)`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``450232 -oexponential`1`n`(Float)->()->Float`pRandomFloatDistributions``450345 -oexponential`1`n`(UnivariatePuiseuxSeries(FE,var,cen))->_$`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``450388 -oexponents`1`n`(_$)->List(Integer)`dExtAlgBasis``450524 -oexprHasAlgebraicWeight`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(List(DoubleFloat),"failed")`pd01WeightsPackage``450685 -oexprHasLogarithmicWeights`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Integer`pd01WeightsPackage``450815 -oexprHasWeightCosWXorSinWX`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(op:BasicOperator,w:DoubleFloat),"failed")`pd01WeightsPackage``450950 -oexprToGenUPS`3`n`(FE,Boolean,String)->Union(%series:UPS,%problem:Record(func:String,prob:String))`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``451176 -oexprToUPS`3`n`(FE,Boolean,String)->Union(%series:UPS,%problem:Record(func:String,prob:String))`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``453282 -oexprToXXP`2`n`(FE,Boolean)->Union(%expansion:ExponentialExpansion(R,FE,x,cen),%problem:Record(func:String,prob:String))`pFunctionSpaceToExponentialExpansion(R,FE,x,cen)``455375 -oexpr`1`x`(_$)->Expr`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``455690 +oexplicitlyFinite?`1`x`(_$)->Boolean`cStreamAggregate(S)``537392 +oexplimitedint`4`n`(Fraction(UP),(UP)->UP,(Integer,F)->Record(ans:F,right:F,sol?:Boolean),List(Fraction(UP)))->Union(Record(answer:Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),a0:F),"failed")`pTranscendentalIntegration(F,UP)``537613 +oexplogs2trigs`1`n`(FG)->Complex(F)`pInnerTrigonometricManipulations(R,F,FG)``538007 +oexponent`1`n`(_$)->E`dModuleMonomial(IS,E,ff)``538144 +oexponent`1`n`(_$)->UnivariatePuiseuxSeries(FE,var,cen)`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``538188 +oexponent`1`x`(_$)->Integer`cFloatingPointSystem``538242 +oexponent`1`x`(_$)->Integer`dFactored(R)``538342 +oexponent`1`x`(_$)->Integer`dMachineFloat``538599 +oexponential1`0`n`()->Float`pRandomFloatDistributions``538658 +oexponential`1`n`(Float)->()->Float`pRandomFloatDistributions``538701 +oexponential`1`n`(UnivariatePuiseuxSeries(FE,var,cen))->_$`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``538744 +oexponentialOrder`1`n`(_$)->Fraction(Integer)`dExponentialOfUnivariatePuiseuxSeries(FE,var,cen)``538880 +oexponents`1`n`(_$)->List(Integer)`dExtAlgBasis``538993 +oexpPot`3`n`(Vector(GF),SingleInteger,SingleInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``539154 +oexpr`1`x`(_$)->Expr`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``539630 oexpressIdealMember`2`n`(List(S),S)->Union(List(S),"failed")`xEuclideanDomain&(S)``0 -oexpressIdealMember`2`x`(List(_$),_$)->Union(List(_$),"failed")`cPrincipalIdealDomain``455813 -oexptMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``456017 -oexptMod`4`x`(U,Integer,U,Integer)->U`pModularDistinctDegreeFactorizer(U)``456137 -oexpt`2`n`(S,PositiveInteger)->S`pRepeatedSquaring(S)``456295 +oexpressIdealMember`2`x`(List(_$),_$)->Union(List(_$),"failed")`cPrincipalIdealDomain``539753 +oexprex`1`x`(OutputForm)->String`dMathMLFormat``539957 +oexprHasAlgebraicWeight`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(List(DoubleFloat),"failed")`pd01WeightsPackage``540361 +oexprHasLogarithmicWeights`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Integer`pd01WeightsPackage``540491 +oexprHasWeightCosWXorSinWX`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(op:BasicOperator,w:DoubleFloat),"failed")`pd01WeightsPackage``540626 +oexprToGenUPS`3`n`(FE,Boolean,String)->Union(%series:UPS,%problem:Record(func:String,prob:String))`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``540852 +oexprToUPS`3`n`(FE,Boolean,String)->Union(%series:UPS,%problem:Record(func:String,prob:String))`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``542958 +oexprToXXP`2`n`(FE,Boolean)->Union(%expansion:ExponentialExpansion(R,FE,x,cen),%problem:Record(func:String,prob:String))`pFunctionSpaceToExponentialExpansion(R,FE,x,cen)``545051 +oexpt`2`n`(S,PositiveInteger)->S`pRepeatedSquaring(S)``545366 +oexptMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``545428 +oexptMod`4`x`(U,Integer,U,Integer)->U`pModularDistinctDegreeFactorizer(U)``545548 +oexquo`2`n`(_$,_$)->_$`dOutputForm``545706 oexquo`2`n`(S,R)->Union(S,"failed")`xComplexCategory&(S,R)``0 oexquo`2`n`(S,R)->Union(S,"failed")`xFiniteAbelianMonoidRing&(S,R,E)``0 oexquo`2`n`(S,R)->Union(S,"failed")`xMatrixCategory&(S,R,Row,Col)``0 @@ -3845,17 +3978,19 @@ oexquo`2`n`(S,S)->Union(S,"failed")`xComplexCategory&(S,R)``0 oexquo`2`n`(S,S)->Union(S,"failed")`xEuclideanDomain&(S)``0 oexquo`2`n`(S,S)->Union(S,"failed")`xField&(S)``0 oexquo`2`n`(S,S)->Union(S,"failed")`xFiniteAbelianMonoidRing&(S,R,E)``0 -oexquo`2`n`(Stream(A),Stream(A))->Union(Stream(A),"failed")`pStreamTaylorSeriesOperations(A)``456357 -oexquo`2`n`(Vector(polR),R)->Vector(polR)`pPseudoRemainderSequence(R,polR)``456494 -oexquo`2`n`(_$,_$)->_$`dOutputForm``456601 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-ofactor`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->List(F))->List(LinearOrdinaryDifferentialOperator1(Fraction(UP)))`pLinearOrdinaryDifferentialOperatorFactorizer(F,UP)``482304 -ofactor`2`n`(P,(SparseUnivariatePolynomial(R))->Factored(SparseUnivariatePolynomial(R)))->Factored(P)`pInnerMultFact(OV,E,R,P)``482413 -ofactor`2`n`(SparseUnivariatePolynomial(P),(SparseUnivariatePolynomial(R))->Factored(SparseUnivariatePolynomial(R)))->Factored(SparseUnivariatePolynomial(P))`pInnerMultFact(OV,E,R,P)``482568 -ofactor`2`n`(UP,List(NonNegativeInteger))->Factored(UP)`pGaloisGroupFactorizer(UP)``482806 -ofactor`2`n`(UP,NonNegativeInteger)->Factored(UP)`pGaloisGroupFactorizer(UP)``483010 -ofactor`2`n`(UP,R)->Factored(UP)`pComplexRootFindingPackage(R,UP)``483170 -ofactor`2`x`(P,List(AlgebraicNumber))->Factored(P)`pAlgebraicMultFact(OV,E,P)``483409 -ofactor`2`x`(SparseUnivariatePolynomial(P),List(AlgebraicNumber))->Factored(SparseUnivariatePolynomial(P))`pAlgebraicMultFact(OV,E,P)``483555 -ofactor`2`x`(U,Integer)->List(U)`pModularDistinctDegreeFactorizer(U)``483782 -ofactor`2`x`(UP,List(AlgebraicNumber))->Factored(UP)`pAlgFactor(UP)``483969 -ofactor`3`n`(UP,List(NonNegativeInteger),NonNegativeInteger)->Factored(UP)`pGaloisGroupFactorizer(UP)``484125 -ofactor`3`n`(UP,NonNegativeInteger,NonNegativeInteger)->Factored(UP)`pGaloisGroupFactorizer(UP)``484380 -ofactor`3`n`(UP,R,Boolean)->Factored(UP)`pComplexRootFindingPackage(R,UP)``484607 -ofactorial`1`n`(F)->F`pCombinatorialFunction(R,F)``484922 -ofactorial`1`n`(S)->S`xIntegerNumberSystem&(S)``0 -ofactorial`1`x`(I)->I`pIntegerCombinatoricFunctions(I)``485015 -ofactorial`1`x`(_$)->_$`cCombinatorialFunctionCategory``485169 -ofactorials`1`n`(F)->F`pCombinatorialFunction(R,F)``485334 -ofactorials`1`x`(_$)->_$`cCombinatorialOpsCategory``485438 -ofactorials`2`n`(F,Symbol)->F`pCombinatorialFunction(R,F)``485542 -ofactorials`2`x`(_$,Symbol)->_$`cCombinatorialOpsCategory``485670 -ofactorsOfCyclicGroupSize`0`x`()->List(Record(factor:Integer,exponent:Integer))`cFiniteFieldCategory``485798 -ofactorsOfDegree`2`n`(PositiveInteger,Factored(UP))->List(UP)`pGaloisGroupPolynomialUtilities(R,UP)``485884 -ofactors`1`n`(_$)->List(Record(gen:S,exp:Integer))`dFreeGroup(S)``485997 -ofactors`1`n`(_$)->List(Record(gen:S,exp:NonNegativeInteger))`dFreeMonoid(S)``486090 -ofactors`1`n`(_$)->List(Record(gen:S,exp:NonNegativeInteger))`dOrderedFreeMonoid(S)``486183 -ofactors`1`x`(_$)->List(Record(factor:R,exponent:Integer))`dFactored(R)``486276 -ofactorset`1`n`(GR)->List(GR)`pParametricLinearEquations(R,Var,Expon,GR)``486576 -ofailed?`1`n`(_$)->Boolean`dPatternMatchListResult(R,S,L)``486655 -ofailed?`1`n`(_$)->Boolean`dPatternMatchResult(R,S)``486717 -ofailed`0`n`()->_$`dPatternMatchListResult(R,S,L)``486779 -ofailed`0`n`()->_$`dPatternMatchResult(R,S)``486826 -ofalse`0`x`()->_$`dBoolean``486873 -offactor`1`n`(UP)->Factored(UP)`pFunctionSpaceUnivariatePolynomialFactor(R,F,UP)``486916 -ofglmIfCan`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->Union(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),"failed")`pLexTriangularPackage(R,ls)``487004 -ofglmIfCan`1`n`(List(Polynomial(R)))->Union(List(Polynomial(R)),"failed")`pFGLMIfCanPackage(R,ls)``487187 -ofi2df`1`x`(Fraction(Integer))->DoubleFloat`pExpertSystemToolsPackage``487372 -ofibonacci`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``487461 +ofactorSquareFreePolynomial`1`x`(SparseUnivariatePolynomial(_$))->Factored(SparseUnivariatePolynomial(_$))`cPolynomialFactorizationExplicit``577808 +ofactorUsingMusser`1`x`(PolK)->Factored(PolK)`pFiniteFieldFactorizationWithSizeParseBySideEffect(K,PolK)``0 +ofactorUsingYun`1`x`(PolK)->Factored(PolK)`pFiniteFieldFactorizationWithSizeParseBySideEffect(K,PolK)``0 +ofailed`0`n`()->_$`dPatternMatchListResult(R,S,L)``578004 +ofailed`0`n`()->_$`dPatternMatchResult(R,S)``578051 +ofailed?`1`n`(_$)->Boolean`dPatternMatchListResult(R,S,L)``578098 +ofailed?`1`n`(_$)->Boolean`dPatternMatchResult(R,S)``578160 +ofalse`0`x`()->_$`dBoolean``578222 +offactor`1`n`(UP)->Factored(UP)`pFunctionSpaceUnivariatePolynomialFactor(R,F,UP)``578265 +offfg`3`x`(List(D),(NonNegativeInteger,Vector(SparseUnivariatePolynomial(D)))->D,List(NonNegativeInteger))->Matrix(SparseUnivariatePolynomial(D))`pFractionFreeFastGaussian(D,V)``578353 +oFG2F`1`n`(FG)->F`pInnerTrigonometricManipulations(R,F,FG)``579100 +ofglmIfCan`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->Union(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),"failed")`pLexTriangularPackage(R,ls)``579159 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-ofilterUntil`2`x`((S)->Boolean,_$)->_$`dStream(S)``488357 -ofilterWhile`2`x`((S)->Boolean,_$)->_$`dInfiniteTuple(S)``488531 -ofilterWhile`2`x`((S)->Boolean,_$)->_$`dStream(S)``488606 -ofindCycle`2`x`(NonNegativeInteger,_$)->Record(cycle?:Boolean,prefix:NonNegativeInteger,period:NonNegativeInteger)`dStream(S)``488783 +ofill!`2`x`(_$,Entry)->_$`cIndexedAggregate(Index,Entry)`has(_$,ATTRIBUTE(shallowlyMutable))`580171 +ofill!`2`x`(_$,R)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``580297 +ofillPascalTriangle`0`n`()->Void`pGaloisGroupUtilities(R)``580477 +ofilterUntil`2`x`((S)->Boolean,_$)->_$`dInfiniteTuple(S)``580536 +ofilterUntil`2`x`((S)->Boolean,_$)->_$`dStream(S)``580615 +ofilterUpTo`2`x`(_$,Integer)->_$`cLocalPowerSeriesCategory(K)``581009 +ofilterWhile`2`x`((S)->Boolean,_$)->_$`dInfiniteTuple(S)``581139 +ofilterWhile`2`x`((S)->Boolean,_$)->_$`dStream(S)``581214 ofind`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->Union(Record(key:Key,entry:Entry),"failed")`xTableAggregate&(S,Key,Entry)``0 ofind`2`n`((S)->Boolean,A)->Union(S,"failed")`xCollection&(A,S)``0 ofind`2`n`((S)->Boolean,A)->Union(S,"failed")`xListAggregate&(A,S)``0 ofind`2`n`((S)->Boolean,A)->Union(S,"failed")`xOneDimensionalArrayAggregate&(A,S)``0 -ofind`2`x`((S)->Boolean,_$)->Union(S,"failed")`cCollection(S)``488868 -ofinite?`1`x`(_$)->Boolean`dCardinalNumber``489012 -ofinite?`1`x`(_$)->Boolean`dOnePointCompletion(R)``489126 -ofinite?`1`x`(_$)->Boolean`dOrderedCompletion(R)``489180 -ofiniteBasis`1`n`(_$)->Vector(R)`dFiniteDivisor(F,UP,UPUP,R)``489234 -ofiniteBound`2`x`(List(OrderedCompletion(DoubleFloat)),DoubleFloat)->List(DoubleFloat)`pe04AgentsPackage``489321 -ofintegrate`3`n`(()->_$,Var,Coef)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)`has(Coef,Algebra(Fraction(Integer)))`489474 -ofintegrate`3`x`(()->_$,Symbol,Coef)->_$`dTaylorSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`489686 -ofirstDenom`1`x`(_$)->Factored(R)`dPartialFraction(R)``489898 -ofirstNumer`1`x`(_$)->R`dPartialFraction(R)``490097 -ofirstSubsetGray`1`n`(PositiveInteger)->Vector(Vector(Integer))`pGrayCode``490294 -ofirstUncouplingMatrix`2`n`(L,PositiveInteger)->Union(Matrix(R),"failed")`pPrecomputedAssociatedEquations(R,L)``490412 +ofind`2`x`((S)->Boolean,_$)->Union(S,"failed")`cCollection(S)``581611 +ofindCoef`2`x`(_$,Integer)->K`cLocalPowerSeriesCategory(K)``0 +ofindCycle`2`x`(NonNegativeInteger,_$)->Record(cycle?:Boolean,prefix:NonNegativeInteger,period:NonNegativeInteger)`dStream(S)``581755 +ofindOrderOfDivisor`3`x`(DIVISOR,Integer,Integer)->Record(ord:Integer,num:PolyRing,den:PolyRing,upTo:Integer)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +ofindOrderOfDivisor`3`x`(Divisor(Places(K)),Integer,Integer)->Record(ord:Integer,num:DistributedMultivariatePolynomial(symb,K),den:DistributedMultivariatePolynomial(symb,K),upTo:Integer)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +ofindOrderOfDivisor`3`x`(Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),Integer,Integer)->Record(ord:Integer,num:DistributedMultivariatePolynomial(symb,K),den:DistributedMultivariatePolynomial(symb,K),upTo:Integer)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +ofindTerm`2`x`(_$,Integer)->Record(k:Integer,c:K)`dNeitherSparseOrDensePowerSeries(K)``0 +ofinite?`1`x`(_$)->Boolean`dCardinalNumber``581987 +ofinite?`1`x`(_$)->Boolean`dOnePointCompletion(R)``582239 +ofinite?`1`x`(_$)->Boolean`dOrderedCompletion(R)``582293 +ofiniteBasis`1`n`(_$)->Vector(R)`dFiniteDivisor(F,UP,UPUP,R)``582347 +ofiniteBound`2`x`(List(OrderedCompletion(DoubleFloat)),DoubleFloat)->List(DoubleFloat)`pe04AgentsPackage``582442 +ofiniteSeries2LinSys`2`x`(List(PCS),Integer)->Matrix(K)`pLinearSystemFromPowerSeriesPackage(K,PCS)``582595 +ofiniteSeries2LinSysWOVectorise`2`x`(List(PCS),Integer)->Matrix(K)`pLinearSystemFromPowerSeriesPackage(K,PCS)``0 +ofiniteSeries2Vector`2`x`(PCS,Integer)->List(K)`pLinearSystemFromPowerSeriesPackage(K,PCS)``0 +ofintegrate`3`n`(()->_$,Var,Coef)->_$`dSparseMultivariateTaylorSeries(Coef,Var,SMP)`has(Coef,Algebra(Fraction(Integer)))`583026 +ofintegrate`3`x`(()->_$,Symbol,Coef)->_$`dTaylorSeries(Coef)`has(Coef,Algebra(Fraction(Integer)))`583238 ofirst`1`n`(A)->S`xLazyStreamAggregate&(A,S)``0 ofirst`1`n`(A)->S`xStreamAggregate&(A,S)``0 +ofirst`1`n`(_$)->LyndonWord(VarSet)`dPoincareBirkhoffWittLyndonBasis(VarSet)``583450 +ofirst`1`n`(_$)->S`dOrderedFreeMonoid(S)``583524 ofirst`1`n`(S)->Entry`xIndexedAggregate&(S,Index,Entry)``0 ofirst`1`n`(S)->Union(P,"failed")`xTriangularSetCategory&(S,R,E,V,P)``0 -ofirst`1`n`(_$)->LyndonWord(VarSet)`dPoincareBirkhoffWittLyndonBasis(VarSet)``490728 -ofirst`1`n`(_$)->S`dOrderedFreeMonoid(S)``490802 -ofirst`1`n`(_$)->VarSet`dMagma(VarSet)``490863 -ofirst`1`x`(_$)->Entry`cIndexedAggregate(Index,Entry)`has(Index,OrderedSet)`490948 -ofirst`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``491139 -ofirst`1`x`(_$)->Union(P,"failed")`cTriangularSetCategory(R,E,V,P)``491249 +ofirst`1`n`(_$)->VarSet`dMagma(VarSet)``583676 +ofirst`1`x`(_$)->Entry`cIndexedAggregate(Index,Entry)`has(Index,OrderedSet)`583761 +ofirst`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``583956 +ofirst`1`x`(_$)->Union(P,"failed")`cTriangularSetCategory(R,E,V,P)``584066 ofirst`2`n`(A,NonNegativeInteger)->A`xLazyStreamAggregate&(A,S)``0 ofirst`2`n`(A,NonNegativeInteger)->A`xStreamAggregate&(A,S)``0 -ofirst`2`x`(_$,NonNegativeInteger)->_$`cUnaryRecursiveAggregate(S)``491426 -ofixPredicate`1`n`((B)->Boolean)->(A)->Boolean`pPatternMatchPushDown(S,A,B)``491543 -ofixedDivisor`1`n`(SparseUnivariatePolynomial(Integer))->Integer`pPolynomialNumberTheoryFunctions``491631 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oflexibleArray`1`x`(List(S))->_$`dFlexibleArray(S)``0 -ofloat?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``493340 -ofloat`1`x`(_$)->Flt`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``493428 +ofloat?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``587756 +ofloat`1`x`(_$)->Flt`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``587844 ofloat`2`n`(Integer,Integer)->S`xFloatingPointSystem&(S)``0 -ofloat`2`x`(Integer,Integer)->_$`cFloatingPointSystem``493564 +ofloat`2`x`(Integer,Integer)->_$`cFloatingPointSystem``587980 ofloat`3`n`(Integer,Integer,PositiveInteger)->S`xFloatingPointSystem&(S)``0 -ofloat`3`x`(Integer,Integer,PositiveInteger)->_$`cFloatingPointSystem``493623 +ofloat`3`x`(Integer,Integer,PositiveInteger)->_$`cFloatingPointSystem``588039 ofloor`1`n`(S)->S`xRealNumberSystem&(S)``0 -ofloor`1`x`(_$)->S`cQuotientFieldCategory(S)`has(S,IntegerNumberSystem)`493681 -ofloor`1`x`(_$)->_$`cRealNumberSystem``493757 -ofmecg`4`n`(_$,E,R,_$)->_$`dPolynomialRing(R,E)`AND(has(R,IntegralDomain),has(E,CancellationAbelianMonoid))`493820 -ofmecg`4`n`(_$,NonNegativeInteger,R,_$)->_$`dNewSparseUnivariatePolynomial(R)``493914 -ofmecg`4`n`(_$,NonNegativeInteger,R,_$)->_$`dSparseUnivariatePolynomial(R)``494086 +ofloor`1`x`(_$)->_$`cRealNumberSystem``588097 +ofloor`1`x`(_$)->S`cQuotientFieldCategory(S)`has(S,IntegerNumberSystem)`588160 +oflush`1`x`(_$)->Void`cFileCategory(Name,S)``588236 +ofmecg`4`n`(_$,E,R,_$)->_$`dPolynomialRing(R,E)`AND(has(R,IntegralDomain),has(E,CancellationAbelianMonoid))`588304 +ofmecg`4`n`(_$,NonNegativeInteger,R,_$)->_$`dNewSparseUnivariatePolynomial(R)``588398 +ofmecg`4`n`(_$,NonNegativeInteger,R,_$)->_$`dSparseUnivariatePolynomial(R)``588570 ofmecg`4`n`(_$,Partition,R,_$)->_$`dSymmetricPolynomial(R)`AND(has(Partition,CancellationAbelianMonoid),has(R,IntegralDomain))`0 -ofmecg`4`x`(_$,NonNegativeInteger,R,_$)->_$`dUnivariatePolynomial(x,R)``494180 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+ogcdPolynomial`2`x`(SparseUnivariatePolynomial(_$),SparseUnivariatePolynomial(_$))->SparseUnivariatePolynomial(_$)`cPolynomialFactorizationExplicit``599357 +ogcdprim`1`n`(List(BP))->BP`pHeuGcd(BP)``599475 +ogcdPrimitive`1`n`(List(P))->P`pPolynomialGcdPackage(E,OV,R,P)``599571 +ogcdPrimitive`2`n`(P,P)->P`pPolynomialGcdPackage(E,OV,R,P)``599673 +ogcdPrimitive`2`n`(SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(P))->SparseUnivariatePolynomial(P)`pPolynomialGcdPackage(E,OV,R,P)``599783 +ogderiv`2`n`((Integer)->A,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``599893 +oGE`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``599990 +ogeneralCoefficient`4`x`((NonNegativeInteger,NonNegativeInteger,V)->D,Vector(V),NonNegativeInteger,Vector(SparseUnivariatePolynomial(D)))->D`pFractionFreeFastGaussian(D,V)``600082 +ogeneralInfiniteProduct`3`n`(Stream(Coef),Integer,Integer)->Stream(Coef)`pStreamInfiniteProduct(Coef)``600471 +ogeneralInfiniteProduct`3`x`(UTS,Integer,Integer)->UTS`pInfiniteProductCharacteristicZero(Coef,UTS)``600641 +ogeneralInfiniteProduct`3`x`(UTS,Integer,Integer)->UTS`pInfiniteProductFiniteField(K,UP,Coef,UTS)``600811 +ogeneralInfiniteProduct`3`x`(UTS,Integer,Integer)->UTS`pInfiniteProductPrimeField(Coef,UTS)``600981 +ogeneralInterpolation`4`x`(List(D),(NonNegativeInteger,NonNegativeInteger,V)->D,Vector(VF),List(NonNegativeInteger))->Matrix(SparseUnivariatePolynomial(D))`pFractionFreeFastGaussianFractions(D,V,VF)``601151 +ogeneralInterpolation`4`x`(List(D),(NonNegativeInteger,NonNegativeInteger,V)->D,Vector(V),List(NonNegativeInteger))->Matrix(SparseUnivariatePolynomial(D))`pFractionFreeFastGaussian(D,V)``601608 +ogeneralInterpolation`5`x`(List(D),(NonNegativeInteger,NonNegativeInteger,V)->D,Vector(VF),NonNegativeInteger,NonNegativeInteger)->Stream(Matrix(SparseUnivariatePolynomial(D)))`pFractionFreeFastGaussianFractions(D,V,VF)``602468 +ogeneralInterpolation`5`x`(List(D),(NonNegativeInteger,NonNegativeInteger,V)->D,Vector(V),NonNegativeInteger,NonNegativeInteger)->Stream(Matrix(SparseUnivariatePolynomial(D)))`pFractionFreeFastGaussian(D,V)``602688 +ogeneralizedContinuumHypothesisAssumed?`0`x`()->Boolean`dCardinalNumber``603320 +ogeneralizedContinuumHypothesisAssumed`1`x`(Boolean)->Boolean`dCardinalNumber``603501 +ogeneralizedEigenvector`2`x`(Record(eigval:Union(Fraction(Polynomial(R)),SuchThat(Symbol,Polynomial(R))),eigmult:NonNegativeInteger,eigvec:List(Matrix(Fraction(Polynomial(R))))),Matrix(Fraction(Polynomial(R))))->List(Matrix(Fraction(Polynomial(R))))`pEigenPackage(R)``603764 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+ogeneralPosition`2`x`(_$,List(VarSet))->Record(mval:Matrix(F),invmval:Matrix(F),genIdeal:_$)`dPolynomialIdeals(F,Expon,VarSet,DPoly)``605356 +ogeneralSqFr`1`n`(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))->Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))`pTwoFactorize(F)``605546 +ogeneralTwoFactor`1`n`(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))->Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))`pTwoFactorize(F)``605702 +ogenerate`1`x`(()->S)->_$`dStream(S)``605851 +ogenerate`2`x`(NonNegativeInteger,NonNegativeInteger)->Vector(List(Integer))`pHallBasis``606124 +ogenerate`2`x`((S)->S,S)->_$`dInfiniteTuple(S)``606437 +ogenerate`2`x`((S)->S,S)->_$`dStream(S)``606510 +ogenerateIrredPoly`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pIrredPolyOverFiniteField(GF)``606899 ogenerator`0`n`()->S`xMonogenicAlgebra&(S,R,UP)``0 -ogenerator`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`504903 -ogenerator`0`x`()->_$`cMonogenicAlgebra(R,UP)``505042 -ogenerator`1`n`(NonNegativeInteger)->_$`dAntiSymm(R,lVar)``505107 -ogenerator`1`n`(NonNegativeInteger)->_$`dDeRhamComplex(CoefRing,listIndVar)``505199 -ogenerator`1`x`(NonNegativeInteger)->_$`dFreeNilpotentLie(n,class,R)``505285 -ogenerator`1`x`(_$)->Union(R,"failed")`cFiniteDivisorCategory(F,UP,UPUP,R)``505349 -ogenerators`1`x`(_$)->List(DPoly)`dPolynomialIdeals(F,Expon,VarSet,DPoly)``505453 -ogenerators`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``505534 -ogeneric?`1`n`(_$)->Boolean`dPattern(R)``505609 -ogenericLeftDiscriminant`0`n`()->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`505684 -ogenericLeftMinimalPolynomial`1`n`(_$)->SparseUnivariatePolynomial(Fraction(Polynomial(R)))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`506018 -ogenericLeftNorm`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`506163 -ogenericLeftTraceForm`2`n`(_$,_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`506436 -ogenericLeftTrace`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`506583 -ogenericPosition`2`n`(List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->Record(dpolys:List(DistributedMultivariatePolynomial(lv,F)),coords:List(Integer))`pGroebnerSolve(lv,F,R)``506825 -ogenericRightDiscriminant`0`n`()->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`506970 -ogenericRightMinimalPolynomial`1`n`(_$)->SparseUnivariatePolynomial(Fraction(Polynomial(R)))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`507305 -ogenericRightNorm`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`507455 -ogenericRightTraceForm`2`n`(_$,_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`507695 -ogenericRightTrace`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`507847 -ogeneric`0`n`()->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508054 -ogeneric`1`n`(Symbol)->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508222 -ogeneric`1`n`(Vector(Symbol))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508387 -ogeneric`1`n`(Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508591 -ogeneric`2`n`(Symbol,Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508761 -ogeneric`2`n`(Vector(Symbol),Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``508923 -ogenus`0`n`()->NonNegativeInteger`xFunctionFieldCategory&(S,F,UP,UPUP)``509151 -ogenus`0`x`()->NonNegativeInteger`cFunctionFieldCategory(F,UP,UPUP)``509231 -ogeometric`1`n`(RationalNumber)->()->Integer`pRandomIntegerDistributions``509311 -ogetBadValues`1`n`(_$)->List(Any)`dPattern(R)``509352 -ogetButtonValue`2`x`(String,String)->Float`dAttributeButtons``509493 -ogetCode`1`x`(_$)->SExpression`dFortranCode``509807 -ogetCurve`1`n`(_$)->Curve`dTubePlot(Curve)``509949 -ogetDatabase`1`x`(String)->Database(IndexCard)`pOperationsQuery``510093 -ogetExplanations`2`x`(_$,String)->List(String)`dRoutinesTable``510352 -ogetGoodPrime`1`n`(Integer)->PositiveInteger`pPointsOfFiniteOrderTools(UP,UPUP)``510463 -ogetGraph`2`n`(_$,PositiveInteger)->GraphImage`dTwoDimensionalViewport``510541 -ogetMatch`2`n`(Pattern(R),_$)->Union(S,"failed")`dPatternMatchResult(R,S)``510786 -ogetMeasure`2`x`(_$,Symbol)->Float`dRoutinesTable``510947 -ogetMultiplicationMatrix`0`n`()->Matrix(GF)`dFiniteFieldNormalBasisExtension(GF,extdeg)``511052 -ogetMultiplicationMatrix`0`n`()->Matrix(GF)`dFiniteFieldNormalBasisExtensionByPolynomial(GF,uni)``511146 -ogetMultiplicationMatrix`0`x`()->Matrix(PrimeField(p))`dFiniteFieldNormalBasis(p,extdeg)``511240 -ogetMultiplicationTable`0`n`()->Vector(List(Record(value:GF,index:SingleInteger)))`dFiniteFieldNormalBasisExtension(GF,extdeg)``511334 -ogetMultiplicationTable`0`n`()->Vector(List(Record(value:GF,index:SingleInteger)))`dFiniteFieldNormalBasisExtensionByPolynomial(GF,uni)``511511 -ogetMultiplicationTable`0`x`()->Vector(List(Record(value:PrimeField(p),index:SingleInteger)))`dFiniteFieldNormalBasis(p,extdeg)``511688 -ogetOrder`0`n`()->Record(low:List(S),high:List(S))`pUserDefinedPartialOrdering(S)``511865 -ogetPickedPoints`1`n`(_$)->List(Point(DoubleFloat))`dTwoDimensionalViewport``512050 -ogetRef`1`n`(_$)->Reference(OrderedCompletion(Integer))`dInnerSparseUnivariatePowerSeries(Coef)``512353 -ogetStream`1`n`(_$)->Stream(Record(k:Integer,c:Coef))`dInnerSparseUnivariatePowerSeries(Coef)``512469 -ogetVariableOrder`0`x`()->Record(high:List(Symbol),low:List(Symbol))`pUserDefinedVariableOrdering``512558 -ogetZechTable`0`n`()->PrimitiveArray(SingleInteger)`dFiniteFieldCyclicGroupExtension(GF,extdeg)``512757 -ogetZechTable`0`n`()->PrimitiveArray(SingleInteger)`dFiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol)``512895 -ogetZechTable`0`x`()->PrimitiveArray(SingleInteger)`dFiniteFieldCyclicGroup(p,extdeg)``513024 -ogethi`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pExpertSystemContinuityPackage``513162 -ogethi`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pExpertSystemToolsPackage``513282 -ogethi`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pd01AgentsPackage``513394 -ogetlo`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pExpertSystemContinuityPackage``513514 -ogetlo`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pExpertSystemToolsPackage``513633 -ogetlo`1`x`(Segment(OrderedCompletion(DoubleFloat)))->DoubleFloat`pd01AgentsPackage``513744 -ogoodPoint`2`n`(UPUP,UPUP)->F`pChangeOfVariable(F,UP,UPUP)``513863 -ogoodnessOfFit`1`x`(NumericalOptimizationProblem)->Result`pAnnaNumericalOptimizationPackage``514008 -ogoodnessOfFit`2`x`(List(Expression(Float)),List(Float))->Result`pAnnaNumericalOptimizationPackage``514668 -ogoto`1`x`(SingleInteger)->_$`dFortranCode``515881 -ogradient`2`x`(F,FLAS)->Vector(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``515956 -ograeffe`1`n`(UP)->UP`pComplexRootFindingPackage(R,UP)``516151 -ogramschmidt`1`x`(List(Matrix(Expression(Integer))))->List(Matrix(Expression(Integer)))`pRadicalEigenPackage``516309 -ographCurves`1`n`(List(List(Point(DoubleFloat))))->GraphImage`pViewportPackage``516481 -ographCurves`2`n`(List(List(Point(DoubleFloat))),List(DrawOption))->GraphImage`pViewportPackage``516642 -ographCurves`5`n`(List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption))->GraphImage`pViewportPackage``516864 -ographImage`0`n`()->_$`dGraphImage``517298 -ographState`14`n`(_$,PositiveInteger,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Palette,Integer,Palette,Integer)->Void`dTwoDimensionalViewport``517483 -ographStates`1`n`(_$)->Vector(Record(scaleX:DoubleFloat,scaleY:DoubleFloat,deltaX:DoubleFloat,deltaY:DoubleFloat,points:Integer,connect:Integer,spline:Integer,axes:Integer,axesColor:Palette,units:Integer,unitsColor:Palette,showing:Integer))`dTwoDimensionalViewport``518577 -ographs`1`n`(_$)->Vector(Union(GraphImage,"undefined"))`dTwoDimensionalViewport``518848 -ographs`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``519188 -ogreen`0`x`()->_$`dColor``519361 -ogroebSolve`2`n`(List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->List(List(DistributedMultivariatePolynomial(lv,F)))`pGroebnerSolve(lv,F,R)``519438 -ogroebgen`1`n`(List(DistributedMultivariatePolynomial(lv,F)))->Record(glbase:List(DistributedMultivariatePolynomial(lv,F)),glval:List(Integer))`pLinGroebnerPackage(lv,F)``519734 -ogroebner?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``519771 -ogroebnerFactorize`1`x`(List(Dpol))->List(List(Dpol))`pGroebnerFactorizationPackage(Dom,Expon,VarSet,Dpol)``519866 -ogroebnerFactorize`2`x`(List(Dpol),Boolean)->List(List(Dpol))`pGroebnerFactorizationPackage(Dom,Expon,VarSet,Dpol)``520368 -ogroebnerFactorize`2`x`(List(Dpol),List(Dpol))->List(List(Dpol))`pGroebnerFactorizationPackage(Dom,Expon,VarSet,Dpol)``520956 -ogroebnerFactorize`3`x`(List(Dpol),List(Dpol),Boolean)->List(List(Dpol))`pGroebnerFactorizationPackage(Dom,Expon,VarSet,Dpol)``521573 -ogroebnerIdeal`1`x`(List(DPoly))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``522282 -ogroebner`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))`pLexTriangularPackage(R,ls)``522494 -ogroebner`1`n`(List(Polynomial(R)))->List(Polynomial(R))`pFGLMIfCanPackage(R,ls)``522734 -ogroebner`1`x`(List(Dpol))->List(Dpol)`pGroebnerPackage(Dom,Expon,VarSet,Dpol)``522977 -ogroebner`1`x`(_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``523101 -ogroebner`2`x`(List(Dpol),String)->List(Dpol)`pGroebnerPackage(Dom,Expon,VarSet,Dpol)``523207 -ogroebner`3`x`(List(Dpol),String,String)->List(Dpol)`pGroebnerPackage(Dom,Expon,VarSet,Dpol)``523672 +ogenerator`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`607033 +ogenerator`0`x`()->_$`cMonogenicAlgebra(R,UP)``607172 +ogenerator`1`n`(NonNegativeInteger)->_$`dAntiSymm(R,lVar)``607237 +ogenerator`1`n`(NonNegativeInteger)->_$`dDeRhamComplex(CoefRing,listIndVar)``607329 +ogenerator`1`x`(NonNegativeInteger)->_$`dFreeNilpotentLie(n,class,R)``607415 +ogenerator`1`x`(_$)->Union(R,"failed")`cFiniteDivisorCategory(F,UP,UPUP,R)``607479 +ogenerators`1`x`(_$)->List(DPoly)`dPolynomialIdeals(F,Expon,VarSet,DPoly)``607583 +ogenerators`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``607664 +ogeneric`0`n`()->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``607740 +ogeneric?`1`n`(_$)->Boolean`dPattern(R)``607908 +ogeneric`1`n`(Symbol)->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``607983 +ogeneric`1`n`(Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``608148 +ogeneric`1`n`(Vector(Symbol))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``608318 +ogeneric`2`n`(Symbol,Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``608522 +ogeneric`2`n`(Vector(Symbol),Vector(_$))->_$`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``608684 +ogenericLeftDiscriminant`0`n`()->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`608912 +ogenericLeftMinimalPolynomial`1`n`(_$)->SparseUnivariatePolynomial(Fraction(Polynomial(R)))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`609246 +ogenericLeftNorm`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`609391 +ogenericLeftTrace`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`609664 +ogenericLeftTraceForm`2`n`(_$,_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`609906 +ogenericPosition`2`n`(List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->Record(dpolys:List(DistributedMultivariatePolynomial(lv,F)),coords:List(Integer))`pGroebnerSolve(lv,F,R)``610053 +ogenericRightDiscriminant`0`n`()->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`610198 +ogenericRightMinimalPolynomial`1`n`(_$)->SparseUnivariatePolynomial(Fraction(Polynomial(R)))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`610533 +ogenericRightNorm`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`610683 +ogenericRightTrace`1`n`(_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`610923 +ogenericRightTraceForm`2`n`(_$,_$)->Fraction(Polynomial(R))`dGenericNonAssociativeAlgebra(R,n,ls,gamma)`has(R,IntegralDomain)`611130 +ogenus`0`n`()->NonNegativeInteger`xFunctionFieldCategory&(S,F,UP,UPUP)``611282 +ogenus`0`x`()->NonNegativeInteger`cFunctionFieldCategory(F,UP,UPUP)``611666 +ogenus`0`x`()->NonNegativeInteger`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``612050 +ogenus`0`x`()->NonNegativeInteger`pPackageForAlgebraicFunctionField(K,symb,BLMET)``612149 +ogenus`0`x`()->NonNegativeInteger`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``612248 +ogenus`1`x`(PolyRing)->NonNegativeInteger`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``612347 +ogenusNeg`0`x`()->Integer`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +ogenusNeg`0`x`()->Integer`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +ogenusNeg`0`x`()->Integer`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +ogenusNeg`1`x`(PolyRing)->Integer`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``612427 +ogenusTree`2`x`(NonNegativeInteger,List(DesTree))->NonNegativeInteger`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``612590 +ogenusTreeNeg`2`x`(NonNegativeInteger,List(DesTree))->Integer`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``612842 +ogeometric`1`n`(RationalNumber)->()->Integer`pRandomIntegerDistributions``613211 +ogetBadValues`1`n`(_$)->List(Any)`dPattern(R)``613252 +ogetButtonValue`2`x`(String,String)->Float`dAttributeButtons``613393 +ogetCode`1`x`(_$)->SExpression`dFortranCode``613707 +ogetCurve`1`n`(_$)->Curve`dTubePlot(Curve)``613849 +ogetDatabase`1`x`(String)->Database(IndexCard)`pOperationsQuery``613993 +ogetDatabase`2`x`(String,String)->String`pAxiomServer``0 +ogetDomains`1`x`(Symbol)->Set(Symbol)`pApplicationProgramInterface``614252 +ogetEq`1`x`(F)->F`pRecurrenceOperator(R,F)``614434 +ogetExplanations`2`x`(_$,String)->List(String)`dRoutinesTable``614555 +ogetGoodPrime`1`n`(Integer)->PositiveInteger`pPointsOfFiniteOrderTools(UP,UPUP)``614666 +ogetGraph`2`n`(_$,PositiveInteger)->GraphImage`dTwoDimensionalViewport``614744 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+ogetMultiplicationMatrix`0`x`()->Matrix(PrimeField(p))`dFiniteFieldNormalBasis(p,extdeg)``616144 +ogetMultiplicationTable`0`n`()->Vector(List(Record(value:GF,index:SingleInteger)))`dFiniteFieldNormalBasisExtensionByPolynomial(GF,uni)``616238 +ogetMultiplicationTable`0`n`()->Vector(List(Record(value:GF,index:SingleInteger)))`dFiniteFieldNormalBasisExtension(GF,extdeg)``616415 +ogetMultiplicationTable`0`x`()->Vector(List(Record(value:PrimeField(p),index:SingleInteger)))`dFiniteFieldNormalBasis(p,extdeg)``616592 +ogetOp`1`x`(F)->BasicOperator`pRecurrenceOperator(R,F)``616769 +ogetOrder`0`n`()->Record(low:List(S),high:List(S))`pUserDefinedPartialOrdering(S)``616906 +ogetPickedPoints`1`n`(_$)->List(Point(DoubleFloat))`dTwoDimensionalViewport``617091 +ogetRef`1`n`(_$)->Reference(OrderedCompletion(Integer))`dInnerSparseUnivariatePowerSeries(Coef)``617394 +ogetShiftRec`3`x`(BasicOperator,Kernel(F),Symbol)->Union(Integer,"failed")`pRecurrenceOperator(R,F)`has(R,Ring)`0 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+ogoppaCode`2`x`(Divisor(Places(K)),List(Places(K)))->Matrix(K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +ogoppaCode`2`x`(Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)))->Matrix(K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +ogoppaCode`2`x`(Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),List(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)))->Matrix(K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +oGospersMethod`3`n`(Q,V,()->V)->Union(Q,"failed")`pGosperSummationMethod(E,V,R,P,Q)``620353 +ogoto`1`x`(SingleInteger)->_$`dFortranCode``620925 +ogradient`2`x`(F,FLAS)->Vector(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``621000 +ograeffe`1`n`(UP)->UP`pComplexRootFindingPackage(R,UP)``621195 +ogramschmidt`1`x`(List(Matrix(Expression(Integer))))->List(Matrix(Expression(Integer)))`pRadicalEigenPackage``621353 +ographCurves`1`n`(List(List(Point(DoubleFloat))))->GraphImage`pViewportPackage``621525 +ographCurves`2`n`(List(List(Point(DoubleFloat))),List(DrawOption))->GraphImage`pViewportPackage``621686 +ographCurves`5`n`(List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger,List(DrawOption))->GraphImage`pViewportPackage``621908 +ographImage`0`n`()->_$`dGraphImage``622342 +ographs`1`n`(_$)->Vector(Union(GraphImage,"undefined"))`dTwoDimensionalViewport``622527 +ographs`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``622867 +ographState`14`n`(_$,PositiveInteger,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Palette,Integer,Palette,Integer)->Void`dTwoDimensionalViewport``623040 +ographStates`1`n`(_$)->Vector(Record(scaleX:DoubleFloat,scaleY:DoubleFloat,deltaX:DoubleFloat,deltaY:DoubleFloat,points:Integer,connect:Integer,spline:Integer,axes:Integer,axesColor:Palette,units:Integer,unitsColor:Palette,showing:Integer))`dTwoDimensionalViewport``624134 +ogreen`0`x`()->_$`dColor``624405 +ogroebgen`1`n`(List(DistributedMultivariatePolynomial(lv,F)))->Record(glbase:List(DistributedMultivariatePolynomial(lv,F)),glval:List(Integer))`pLinGroebnerPackage(lv,F)``624482 +ogroebner`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls)))`pLexTriangularPackage(R,ls)``624519 +ogroebner`1`n`(List(Polynomial(R)))->List(Polynomial(R))`pFGLMIfCanPackage(R,ls)``624747 +ogroebner?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``624978 +ogroebner`1`x`(_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``625073 +ogroebner`1`x`(List(Dpol))->List(Dpol)`pGroebnerPackage(Dom,Expon,VarSet,Dpol)``625179 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+ogroebSolve`2`n`(List(DistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->List(List(DistributedMultivariatePolynomial(lv,F)))`pGroebnerSolve(lv,F,R)``633029 oground?`1`n`(S)->Boolean`xFiniteAbelianMonoidRing&(S,R,E)``0 oground?`1`n`(S)->Boolean`xFunctionSpace&(S,R)``0 -oground?`1`x`(_$)->Boolean`cFiniteAbelianMonoidRing(R,E)``524060 -oground?`1`x`(_$)->Boolean`cFunctionSpace(R)``524151 oground`1`n`(S)->R`xFiniteAbelianMonoidRing&(S,R,E)``0 oground`1`n`(S)->R`xFunctionSpace&(S,R)``0 -oground`1`x`(_$)->R`cFiniteAbelianMonoidRing(R,E)``524221 -oground`1`x`(_$)->R`cFunctionSpace(R)``524299 -ohMonic`1`n`(Dpol)->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``524426 -ohalfExtendedResultant1`2`n`(_$,_$)->Record(resultant:R,coef1:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`524461 -ohalfExtendedResultant2`2`n`(_$,_$)->Record(resultant:R,coef2:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`524647 -ohalfExtendedSubResultantGcd1`2`n`(_$,_$)->Record(gcd:_$,coef1:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`524833 -ohalfExtendedSubResultantGcd1`2`x`(_$,_$)->Record(gcd:_$,coef1:_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`525031 -ohalfExtendedSubResultantGcd2`2`n`(_$,_$)->Record(gcd:_$,coef2:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`525250 -ohalfExtendedSubResultantGcd2`2`x`(_$,_$)->Record(gcd:_$,coef2:_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`525455 -oharmonic`1`x`(Integer)->Fraction(Integer)`pIntegerNumberTheoryFunctions``525681 -ohas?`2`x`(_$,String)->Boolean`dBasicOperator``525788 -ohasHi`1`x`(_$)->Boolean`dUniversalSegment(S)``525869 -ohasPredicate?`1`n`(_$)->Boolean`dPattern(R)``525947 -ohasSolution?`2`x`(M,Col)->Boolean`pLinearSystemMatrixPackage(F,Row,Col,M)``526027 -ohasSolution?`2`x`(Matrix(F),Vector(F))->Boolean`pLinearSystemMatrixPackage1(F)``526118 -ohasTopPredicate?`1`n`(_$)->Boolean`dPattern(R)``526209 +oground?`1`x`(_$)->Boolean`cFiniteAbelianMonoidRing(R,E)``633325 +oground?`1`x`(_$)->Boolean`cFunctionSpace(R)``633416 +oground?`1`x`(_$)->Boolean`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +oground?`1`x`(_$)->Boolean`dMyExpression(q,R)``0 +oground`1`x`(_$)->R`cFiniteAbelianMonoidRing(R,E)``633486 +oground`1`x`(_$)->R`cFunctionSpace(R)``633564 +oGT`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``633691 +oguess`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguess`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguess`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``633782 +oguess`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguess`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``633998 +oguess`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguess`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguess`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguess`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``634214 +oguess`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguess`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``634395 +oguess`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguess`3`x`(List(AlgebraicNumber),List((List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguess`3`x`(List(F),List((List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguess`3`x`(List(F),List((List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))),List(Symbol))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``634576 +oguess`3`x`(List(Fraction(Integer)),List((List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguess`3`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))),List(Symbol))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``634882 +oguess`3`x`(List(Fraction(Polynomial(Integer))),List((List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguess`4`x`(List(AlgebraicNumber),List((List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguess`4`x`(List(F),List((List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguess`4`x`(List(F),List((List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``635188 +oguess`4`x`(List(Fraction(Integer)),List((List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguess`4`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List((List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``635451 +oguess`4`x`(List(Fraction(Polynomial(Integer))),List((List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))),List(Symbol),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessADE`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessADE`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessADE`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``635724 +oguessADE`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessADE`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``635954 +oguessADE`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessADE`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessADE`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessADE`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`636184 +oguessADE`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessADE`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``636389 +oguessADE`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessADE`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessADE`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessADE`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``636594 +oguessADE`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessADE`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``636788 +oguessADE`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessAlg`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessAlg`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessAlg`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``636982 +oguessAlg`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessAlg`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``637278 +oguessAlg`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessAlg`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessAlg`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessAlg`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``637574 +oguessAlg`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessAlg`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``637847 +oguessAlg`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessBinRat`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessBinRat`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessBinRat`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``638120 +oguessBinRat`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessBinRat`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``638336 +oguessBinRat`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessBinRat`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessBinRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessBinRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`638552 +oguessBinRat`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessBinRat`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``638791 +oguessBinRat`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessBinRat`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessBinRat`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessBinRat`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``639030 +oguessBinRat`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessBinRat`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``639246 +oguessBinRat`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessExpRat`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessExpRat`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessExpRat`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``639462 +oguessExpRat`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessExpRat`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``639655 +oguessExpRat`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessExpRat`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessExpRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessExpRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`639848 +oguessExpRat`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessExpRat`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``640079 +oguessExpRat`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessExpRat`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessExpRat`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessExpRat`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``640310 +oguessExpRat`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessExpRat`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``640515 +oguessExpRat`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessHolo`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessHolo`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessHolo`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``640720 +oguessHolo`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessHolo`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``641024 +oguessHolo`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessHolo`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessHolo`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessHolo`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``641328 +oguessHolo`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessHolo`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``641616 +oguessHolo`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessHP`1`x`((List(GuessOption))->HPSPEC)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``641904 +oguessHP`1`x`((List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(AlgebraicNumber))->Stream(UnivariateFormalPowerSeries(AlgebraicNumber)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(--AlgebraicNumber))->AlgebraicNumber,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->SparseUnivariatePolynomial(AlgebraicNumber),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(AlgebraicNumber)))->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessHP`1`x`((List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Integer)))->Stream(UnivariateFormalPowerSeries(Fraction(Integer))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePol--ynomial(Integer))->Integer,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->SparseUnivariatePolynomial(Fraction(Integer)),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Integer)))->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessHP`1`x`((List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))->Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegati--veInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer)))->Polynomial(Integer),AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->SparseUnivariatePolynomial(Fraction(Polynomial(Integer))),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Polynomial(Integer))))->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Express--ion(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessHP`1`x`((List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F))->F,AF:(NonNegativeInteger,NonNegativeInteger,Univari--ateFormalPowerSeries(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(F)))->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessHP`1`x`((List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(EXPRR,Symbol)->Stream(EXPRR),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S))->S,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseU--nivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,EXPRR)->EXPRR,C:(NonNegativeInteger)->List(S)))->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``642048 +oguessPade`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessPade`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessPade`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``642192 +oguessPade`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessPade`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``642525 +oguessPade`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessPade`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessPade`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessPade`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``642858 +oguessPade`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessPade`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``643123 +oguessPade`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessPRec`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessPRec`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessPRec`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``643388 +oguessPRec`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessPRec`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``643661 +oguessPRec`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessPRec`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessPRec`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessPRec`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`643934 +oguessPRec`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessPRec`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``644200 +oguessPRec`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessPRec`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessPRec`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessPRec`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``644466 +oguessPRec`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessPRec`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``644723 +oguessPRec`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessRat`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessRat`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessRat`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``644980 +oguessRat`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessRat`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``645262 +oguessRat`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessRat`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessRat`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`645544 +oguessRat`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessRat`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``645816 +oguessRat`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessRat`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessRat`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessRat`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``646088 +oguessRat`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessRat`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``646334 +oguessRat`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessRec`1`x`(List(AlgebraicNumber))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessRec`1`x`(List(F))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessRec`1`x`(List(F))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``646580 +oguessRec`1`x`(List(Fraction(Integer)))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessRec`1`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``646768 +oguessRec`1`x`(List(Fraction(Polynomial(Integer))))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +oguessRec`1`x`(Symbol)->(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oguessRec`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oguessRec`1`x`(Symbol)->(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`646956 +oguessRec`1`x`(Symbol)->(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oguessRec`1`x`(Symbol)->(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``647120 +oguessRec`1`x`(Symbol)->(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oguessRec`2`x`(List(AlgebraicNumber),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessAlgebraicNumber``0 +oguessRec`2`x`(List(F),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessFinite(F)``0 +oguessRec`2`x`(List(F),List(GuessOption))->List(Record(function:EXPRR,order:NonNegativeInteger))`pGuess(F,S,EXPRR,R,retract,coerce)``647284 +oguessRec`2`x`(List(Fraction(Integer)),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessInteger``0 +oguessRec`2`x`(List(Fraction(MyUnivariatePolynomial(q,Integer))),List(GuessOption))->List(Record(function:MyExpression(q,Integer),order:NonNegativeInteger))`pGuessUnivariatePolynomial(q)``647436 +oguessRec`2`x`(List(Fraction(Polynomial(Integer))),List(GuessOption))->List(Record(function:Expression(Integer),order:NonNegativeInteger))`pGuessPolynomial``0 +ohadamard`2`x`(UnivariateFormalPowerSeries(Coef),UnivariateFormalPowerSeries(Coef))->UnivariateFormalPowerSeries(Coef)`pUnivariateFormalPowerSeriesFunctions(Coef)``0 +ohalfExtendedResultant1`2`n`(_$,_$)->Record(resultant:R,coef1:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`647588 +ohalfExtendedResultant2`2`n`(_$,_$)->Record(resultant:R,coef2:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`647774 +ohalfExtendedSubResultantGcd1`2`n`(_$,_$)->Record(gcd:_$,coef1:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`647960 +ohalfExtendedSubResultantGcd1`2`x`(_$,_$)->Record(gcd:_$,coef1:_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`648158 +ohalfExtendedSubResultantGcd2`2`n`(_$,_$)->Record(gcd:_$,coef2:_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`648377 +ohalfExtendedSubResultantGcd2`2`x`(_$,_$)->Record(gcd:_$,coef2:_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`648582 +oharmonic`1`x`(Integer)->Fraction(Integer)`pIntegerNumberTheoryFunctions``648808 +ohas?`2`x`(_$,String)->Boolean`dBasicOperator``648915 +ohash`1`n`(_$)->Integer`dIndexedString(mn)``648996 ohash`1`n`(S)->SingleInteger`xSetCategory&(S)``0 -ohash`1`n`(_$)->Integer`dIndexedString(mn)``526288 -ohash`1`x`(_$)->Integer`dDoubleFloat``526350 -ohash`1`x`(_$)->SingleInteger`cSetCategory``526406 -ohash`1`x`(_$)->_$`cIntegerNumberSystem``526465 -ohasoln`2`n`(List(GR),List(GR))->Record(sysok:Boolean,z0:List(GR),n0:List(GR))`pParametricLinearEquations(R,Var,Expon,GR)``526522 -ohclf`2`n`(_$,_$)->_$`dFreeMonoid(S)``526767 -ohclf`2`n`(_$,_$)->_$`dOrderedFreeMonoid(S)``526945 -ohconcat`1`n`(List(_$))->_$`dOutputForm``527113 -ohconcat`2`n`(_$,_$)->_$`dOutputForm``527192 -ohcrf`2`n`(_$,_$)->_$`dFreeMonoid(S)``527275 -ohcrf`2`n`(_$,_$)->_$`dOrderedFreeMonoid(S)``527454 -ohdmpToDmp`1`n`(HomogeneousDistributedMultivariatePolynomial(lv,R))->DistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``527623 -ohdmpToP`1`n`(HomogeneousDistributedMultivariatePolynomial(lv,R))->Polynomial(R)`pPolToPol(lv,R)``527712 +ohash`1`x`(_$)->_$`cIntegerNumberSystem``649058 +ohash`1`x`(_$)->Integer`dDoubleFloat``649115 +ohash`1`x`(_$)->SingleInteger`cSetCategory``649171 +ohash`1`x`(_$)->SingleInteger`dArrayStack(S)`has(S,SetCategory)`649230 +ohash`1`x`(_$)->SingleInteger`dDequeue(S)`has(S,SetCategory)`649323 +ohash`1`x`(_$)->SingleInteger`dHeap(S)`has(S,SetCategory)`649410 +ohash`1`x`(_$)->SingleInteger`dQueue(S)`has(S,SetCategory)`649491 +ohash`1`x`(_$)->SingleInteger`dStack(S)`has(S,SetCategory)`649574 +ohasHi`1`x`(_$)->Boolean`dUniversalSegment(S)``649657 +ohasoln`2`n`(List(GR),List(GR))->Record(sysok:Boolean,z0:List(GR),n0:List(GR))`pParametricLinearEquations(R,Var,Expon,GR)``649735 +ohasPredicate?`1`n`(_$)->Boolean`dPattern(R)``649980 +ohasSolution?`2`x`(Matrix(F),Vector(F))->Boolean`pLinearSystemMatrixPackage1(F)``650060 +ohasSolution?`2`x`(M,Col)->Boolean`pLinearSystemMatrixPackage(F,Row,Col,M)``650151 +ohasTopPredicate?`1`n`(_$)->Boolean`dPattern(R)``650242 +oHausdorff`3`n`(XPOLY,XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``650321 +ohclf`2`n`(_$,_$)->_$`dFreeMonoid(S)``650442 +ohclf`2`n`(_$,_$)->_$`dOrderedFreeMonoid(S)``650620 +ohconcat`1`n`(List(_$))->_$`dOutputForm``650968 +ohconcat`2`n`(_$,_$)->_$`dOutputForm``651047 +ohcrf`2`n`(_$,_$)->_$`dFreeMonoid(S)``651130 +ohcrf`2`n`(_$,_$)->_$`dOrderedFreeMonoid(S)``651309 +ohdmpToDmp`1`n`(HomogeneousDistributedMultivariatePolynomial(lv,R))->DistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``651665 +ohdmpToP`1`n`(HomogeneousDistributedMultivariatePolynomial(lv,R))->Polynomial(R)`pPolToPol(lv,R)``651754 +ohead`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +ohead`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``651842 +ohead`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``651958 +ohead`1`x`(_$)->Record(gen:S,exp:Integer)`dDivisor(S)``0 oheadReduce`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 oheadReduce`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oheadReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``527800 -oheadReduce`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``528112 +oheadReduce`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``652228 +oheadReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``652490 oheadReduced?`1`n`(S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -oheadReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``528374 +oheadReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``652802 oheadReduced?`2`n`(P,S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 oheadReduced?`2`n`(S,List(S))->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 oheadReduced?`2`n`(S,S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -oheadReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``528557 -oheadReduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``528718 -oheadReduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``528889 +oheadReduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``652985 +oheadReduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``653110 +oheadReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``653281 oheadRemainder`2`n`(P,S)->Record(num:P,den:R)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -oheadRemainder`2`x`(P,_$)->Record(num:P,den:R)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`529014 -ohead`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -ohead`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``529312 -ohead`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``529428 -oheapSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``529684 -oheap`1`x`(List(S))->_$`dHeap(S)``529807 -oheight`0`n`()->Integer`dOutputForm``529898 +oheadRemainder`2`x`(P,_$)->Record(num:P,den:R)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`653442 +oheap`1`x`(List(S))->_$`dHeap(S)``653740 +oheapSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``653933 +oheight`0`n`()->Integer`dOutputForm``654056 +oheight`1`n`(_$)->Integer`dOutputForm``654132 +oheight`1`n`(_$)->NonNegativeInteger`dKernel(S)``654206 oheight`1`n`(S)->NonNegativeInteger`xExpressionSpace&(S)``0 -oheight`1`n`(UP)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``529974 -oheight`1`n`(_$)->Integer`dOutputForm``530081 -oheight`1`n`(_$)->NonNegativeInteger`dKernel(S)``530155 -oheight`1`x`(_$)->NonNegativeInteger`cDequeueAggregate(S)``530218 -oheight`1`x`(_$)->NonNegativeInteger`cExpressionSpace``530340 -ohenselFact`2`n`(UP,Boolean)->Record(contp:Integer,factors:List(Record(irr:UP,pow:Integer)))`pGaloisGroupFactorizer(UP)``530628 -ohenselFact`2`n`(ZP,Boolean)->Record(contp:Integer,factors:List(Record(irr:ZP,pow:Integer)))`pUnivariateFactorize(ZP)``530948 -ohermiteH`2`x`(NonNegativeInteger,R)->R`pOrthogonalPolynomialFunctions(R)``531237 -ohermite`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pPolynomialNumberTheoryFunctions``531403 -ohermite`1`x`(M)->M`pSmithNormalForm(R,Row,Col,M)``531676 -ohessian`2`x`(F,FLAS)->Matrix(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``531757 -ohexDigit?`1`x`(_$)->Boolean`dCharacter``531951 -ohexDigit`0`x`()->_$`dCharacterClass``532085 -ohex`1`x`(Fraction(Integer))->_$`dHexadecimalExpansion``532207 -ohi`1`x`(_$)->S`cSegmentCategory(S)``532283 -ohighCommonTerms`2`x`(_$,_$)->_$`cFreeAbelianMonoidCategory(S,E)`has(E,OrderedAbelianMonoid)`532385 -ohigh`1`x`(_$)->S`cSegmentCategory(S)``532637 -ohitherPlane`2`x`(_$,Float)->Void`dThreeDimensionalViewport``532729 -ohomogeneous?`1`n`(_$)->Boolean`dAntiSymm(R,lVar)``532910 -ohomogeneous?`1`n`(_$)->Boolean`dDeRhamComplex(CoefRing,listIndVar)``533000 +oheight`1`n`(UP)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``654269 +oheight`1`x`(_$)->NonNegativeInteger`cDequeueAggregate(S)``654376 +oheight`1`x`(_$)->NonNegativeInteger`cExpressionSpace``654502 +oheight`1`x`(_$)->NonNegativeInteger`dDequeue(S)``654790 +ohenselFact`2`n`(UP,Boolean)->Record(contp:Integer,factors:List(Record(irr:UP,pow:Integer)))`pGaloisGroupFactorizer(UP)``654879 +ohenselFact`2`n`(ZP,Boolean)->Record(contp:Integer,factors:List(Record(irr:ZP,pow:Integer)))`pUnivariateFactorize(ZP)``655199 +oHenselLift`4`n`(TP,List(TP),RP,PositiveInteger)->Record(plist:List(TP),modulo:RP)`pGeneralHenselPackage(RP,TP)``655488 +ohermite`1`n`(Integer)->SparseUnivariatePolynomial(Integer)`pPolynomialNumberTheoryFunctions``655700 +ohermite`1`x`(M)->M`pSmithNormalForm(R,Row,Col,M)``655977 +ohermiteH`2`x`(NonNegativeInteger,R)->R`pOrthogonalPolynomialFunctions(R)``656058 +oHermiteIntegrate`2`n`(Fraction(UP),(UP)->UP)->Record(answer:Fraction(UP),logpart:Fraction(UP),specpart:Fraction(UP),polypart:UP)`pTranscendentalHermiteIntegration(F,UP)``656224 +oHermiteIntegrate`2`n`(R,(UP)->UP)->Record(answer:R,logpart:R)`pAlgebraicHermiteIntegration(F,UP,UPUP,R)``656658 +ohessian`2`x`(F,FLAS)->Matrix(F)`pMultiVariableCalculusFunctions(S,F,FLAF,FLAS)``656800 +ohex`1`x`(Fraction(Integer))->_$`dHexadecimalExpansion``656994 +ohexDigit`0`x`()->_$`dCharacterClass``657070 +ohexDigit?`1`x`(_$)->Boolean`dCharacter``657167 +ohi`1`x`(_$)->S`cSegmentCategory(S)``657497 +ohigh`1`x`(_$)->S`cSegmentCategory(S)``657603 +ohighCommonTerms`2`x`(_$,_$)->_$`cFreeAbelianMonoidCategory(S,E)`has(E,OrderedAbelianMonoid)`657699 +ohitherPlane`2`x`(_$,Float)->Void`dThreeDimensionalViewport``657937 +ohMonic`1`n`(Dpol)->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``658118 +ohomogeneous?`1`n`(_$)->Boolean`dAntiSymm(R,lVar)``658153 +ohomogeneous?`1`n`(_$)->Boolean`dDeRhamComplex(CoefRing,listIndVar)``658243 +ohomogeneous`1`x`(Boolean)->_$`dGuessOption``658353 +ohomogeneous`1`x`(List(GuessOption))->Boolean`dGuessOptionFunctions0``658522 +ohomogenize`1`x`(_$)->_$`cProjectiveSpaceCategory(K)``658653 +ohomogenize`2`x`(DistributedMultivariatePolynomial(symb,K),Integer)->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +ohomogenize`2`x`(DistributedMultivariatePolynomial(symb,K),Integer)->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +ohomogenize`2`x`(_$,Integer)->_$`cProjectiveSpaceCategory(K)``658748 +ohomogenize`2`x`(PolyRing,Integer)->PolyRing`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +ohomogenize`2`x`(PolyRing,Integer)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``658836 ohorizConcat`2`n`(S,S)->S`xMatrixCategory&(S,R,Row,Col)``0 -ohorizConcat`2`x`(_$,_$)->_$`cMatrixCategory(R,Row,Col)``533110 -ohspace`1`n`(Integer)->_$`dOutputForm``533344 -ohtrigs`1`x`(F)->F`pTranscendentalManipulations(R,F)``533407 -ohue`1`n`(Point(R))->R`pPointPackage(R)``533508 -ohue`1`x`(_$)->Color`dPalette``533831 -ohue`1`x`(_$)->Integer`dColor``533909 -ohyperelliptic`0`n`()->Union(UP,"failed")`xFunctionFieldCategory&(S,F,UP,UPUP)``533985 -ohyperelliptic`0`x`()->Union(UP,"failed")`cFunctionFieldCategory(F,UP,UPUP)``534122 -ohypergeometric0F1`2`x`(Complex(DoubleFloat),Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``534259 -ohypergeometric0F1`2`x`(DoubleFloat,DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``534349 -oiCompose`2`n`(_$,_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)``534439 -oiExquo`3`n`(_$,_$,Boolean)->Union(_$,"failed")`dInnerSparseUnivariatePowerSeries(Coef)``534655 -oiFTable`1`x`(List(Record(key:Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float))))->_$`dODEIntensityFunctionsTable``534835 -oid`1`x`(A)->A`pMappingPackage1(A)``534928 -oidealSimplify`1`n`(_$)->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``534960 -oideal`1`n`(Vector(A))->_$`dFractionalIdeal(R,F,UP,A)``535258 -oideal`1`x`(List(DPoly))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``535337 -oideal`1`x`(_$)->FractionalIdeal(UP,Fraction(UP),UPUP,R)`cFiniteDivisorCategory(F,UP,UPUP,R)``535442 -oidealiserMatrix`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pIntegralBasisTools(R,UP,F)``535520 -oidealiser`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pIntegralBasisTools(R,UP,F)``535688 -oidealiser`3`n`(Matrix(R),Matrix(R),R)->Matrix(R)`pIntegralBasisTools(R,UP,F)``535787 -oidentification`2`n`(_$,_$)->List(Equation(R))`dLieExponentials(VarSet,R,Order)``535942 -oidentityMatrix`1`x`(NonNegativeInteger)->_$`dThreeDimensionalMatrix(R)`has(R,Ring)`536156 -oidentitySquareMatrix`2`x`(Symbol,Polynomial(Integer))->FortranCode`pFortranCodePackage1``536247 -oiflist2Result`1`x`(Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float))->Result`pExpertSystemToolsPackage``536305 -oignore?`1`n`(String)->Boolean`pDefiniteIntegrationTools(R,F)``536391 -oiiGamma`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``536552 -oiiabs`1`n`(F)->F`pFunctionalSpecialFunction(R,F)``536610 -oiiacos`1`n`(F)->F`pElementaryFunction(R,F)``536666 -oiiacosh`1`n`(F)->F`pElementaryFunction(R,F)``536722 -oiiacot`1`n`(F)->F`pElementaryFunction(R,F)``536779 -oiiacoth`1`n`(F)->F`pElementaryFunction(R,F)``536835 -oiiacsc`1`n`(F)->F`pElementaryFunction(R,F)``536892 -oiiacsch`1`n`(F)->F`pElementaryFunction(R,F)``536948 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-oiiperm`1`n`(List(F))->F`pCombinatorialFunction(R,F)``538017 -oiipow`1`n`(List(F))->F`pCombinatorialFunction(R,F)``538074 -oiisec`1`n`(F)->F`pElementaryFunction(R,F)``538130 -oiisech`1`n`(F)->F`pElementaryFunction(R,F)``538185 -oiisin`1`n`(F)->F`pElementaryFunction(R,F)``538241 -oiisinh`1`n`(F)->F`pElementaryFunction(R,F)``538296 -oiisqrt2`0`n`()->F`pElementaryFunction(R,F)``538352 -oiisqrt3`0`n`()->F`pElementaryFunction(R,F)``538408 -oiitan`1`n`(F)->F`pElementaryFunction(R,F)``538464 -oiitanh`1`n`(F)->F`pElementaryFunction(R,F)``538519 -oimagE`1`x`(_$)->R`cOctonionCategory(R)``538575 -oimagI`1`x`(_$)->R`cOctonionCategory(R)``538657 -oimagI`1`x`(_$)->R`cQuaternionCategory(R)``538739 -oimagJ`1`x`(_$)->R`cOctonionCategory(R)``538823 -oimagJ`1`x`(_$)->R`cQuaternionCategory(R)``538905 -oimagK`1`x`(_$)->R`cOctonionCategory(R)``538989 -oimagK`1`x`(_$)->R`cQuaternionCategory(R)``539071 -oimag`1`x`(F)->Expression(R)`pComplexTrigonometricManipulations(R,F)``539155 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-oindicialEquations`2`n`(LQ,UP)->List(Record(center:UP,equation:UP))`pPrimitiveRatDE(F,UP,L,LQ)``544242 -oinfLex?`4`n`(_$,_$,(V,V)->Boolean,(C,C)->Boolean)->Boolean`dSplittingNode(V,C)``544506 +oindices`1`x`(_$)->List(Index)`cIndexedAggregate(Index,Entry)``669250 +oindiceSubResultant`3`n`(polR,polR,NonNegativeInteger)->polR`pPseudoRemainderSequence(R,polR)``669366 +oindiceSubResultantEuclidean`3`n`(polR,polR,NonNegativeInteger)->Record(coef1:polR,coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``669486 +oindicialEquation`2`n`(L,F)->UP`pPrimitiveRatDE(F,UP,L,LQ)``669694 +oindicialEquation`2`n`(LQ,F)->UP`pPrimitiveRatDE(F,UP,L,LQ)``669790 +oindicialEquationAtInfinity`1`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)))->UP`pRationalLODE(F,UP)``669886 +oindicialEquationAtInfinity`1`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)))->UP`pRationalLODE(F,UP)``669986 +oindicialEquations`1`n`(L)->List(Record(center:UP,equation:UP))`pPrimitiveRatDE(F,UP,L,LQ)``670086 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-oinfRittWu?`2`x`(_$,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``545191 -oinf`1`x`(_$)->R`cIntervalCategory(R)``545347 -oinfieldIntegrate`2`x`(Fraction(Polynomial(F)),Symbol)->Union(Fraction(Polynomial(F)),"failed")`pRationalFunctionIntegration(F)``545409 -oinfieldint`1`n`(Fraction(UP))->Union(Fraction(UP),"failed")`pRationalIntegration(F,UP)``545545 -oinfinite?`1`x`(_$)->Boolean`dOnePointCompletion(R)``545682 -oinfinite?`1`x`(_$)->Boolean`dOrderedCompletion(R)``545740 -oinfiniteProduct`1`n`(Stream(Coef))->Stream(Coef)`pStreamInfiniteProduct(Coef)``545814 -oinfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductCharacteristicZero(Coef,UTS)``545960 -oinfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductFiniteField(K,UP,Coef,UTS)``546106 -oinfiniteProduct`1`x`(UTS)->UTS`pInfiniteProductPrimeField(Coef,UTS)``546252 -oinfinityNorm`1`n`(UP)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``546398 -oinfinity`0`x`()->OnePointCompletion(Integer)`pInfinity``546511 -oinfinity`0`x`()->_$`dOnePointCompletion(R)``546554 -oinfix?`1`n`(_$)->Boolean`dOutputForm``546597 -oinfix`2`n`(_$,List(_$))->_$`dOutputForm``546707 -oinfix`3`n`(_$,_$,_$)->_$`dOutputForm``546850 -oinitTable!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``546938 +oinfRittWu?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``672929 +oinfRittWu?`2`x`(_$,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``673126 +oinfRittWu?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``673282 +oinfRittWu?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``673394 +oinGroundField?`1`x`(_$)->Boolean`cExtensionField(F)``673506 +oinHallBasis?`4`x`(Integer,Integer,Integer,Integer)->Boolean`pHallBasis``673613 oinit`0`n`()->A`xQuotientFieldCategory&(A,S)``0 oinit`0`n`()->S`xFiniteFieldCategory&(S)``0 oinit`0`n`()->S`xIntegerNumberSystem&(S)``0 oinit`0`n`()->S`xUnivariatePolynomialCategory&(S,R)``0 -oinit`0`x`()->_$`cStepThrough``546994 +oinit`0`x`()->_$`cStepThrough``674010 oinit`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oinit`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``547055 +oinit`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``674071 oinitial`1`n`(A)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -oinitial`1`x`(_$)->_$`cDifferentialPolynomialCategory(R,S,V,E)``547280 -oinitializeGroupForWordProblem`1`x`(_$)->Void`dPermutationGroup(S)``547432 -oinitializeGroupForWordProblem`3`x`(_$,Integer,Integer)->Void`dPermutationGroup(S)``547870 +oinitial`1`x`(_$)->_$`cDifferentialPolynomialCategory(R,S,V,E)``674296 +oinitializeGroupForWordProblem`1`x`(_$)->Void`dPermutationGroup(S)``674448 +oinitializeGroupForWordProblem`3`x`(_$,Integer,Integer)->Void`dPermutationGroup(S)``674888 +oinitializeParamOfPlaces`1`x`(DesTree)->Void`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``675354 +oinitializeParamOfPlaces`2`x`(DesTree,List(PolyRing))->Void`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``675478 oinitiallyReduce`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 oinitiallyReduce`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oinitiallyReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``548335 -oinitiallyReduce`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``548658 +oinitiallyReduce`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``675668 +oinitiallyReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``675940 oinitiallyReduced?`1`n`(S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -oinitiallyReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``548930 +oinitiallyReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``676263 oinitiallyReduced?`2`n`(P,S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 oinitiallyReduced?`2`n`(S,List(S))->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 oinitiallyReduced?`2`n`(S,S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -oinitiallyReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``549205 -oinitiallyReduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``549437 -oinitiallyReduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``549618 +oinitiallyReduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``676539 +oinitiallyReduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``676723 +oinitiallyReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``676904 oinitials`1`n`(S)->List(P)`xTriangularSetCategory&(S,R,E,V,P)``0 -oinitials`1`x`(_$)->List(P)`cTriangularSetCategory(R,E,V,P)``549802 -oinnerEigenvectors`3`n`(Matrix(K),Par,(SparseUnivariatePolynomial(K))->Factored(SparseUnivariatePolynomial(K)))->List(Record(outval:F,outmult:Integer,outvect:List(Matrix(F))))`pInnerNumericEigenPackage(K,F,Par)``549920 -oinnerSolve1`2`n`(Polynomial(K),Par)->List(F)`pInnerNumericFloatSolvePackage(K,F,Par)``550264 -oinnerSolve1`2`n`(SparseUnivariatePolynomial(K),Par)->List(F)`pInnerNumericFloatSolvePackage(K,F,Par)``550383 -oinnerSolve`4`n`(List(Polynomial(K)),List(Polynomial(K)),List(Symbol),Par)->List(List(F))`pInnerNumericFloatSolvePackage(K,F,Par)``550515 -oinnerint`5`x`(F,Symbol,OrderedCompletion(F),OrderedCompletion(F),Boolean)->Union(f1:OrderedCompletion(F),f2:List(OrderedCompletion(F)),fail:"failed",pole:"potentialPole")`pElementaryFunctionDefiniteIntegration(R,F)``550873 -oinput`1`x`(_$)->Union((List(InputForm))->InputForm,"failed")`dBasicOperator``550957 -oinput`2`x`(_$,(List(InputForm))->InputForm)->_$`dBasicOperator``551071 -oinrootof`2`n`(SparseUnivariatePolynomial(F),F)->F`pAlgebraicFunction(R,F)``551291 -oinsert!`1`x`(Record(key:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(st--r:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))))->_$`dIntegrationFunctionsTable``551357 -oinsert!`1`x`(Record(key:Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float)))->_$`dODEIntensityFunctionsTable``551424 -oinsert!`2`n`(Key,Entry)->Void`pTabulatedComputationPackage(Key,Entry)``551491 +oinitials`1`x`(_$)->List(P)`cTriangularSetCategory(R,E,V,P)``677136 +oinitParLocLeaves`1`x`(DesTree)->Void`pDesingTreePackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``677254 +oinitTable!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``677385 +oinnerEigenvectors`3`n`(Matrix(K),Par,(SparseUnivariatePolynomial(K))->Factored(SparseUnivariatePolynomial(K)))->List(Record(outval:F,outmult:Integer,outvect:List(Matrix(F))))`pInnerNumericEigenPackage(K,F,Par)``677441 +oinnerint`5`x`(F,Symbol,OrderedCompletion(F),OrderedCompletion(F),Boolean)->Union(f1:OrderedCompletion(F),f2:List(OrderedCompletion(F)),fail:"failed",pole:"potentialPole")`pElementaryFunctionDefiniteIntegration(R,F)``677785 +oinnerSolve1`2`n`(Polynomial(K),Par)->List(F)`pInnerNumericFloatSolvePackage(K,F,Par)``677869 +oinnerSolve1`2`n`(SparseUnivariatePolynomial(K),Par)->List(F)`pInnerNumericFloatSolvePackage(K,F,Par)``677988 +oinnerSolve`4`n`(List(Polynomial(K)),List(Polynomial(K)),List(Symbol),Par)->List(List(F))`pInnerNumericFloatSolvePackage(K,F,Par)``678120 +oinput`1`x`(_$)->Union((List(InputForm))->InputForm,"failed")`dBasicOperator``678478 +oinput`2`x`(_$,(List(InputForm))->InputForm)->_$`dBasicOperator``678592 +oinR?`1`n`(_$)->Boolean`dPattern(R)``678812 +oinRadical?`2`x`(DPoly,_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``678907 +oinrootof`2`n`(SparseUnivariatePolynomial(F),F)->F`pAlgebraicFunction(R,F)``679017 +oinsert!`1`x`(Record(key:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(st--r:Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated"))))->_$`dIntegrationFunctionsTable``679083 +oinsert!`1`x`(Record(key:Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat),entry:Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float)))->_$`dODEIntensityFunctionsTable``679150 +oinsert!`2`n`(Key,Entry)->Void`pTabulatedComputationPackage(Key,Entry)``679217 oinsert!`2`n`(Record(key:Key,entry:Entry),S)->S`xTableAggregate&(S,Key,Entry)``0 -oinsert!`2`x`(S,_$)->_$`cBagAggregate(S)``551618 -oinsert!`2`x`(S,_$)->_$`dBinarySearchTree(S)``551688 -oinsert!`2`x`(S,_$)->_$`dBinaryTournament(S)``551786 -oinsert!`3`n`(A,A,Integer)->A`xListAggregate&(A,S)``0 -oinsert!`3`n`(S,A,Integer)->A`xListAggregate&(A,S)``0 -oinsert!`3`x`(S,_$,Integer)->_$`cExtensibleLinearAggregate(S)``551883 -oinsert!`3`x`(S,_$,NonNegativeInteger)->_$`cMultiDictionary(S)``551983 -oinsert!`3`x`(_$,_$,Integer)->_$`cExtensibleLinearAggregate(S)``552092 -oinsertBottom!`2`x`(S,_$)->S`cDequeueAggregate(S)``552202 -oinsertMatch`3`n`(Pattern(R),S,_$)->_$`dPatternMatchResult(R,S)``552331 -oinsertRoot!`2`x`(S,_$)->_$`dBinarySearchTree(S)``552497 -oinsertTop!`2`x`(S,_$)->S`cDequeueAggregate(S)``552597 +oinsert!`2`x`(S,_$)->_$`cBagAggregate(S)``679344 +oinsert!`2`x`(S,_$)->_$`dArrayStack(S)``679414 +oinsert!`2`x`(S,_$)->_$`dBinarySearchTree(S)``679526 +oinsert!`2`x`(S,_$)->_$`dBinaryTournament(S)``679734 +oinsert!`2`x`(S,_$)->_$`dDequeue(S)``679960 +oinsert!`2`x`(S,_$)->_$`dHeap(S)``680067 +oinsert!`2`x`(S,_$)->_$`dQueue(S)``680167 +oinsert!`2`x`(S,_$)->_$`dStack(S)``680270 oinsert`3`n`(A,A,Integer)->A`xExtensibleLinearAggregate&(A,S)``0 oinsert`3`n`(A,A,Integer)->A`xLazyStreamAggregate&(A,S)``0 oinsert`3`n`(A,A,Integer)->A`xLinearAggregate&(A,S)``0 +oinsert!`3`n`(A,A,Integer)->A`xListAggregate&(A,S)``0 oinsert`3`n`(A,A,Integer)->A`xOneDimensionalArrayAggregate&(A,S)``0 oinsert`3`n`(S,A,Integer)->A`xExtensibleLinearAggregate&(A,S)``0 oinsert`3`n`(S,A,Integer)->A`xLazyStreamAggregate&(A,S)``0 oinsert`3`n`(S,A,Integer)->A`xLinearAggregate&(A,S)``0 +oinsert!`3`n`(S,A,Integer)->A`xListAggregate&(A,S)``0 oinsert`3`n`(S,A,Integer)->A`xOneDimensionalArrayAggregate&(A,S)``0 -oinsert`3`x`(S,_$,Integer)->_$`cLinearAggregate(S)``552832 -oinsert`3`x`(_$,_$,Integer)->_$`cLinearAggregate(S)``553051 -oinsertionSort!`1`n`(A)->A`pSortPackage(S,A)`has(S,OrderedSet)`553306 -oinsertionSort!`2`n`(A,(S,S)->Boolean)->A`pSortPackage(S,A)``553349 +oinsert!`3`x`(_$,_$,Integer)->_$`cExtensibleLinearAggregate(S)``680372 +oinsert`3`x`(_$,_$,Integer)->_$`cLinearAggregate(S)``680482 +oinsert!`3`x`(S,_$,Integer)->_$`cExtensibleLinearAggregate(S)``680741 +oinsert`3`x`(S,_$,Integer)->_$`cLinearAggregate(S)``680841 +oinsert!`3`x`(S,_$,NonNegativeInteger)->_$`cMultiDictionary(S)``681064 +oinsertBottom!`2`x`(S,_$)->S`cDequeueAggregate(S)``681173 +oinsertBottom!`2`x`(S,_$)->S`dDequeue(S)``681302 +oinsertionSort!`1`n`(A)->A`pSortPackage(S,A)`has(S,OrderedSet)`681409 +oinsertionSort!`2`n`(A,(S,S)->Boolean)->A`pSortPackage(S,A)``681452 +oinsertMatch`3`n`(Pattern(R),S,_$)->_$`dPatternMatchResult(R,S)``681502 +oinsertRoot!`2`x`(S,_$)->_$`dBinarySearchTree(S)``681668 +oinsertTop!`2`x`(S,_$)->S`cDequeueAggregate(S)``681882 +oinsertTop!`2`x`(S,_$)->S`dDequeue(S)``682117 oinspect`1`n`(S)->Record(key:Key,entry:Entry)`xTableAggregate&(S,Key,Entry)``0 -oinspect`1`x`(_$)->S`cBagAggregate(S)``553399 -ointChoose`3`n`(SparseUnivariatePolynomial(P),List(OV),List(List(R)))->Record(upol:SparseUnivariatePolynomial(R),Lval:List(R),Lfact:List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)),ctpol:R)`pMultivariateSquareFree(E,OV,R,P)``553464 -ointPatternMatch`4`n`(F,Symbol,(F,Symbol)->IntegrationResult(F),(F,Symbol)->Union(Record(special:F,integrand:F),"failed"))->IntegrationResult(F)`pIntegrationTools(R,F)`AND(has(R,ConvertibleTo(Pattern(Integer))),has(R,GcdDomain),has(R,PatternMatchable(Integer)),has(F,ElementaryFunctionCategory),has(F,LiouvillianFunctionCategory),has(F,RetractableTo(Symbol)))`553504 -oint`1`n`(A)->Stream(A)`pStreamTaylorSeriesOperations(A)``553757 -oint`1`n`(_$)->_$`dOutputForm``553866 -oint`2`n`(F,Symbol)->F`pODEIntegration(R,F)``553952 -oint`2`n`(_$,_$)->_$`dOutputForm``554037 -oint`3`n`(_$,_$,_$)->_$`dOutputForm``554159 -ointcompBasis`3`n`(OrderedVariableList(lv),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(HomogeneousDistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``554321 -ointeger?`1`x`(S)->Boolean`pIntegerRetractions(S)``554362 -ointeger?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``554456 -ointeger?`1`x`(_$)->Boolean`dFortranScalarType``554539 -ointegerBound`1`n`(UP)->Integer`pBoundIntegerRoots(F,UP)``554631 -ointegerIfCan`1`x`(S)->Union(Integer,"failed")`pIntegerRetractions(S)``554777 -ointeger`1`x`(S)->Integer`pIntegerRetractions(S)``554881 -ointeger`1`x`(_$)->Int`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``554975 -ointegers`1`n`(Integer)->Stream(Integer)`pStreamTaylorSeriesOperations(A)``555099 +oinspect`1`x`(_$)->S`cBagAggregate(S)``682221 +oinspect`1`x`(_$)->S`dArrayStack(S)``682286 +oinspect`1`x`(_$)->S`dDequeue(S)``682382 +oinspect`1`x`(_$)->S`dHeap(S)``682472 +oinspect`1`x`(_$)->S`dQueue(S)``682556 +oinspect`1`x`(_$)->S`dStack(S)``682642 +oint`1`n`(A)->Stream(A)`pStreamTaylorSeriesOperations(A)``682728 +oint`1`n`(_$)->_$`dOutputForm``682837 +oint`2`n`(_$,_$)->_$`dOutputForm``682923 +oint`2`n`(F,Symbol)->F`pODEIntegration(R,F)``683045 +oint`3`n`(_$,_$,_$)->_$`dOutputForm``683130 +ointChoose`3`n`(SparseUnivariatePolynomial(P),List(OV),List(List(R)))->Record(upol:SparseUnivariatePolynomial(R),Lval:List(R),Lfact:List(Record(factor:SparseUnivariatePolynomial(R),exponent:Integer)),ctpol:R)`pMultivariateSquareFree(E,OV,R,P)``683292 +ointcompBasis`3`n`(OrderedVariableList(lv),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(HomogeneousDistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``683332 +ointeger?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``683373 +ointeger?`1`x`(_$)->Boolean`dFortranScalarType``683456 +ointeger`1`x`(_$)->Int`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``683548 +ointeger?`1`x`(S)->Boolean`pIntegerRetractions(S)``683672 +ointeger`1`x`(S)->Integer`pIntegerRetractions(S)``683766 +ointegerBound`1`n`(UP)->Integer`pBoundIntegerRoots(F,UP)``683860 +ointegerDecode`1`x`(_$)->List(Integer)`dDoubleFloat``684006 +ointegerIfCan`1`x`(S)->Union(Integer,"failed")`pIntegerRetractions(S)``684426 +ointegers`1`n`(Integer)->Stream(Integer)`pStreamTaylorSeriesOperations(A)``684530 ointegral?`1`n`(S)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -ointegral?`1`x`(_$)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``555163 +ointegral?`1`x`(_$)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``684594 +ointegral`2`n`(F,F)->_$`dIntegrationResult(F)``684668 +ointegral`2`n`(F,SegmentBinding(F))->F`pLiouvillianFunction(R,F)``684763 +ointegral`2`n`(F,Symbol)->_$`dIntegrationResult(F)`has(F,RetractableTo(Symbol))`684894 +ointegral`2`n`(F,Symbol)->F`pLiouvillianFunction(R,F)``684989 ointegral?`2`n`(S,F)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``0 ointegral?`2`n`(S,UP)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -ointegral?`2`x`(_$,F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``555237 -ointegral?`2`x`(_$,UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``555329 +ointegral?`2`x`(_$,F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``685077 +ointegral`2`x`(_$,SegmentBinding(_$))->_$`cPrimitiveFunctionCategory``685169 +ointegral`2`x`(_$,Symbol)->_$`cPrimitiveFunctionCategory``685310 +ointegral?`2`x`(_$,UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``685392 ointegralAtInfinity?`1`n`(S)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -ointegralAtInfinity?`1`x`(_$)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``555424 -ointegralBasisAtInfinity`0`x`()->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``555511 -ointegralBasis`0`n`()->Record(basis:Matrix(Integer),basisDen:Integer,basisInv:Matrix(Integer))`pNumberFieldIntegralBasis(UP,F)``555597 -ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pFunctionFieldIntegralBasis(R,UP,F)``556458 -ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``557319 -ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pWildFunctionFieldIntegralBasis(K,R,UP,F)``558172 -ointegralBasis`0`x`()->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``559033 -ointegralCoordinates`1`x`(_$)->Record(num:Vector(UP),den:UP)`cFunctionFieldCategory(F,UP,UPUP)``559105 -ointegralDerivationMatrix`1`x`((UP)->UP)->Record(num:Matrix(UP),den:UP)`cFunctionFieldCategory(F,UP,UPUP)``559312 -ointegralLastSubResultant`3`x`(P,P,TS)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``559653 -ointegralMatrixAtInfinity`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``559789 -ointegralMatrix`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``560015 -ointegralRepresents`2`x`(Vector(UP),UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``560237 -ointegral`2`n`(F,F)->_$`dIntegrationResult(F)``560405 -ointegral`2`n`(F,SegmentBinding(F))->F`pLiouvillianFunction(R,F)``560500 -ointegral`2`n`(F,Symbol)->F`pLiouvillianFunction(R,F)``560631 -ointegral`2`n`(F,Symbol)->_$`dIntegrationResult(F)`has(F,RetractableTo(Symbol))`560719 -ointegral`2`x`(_$,SegmentBinding(_$))->_$`cPrimitiveFunctionCategory``560814 -ointegral`2`x`(_$,Symbol)->_$`cPrimitiveFunctionCategory``560955 -ointegrate`1`n`(Fraction(UP))->IntegrationResult(Fraction(UP))`pRationalIntegration(F,UP)``561037 +ointegralAtInfinity?`1`x`(_$)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``685486 +ointegralBasis`0`n`()->Record(basis:Matrix(Integer),basisDen:Integer,basisInv:Matrix(Integer))`pNumberFieldIntegralBasis(UP,F)``685573 +ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pFunctionFieldIntegralBasis(R,UP,F)``686434 +ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``687295 +ointegralBasis`0`n`()->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pWildFunctionFieldIntegralBasis(K,R,UP,F)``688148 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-ointernalLastSubResultant`3`x`(List(Record(val:List(P),tower:TS)),V,Boolean)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``576238 -ointernalLastSubResultant`5`x`(P,P,TS,Boolean,Boolean)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``576363 -ointernalSubPolSet?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``576515 -ointernalSubPolSet?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``576785 -ointernalSubQuasiComponent?`2`x`(TS,TS)->Union(Boolean,"failed")`pQuasiComponentPackage(R,E,V,P,TS)``577055 -ointernalSubQuasiComponent?`2`x`(TS,TS)->Union(Boolean,"failed")`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``577341 -ointernalZeroSetSplit`4`x`(List(P),Boolean,Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``577622 -ointernalZeroSetSplit`4`x`(List(P),Boolean,Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``577766 -ointerpolate`2`n`(List(F),List(F))->SparseUnivariatePolynomial(F)`pPolynomialInterpolation(xx,F)``577910 -ointerpolate`3`n`(UnivariatePolynomial(xx,F),List(F),List(F))->UnivariatePolynomial(xx,F)`pPolynomialInterpolation(xx,F)``577959 -ointerpretString`1`x`(String)->Any`pTemplateUtilities``578012 -ointerpret`1`n`(InputForm)->R`pInputFormFunctions1(R)``578122 -ointerpret`1`n`(_$)->Any`dInputForm``578246 -ointersect`1`x`(List(_$))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``578309 +ointernalInfRittWu?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``706364 +ointernalInfRittWu?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``706484 +ointernalIntegrate0`2`x`(F,Symbol)->IntegrationResult(F)`pFunctionSpaceComplexIntegration(R,F)``706604 +ointernalIntegrate`2`x`(Fraction(Polynomial(F)),Symbol)->IntegrationResult(Fraction(Polynomial(F)))`pRationalFunctionIntegration(F)``706687 +ointernalIntegrate`2`x`(F,Symbol)->IntegrationResult(F)`pFunctionSpaceComplexIntegration(R,F)``706772 +ointernalLastSubResultant`3`x`(List(Record(val:List(P),tower:TS)),V,Boolean)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``706898 +ointernalLastSubResultant`5`x`(P,P,TS,Boolean,Boolean)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``707023 +ointernalSubPolSet?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``707175 +ointernalSubPolSet?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``707435 +ointernalSubQuasiComponent?`2`x`(TS,TS)->Union(Boolean,"failed")`pQuasiComponentPackage(R,E,V,P,TS)``707695 +ointernalSubQuasiComponent?`2`x`(TS,TS)->Union(Boolean,"failed")`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``707981 +ointernalZeroSetSplit`4`x`(List(P),Boolean,Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``708262 +ointernalZeroSetSplit`4`x`(List(P),Boolean,Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``708406 +ointerpolate`2`n`(List(F),List(F))->SparseUnivariatePolynomial(F)`pPolynomialInterpolation(xx,F)``708550 +ointerpolate`3`n`(UnivariatePolynomial(xx,F),List(F),List(F))->UnivariatePolynomial(xx,F)`pPolynomialInterpolation(xx,F)``708599 +ointerpolate`3`x`(List(D),List(D),NonNegativeInteger)->Fraction(SparseUnivariatePolynomial(D))`pFractionFreeFastGaussian(D,V)``708652 +ointerpolate`3`x`(List(Fraction(D)),List(Fraction(D)),NonNegativeInteger)->Fraction(SparseUnivariatePolynomial(D))`pFractionFreeFastGaussian(D,V)``709048 +ointerpolate`4`n`(List(F),List(F),NonNegativeInteger,NonNegativeInteger)->Fraction(Polynomial(F))`pRationalInterpolation(xx,F)``0 +ointerpolateForms`2`x`(DIVISOR,NonNegativeInteger)->List(PolyRing)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``709226 +ointerpolateForms`2`x`(Divisor(Places(K)),NonNegativeInteger)->List(DistributedMultivariatePolynomial(symb,K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``709349 +ointerpolateForms`2`x`(Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),NonNegativeInteger)->List(DistributedMultivariatePolynomial(symb,K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``709472 +ointerpolateForms`4`x`(DIVISOR,NonNegativeInteger,PolyRing,List(PolyRing))->List(PolyRing)`pInterpolateFormsPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR)``709595 +ointerpolateFormsForFact`2`x`(DIVISOR,List(PolyRing))->List(PolyRing)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +ointerpolateFormsForFact`2`x`(DIVISOR,List(PolyRing))->List(PolyRing)`pInterpolateFormsPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR)``0 +ointerpolateFormsForFact`2`x`(Divisor(Places(K)),List(DistributedMultivariatePolynomial(symb,K)))->List(DistributedMultivariatePolynomial(symb,K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +ointerpolateFormsForFact`2`x`(Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K)),List(DistributedMultivariatePolynomial(symb,K)))->List(DistributedMultivariatePolynomial(symb,PseudoAlgebraicClosureOfFiniteField(K)))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +ointerpret`1`n`(_$)->Any`dInputForm``710268 +ointerpret`1`n`(InputForm)->R`pInputFormFunctions1(R)``710331 +ointerpretString`1`x`(String)->Any`pTemplateUtilities``710455 +ointerReduce`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``710565 +ointersect`1`x`(List(_$))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``710903 ointersect`2`n`(A,A)->A`xFiniteSetAggregate&(A,S)``0 ointersect`2`n`(List(P),List(S))->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 ointersect`2`n`(List(P),S)->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 ointersect`2`n`(P,List(S))->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 ointersect`2`n`(P,S)->List(S)`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -ointersect`2`x`(List(P),List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``578396 -ointersect`2`x`(List(P),_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``578501 -ointersect`2`x`(P,List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``578678 -ointersect`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``578759 -ointersect`2`x`(_$,_$)->_$`cSetAggregate(S)``578838 -ointersect`2`x`(_$,_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``579107 -ointerval`1`x`(Fraction(Integer))->_$`cIntervalCategory(R)``579201 -ointerval`1`x`(R)->_$`cIntervalCategory(R)``579267 -ointerval`2`x`(R,R)->_$`cIntervalCategory(R)``579333 +ointersect`2`x`(_$,_$)->_$`cSetAggregate(S)``710990 +ointersect`2`x`(_$,_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``711263 +ointersect`2`x`(List(P),_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``711357 +ointersect`2`x`(List(P),List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``711534 +ointersect`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``711639 +ointersect`2`x`(P,List(_$))->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``711718 +ointersectionDivisor`1`x`(DistributedMultivariatePolynomial(symb,K))->Divisor(Places(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``711799 +ointersectionDivisor`1`x`(DistributedMultivariatePolynomial(symb,K))->Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``712169 +ointersectionDivisor`1`x`(PolyRing)->DIVISOR`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``712343 +ointersectionDivisor`4`x`(PolyRing,PolyRing,List(DesTree),List(ProjPt))->DIVISOR`pIntersectionDivisorPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``712723 +ointerval`1`x`(Fraction(Integer))->_$`cIntervalCategory(R)``712996 +ointerval`1`x`(R)->_$`cIntervalCategory(R)``713062 +ointerval`2`x`(R,R)->_$`cIntervalCategory(R)``713128 +ointPatternMatch`4`n`(F,Symbol,(F,Symbol)->IntegrationResult(F),(F,Symbol)->Union(Record(special:F,integrand:F),"failed"))->IntegrationResult(F)`pIntegrationTools(R,F)`AND(has(R,ConvertibleTo(Pattern(Integer))),has(R,GcdDomain),has(R,PatternMatchable(Integer)),has(F,ElementaryFunctionCategory),has(F,LiouvillianFunctionCategory),has(F,RetractableTo(Symbol)))`713312 +oinv`1`n`(_$)->_$`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``713565 +oinv`1`n`(_$)->_$`dModularRing(R,Mod,reduction,merge,exactQuo)``713604 oinv`1`n`(S)->S`xComplexCategory&(S,R)``0 oinv`1`n`(S)->S`xField&(S)``0 oinv`1`n`(S)->S`xOctonionCategory&(S,R)``0 oinv`1`n`(S)->S`xQuaternionCategory&(S,R)``0 -oinv`1`n`(Vector(GF))->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``579517 -oinv`1`n`(_$)->_$`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``579590 -oinv`1`n`(_$)->_$`dModularRing(R,Mod,reduction,merge,exactQuo)``579625 -oinv`1`x`(_$)->_$`cDivisionRing``579660 -oinv`1`x`(_$)->_$`cGroup``579753 -oinv`1`x`(_$)->_$`cOctonionCategory(R)`has(R,Field)`579807 -oinv`1`x`(_$)->_$`dEquation(S)`has(S,Field)`579874 -oinverseColeman`3`x`(List(Integer),List(Integer),Matrix(Integer))->List(Integer)`pSymmetricGroupCombinatoricFunctions``579943 -oinverseIntegralMatrixAtInfinity`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``580652 -oinverseIntegralMatrix`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``580885 -oinverseLaplace`3`x`(F,Symbol,Symbol)->Union(F,"failed")`pInverseLaplaceTransform(R,F)``581111 -oinverse`1`n`(List(S))->List(S)`pTableauxBumpers(S)``581286 -oinverse`1`n`(M)->Union(M,"failed")`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``581354 -oinverse`1`n`(M)->Union(M2,"failed")`pInnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2)``581516 -oinverse`1`x`(M)->Union(M,"failed")`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,Field)`581736 -oinverse`1`x`(_$)->Union(_$,"failed")`cMatrixCategory(R,Row,Col)`has(R,Field)`581889 -oinverse`1`x`(_$)->Union(_$,"failed")`cSquareMatrixCategory(ndim,R,Row,Col)`has(R,Field)`582051 -oinverse`1`x`(_$)->Union(_$,"failed")`dMatrix(R)`has(R,Field)`582183 -oinvertIfCan`1`x`(M)->Union(M,"failed")`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`582345 -oinvertible?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``582420 -oinvertible?`2`x`(P,_$)->List(Record(val:Boolean,tower:_$))`cRegularTriangularSetCategory(R,E,V,P)``582541 -oinvertibleElseSplit?`2`x`(P,_$)->Union(Boolean,List(_$))`cRegularTriangularSetCategory(R,E,V,P)``582760 -oinvertibleSet`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``582956 +oinv`1`n`(Vector(GF))->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``713643 +oinv`1`x`(_$)->_$`cDivisionRing``713716 +oinv`1`x`(_$)->_$`cGroup``713809 +oinv`1`x`(_$)->_$`cOctonionCategory(R)`has(R,Field)`713863 +oinv`1`x`(_$)->_$`dEquation(S)`has(S,Field)`713930 +oinverse`1`n`(List(S))->List(S)`pTableauxBumpers(S)``713999 +oinverse`1`n`(M)->Union(M2,"failed")`pInnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2)``714067 +oinverse`1`n`(M)->Union(M,"failed")`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``714291 +oinverse`1`x`(M)->Union(M,"failed")`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,Field)`714453 +oinverse`1`x`(_$)->Union(_$,"failed")`cMatrixCategory(R,Row,Col)`has(R,Field)`714606 +oinverse`1`x`(_$)->Union(_$,"failed")`cSquareMatrixCategory(ndim,R,Row,Col)`has(R,Field)`714896 +oinverse`1`x`(_$)->Union(_$,"failed")`dMatrix(R)`has(R,Field)`715028 +oinverseColeman`3`x`(List(Integer),List(Integer),Matrix(Integer))->List(Integer)`pSymmetricGroupCombinatoricFunctions``715190 +oinverseIntegralMatrix`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``715878 +oinverseIntegralMatrixAtInfinity`0`x`()->Matrix(Fraction(UP))`cFunctionFieldCategory(F,UP,UPUP)``716476 +oinverseLaplace`3`x`(F,Symbol,Symbol)->Union(F,"failed")`pInverseLaplaceTransform(R,F)``717091 +oinvertible?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``717301 +oinvertible?`2`x`(P,_$)->List(Record(val:Boolean,tower:_$))`cRegularTriangularSetCategory(R,E,V,P)``717422 +oinvertibleElseSplit?`2`x`(P,_$)->Union(Boolean,List(_$))`cRegularTriangularSetCategory(R,E,V,P)``717641 +oinvertibleSet`2`x`(P,_$)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``717837 +oinvertIfCan`1`x`(M)->Union(M,"failed")`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`718024 oinvmod`2`n`(S,S)->S`xIntegerNumberSystem&(S)``0 -oinvmod`2`x`(_$,_$)->_$`cIntegerNumberSystem``583143 -oinvmultisect`3`n`(Integer,Integer,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``583234 -oinvmultisect`3`n`(Integer,Integer,_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``583352 -oiomode`1`x`(_$)->String`cFileCategory(Name,S)``583482 -oipow`1`n`(List(F))->F`pCombinatorialFunction(R,F)``583628 -oiprint`1`n`(String)->Void`pInternalPrintPackage``583683 -oiroot`2`n`(R,Integer)->F`pAlgebraicFunction(R,F)`has(R,RetractableTo(Integer))`583778 -oirreducible?`1`x`(FP)->Boolean`pDistinctDegreeFactorize(F,FP)``583841 -oirreducibleFactor`2`x`(R,Integer)->_$`dFactored(R)``583925 -oirreducibleFactors`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`584087 -oirreducibleRepresentation`1`x`(List(Integer))->List(Matrix(Integer))`pIrrRepSymNatPackage``584440 -oirreducibleRepresentation`2`x`(List(Integer),List(Permutation(Integer)))->List(Matrix(Integer))`pIrrRepSymNatPackage``584792 -oirreducibleRepresentation`2`x`(List(Integer),Permutation(Integer))->Matrix(Integer)`pIrrRepSymNatPackage``585017 +oinvmod`2`x`(_$,_$)->_$`cIntegerNumberSystem``718099 +oinvmultisect`3`n`(Integer,Integer,_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``718190 +oinvmultisect`3`n`(Integer,Integer,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``718320 +oinvmultisect`3`x`(Integer,Integer,_$)->_$`dUnivariateFormalPowerSeries(Coef)``0 +oinvmultisect`3`x`(Integer,Integer,_$)->_$`dUnivariateTaylorSeriesCZero(Coef,var)``718438 +oiomode`1`x`(_$)->String`cFileCategory(Name,S)``718568 +oipow`1`n`(List(F))->F`pCombinatorialFunction(R,F)``718714 +oiprint`1`n`(String)->Void`pInternalPrintPackage``718769 +oiroot`2`n`(R,Integer)->F`pAlgebraicFunction(R,F)`has(R,RetractableTo(Integer))`718864 +oirreducible?`1`x`(FP)->Boolean`pDistinctDegreeFactorize(F,FP)``718927 +oirreducible?`1`x`(PolK)->Boolean`pFiniteFieldFactorizationWithSizeParseBySideEffect(K,PolK)``0 +oirreducibleFactor`2`x`(R,Integer)->_$`dFactored(R)``719011 +oirreducibleFactors`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`719273 +oirreducibleRepresentation`1`x`(List(Integer))->List(Matrix(Integer))`pIrrRepSymNatPackage``719626 +oirreducibleRepresentation`2`x`(List(Integer),List(Permutation(Integer)))->List(Matrix(Integer))`pIrrRepSymNatPackage``719975 +oirreducibleRepresentation`2`x`(List(Integer),Permutation(Integer))->Matrix(Integer)`pIrrRepSymNatPackage``720202 +ois?`2`n`(_$,BasicOperator)->Boolean`dKernel(S)``720472 ois?`2`n`(S,BasicOperator)->Boolean`xExpressionSpace&(S)``0 ois?`2`n`(S,Symbol)->Boolean`xExpressionSpace&(S)``0 -ois?`2`n`(_$,BasicOperator)->Boolean`dKernel(S)``585291 -ois?`2`n`(_$,Symbol)->Boolean`dKernel(S)``585357 -ois?`2`x`(List(Subject),Pat)->Boolean`pPatternMatch(Base,Subject,Pat)``585436 -ois?`2`x`(Subject,Pat)->Boolean`pPatternMatch(Base,Subject,Pat)``585559 -ois?`2`x`(_$,BasicOperator)->Boolean`cExpressionSpace``585651 -ois?`2`x`(_$,Symbol)->Boolean`cExpressionSpace``585735 -ois?`2`x`(_$,Symbol)->Boolean`dBasicOperator``585836 -oisAbsolutelyIrreducible?`1`x`(List(Matrix(R)))->Boolean`pRepresentationPackage2(R)`has(R,Field)`585907 -oisAbsolutelyIrreducible?`2`x`(List(Matrix(R)),Integer)->Boolean`pRepresentationPackage2(R)`has(R,Field)`586042 -oisExpt`1`n`(F)->Union(Record(var:V,exponent:Integer),"failed")`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``586542 +ois?`2`n`(_$,Symbol)->Boolean`dKernel(S)``720538 +ois?`2`x`(_$,BasicOperator)->Boolean`cExpressionSpace``720617 +ois?`2`x`(List(Subject),Pat)->Boolean`pPatternMatch(Base,Subject,Pat)``720701 +oIs`2`x`(List(Subject),Pat)->PatternMatchListResult(Base,Subject,List(Subject))`pPatternMatch(Base,Subject,Pat)``720824 +ois?`2`x`(Subject,Pat)->Boolean`pPatternMatch(Base,Subject,Pat)``720963 +oIs`2`x`(Subject,Pat)->List(Equation(Polynomial(Subject)))`pPatternMatch(Base,Subject,Pat)`AND(has(Subject,Ring),not(has(Subject,RetractableTo(Symbol))))`721055 +oIs`2`x`(Subject,Pat)->List(Equation(Subject))`pPatternMatch(Base,Subject,Pat)`has(Subject,RetractableTo(Symbol))`721309 +oIs`2`x`(Subject,Pat)->PatternMatchResult(Base,Subject)`pPatternMatch(Base,Subject,Pat)`AND(not(has(Subject,RetractableTo(Symbol))),not(has(Subject,Ring)))`721563 +ois?`2`x`(_$,Symbol)->Boolean`cExpressionSpace``721844 +ois?`2`x`(_$,Symbol)->Boolean`dBasicOperator``721945 +oisAbsolutelyIrreducible?`1`x`(List(Matrix(R)))->Boolean`pRepresentationPackage2(R)`has(R,Field)`722016 +oisAbsolutelyIrreducible?`2`x`(List(Matrix(R)),Integer)->Boolean`pRepresentationPackage2(R)`has(R,Field)`722156 +oisExpt`1`n`(F)->Union(Record(var:V,exponent:Integer),"failed")`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``722650 oisExpt`1`n`(S)->Union(Record(var:Kernel(S),exponent:Integer),"failed")`xFunctionSpace&(S,R)``0 oisExpt`1`n`(S)->Union(Record(var:VarSet,exponent:NonNegativeInteger),"failed")`xPolynomialCategory&(S,R,E,VarSet)``0 -oisExpt`1`n`(_$)->Union(Record(val:_$,exponent:NonNegativeInteger),"failed")`dPattern(R)``586650 -oisExpt`1`x`(_$)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,SemiGroup)`586763 -oisExpt`1`x`(_$)->Union(Record(var:VarSet,exponent:NonNegativeInteger),"failed")`cPolynomialCategory(R,E,VarSet)``586849 +oisExpt`1`n`(_$)->Union(Record(val:_$,exponent:NonNegativeInteger),"failed")`dPattern(R)``722758 +oisExpt`1`x`(_$)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,SemiGroup)`722871 +oisExpt`1`x`(_$)->Union(Record(var:VarSet,exponent:NonNegativeInteger),"failed")`cPolynomialCategory(R,E,VarSet)``722957 oisExpt`2`n`(S,BasicOperator)->Union(Record(var:Kernel(S),exponent:Integer),"failed")`xFunctionSpace&(S,R)``0 oisExpt`2`n`(S,Symbol)->Union(Record(var:Kernel(S),exponent:Integer),"failed")`xFunctionSpace&(S,R)``0 -oisExpt`2`x`(_$,BasicOperator)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,Ring)`586963 -oisExpt`2`x`(_$,Symbol)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,Ring)`587075 -oisList`1`n`(_$)->Union(List(_$),"failed")`dPattern(R)``587185 +oisExpt`2`x`(_$,BasicOperator)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,Ring)`723071 +oisExpt`2`x`(_$,Symbol)->Union(Record(var:Kernel(_$),exponent:Integer),"failed")`cFunctionSpace(R)`has(R,Ring)`723183 +oisList`1`n`(_$)->Union(List(_$),"failed")`dPattern(R)``723293 oisMult`1`n`(S)->Union(Record(coef:Integer,var:Kernel(S)),"failed")`xFunctionSpace&(S,R)``0 -oisMult`1`x`(_$)->Union(Record(coef:Integer,var:Kernel(_$)),"failed")`cFunctionSpace(R)`has(R,AbelianSemiGroup)`587293 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+olfextlimint`4`n`(F,Symbol,Kernel(F),List(Kernel(F)))->Union(Record(ratpart:F,coeff:F),"failed")`pElementaryIntegration(R,F)``764836 +olfinfieldint`2`n`(F,Symbol)->Union(F,"failed")`pElementaryIntegration(R,F)``765094 +olfintegrate`2`n`(F,Symbol)->IntegrationResult(F)`pElementaryIntegration(R,F)``765226 +olflimitedint`3`n`(F,Symbol,List(F))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed")`pElementaryIntegration(R,F)``765299 +olfunc`2`x`(Integer,Integer)->Integer`pHallBasis``765569 +olhs`1`n`(_$)->S1`dSuchThat(S1,S2)``765794 +olhs`1`x`(_$)->F`dRewriteRule(Base,R,F)``765849 +olhs`1`x`(_$)->S`dEquation(S)``765919 +oli`1`n`(F)->F`pLiouvillianFunction(R,F)``765993 +oli`1`x`(_$)->_$`cLiouvillianFunctionCategory``766053 +olibrary`1`x`(FileName)->_$`dLibrary``766182 +olieAdmissible?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``766236 +olieAdmissible?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``766443 +olieAlgebra?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``766650 +olieAlgebra?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``766974 +oLiePoly`1`x`(LyndonWord(VarSet))->_$`cFreeLieAlgebra(VarSet,R)``767298 +oLiePolyIfCan`1`n`(_$)->Union(LiePolynomial(VarSet,R),"failed")`dXPBWPolynomial(VarSet,R)``767399 +oLiePolyIfCan`1`n`(XDistributedPolynomial(VarSet,R))->Union(_$,"failed")`dLiePolynomial(VarSet,R)``767502 +olift`1`n`(_$)->FPol`dResidueRing(F,Expon,VarSet,FPol,LFPol)``767664 +olift`1`n`(_$)->Rep`dModMonic(R,Rep)``767756 olift`1`n`(S)->SparseUnivariatePolynomial(R)`xComplexCategory&(S,R)``0 -olift`1`n`(_$)->FPol`dResidueRing(F,Expon,VarSet,FPol,LFPol)``627770 -olift`1`n`(_$)->Rep`dModMonic(R,Rep)``627862 -olift`1`x`(_$)->UP`cMonogenicAlgebra(R,UP)``627898 -olift`2`n`(SparseUnivariatePolynomial(F),Kernel(F))->SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F)))`pGenusZeroIntegration(R,F,L)``628000 -olift`7`n`(SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),SparseUnivariatePolynomial(R),P,List(OV),List(NonNegativeInteger),List(R))->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateSquareFree(E,OV,R,P)``628040 -olifting1`9`n`(SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(P)),List(R),List(P),List(List(Record(expt:NonNegativeInteger,pcoef:P))),List(NonNegativeInteger),Vector(List(SparseUnivariatePolynomial(R))),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``628075 -olifting`7`n`(SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(R)),List(R),List(P),List(NonNegativeInteger),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``628153 -olight`1`x`(Color)->_$`dPalette``628221 -olighting`4`x`(_$,Float,Float,Float)->Void`dThreeDimensionalViewport``628313 -olimitPlus`1`n`(_$)->Union(OrderedCompletion(FE),"failed")`dExponentialExpansion(R,FE,var,cen)``628580 -olimitPlus`1`n`(_$)->Union(OrderedCompletion(FE),"failed")`dUnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)``628654 -olimit`2`x`(FE,Equation(OrderedCompletion(FE)))->Union(OrderedCompletion(FE),Record(leftHandLimit:Union(OrderedCompletion(FE),"failed"),rightHandLimit:Union(OrderedCompletion(FE),"failed")),"failed")`pPowerSeriesLimitPackage(R,FE)``628730 -olimit`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed")`pRationalFunctionLimitPackage(R)``628815 -olimit`2`x`(Fraction(Polynomial(R)),Equation(OrderedCompletion(Polynomial(R))))->Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed")`pRationalFunctionLimitPackage(R)``628941 -olimit`3`x`(FE,Equation(FE),String)->Union(OrderedCompletion(FE),"failed")`pPowerSeriesLimitPackage(R,FE)``629067 -olimit`3`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))),String)->Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")`pRationalFunctionLimitPackage(R)``629268 -olimitedIntegrate`3`x`(Fraction(Polynomial(F)),Symbol,List(Fraction(Polynomial(F))))->Union(Record(mainpart:Fraction(Polynomial(F)),limitedlogs:List(Record(coeff:Fraction(Polynomial(F)),logand:Fraction(Polynomial(F))))),"failed")`pRationalFunctionIntegration(F)``629539 -olimitedint`2`n`(Fraction(UP),List(Fraction(UP)))->Union(Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),"failed")`pRationalIntegration(F,UP)``629845 -olinGenPos`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->Record(gblist:List(DistributedMultivariatePolynomial(lv,F)),gvlist:List(Integer))`pLinGroebnerPackage(lv,F)``630125 -olinSolve`2`x`(List(P),List(OV))->Record(particular:Union(Vector(Fraction(P)),"failed"),basis:List(Vector(Fraction(P))))`pLinearSystemPolynomialPackage(R,E,OV,P)``630163 -olineColorDefault`0`x`()->Palette`pViewDefaultsPackage``630316 -olineColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``630420 -olinear?`1`n`(P)->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``630546 -olinear?`1`x`(Expression(DoubleFloat))->Boolean`pe04AgentsPackage``630698 -olinear?`1`x`(List(Expression(DoubleFloat)))->Boolean`pe04AgentsPackage``630771 +olift`1`x`(_$)->SparseUnivariatePolynomial(_$)`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +olift`1`x`(_$)->UP`cMonogenicAlgebra(R,UP)``767796 +olift`2`n`(SparseUnivariatePolynomial(F),Kernel(F))->SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F)))`pGenusZeroIntegration(R,F,L)``767898 +olift`2`x`(_$,_$)->SparseUnivariatePolynomial(_$)`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +olift`7`n`(SparseUnivariatePolynomial(P),SparseUnivariatePolynomial(R),SparseUnivariatePolynomial(R),P,List(OV),List(NonNegativeInteger),List(R))->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateSquareFree(E,OV,R,P)``767938 +olifting1`9`n`(SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(P)),List(R),List(P),List(List(Record(expt:NonNegativeInteger,pcoef:P))),List(NonNegativeInteger),Vector(List(SparseUnivariatePolynomial(R))),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``767973 +olifting`7`n`(SparseUnivariatePolynomial(P),List(OV),List(SparseUnivariatePolynomial(R)),List(R),List(P),List(NonNegativeInteger),R)->Union(List(SparseUnivariatePolynomial(P)),"failed")`pMultivariateLifting(E,OV,R,P)``768051 +olight`1`x`(Color)->_$`dPalette``768119 +olighting`4`x`(_$,Float,Float,Float)->Void`dThreeDimensionalViewport``768211 +olimit`2`x`(FE,Equation(OrderedCompletion(FE)))->Union(OrderedCompletion(FE),Record(leftHandLimit:Union(OrderedCompletion(FE),"failed"),rightHandLimit:Union(OrderedCompletion(FE),"failed")),"failed")`pPowerSeriesLimitPackage(R,FE)``768478 +olimit`2`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))))->Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed")`pRationalFunctionLimitPackage(R)``768563 +olimit`2`x`(Fraction(Polynomial(R)),Equation(OrderedCompletion(Polynomial(R))))->Union(OrderedCompletion(Fraction(Polynomial(R))),Record(leftHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed"),rightHandLimit:Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")),"failed")`pRationalFunctionLimitPackage(R)``768689 +olimit`3`x`(FE,Equation(FE),String)->Union(OrderedCompletion(FE),"failed")`pPowerSeriesLimitPackage(R,FE)``768815 +olimit`3`x`(Fraction(Polynomial(R)),Equation(Fraction(Polynomial(R))),String)->Union(OrderedCompletion(Fraction(Polynomial(R))),"failed")`pRationalFunctionLimitPackage(R)``769016 +olimitedint`2`n`(Fraction(UP),List(Fraction(UP)))->Union(Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),"failed")`pRationalIntegration(F,UP)``769287 +olimitedIntegrate`3`x`(Fraction(Polynomial(F)),Symbol,List(Fraction(Polynomial(F))))->Union(Record(mainpart:Fraction(Polynomial(F)),limitedlogs:List(Record(coeff:Fraction(Polynomial(F)),logand:Fraction(Polynomial(F))))),"failed")`pRationalFunctionIntegration(F)``769567 +olimitPlus`1`n`(_$)->Union(OrderedCompletion(FE),"failed")`dExponentialExpansion(R,FE,var,cen)``769873 +olimitPlus`1`n`(_$)->Union(OrderedCompletion(FE),"failed")`dUnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen)``769947 +olinear?`1`n`(P)->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``770023 +olinear`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``770175 +olinear?`1`x`(Expression(DoubleFloat))->Boolean`pe04AgentsPackage``770213 +olinear?`1`x`(List(Expression(DoubleFloat)))->Boolean`pe04AgentsPackage``770286 +olinear`2`n`(F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``770387 olinearAssociatedExp`2`n`(S,SparseUnivariatePolynomial(F))->S`xFiniteAlgebraicExtensionField&(S,F)``0 -olinearAssociatedExp`2`x`(_$,SparseUnivariatePolynomial(F))->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`630872 +olinearAssociatedExp`2`x`(_$,SparseUnivariatePolynomial(F))->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`770429 olinearAssociatedLog`1`n`(S)->SparseUnivariatePolynomial(F)`xFiniteAlgebraicExtensionField&(S,F)``0 -olinearAssociatedLog`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`631550 +olinearAssociatedLog`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`771133 olinearAssociatedLog`2`n`(S,S)->Union(SparseUnivariatePolynomial(F),"failed")`xFiniteAlgebraicExtensionField&(S,F)``0 -olinearAssociatedLog`2`x`(_$,_$)->Union(SparseUnivariatePolynomial(F),"failed")`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`631703 +olinearAssociatedLog`2`x`(_$,_$)->Union(SparseUnivariatePolynomial(F),"failed")`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`771281 olinearAssociatedOrder`1`n`(S)->SparseUnivariatePolynomial(F)`xFiniteAlgebraicExtensionField&(S,F)``0 -olinearAssociatedOrder`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`631941 -olinearDependenceOverZ`1`x`(Vector(R))->Union(Vector(Integer),"failed")`pIntegerLinearDependence(R)``632096 -olinearDependence`1`n`(Vector(R))->Union(Vector(S),"failed")`pLinearDependence(S,R)``632339 -olinearMatrix`2`x`(List(Expression(DoubleFloat)),NonNegativeInteger)->Matrix(DoubleFloat)`pe04AgentsPackage``632571 -olinearPart`1`x`(List(Expression(DoubleFloat)))->List(Expression(DoubleFloat))`pe04AgentsPackage``632740 -olinearPolynomials`1`n`(List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``632826 -olinear`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``633018 -olinear`2`n`(F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``633056 -olinearlyDependent?`1`n`(Vector(R))->Boolean`pLinearDependence(S,R)``633098 -olinearlyDependentOverZ?`1`x`(Vector(R))->Boolean`pIntegerLinearDependence(R)``633258 -olinears`2`x`(U,Integer)->U`pModularDistinctDegreeFactorizer(U)``633427 -olinkToFortran`4`x`(Symbol,List(Symbol),TheSymbolTable,List(Symbol))->SExpression`pFortranPackage``633608 -olinkToFortran`4`x`(Symbol,List(Union(array:List(Symbol),scalar:Symbol)),List(List(Union(array:List(Symbol),scalar:Symbol))),List(Symbol))->SExpression`pFortranPackage``633668 -olinkToFortran`5`x`(Symbol,List(Union(array:List(Symbol),scalar:Symbol)),List(List(Union(array:List(Symbol),scalar:Symbol))),List(Symbol),Symbol)->SExpression`pFortranPackage``633729 -olintgcd`1`n`(List(Integer))->Integer`pHeuGcd(BP)``633794 -olist?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``633867 -olistBranches`1`x`(_$)->List(List(Point(DoubleFloat)))`cPlottablePlaneCurveCategory``633948 -olistBranches`1`x`(_$)->List(List(Point(DoubleFloat)))`cPlottableSpaceCurveCategory``634064 -olistConjugateBases`3`n`(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)),NonNegativeInteger,NonNegativeInteger)->List(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)))`pChineseRemainderToolsForIntegralBases(K,R,UP)``634180 -olistLoops`1`n`(_$)->List(List(Point(DoubleFloat)))`dTubePlot(Curve)``634427 -olistOfLists`1`n`(S)->List(List(R))`xMatrixCategory&(S,R,Row,Col)``0 -olistOfLists`1`x`(_$)->List(List(R))`cMatrixCategory(R,Row,Col)``634544 -olistOfLists`1`x`(_$)->List(List(R))`cRectangularMatrixCategory(m,n,R,Row,Col)``634633 -olistOfLists`1`x`(_$)->List(List(S))`dTableau(S)``634722 -olistOfMonoms`1`n`(_$)->List(Record(gen:S,exp:E))`dListMonoidOps(S,E,un)``634798 -olistRepresentation`1`x`(_$)->Record(preimage:List(S),image:List(S))`dPermutation(S)``634880 -olistYoungTableaus`1`x`(List(Integer))->List(Matrix(Integer))`pSymmetricGroupCombinatoricFunctions``635121 +olinearAssociatedOrder`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`771515 +olinearBezier`2`x`(List(R),List(R))->(R)->List(R)`pBezier(R)``771671 +olinearDependence`1`n`(Vector(R))->Union(Vector(S),"failed")`pLinearDependence(S,R)``772199 +olinearDependenceOverZ`1`x`(Vector(R))->Union(Vector(Integer),"failed")`pIntegerLinearDependence(R)``772431 +olinearlyDependent?`1`n`(Vector(R))->Boolean`pLinearDependence(S,R)``772674 +olinearlyDependentOverZ?`1`x`(Vector(R))->Boolean`pIntegerLinearDependence(R)``772834 +olinearMatrix`2`x`(List(Expression(DoubleFloat)),NonNegativeInteger)->Matrix(DoubleFloat)`pe04AgentsPackage``773003 +olinearPart`1`x`(List(Expression(DoubleFloat)))->List(Expression(DoubleFloat))`pe04AgentsPackage``773172 +olinearPolynomials`1`n`(List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``773258 +olinears`2`x`(U,Integer)->U`pModularDistinctDegreeFactorizer(U)``773450 +olineColorDefault`0`x`()->Palette`pViewDefaultsPackage``773631 +olineColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``773735 +olinGenPos`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->Record(gblist:List(DistributedMultivariatePolynomial(lv,F)),gvlist:List(Integer))`pLinGroebnerPackage(lv,F)``773861 +olinkToFortran`4`x`(Symbol,List(Symbol),TheSymbolTable,List(Symbol))->SExpression`pFortranPackage``773899 +olinkToFortran`4`x`(Symbol,List(Union(array:List(Symbol),scalar:Symbol)),List(List(Union(array:List(Symbol),scalar:Symbol))),List(Symbol))->SExpression`pFortranPackage``773959 +olinkToFortran`5`x`(Symbol,List(Union(array:List(Symbol),scalar:Symbol)),List(List(Union(array:List(Symbol),scalar:Symbol))),List(Symbol),Symbol)->SExpression`pFortranPackage``774020 +olinSolve`2`x`(List(P),List(OV))->Record(particular:Union(Vector(Fraction(P)),"failed"),basis:List(Vector(Fraction(P))))`pLinearSystemPolynomialPackage(R,E,OV,P)``774085 +olintgcd`1`n`(List(Integer))->Integer`pHeuGcd(BP)``774238 olist`1`n`(S)->A`xListAggregate&(A,S)``0 -olist`1`x`(S)->_$`cListAggregate(S)``635598 -olist`1`x`(_$)->List(_$)`dSymbol``635662 -olistexp`1`n`(BP)->List(NonNegativeInteger)`pNPCoef(BP,E,OV,R,P)``635766 -olists`1`n`(_$)->PatternMatchResult(R,L)`dPatternMatchListResult(R,S,L)``635802 -olllip`1`x`(_$)->List(List(List(NonNegativeInteger)))`cThreeSpaceCategory(R)``635871 -olllp`1`x`(_$)->List(List(List(Point(R))))`cThreeSpaceCategory(R)``636141 -ollprop`1`x`(_$)->List(List(SubSpaceComponentProperty))`cThreeSpaceCategory(R)``636399 -olo`1`x`(_$)->S`cSegmentCategory(S)``636655 -olocalAbs`1`n`(FE)->FE`pFunctionSpaceToExponentialExpansion(R,FE,x,cen)``636742 -olocalAbs`1`n`(FE)->FE`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``636944 -olocalIntegralBasis`1`n`(Integer)->Record(basis:Matrix(Integer),basisDen:Integer,basisInv:Matrix(Integer))`pNumberFieldIntegralBasis(UP,F)``637146 -olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pFunctionFieldIntegralBasis(R,UP,F)``638046 -olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``638942 -olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pWildFunctionFieldIntegralBasis(K,R,UP,F)``639840 -olocalReal?`1`n`(F)->Boolean`pElementaryFunction(R,F)``640746 -olocalUnquote`2`n`(F,List(Symbol))->F`pApplyRules(Base,R,F)``640806 -olog10`0`x`()->_$`dFloat``640862 -olog10`1`x`(_$)->_$`dDoubleFloat``640930 -olog10`1`x`(_$)->_$`dFloat``641003 -olog10`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``641074 -olog2`0`x`()->_$`dFloat``641152 -olog2`1`x`(_$)->_$`dDoubleFloat``641238 -olog2`1`x`(_$)->_$`dFloat``641309 -ologGamma`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``641378 -ologGamma`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``641502 -ologIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``641626 -olog`1`n`(F)->F`pElementaryFunction(R,F)``641713 -olog`1`n`(Factored(M))->List(Record(coef:NonNegativeInteger,logand:M))`pFactoredFunctions(M)``641777 +olist?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``774311 +olist`1`x`(_$)->List(_$)`dSymbol``774392 +olist`1`x`(_$)->List(K)`cAffineSpaceCategory(K)``774496 +olist`1`x`(_$)->List(K)`cProjectiveSpaceCategory(K)``774551 +olist`1`x`(S)->_$`cListAggregate(S)``774606 +olistAllMono`1`x`(NonNegativeInteger)->List(PolyRing)`pPackageForPoly(R,PolyRing,E,dim)``774670 +olistAllMonoExp`1`x`(Integer)->List(E)`pPackageForPoly(R,PolyRing,E,dim)``774744 +olistBranches`1`x`(_$)->List(List(Point(DoubleFloat)))`cPlottablePlaneCurveCategory``774821 +olistBranches`1`x`(_$)->List(List(Point(DoubleFloat)))`cPlottableSpaceCurveCategory``774937 +olistConjugateBases`3`n`(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)),NonNegativeInteger,NonNegativeInteger)->List(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)))`pChineseRemainderToolsForIntegralBases(K,R,UP)``775053 +olistexp`1`n`(BP)->List(NonNegativeInteger)`pNPCoef(BP,E,OV,R,P)``775300 +olistLoops`1`n`(_$)->List(List(Point(DoubleFloat)))`dTubePlot(Curve)``775336 +olistOfLists`1`n`(S)->List(List(R))`xMatrixCategory&(S,R,Row,Col)``0 +olistOfLists`1`x`(_$)->List(List(R))`cMatrixCategory(R,Row,Col)``775453 +olistOfLists`1`x`(_$)->List(List(R))`cRectangularMatrixCategory(m,n,R,Row,Col)``775681 +olistOfLists`1`x`(_$)->List(List(S))`dTableau(S)``775770 +olistOfMonoms`1`n`(_$)->List(Record(gen:S,exp:E))`dListMonoidOps(S,E,un)``775846 +olistOfTerms`1`n`(_$)->List(LyndonWord(VarSet))`dPoincareBirkhoffWittLyndonBasis(VarSet)``775928 +olistOfTerms`1`n`(_$)->List(Record(k:PoincareBirkhoffWittLyndonBasis(VarSet),c:R))`dLieExponentials(VarSet,R,Order)``776027 +olistOfTerms`1`x`(_$)->List(Record(k:Basis,c:R))`cFreeModuleCat(R,Basis)``776121 +olistRepresentation`1`x`(_$)->Record(preimage:List(S),image:List(S))`dPermutation(S)``776308 +olists`1`n`(_$)->PatternMatchResult(R,L)`dPatternMatchListResult(R,S,L)``776673 +olistVariable`0`x`()->List(PolyRing)`pPackageForPoly(R,PolyRing,E,dim)``0 +olistYoungTableaus`1`x`(List(Integer))->List(Matrix(Integer))`pSymmetricGroupCombinatoricFunctions``776742 +olllip`1`x`(_$)->List(List(List(NonNegativeInteger)))`cThreeSpaceCategory(R)``777211 +olllp`1`x`(_$)->List(List(List(Point(R))))`cThreeSpaceCategory(R)``777481 +ollprop`1`x`(_$)->List(List(SubSpaceComponentProperty))`cThreeSpaceCategory(R)``777739 +olo`1`x`(_$)->S`cSegmentCategory(S)``777995 +olocalAbs`1`n`(FE)->FE`pFunctionSpaceToExponentialExpansion(R,FE,x,cen)``778086 +olocalAbs`1`n`(FE)->FE`pFunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x)``778288 +olocalIntegralBasis`1`n`(Integer)->Record(basis:Matrix(Integer),basisDen:Integer,basisInv:Matrix(Integer))`pNumberFieldIntegralBasis(UP,F)``778490 +olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pFunctionFieldIntegralBasis(R,UP,F)``779390 +olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``780286 +olocalIntegralBasis`1`n`(R)->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pWildFunctionFieldIntegralBasis(K,R,UP,F)``781184 +olocalize`4`x`(PolyRing,ProjPt,PolyRing,Integer)->Record(fnc:PolyRing,crv:PolyRing,chart:List(Integer))`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``782090 +olocalParam`1`x`(_$)->List(PCS)`cPlacesCategory(K,PCS)``782505 +olocalParamOfSimplePt`3`x`(ProjPt,PolyRing,Integer)->List(PCS)`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``782603 +olocalParamV`1`x`(_$)->List(PCS)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +olocalPointV`1`x`(_$)->AffinePlane(K)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``782848 +olocalReal?`1`n`(F)->Boolean`pElementaryFunction(R,F)``782933 +olocalUnquote`2`n`(F,List(Symbol))->F`pApplyRules(Base,R,F)``782993 +oLODO2FUN`1`n`(L)->(List(UTS))->UTS`pUTSodetools(F,UP,L,UTS)``783049 +olog10`0`x`()->_$`dFloat``783165 +olog10`1`x`(_$)->_$`dDoubleFloat``783233 +olog10`1`x`(_$)->_$`dFloat``783306 +olog10`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``783377 +olog`1`n`(Factored(M))->List(Record(coef:NonNegativeInteger,logand:M))`pFactoredFunctions(M)``783455 +olog`1`n`(F)->F`pElementaryFunction(R,F)``783607 +olog`1`n`(_$)->LiePolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``783671 olog`1`n`(S)->S`xComplexCategory&(S,R)``0 olog`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -olog`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``641929 -olog`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``641987 -olog`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``642045 -olog`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``642116 -olog`1`n`(_$)->LiePolynomial(VarSet,R)`dLieExponentials(VarSet,R,Order)``642189 -olog`1`x`(_$)->_$`cElementaryFunctionCategory``642261 -olog`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``642325 -olog`2`n`(XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``642392 -olog`2`n`(_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)`has(R,Module(Fraction(Integer)))`642512 -ological?`1`x`(_$)->Boolean`dFortranScalarType``642636 -ologpart`1`n`(_$)->List(Record(scalar:Fraction(Integer),coeff:SparseUnivariatePolynomial(F),logand:SparseUnivariatePolynomial(F)))`dIntegrationResult(F)``642728 +olog`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``783743 +olog`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``783801 +olog`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``783859 +olog`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``783930 +olog`1`x`(_$)->_$`cElementaryFunctionCategory``784003 +olog`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``784067 +olog2`0`x`()->_$`dFloat``784134 +olog2`1`x`(_$)->_$`dDoubleFloat``784220 +olog2`1`x`(_$)->_$`dFloat``784291 +olog`2`n`(_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)`has(R,Module(Fraction(Integer)))`784360 +olog`2`n`(XPOLY,NonNegativeInteger)->XPOLY`pXExponentialPackage(R,VarSet,XPOLY)``784484 +ologGamma`1`x`(Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``784604 +ologGamma`1`x`(DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``784728 +ological?`1`x`(_$)->Boolean`dFortranScalarType``784852 +ologIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``784944 +ologpart`1`n`(_$)->List(Record(scalar:Fraction(Integer),coeff:SparseUnivariatePolynomial(F),logand:SparseUnivariatePolynomial(F)))`dIntegrationResult(F)``785031 olookup`1`n`(A)->PositiveInteger`xFiniteSetAggregate&(A,S)``0 -olookup`1`n`(Vector(GF))->PositiveInteger`pInnerNormalBasisFieldFunctions(GF)``642808 -olookup`1`x`(_$)->PositiveInteger`cFinite``642882 -oloopPoints`5`n`(Point(DoubleFloat),Point(DoubleFloat),Point(DoubleFloat),DoubleFloat,List(List(DoubleFloat)))->List(Point(DoubleFloat))`pTubePlotTools``642970 -olow`1`x`(_$)->S`cSegmentCategory(S)``643452 -olowerCase!`1`x`(_$)->_$`cStringAggregate``643541 -olowerCase?`1`x`(_$)->Boolean`dCharacter``643645 -olowerCase`0`x`()->_$`dCharacterClass``643756 +olookup`1`n`(Vector(GF))->PositiveInteger`pInnerNormalBasisFieldFunctions(GF)``785111 +olookup`1`x`(_$)->PositiveInteger`cFinite``785185 +oloopPoints`5`n`(Point(DoubleFloat),Point(DoubleFloat),Point(DoubleFloat),DoubleFloat,List(List(DoubleFloat)))->List(Point(DoubleFloat))`pTubePlotTools``785273 +olow`1`x`(_$)->S`cSegmentCategory(S)``785755 +olowerCase`0`x`()->_$`dCharacterClass``785848 olowerCase`1`n`(S)->S`xStringAggregate&(S)``0 -olowerCase`1`x`(_$)->_$`cStringAggregate``643880 -olowerCase`1`x`(_$)->_$`dCharacter``643961 -olowerPolynomial`1`n`(SparseUnivariatePolynomial(P))->SparseUnivariatePolynomial(R)`pFactoringUtilities(E,OV,R,P)``644132 -olp`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``644284 -olprop`1`x`(_$)->List(SubSpaceComponentProperty)`cThreeSpaceCategory(R)``644580 -olquo`2`n`(_$,S)->Union(_$,"failed")`dOrderedFreeMonoid(S)``644782 -olquo`2`n`(_$,_$)->Union(_$,"failed")`dFreeMonoid(S)``644866 -olquo`2`n`(_$,_$)->Union(_$,"failed")`dOrderedFreeMonoid(S)``645060 -olquo`2`x`(XRecursivePolynomial(VarSet,R),_$)->XRecursivePolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``645258 -olquo`2`x`(_$,OrderedFreeMonoid(vl))->_$`cXFreeAlgebra(vl,R)``645372 -olquo`2`x`(_$,_$)->_$`cXFreeAlgebra(vl,R)``645464 -olquo`2`x`(_$,vl)->_$`cXFreeAlgebra(vl,R)``645547 -olyndon?`1`n`(OrderedFreeMonoid(VarSet))->Boolean`dLyndonWord(VarSet)``645643 -olyndonIfCan`1`n`(OrderedFreeMonoid(VarSet))->Union(_$,"failed")`dLyndonWord(VarSet)``645719 -olyndon`1`n`(OrderedFreeMonoid(VarSet))->_$`dLyndonWord(VarSet)``645801 +olowerCase?`1`x`(_$)->Boolean`dCharacter``785947 +olowerCase!`1`x`(_$)->_$`cStringAggregate``786255 +olowerCase`1`x`(_$)->_$`cStringAggregate``786359 +olowerCase`1`x`(_$)->_$`dCharacter``786440 +olowerPolynomial`1`n`(SparseUnivariatePolynomial(P))->SparseUnivariatePolynomial(R)`pFactoringUtilities(E,OV,R,P)``786829 +oLowTriBddDenomInv`2`n`(M,R)->M`pTriangularMatrixOperations(R,Row,Col,M)``786981 +olp`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``787193 +oLPolynomial`0`x`()->SparseUnivariatePolynomial(Integer)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)`has(K,Finite)`787489 +oLPolynomial`0`x`()->SparseUnivariatePolynomial(Integer)`pPackageForAlgebraicFunctionField(K,symb,BLMET)`has(K,Finite)`787542 +oLPolynomial`0`x`()->SparseUnivariatePolynomial(Integer)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)`has(PseudoAlgebraicClosureOfFiniteField(K),Finite)`787595 +oLPolynomial`1`x`(PositiveInteger)->SparseUnivariatePolynomial(Integer)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)`has(K,Finite)`787648 +oLPolynomial`1`x`(PositiveInteger)->SparseUnivariatePolynomial(Integer)`pPackageForAlgebraicFunctionField(K,symb,BLMET)`has(K,Finite)`787770 +oLPolynomial`1`x`(PositiveInteger)->SparseUnivariatePolynomial(Integer)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)`has(PseudoAlgebraicClosureOfFiniteField(K),Finite)`787892 +olprop`1`x`(_$)->List(SubSpaceComponentProperty)`cThreeSpaceCategory(R)``788014 +olquo`2`n`(_$,S)->Union(_$,"failed")`dOrderedFreeMonoid(S)``788216 +olquo`2`n`(_$,_$)->Union(_$,"failed")`dFreeMonoid(S)``788416 +olquo`2`n`(_$,_$)->Union(_$,"failed")`dOrderedFreeMonoid(S)``788610 +olquo`2`x`(_$,_$)->_$`cXFreeAlgebra(vl,R)``788962 +olquo`2`x`(_$,OrderedFreeMonoid(vl))->_$`cXFreeAlgebra(vl,R)``789045 +olquo`2`x`(_$,vl)->_$`cXFreeAlgebra(vl,R)``789137 +olquo`2`x`(XRecursivePolynomial(VarSet,R),_$)->XRecursivePolynomial(VarSet,R)`cFreeLieAlgebra(VarSet,R)``789233 +olSpaceBasis`1`n`(_$)->Vector(R)`dFiniteDivisor(F,UP,UPUP,R)``789347 +oLT`2`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$),Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``789456 +olyndon?`1`n`(OrderedFreeMonoid(VarSet))->Boolean`dLyndonWord(VarSet)``789547 +olyndon`1`n`(OrderedFreeMonoid(VarSet))->_$`dLyndonWord(VarSet)``789623 +oLyndonBasis`1`n`(List(VarSet))->List(LiePolynomial(VarSet,R))`dLieExponentials(VarSet,R,Order)``789750 +oLyndonCoordinates`1`n`(_$)->List(Record(k:LyndonWord(VarSet),c:R))`dLieExponentials(VarSet,R,Order)``789848 +olyndonIfCan`1`n`(OrderedFreeMonoid(VarSet))->Union(_$,"failed")`dLyndonWord(VarSet)``789948 +oLyndonWordsList1`2`n`(List(VarSet),PositiveInteger)->OneDimensionalArray(List(_$))`dLyndonWord(VarSet)``790030 +oLyndonWordsList`2`n`(List(VarSet),PositiveInteger)->List(_$)`dLyndonWord(VarSet)``790203 +omachineFraction`1`x`(_$)->Fraction(Integer)`dDoubleFloat``790359 omagnitude`1`n`(S)->R`xVectorCategory&(S,R)``0 -omagnitude`1`x`(_$)->R`cVectorCategory(R)`AND(has(R,RadicalCategory),has(R,Ring))`645928 -omainCharacterization`1`x`(_$)->Union(RightOpenIntervalRootCharacterization(_$,SparseUnivariatePolynomial(_$)),"failed")`dRealClosure(TheField)``646031 +omagnitude`1`x`(_$)->R`cVectorCategory(R)`AND(has(R,RadicalCategory),has(R,Ring))`790788 +omainCharacterization`1`x`(_$)->Union(RightOpenIntervalRootCharacterization(_$,SparseUnivariatePolynomial(_$)),"failed")`dRealClosure(TheField)``790891 omainCoefficients`1`n`(S)->List(S)`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainCoefficients`1`x`(_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)``646142 +omainCoefficients`1`x`(_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)``791002 omainContent`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainContent`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`646479 -omainDefiningPolynomial`1`x`(_$)->Union(SparseUnivariatePolynomial(_$),"failed")`cRealClosedField``646712 -omainForm`1`x`(_$)->Union(OutputForm,"failed")`cRealClosedField``646839 +omainContent`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`791339 +omainDefiningPolynomial`1`x`(_$)->Union(SparseUnivariatePolynomial(_$),"failed")`cRealClosedField``791572 +omainForm`1`x`(_$)->Union(OutputForm,"failed")`cRealClosedField``791699 omainKernel`1`n`(S)->Union(Kernel(S),"failed")`xExpressionSpace&(S)``0 omainKernel`1`n`(S)->Union(Kernel(S),"failed")`xFunctionSpace&(S,R)``0 -omainKernel`1`x`(_$)->Union(Kernel(_$),"failed")`cExpressionSpace``646929 +omainKernel`1`x`(_$)->Union(Kernel(_$),"failed")`cExpressionSpace``791789 omainMonomial`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainMonomial`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``647090 +omainMonomial`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``791950 omainMonomials`1`n`(S)->List(S)`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainMonomials`1`x`(_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)``647350 +omainMonomials`1`x`(_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)``792210 omainPrimitivePart`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainPrimitivePart`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`647674 +omainPrimitivePart`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`792534 omainSquareFreePart`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -omainSquareFreePart`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`647920 -omainValue`1`x`(_$)->Union(SparseUnivariatePolynomial(_$),"failed")`cRealClosedField``648169 -omainVariable?`2`n`(VarSet,S)->Boolean`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -omainVariable?`2`x`(VarSet,_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)``648293 -omainVariable`1`n`(F)->Union(V,"failed")`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``648447 +omainSquareFreePart`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`792780 +omainValue`1`x`(_$)->Union(SparseUnivariatePolynomial(_$),"failed")`cRealClosedField``793029 +omainVariable`1`n`(F)->Union(V,"failed")`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``793153 omainVariable`1`n`(S)->Union(SingletonAsOrderedSet,"failed")`xUnivariatePolynomialCategory&(S,R)``0 -omainVariable`1`x`(Fraction(Polynomial(R)))->Union(Symbol,"failed")`pRationalFunction(R)``648606 -omainVariable`1`x`(_$)->Union(VarSet,"failed")`cPolynomialCategory(R,E,VarSet)``648765 +omainVariable`1`x`(Fraction(Polynomial(R)))->Union(Symbol,"failed")`pRationalFunction(R)``793312 +omainVariable`1`x`(_$)->Union(VarSet,"failed")`cPolynomialCategory(R,E,VarSet)``793471 +omainVariable?`2`n`(VarSet,S)->Boolean`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 +omainVariable?`2`x`(VarSet,_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)``793671 omainVariables`1`n`(S)->List(VarSet)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -omainVariables`1`x`(_$)->List(VarSet)`cPolynomialSetCategory(R,E,VarSet,P)``648965 -omakeCos`2`x`(E,R)->_$`dFourierSeries(R,E)``649125 -omakeCrit`3`n`(Record(totdeg:NonNegativeInteger,pol:Dpol),Dpol,NonNegativeInteger)->Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``649213 -omakeEq`2`n`(List(F),List(Symbol))->List(Equation(Polynomial(F)))`pInnerNumericFloatSolvePackage(K,F,Par)``649250 -omakeFR`1`n`(Record(contp:Integer,factors:List(Record(irr:UP,pow:Integer))))->Factored(UP)`pGaloisGroupFactorizer(UP)``649376 -omakeFR`2`x`(R,List(Record(flg:Union("nil","sqfr","irred","prime"),fctr:R,xpnt:Integer)))->_$`dFactored(R)``649483 -omakeFloatFunction`2`x`(S,Symbol)->(DoubleFloat)->DoubleFloat`pMakeFloatCompiledFunction(S)``649581 -omakeFloatFunction`3`x`(S,Symbol,Symbol)->(DoubleFloat,DoubleFloat)->DoubleFloat`pMakeFloatCompiledFunction(S)``649839 -omakeGraphImage`1`n`(List(List(Point(DoubleFloat))))->_$`dGraphImage``650172 -omakeGraphImage`1`n`(_$)->_$`dGraphImage``650530 -omakeGraphImage`4`n`(List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger))->_$`dGraphImage``650969 -omakeGraphImage`5`n`(List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger),List(DrawOption))->_$`dGraphImage``651553 -omakeMulti`1`n`(List(Record(gen:S,exp:E)))->_$`dListMonoidOps(S,E,un)``652199 -omakeObject`2`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``652283 -omakeObject`2`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``652561 -omakeObject`2`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``652839 -omakeObject`3`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``653155 -omakeObject`3`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``653502 -omakeObject`3`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``653772 -omakeObject`3`x`(Ex,SegmentBinding(Float),SegmentBinding(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``654065 -omakeObject`3`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``654396 -omakeObject`3`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``654753 -omakeObject`3`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``655177 -omakeObject`3`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``655547 -omakeObject`4`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``655976 -omakeObject`4`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``656354 -omakeObject`4`x`(Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``656745 -omakeObject`4`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``657176 -omakeObject`4`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``657634 -omakeRecord`2`x`(S,T)->Record(part1:S,part2:T)`pMakeRecord(S,T)``658161 -omakeResult`2`n`(PatternMatchResult(R,S),PatternMatchResult(R,L))->_$`dPatternMatchListResult(R,S,L)``658318 +omainVariables`1`x`(_$)->List(VarSet)`cPolynomialSetCategory(R,E,VarSet,P)``793825 +omakeCos`2`x`(E,R)->_$`dFourierSeries(R,E)``793985 +omakeCrit`3`n`(Record(totdeg:NonNegativeInteger,pol:Dpol),Dpol,NonNegativeInteger)->Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``794094 +omakeEq`2`n`(List(F),List(Symbol))->List(Equation(Polynomial(F)))`pInnerNumericFloatSolvePackage(K,F,Par)``794131 +omakeFloatFunction`2`x`(S,Symbol)->(DoubleFloat)->DoubleFloat`pMakeFloatCompiledFunction(S)``794257 +omakeFloatFunction`3`x`(S,Symbol,Symbol)->(DoubleFloat,DoubleFloat)->DoubleFloat`pMakeFloatCompiledFunction(S)``794515 +omakeFR`1`n`(Record(contp:Integer,factors:List(Record(irr:UP,pow:Integer))))->Factored(UP)`pGaloisGroupFactorizer(UP)``794848 +omakeFR`2`x`(R,List(Record(flg:Union("nil","sqfr","irred","prime"),fctr:R,xpnt:Integer)))->_$`dFactored(R)``794955 +omakeGraphImage`1`n`(_$)->_$`dGraphImage``795199 +omakeGraphImage`1`n`(List(List(Point(DoubleFloat))))->_$`dGraphImage``795638 +omakeGraphImage`4`n`(List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger))->_$`dGraphImage``795996 +omakeGraphImage`5`n`(List(List(Point(DoubleFloat))),List(Palette),List(Palette),List(PositiveInteger),List(DrawOption))->_$`dGraphImage``796580 +omakeMulti`1`n`(List(Record(gen:S,exp:E)))->_$`dListMonoidOps(S,E,un)``797226 +omakeObject`2`x`((DoubleFloat)->Point(DoubleFloat),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``797310 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+omakeObject`3`x`(ParametricSpaceCurve((DoubleFloat)->DoubleFloat),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``799423 +omakeObject`3`x`(ParametricSpaceCurve(Ex),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``799780 +omakeObject`3`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``800204 +omakeObject`3`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``800574 +omakeObject`4`x`((DoubleFloat,DoubleFloat)->DoubleFloat,Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``801003 +omakeObject`4`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``801381 +omakeObject`4`x`(Ex,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``801772 +omakeObject`4`x`(ParametricSurface((DoubleFloat,DoubleFloat)->DoubleFloat),Segment(Float),Segment(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``802203 +omakeObject`4`x`(ParametricSurface(Ex),SegmentBinding(Float),SegmentBinding(Float),List(DrawOption))->ThreeSpace(DoubleFloat)`pTopLevelDrawFunctions(Ex)``802661 +omakeop`2`n`(R,FreeGroup(BasicOperator))->_$`dOperator(R)``0 +omakeop`2`x`(R,FreeGroup(BasicOperator))->_$`dModuleOperator(R,M)``803188 +omakeprod`2`n`(A,B)->_$`dProduct(A,B)``803241 +omakeRecord`2`x`(S,T)->Record(part1:S,part2:T)`pMakeRecord(S,T)``803543 +omakeResult`2`n`(PatternMatchResult(R,S),PatternMatchResult(R,L))->_$`dPatternMatchListResult(R,S,L)``803700 +omakeSeries`2`n`(Reference(OrderedCompletion(Integer)),Stream(Record(k:Integer,c:Coef)))->_$`dInnerSparseUnivariatePowerSeries(Coef)``803785 +omakeSin`2`x`(E,R)->_$`dFourierSeries(R,E)``803905 +omakeSketch`5`n`(Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer)))->_$`dPlaneAlgebraicCurvePlot``803993 omakeSUP`1`n`(S)->SparseUnivariatePolynomial(R)`xUnivariatePolynomialCategory&(S,R)``0 -omakeSUP`1`x`(_$)->SparseUnivariatePolynomial(R)`cUnivariatePolynomialCategory(R)``658403 -omakeSeries`2`n`(Reference(OrderedCompletion(Integer)),Stream(Record(k:Integer,c:Coef)))->_$`dInnerSparseUnivariatePowerSeries(Coef)``658530 -omakeSin`2`x`(E,R)->_$`dFourierSeries(R,E)``658650 -omakeSketch`5`n`(Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer)))->_$`dPlaneAlgebraicCurvePlot``658738 -omakeTerm`2`n`(S,E)->_$`dListMonoidOps(S,E,un)``659649 -omakeUnit`0`n`()->_$`dListMonoidOps(S,E,un)``659784 +omakeSUP`1`x`(_$)->SparseUnivariatePolynomial(R)`cUnivariatePolynomialCategory(R)``805364 +omakeTerm`2`n`(S,E)->_$`dListMonoidOps(S,E,un)``805491 +omakeUnit`0`n`()->_$`dListMonoidOps(S,E,un)``805626 omakeVariable`1`n`(A)->(NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 omakeVariable`1`n`(S)->(NonNegativeInteger)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -omakeVariable`1`x`(S)->(NonNegativeInteger)->_$`cDifferentialPolynomialCategory(R,S,V,E)``659851 -omakeVariable`1`x`(_$)->(NonNegativeInteger)->_$`cDifferentialPolynomialCategory(R,S,V,E)`has(R,DifferentialRing)`660166 -omakeVariable`2`x`(S,NonNegativeInteger)->_$`cDifferentialVariableCategory(S)``660494 -omakeViewport2D`1`n`(_$)->_$`dTwoDimensionalViewport``660636 -omakeViewport2D`2`n`(GraphImage,List(DrawOption))->_$`dTwoDimensionalViewport``660858 -omakeViewport3D`1`x`(_$)->_$`dThreeDimensionalViewport``661207 -omakeViewport3D`2`x`(ThreeSpace(DoubleFloat),List(DrawOption))->_$`dThreeDimensionalViewport``661433 -omakeViewport3D`2`x`(ThreeSpace(DoubleFloat),String)->_$`dThreeDimensionalViewport``661768 -omakeYoungTableau`2`x`(List(Integer),List(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``662012 -omakeop`2`n`(R,FreeGroup(BasicOperator))->_$`dOperator(R)``0 -omakeop`2`x`(R,FreeGroup(BasicOperator))->_$`dModuleOperator(R,M)``662293 -omakeprod`2`n`(A,B)->_$`dProduct(A,B)``662346 -omakingStats?`0`n`()->Boolean`pTabulatedComputationPackage(Key,Entry)``662390 -omantissa`1`x`(_$)->Integer`cFloatingPointSystem``662480 -omantissa`1`x`(_$)->Integer`dMachineFloat``662545 +omakeVariable`1`x`(_$)->(NonNegativeInteger)->_$`cDifferentialPolynomialCategory(R,S,V,E)`has(R,DifferentialRing)`805693 +omakeVariable`1`x`(S)->(NonNegativeInteger)->_$`cDifferentialPolynomialCategory(R,S,V,E)``806025 +omakeVariable`2`x`(S,NonNegativeInteger)->_$`cDifferentialVariableCategory(S)``806344 +omakeViewport2D`1`n`(_$)->_$`dTwoDimensionalViewport``806486 +omakeViewport2D`2`n`(GraphImage,List(DrawOption))->_$`dTwoDimensionalViewport``806708 +omakeViewport3D`1`x`(_$)->_$`dThreeDimensionalViewport``807057 +omakeViewport3D`2`x`(ThreeSpace(DoubleFloat),List(DrawOption))->_$`dThreeDimensionalViewport``807283 +omakeViewport3D`2`x`(ThreeSpace(DoubleFloat),String)->_$`dThreeDimensionalViewport``807618 +omakeYoungTableau`2`x`(List(Integer),List(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``807862 +omakingStats?`0`n`()->Boolean`pTabulatedComputationPackage(Key,Entry)``808141 +omantissa`1`x`(_$)->Integer`cFloatingPointSystem``808231 +omantissa`1`x`(_$)->Integer`dMachineFloat``808296 +omap`2`n`((Entry)->Entry,S)->S`xIndexedAggregate&(S,Index,Entry)``0 omap!`2`n`((Entry)->Entry,S)->S`xIndexedAggregate&(S,Index,Entry)``0 +omap`2`n`((Entry)->Entry,S)->S`xTableAggregate&(S,Key,Entry)``0 omap!`2`n`((Entry)->Entry,S)->S`xTableAggregate&(S,Key,Entry)``0 -omap!`2`n`((R)->R,S)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 +omap`2`n`((Expression(CoefRing))->Expression(CoefRing),_$)->_$`dDeRhamComplex(CoefRing,listIndVar)``808355 +omap`2`n`((Polynomial(R))->PPR,PPR)->PPR`pPushVariables(R,E,OV,PPR)``808463 +omap`2`n`((R1)->R2,UPUP1)->UPUP2`pMultipleMap(R1,UP1,UPUP1,R2,UP2,UPUP2)``808504 +omap`2`n`((Record(key:Key,entry:Entry))->Record(key:Key,entry:Entry),S)->S`xTableAggregate&(S,Key,Entry)``0 omap!`2`n`((Record(key:Key,entry:Entry))->Record(key:Key,entry:Entry),S)->S`xTableAggregate&(S,Key,Entry)``0 -omap!`2`n`((S)->S,A)->A`xBinaryTreeCategory&(A,S)``0 -omap!`2`n`((S)->S,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -omap!`2`n`((S)->S,A)->A`xStreamAggregate&(A,S)``0 -omap!`2`x`((R)->R,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``662604 -omap!`2`x`((S)->S,_$)->_$`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`662697 -omapBivariate`2`n`((K)->L,UP)->SparseUnivariatePolynomial(SparseUnivariatePolynomial(L))`pIntegralBasisPolynomialTools(K,R,UP,L)``662811 -omapCoef`2`x`((E)->E,_$)->_$`cFreeAbelianMonoidCategory(S,E)``662922 -omapDown!`3`x`(_$,S,(S,S)->S)->_$`dBalancedBinaryTree(S)``663008 -omapDown!`3`x`(_$,S,(S,S,S)->List(S))->_$`dBalancedBinaryTree(S)``663447 -omapExpon`2`n`((E)->E,_$)->_$`dListMonoidOps(S,E,un)``664051 -omapExpon`2`n`((Integer)->Integer,_$)->_$`dFreeGroup(S)``664138 -omapExpon`2`n`((NonNegativeInteger)->NonNegativeInteger,_$)->_$`dFreeMonoid(S)``664225 -omapExponents`2`n`((E)->E,S)->S`xFiniteAbelianMonoidRing&(S,R,E)``0 -omapExponents`2`x`((E)->E,_$)->_$`cFiniteAbelianMonoidRing(R,E)``664312 -omapGen`2`n`((S)->S,_$)->_$`dFreeGroup(S)``664440 -omapGen`2`n`((S)->S,_$)->_$`dFreeMonoid(S)``664525 -omapGen`2`n`((S)->S,_$)->_$`dListMonoidOps(S,E,un)``664610 -omapGen`2`x`((S)->S,_$)->_$`cFreeAbelianMonoidCategory(S,E)``664695 -omapMatrixIfCan`2`n`((L)->Union(K,"failed"),Matrix(SparseUnivariatePolynomial(L)))->Union(Matrix(R),"failed")`pIntegralBasisPolynomialTools(K,R,UP,L)``664780 -omapSolve`2`n`(UP,(F)->F)->Record(solns:List(F),maps:List(Record(arg:F,res:F)))`pPolynomialSolveByFormulas(UP,F)``664951 -omapUnivariateIfCan`2`n`((L)->Union(K,"failed"),SparseUnivariatePolynomial(L))->Union(R,"failed")`pIntegralBasisPolynomialTools(K,R,UP,L)``664995 -omapUnivariate`2`n`((K)->L,R)->SparseUnivariatePolynomial(L)`pIntegralBasisPolynomialTools(K,R,UP,L)``665160 -omapUnivariate`2`n`((L)->K,SparseUnivariatePolynomial(L))->R`pIntegralBasisPolynomialTools(K,R,UP,L)``665264 -omapUp!`2`x`(_$,(S,S)->S)->S`dBalancedBinaryTree(S)``665368 -omapUp!`3`x`(_$,_$,(S,S,S,S)->S)->_$`dBalancedBinaryTree(S)``665692 -omap`2`n`((Entry)->Entry,S)->S`xIndexedAggregate&(S,Index,Entry)``0 -omap`2`n`((Entry)->Entry,S)->S`xTableAggregate&(S,Key,Entry)``0 -omap`2`n`((Expression(CoefRing))->Expression(CoefRing),_$)->_$`dDeRhamComplex(CoefRing,listIndVar)``666174 -omap`2`n`((Polynomial(R))->PPR,PPR)->PPR`pPushVariables(R,E,OV,PPR)``666282 +omap`2`n`((R)->R,_$)->_$`dAntiSymm(R,lVar)``808600 +omap`2`n`((R)->R,_$)->_$`dMonoidRing(R,M)``808694 +omap`2`n`((R)->R,_$)->_$`dXPolynomialRing(R,E)``808805 omap`2`n`((R)->R,S)->S`xAbelianMonoidRing&(S,R,E)``0 omap`2`n`((R)->R,S)->S`xComplexCategory&(S,R)``0 omap`2`n`((R)->R,S)->S`xOctonionCategory&(S,R)``0 omap`2`n`((R)->R,S)->S`xQuaternionCategory&(S,R)``0 omap`2`n`((R)->R,S)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -omap`2`n`((R)->R,_$)->_$`dAntiSymm(R,lVar)``666323 -omap`2`n`((R)->R,_$)->_$`dMonoidRing(R,M)``666417 -omap`2`n`((R)->R,_$)->_$`dXPolynomialRing(R,E)``666528 -omap`2`n`((R)->S,NewSparseUnivariatePolynomial(R))->NewSparseUnivariatePolynomial(S)`pNewSparseUnivariatePolynomialFunctions2(R,S)``666626 -omap`2`n`((R1)->R2,UPUP1)->UPUP2`pMultipleMap(R1,UP1,UPUP1,R2,UP2,UPUP2)``666755 -omap`2`n`((Record(key:Key,entry:Entry))->Record(key:Key,entry:Entry),S)->S`xTableAggregate&(S,Key,Entry)``0 +omap!`2`n`((R)->R,S)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 +omap`2`n`((R)->S,NewSparseUnivariatePolynomial(R))->NewSparseUnivariatePolynomial(S)`pNewSparseUnivariatePolynomialFunctions2(R,S)``808903 +omap!`2`n`((S)->S,A)->A`xBinaryTreeCategory&(A,S)``0 omap`2`n`((S)->S,A)->A`xListAggregate&(A,S)``0 omap`2`n`((S)->S,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 +omap!`2`n`((S)->S,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 omap`2`n`((S)->S,A)->A`xQuotientFieldCategory&(A,S)``0 +omap!`2`n`((S)->S,A)->A`xStreamAggregate&(A,S)``0 omap`2`n`((S)->S,Kernel(S))->S`xExpressionSpace&(S)``0 -omap`2`n`((Vars1)->Vars2,PR1)->PR2`pMPolyCatFunctions3(Vars1,Vars2,E1,E2,R,PR1,PR2)``666851 -omap`2`x`((A)->A,_$)->_$`cIndexedDirectProductCategory(A,S)``666890 -omap`2`x`((A)->B,DirectProduct(dim,A))->DirectProduct(dim,B)`pDirectProductFunctions2(dim,A,B)``667039 -omap`2`x`((A)->B,Fraction(A))->Fraction(B)`pFractionFunctions2(A,B)``667181 -omap`2`x`((A)->B,InfiniteTuple(A))->InfiniteTuple(B)`pInfiniteTupleFunctions2(A,B)``667307 -omap`2`x`((A)->B,List(A))->List(B)`pListFunctions2(A,B)``667396 -omap`2`x`((A)->B,OneDimensionalArray(A))->OneDimensionalArray(B)`pOneDimensionalArrayFunctions2(A,B)``667574 -omap`2`x`((A)->B,PatternMatchResult(R,A))->PatternMatchResult(R,B)`pPatternMatchResultFunctions2(R,A,B)``667760 -omap`2`x`((A)->B,PrimitiveArray(A))->PrimitiveArray(B)`pPrimitiveArrayFunctions2(A,B)``667914 -omap`2`x`((A)->B,R)->S`pQuotientFieldCategoryFunctions2(A,B,R,S)``668088 -omap`2`x`((A)->B,Stream(A))->Stream(B)`pStreamFunctions2(A,B)``668201 -omap`2`x`((A)->B,Vector(A))->Vector(B)`pVectorFunctions2(A,B)``668410 -omap`2`x`((A)->Union(B,"failed"),Vector(A))->Union(Vector(B),"failed")`pVectorFunctions2(A,B)``668552 -omap`2`x`((CF1)->CF2,ParametricPlaneCurve(CF1))->ParametricPlaneCurve(CF2)`pParametricPlaneCurveFunctions2(CF1,CF2)``668713 -omap`2`x`((CF1)->CF2,ParametricSpaceCurve(CF1))->ParametricSpaceCurve(CF2)`pParametricSpaceCurveFunctions2(CF1,CF2)``668752 -omap`2`x`((CF1)->CF2,ParametricSurface(CF1))->ParametricSurface(CF2)`pParametricSurfaceFunctions2(CF1,CF2)``668791 -omap`2`x`((Coef1)->Coef2,UTS1)->UTS2`pUnivariateTaylorSeriesFunctions2(Coef1,Coef2,UTS1,UTS2)``668830 -omap`2`x`((Coef1)->Coef2,UnivariateLaurentSeries(Coef1,var1,cen1))->UnivariateLaurentSeries(Coef2,var2,cen2)`pUnivariateLaurentSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2)``668951 -omap`2`x`((Coef1)->Coef2,UnivariatePuiseuxSeries(Coef1,var1,cen1))->UnivariatePuiseuxSeries(Coef2,var2,cen2)`pUnivariatePuiseuxSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2)``669059 -omap`2`x`((E)->F,IntegrationResult(E))->IntegrationResult(F)`pIntegrationResultFunctions2(E,F)``669167 -omap`2`x`((E)->F,Kernel(E))->F`pExpressionSpaceFunctions2(E,F)``669208 -omap`2`x`((E)->F,Union(E,"failed"))->Union(F,"failed")`pIntegrationResultFunctions2(E,F)``669313 -omap`2`x`((E)->F,Union(Record(mainpart:E,limitedlogs:List(Record(coeff:E,logand:E))),"failed"))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed")`pIntegrationResultFunctions2(E,F)``669353 -omap`2`x`((E)->F,Union(Record(ratpart:E,coeff:E),"failed"))->Union(Record(ratpart:F,coeff:F),"failed")`pIntegrationResultFunctions2(E,F)``669394 -omap`2`x`((R)->R,_$)->_$`cAbelianMonoidRing(R,E)``669435 -omap`2`x`((R)->R,_$)->_$`cFreeModuleCat(R,Basis)``669546 -omap`2`x`((R)->R,_$)->_$`cFullyEvalableOver(R)``669671 -omap`2`x`((R)->R,_$)->_$`cRectangularMatrixCategory(m,n,R,Row,Col)``669766 -omap`2`x`((R)->R,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``669874 -omap`2`x`((R)->R,_$)->_$`cXFreeAlgebra(vl,R)``669977 -omap`2`x`((R)->R,_$)->_$`dFactored(R)``670075 -omap`2`x`((R)->S,A)->B`pFunctionSpaceFunctions2(R,A,S,B)``670351 -omap`2`x`((R)->S,AR)->AS`pFramedNonAssociativeAlgebraFunctions2(AR,R,AS,S)``670450 -omap`2`x`((R)->S,Complex(R))->Complex(S)`pComplexFunctions2(R,S)``670643 -omap`2`x`((R)->S,Expression(R))->Expression(S)`pExpressionFunctions2(R,S)``670725 -omap`2`x`((R)->S,Factored(R))->Factored(S)`pFactoredFunctions2(R,S)``670812 -omap`2`x`((R)->S,MonoidRing(R,M))->MonoidRing(S,M)`pMonoidRingFunctions2(R,S,M)``671086 -omap`2`x`((R)->S,OR)->OS`pOctonionCategoryFunctions2(OR,R,OS,S)``671265 -omap`2`x`((R)->S,OnePointCompletion(R))->OnePointCompletion(S)`pOnePointCompletionFunctions2(R,S)``671355 -omap`2`x`((R)->S,OrderedCompletion(R))->OrderedCompletion(S)`pOrderedCompletionFunctions2(R,S)``671471 -omap`2`x`((R)->S,PR)->PS`pMPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS)``671644 -omap`2`x`((R)->S,PR)->PS`pUnivariatePolynomialCategoryFunctions2(R,PR,S,PS)``671683 -omap`2`x`((R)->S,Pattern(R))->Pattern(S)`pPatternFunctions2(R,S)``671972 -omap`2`x`((R)->S,Polynomial(R))->Polynomial(S)`pPolynomialFunctions2(R,S)``672096 -omap`2`x`((R)->S,QR)->QS`pQuaternionCategoryFunctions2(QR,R,QS,S)``672243 -omap`2`x`((R)->S,Segment(R))->List(S)`pSegmentFunctions2(R,S)`has(R,OrderedRing)`672335 -omap`2`x`((R)->S,Segment(R))->Segment(S)`pSegmentFunctions2(R,S)``672564 -omap`2`x`((R)->S,SegmentBinding(R))->SegmentBinding(S)`pSegmentBindingFunctions2(R,S)``672633 -omap`2`x`((R)->S,SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(S)`pSparseUnivariatePolynomialFunctions2(R,S)``672711 -omap`2`x`((R)->S,UnivariatePolynomial(x,R))->UnivariatePolynomial(y,S)`pUnivariatePolynomialFunctions2(x,R,y,S)``672846 -omap`2`x`((R)->S,UniversalSegment(R))->Stream(S)`pUniversalSegmentFunctions2(R,S)`has(R,OrderedRing)`672981 -omap`2`x`((R)->S,UniversalSegment(R))->UniversalSegment(S)`pUniversalSegmentFunctions2(R,S)``673071 -omap`2`x`((R1)->R2,F1)->F2`pFunctionFieldCategoryFunctions2(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)``673184 -omap`2`x`((R1)->R2,FiniteDivisor(R1,UP1,UPUP1,F1))->FiniteDivisor(R2,UP2,UPUP2,F2)`pFiniteDivisorFunctions2(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)``673266 -omap`2`x`((R1)->R2,FractionalIdeal(R1,F1,U1,A1))->FractionalIdeal(R2,F2,U2,A2)`pFractionalIdealFunctions2(R1,F1,U1,A1,R2,F2,U2,A2)``673307 -omap`2`x`((R1)->R2,M1)->M2`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``673348 -omap`2`x`((R1)->R2,M1)->M2`pRectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2)``673443 -omap`2`x`((R1)->R2,Matrix(R1))->Matrix(R2)`pExpertSystemToolsPackage2(R1,R2)``673538 -omap`2`x`((R1)->R2,Point(R1))->Point(R2)`pPointFunctions2(R1,R2)``673681 -omap`2`x`((R1)->Union(R2,"failed"),M1)->Union(M2,"failed")`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``673720 -omap`2`x`((S)->R,A)->B`pFiniteLinearAggregateFunctions2(S,A,R,B)``673815 -omap`2`x`((S)->R,A)->B`pFiniteSetAggregateFunctions2(S,A,R,B)``673977 -omap`2`x`((S)->R,Equation(S))->Equation(R)`pEquationFunctions2(S,R)``674138 -omap`2`x`((S)->S,_$)->L`cSegmentExpansionCategory(S,L)``674236 -omap`2`x`((S)->S,_$)->_$`cHomogeneousAggregate(S)``674459 -omap`2`x`((S)->S,_$)->_$`dEquation(S)``674671 -omap`2`x`((S)->S,_$)->_$`dInfiniteTuple(S)``674774 -omap`2`x`((S)->T,CartesianTensor(minix,dim,S))->CartesianTensor(minix,dim,T)`pCartesianTensorFunctions2(minix,dim,S,T)``674856 -omap`2`x`((_$)->_$,Kernel(_$))->_$`cExpressionSpace``674984 +omap`2`n`((Vars1)->Vars2,PR1)->PR2`pMPolyCatFunctions3(Vars1,Vars2,E1,E2,R,PR1,PR2)``809032 +omap`2`x`((A)->A,_$)->_$`cIndexedDirectProductCategory(A,S)``809071 +omap`2`x`((A)->B,DirectProduct(dim,A))->DirectProduct(dim,B)`pDirectProductFunctions2(dim,A,B)``809220 +omap`2`x`((A)->B,Fraction(A))->Fraction(B)`pFractionFunctions2(A,B)``809362 +omap`2`x`((A)->B,InfiniteTuple(A))->InfiniteTuple(B)`pInfiniteTupleFunctions2(A,B)``809488 +omap`2`x`((A)->B,List(A))->List(B)`pListFunctions2(A,B)``809577 +omap`2`x`((A)->B,OneDimensionalArray(A))->OneDimensionalArray(B)`pOneDimensionalArrayFunctions2(A,B)``809755 +omap`2`x`((A)->B,PatternMatchResult(R,A))->PatternMatchResult(R,B)`pPatternMatchResultFunctions2(R,A,B)``810145 +omap`2`x`((A)->B,PrimitiveArray(A))->PrimitiveArray(B)`pPrimitiveArrayFunctions2(A,B)``810299 +omap`2`x`((A)->B,R)->S`pQuotientFieldCategoryFunctions2(A,B,R,S)``810672 +omap`2`x`((A)->B,Stream(A))->Stream(B)`pStreamFunctions2(A,B)``810785 +omap`2`x`((A)->B,Vector(A))->Vector(B)`pVectorFunctions2(A,B)``811208 +omap`2`x`((A)->Union(B,"failed"),Vector(A))->Union(Vector(B),"failed")`pVectorFunctions2(A,B)``811350 +omap`2`x`((CF1)->CF2,ParametricPlaneCurve(CF1))->ParametricPlaneCurve(CF2)`pParametricPlaneCurveFunctions2(CF1,CF2)``811511 +omap`2`x`((CF1)->CF2,ParametricSpaceCurve(CF1))->ParametricSpaceCurve(CF2)`pParametricSpaceCurveFunctions2(CF1,CF2)``811550 +omap`2`x`((CF1)->CF2,ParametricSurface(CF1))->ParametricSurface(CF2)`pParametricSurfaceFunctions2(CF1,CF2)``811589 +omap`2`x`((Coef1)->Coef2,UnivariateLaurentSeries(Coef1,var1,cen1))->UnivariateLaurentSeries(Coef2,var2,cen2)`pUnivariateLaurentSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2)``811628 +omap`2`x`((Coef1)->Coef2,UnivariatePuiseuxSeries(Coef1,var1,cen1))->UnivariatePuiseuxSeries(Coef2,var2,cen2)`pUnivariatePuiseuxSeriesFunctions2(Coef1,Coef2,var1,var2,cen1,cen2)``811736 +omap`2`x`((Coef1)->Coef2,UTS1)->UTS2`pUnivariateTaylorSeriesFunctions2(Coef1,Coef2,UTS1,UTS2)``811844 +omap`2`x`((E)->F,IntegrationResult(E))->IntegrationResult(F)`pIntegrationResultFunctions2(E,F)``811965 +omap`2`x`((E)->F,Kernel(E))->F`pExpressionSpaceFunctions2(E,F)``812006 +omap`2`x`((E)->F,Union(E,"failed"))->Union(F,"failed")`pIntegrationResultFunctions2(E,F)``812111 +omap`2`x`((E)->F,Union(Record(mainpart:E,limitedlogs:List(Record(coeff:E,logand:E))),"failed"))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed")`pIntegrationResultFunctions2(E,F)``812151 +omap`2`x`((E)->F,Union(Record(ratpart:E,coeff:E),"failed"))->Union(Record(ratpart:F,coeff:F),"failed")`pIntegrationResultFunctions2(E,F)``812192 +omap`2`x`((_$)->_$,Kernel(_$))->_$`cExpressionSpace``812233 +omap`2`x`((R1)->R2,A1)->A2`pFiniteAbelianMonoidRingFunctions2(E,R1,A1,R2,A2)``812334 +omap`2`x`((R1)->R2,F1)->F2`pFunctionFieldCategoryFunctions2(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)``812458 +omap`2`x`((R1)->R2,FiniteDivisor(R1,UP1,UPUP1,F1))->FiniteDivisor(R2,UP2,UPUP2,F2)`pFiniteDivisorFunctions2(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)``812540 +omap`2`x`((R1)->R2,FractionalIdeal(R1,F1,U1,A1))->FractionalIdeal(R2,F2,U2,A2)`pFractionalIdealFunctions2(R1,F1,U1,A1,R2,F2,U2,A2)``812581 +omap`2`x`((R1)->R2,M1)->M2`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``812622 +omap`2`x`((R1)->R2,M1)->M2`pRectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2)``812717 +omap`2`x`((R1)->R2,Matrix(R1))->Matrix(R2)`pExpertSystemToolsPackage2(R1,R2)``812812 +omap`2`x`((R1)->R2,Point(R1))->Point(R2)`pPointFunctions2(R1,R2)``812955 +omap`2`x`((R1)->Union(R2,"failed"),M1)->Union(M2,"failed")`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``812994 +omap`2`x`((R)->R,_$)->_$`cAbelianMonoidRing(R,E)``813089 +omap`2`x`((R)->R,_$)->_$`cFreeModuleCat(R,Basis)``813200 +omap`2`x`((R)->R,_$)->_$`cFullyEvalableOver(R)``813325 +omap`2`x`((R)->R,_$)->_$`cRectangularMatrixCategory(m,n,R,Row,Col)``813420 +omap`2`x`((R)->R,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``813528 +omap!`2`x`((R)->R,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``813806 +omap`2`x`((R)->R,_$)->_$`cXFreeAlgebra(vl,R)``814017 +omap`2`x`((R)->R,_$)->_$`dFactored(R)``814115 +omap`2`x`((R)->S,A)->B`pFunctionSpaceFunctions2(R,A,S,B)``814746 +omap`2`x`((R)->S,AR)->AS`pFramedNonAssociativeAlgebraFunctions2(AR,R,AS,S)``814845 +omap`2`x`((R)->S,Complex(R))->Complex(S)`pComplexFunctions2(R,S)``815038 +omap`2`x`((R)->S,Expression(R))->Expression(S)`pExpressionFunctions2(R,S)``815120 +omap`2`x`((R)->S,Factored(R))->Factored(S)`pFactoredFunctions2(R,S)``815207 +omap`2`x`((R)->S,MonoidRing(R,M))->MonoidRing(S,M)`pMonoidRingFunctions2(R,S,M)``815481 +omap`2`x`((R)->S,OnePointCompletion(R))->OnePointCompletion(S)`pOnePointCompletionFunctions2(R,S)``815660 +omap`2`x`((R)->S,OrderedCompletion(R))->OrderedCompletion(S)`pOrderedCompletionFunctions2(R,S)``815776 +omap`2`x`((R)->S,OR)->OS`pOctonionCategoryFunctions2(OR,R,OS,S)``815949 +omap`2`x`((R)->S,Pattern(R))->Pattern(S)`pPatternFunctions2(R,S)``816039 +omap`2`x`((R)->S,Polynomial(R))->Polynomial(S)`pPolynomialFunctions2(R,S)``816163 +omap`2`x`((R)->S,PR)->PS`pMPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS)``816310 +omap`2`x`((R)->S,PR)->PS`pUnivariatePolynomialCategoryFunctions2(R,PR,S,PS)``816349 +omap`2`x`((R)->S,QR)->QS`pQuaternionCategoryFunctions2(QR,R,QS,S)``816642 +omap`2`x`((R)->S,SegmentBinding(R))->SegmentBinding(S)`pSegmentBindingFunctions2(R,S)``817016 +omap`2`x`((R)->S,Segment(R))->List(S)`pSegmentFunctions2(R,S)`has(R,OrderedRing)`817094 +omap`2`x`((R)->S,Segment(R))->Segment(S)`pSegmentFunctions2(R,S)``817323 +omap`2`x`((R)->S,SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(S)`pSparseUnivariatePolynomialFunctions2(R,S)``817392 +omap`2`x`((R)->S,UnivariatePolynomial(x,R))->UnivariatePolynomial(y,S)`pUnivariatePolynomialFunctions2(x,R,y,S)``817527 +omap`2`x`((R)->S,UniversalSegment(R))->Stream(S)`pUniversalSegmentFunctions2(R,S)`has(R,OrderedRing)`817662 +omap`2`x`((R)->S,UniversalSegment(R))->UniversalSegment(S)`pUniversalSegmentFunctions2(R,S)``817752 +omap`2`x`((S)->R,A)->B`pFiniteLinearAggregateFunctions2(S,A,R,B)``817865 +omap`2`x`((S)->R,A)->B`pFiniteSetAggregateFunctions2(S,A,R,B)``818027 +omap`2`x`((S)->R,Equation(S))->Equation(R)`pEquationFunctions2(S,R)``818188 +omap!`2`x`((S)->S,_$)->_$`cHomogeneousAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`818286 +omap`2`x`((S)->S,_$)->_$`cHomogeneousAggregate(S)``818400 +omap`2`x`((S)->S,_$)->_$`dArrayStack(S)``818612 +omap!`2`x`((S)->S,_$)->_$`dArrayStack(S)`has(_$,ATTRIBUTE(shallowlyMutable))`818741 +omap`2`x`((S)->S,_$)->_$`dDequeue(S)``818871 +omap!`2`x`((S)->S,_$)->_$`dDequeue(S)`has(_$,ATTRIBUTE(shallowlyMutable))`818994 +omap`2`x`((S)->S,_$)->_$`dEquation(S)``819118 +omap`2`x`((S)->S,_$)->_$`dHeap(S)``819221 +omap!`2`x`((S)->S,_$)->_$`dHeap(S)`has(_$,ATTRIBUTE(shallowlyMutable))`819338 +omap`2`x`((S)->S,_$)->_$`dInfiniteTuple(S)``819456 +omap`2`x`((S)->S,_$)->_$`dQueue(S)``819538 +omap!`2`x`((S)->S,_$)->_$`dQueue(S)`has(_$,ATTRIBUTE(shallowlyMutable))`819657 +omap`2`x`((S)->S,_$)->_$`dStack(S)``819777 +omap!`2`x`((S)->S,_$)->_$`dStack(S)`has(_$,ATTRIBUTE(shallowlyMutable))`819896 +omap`2`x`((S)->S,_$)->L`cSegmentExpansionCategory(S,L)``820016 +omap`2`x`((S)->T,CartesianTensor(minix,dim,S))->CartesianTensor(minix,dim,T)`pCartesianTensorFunctions2(minix,dim,S,T)``820239 omap`3`n`((Entry,Entry)->Entry,S,S)->S`xTableAggregate&(S,Key,Entry)``0 -omap`3`n`((F)->S,String,Kernel(F))->S`pExpressionSpaceFunctions1(F,S)``675085 +omap`3`n`((F)->S,String,Kernel(F))->S`pExpressionSpaceFunctions1(F,S)``820367 omap`3`n`((R,R)->R,S,S)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 omap`3`n`((S,S)->S,A,A)->A`xListAggregate&(A,S)``0 omap`3`n`((S,S)->S,A,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -omap`3`n`((Vars)->S,(R)->S,P)->S`pPolynomialCategoryLifting(E,Vars,R,P,S)``675226 -omap`3`x`((A,B)->C,InfiniteTuple(A),InfiniteTuple(B))->InfiniteTuple(C)`pInfiniteTupleFunctions3(A,B,C)``675535 -omap`3`x`((A,B)->C,InfiniteTuple(A),Stream(B))->Stream(C)`pInfiniteTupleFunctions3(A,B,C)``675578 -omap`3`x`((A,B)->C,List(A),List(B))->List(C)`pListFunctions3(A,B,C)``675621 -omap`3`x`((A,B)->C,Stream(A),InfiniteTuple(B))->Stream(C)`pInfiniteTupleFunctions3(A,B,C)``676052 -omap`3`x`((A,B)->C,Stream(A),Stream(B))->Stream(C)`pStreamFunctions3(A,B,C)``676095 -omap`3`x`((Entry,Entry)->Entry,_$,_$)->_$`cTableAggregate(Key,Entry)``676354 -omap`3`x`((R)->S,OnePointCompletion(R),OnePointCompletion(S))->OnePointCompletion(S)`pOnePointCompletionFunctions2(R,S)``676600 -omap`3`x`((R,R)->R,_$,_$)->_$`cRectangularMatrixCategory(m,n,R,Row,Col)``676721 -omap`3`x`((R,R)->R,_$,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``676869 -omap`3`x`((S,S)->S,_$,_$)->_$`cLinearAggregate(S)``676987 +omap`3`n`((Vars)->S,(R)->S,P)->S`pPolynomialCategoryLifting(E,Vars,R,P,S)``820508 +omap`3`x`((A,B)->C,InfiniteTuple(A),InfiniteTuple(B))->InfiniteTuple(C)`pInfiniteTupleFunctions3(A,B,C)``820817 +omap`3`x`((A,B)->C,InfiniteTuple(A),Stream(B))->Stream(C)`pInfiniteTupleFunctions3(A,B,C)``820860 +omap`3`x`((A,B)->C,List(A),List(B))->List(C)`pListFunctions3(A,B,C)``820903 +omap`3`x`((A,B)->C,Stream(A),InfiniteTuple(B))->Stream(C)`pInfiniteTupleFunctions3(A,B,C)``821334 +omap`3`x`((A,B)->C,Stream(A),Stream(B))->Stream(C)`pStreamFunctions3(A,B,C)``821377 +omap`3`x`((Entry,Entry)->Entry,_$,_$)->_$`cTableAggregate(Key,Entry)``821958 +omap`3`x`((R,R)->R,_$,_$)->_$`cRectangularMatrixCategory(m,n,R,Row,Col)``822204 +omap`3`x`((R,R)->R,_$,_$)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``822352 +omap`3`x`((R)->S,OnePointCompletion(R),OnePointCompletion(S))->OnePointCompletion(S)`pOnePointCompletionFunctions2(R,S)``822667 +omap`3`x`((S,S)->S,_$,_$)->_$`cLinearAggregate(S)``822788 omap`4`n`((R,R)->R,S,S,R)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -omap`4`x`((R)->S,OrderedCompletion(R),OrderedCompletion(S),OrderedCompletion(S))->OrderedCompletion(S)`pOrderedCompletionFunctions2(R,S)``677298 -omap`4`x`((R,R)->R,_$,_$,R)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``677472 -omapdiv`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Field)`677816 -omapmult`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``677907 +omap`4`x`((R,R)->R,_$,_$,R)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``823103 +omap`4`x`((R)->S,OrderedCompletion(R),OrderedCompletion(S),OrderedCompletion(S))->OrderedCompletion(S)`pOrderedCompletionFunctions2(R,S)``823799 +omapBivariate`2`n`((K)->L,UP)->SparseUnivariatePolynomial(SparseUnivariatePolynomial(L))`pIntegralBasisPolynomialTools(K,R,UP,L)``823973 +omapCoef`2`x`((E)->E,_$)->_$`cFreeAbelianMonoidCategory(S,E)``824084 +omapdiv`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Field)`824170 +omapDown!`3`x`(_$,S,(S,S)->S)->_$`dBalancedBinaryTree(S)``824261 +omapDown!`3`x`(_$,S,(S,S,S)->List(S))->_$`dBalancedBinaryTree(S)``825099 +omapExpon`2`n`((E)->E,_$)->_$`dListMonoidOps(S,E,un)``826178 +omapExpon`2`n`((Integer)->Integer,_$)->_$`dFreeGroup(S)``826265 +omapExpon`2`n`((NonNegativeInteger)->NonNegativeInteger,_$)->_$`dFreeMonoid(S)``826352 +omapExponents`2`n`((E)->E,S)->S`xFiniteAbelianMonoidRing&(S,R,E)``0 +omapExponents`2`x`((E)->E,_$)->_$`cFiniteAbelianMonoidRing(R,E)``826439 +omapExponents`2`x`((E)->E,PolyRing)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``0 +omapGen`2`n`((S)->S,_$)->_$`dFreeGroup(S)``826567 +omapGen`2`n`((S)->S,_$)->_$`dFreeMonoid(S)``826652 +omapGen`2`n`((S)->S,_$)->_$`dListMonoidOps(S,E,un)``826737 +omapGen`2`x`((S)->S,_$)->_$`cFreeAbelianMonoidCategory(S,E)``826822 +omapMatrixIfCan`2`n`((L)->Union(K,"failed"),Matrix(SparseUnivariatePolynomial(L)))->Union(Matrix(R),"failed")`pIntegralBasisPolynomialTools(K,R,UP,L)``826907 +omapmult`2`n`(Stream(A),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``827078 +omapSolve`2`n`(UP,(F)->F)->Record(solns:List(F),maps:List(Record(arg:F,res:F)))`pPolynomialSolveByFormulas(UP,F)``827170 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-omerge`1`x`(List(_$))->_$`cThreeSpaceCategory(R)``699505 omerge`2`n`(A,A)->A`xFiniteLinearAggregate&(A,S)``0 omerge`2`n`(A,A)->A`xListAggregate&(A,S)``0 +omerge!`2`n`(A,A)->A`xListAggregate&(A,S)``0 omerge`2`n`(A,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -omerge`2`n`(_$,_$)->_$`dSubSpace(n,R)``699696 -omerge`2`x`(_$,_$)->_$`cFiniteLinearAggregate(S)`has(S,OrderedSet)`699787 -omerge`2`x`(_$,_$)->_$`cPriorityQueueAggregate(S)``699946 -omerge`2`x`(_$,_$)->_$`cThreeSpaceCategory(R)``700076 +omerge`2`n`(_$,_$)->_$`dSubSpace(n,R)``853401 +omerge!`2`x`(_$,_$)->_$`cExtensibleLinearAggregate(S)`has(S,OrderedSet)`853492 +omerge`2`x`(_$,_$)->_$`cFiniteLinearAggregate(S)`has(S,OrderedSet)`853583 +omerge`2`x`(_$,_$)->_$`cPriorityQueueAggregate(S)``853746 +omerge!`2`x`(_$,_$)->_$`cPriorityQueueAggregate(S)``853876 +omerge`2`x`(_$,_$)->_$`cThreeSpaceCategory(R)``854004 +omerge`2`x`(_$,_$)->_$`dHeap(S)``854181 +omerge!`2`x`(_$,_$)->_$`dHeap(S)``854323 +omerge!`3`n`((S,S)->Boolean,A,A)->A`xExtensibleLinearAggregate&(A,S)``0 omerge`3`n`((S,S)->Boolean,A,A)->A`xFiniteLinearAggregate&(A,S)``0 omerge`3`n`((S,S)->Boolean,A,A)->A`xListAggregate&(A,S)``0 +omerge!`3`n`((S,S)->Boolean,A,A)->A`xListAggregate&(A,S)``0 omerge`3`n`((S,S)->Boolean,A,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -omerge`3`x`((S,S)->Boolean,_$,_$)->_$`cFiniteLinearAggregate(S)``700253 -omesh?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``700884 -omeshFun2Var`5`n`((DoubleFloat,DoubleFloat)->DoubleFloat,Union((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat,"undefined"),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``701098 -omeshPar1Var`6`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``701159 -omeshPar2Var`4`n`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``701223 -omeshPar2Var`5`n`(ThreeSpace(DoubleFloat),(DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``701280 -omeshPar2Var`7`n`((DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,Union((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat,"undefined"),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``701342 -omesh`1`x`(List(List(Point(R))))->_$`cThreeSpaceCategory(R)``701411 -omesh`1`x`(_$)->List(List(Point(R)))`cThreeSpaceCategory(R)``701635 -omesh`3`x`(List(List(Point(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``701897 -omesh`4`x`(_$,List(List(List(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``702640 -omesh`4`x`(_$,List(List(List(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty)->_$`cThreeSpaceCategory(R)``703556 -omesh`4`x`(_$,List(List(Point(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``704115 -omesh`4`x`(_$,List(List(Point(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty)->_$`cThreeSpaceCategory(R)``704892 -omessagePrint`1`n`(String)->Void`dOutputForm``705267 -omessage`1`n`(String)->_$`dOutputForm``705407 -omiddle`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``705492 -omidpoint`1`x`(Record(left:Fraction(Integer),right:Fraction(Integer)))->Fraction(Integer)`pRealZeroPackage(Pol)``705564 -omidpoints`1`x`(List(Record(left:Fraction(Integer),right:Fraction(Integer))))->List(Fraction(Integer))`pRealZeroPackage(Pol)``705641 -omightHaveRoots`2`x`(ThePolDom,_$)->Boolean`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``705746 -ominColIndex`1`x`(_$)->Integer`cRectangularMatrixCategory(m,n,R,Row,Col)``705851 -ominColIndex`1`x`(_$)->Integer`cTwoDimensionalArrayCategory(R,Row,Col)``705944 -ominGbasis`1`n`(List(Dpol))->List(Dpol)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``706035 -ominIndex`1`n`(A)->Integer`xLazyStreamAggregate&(A,S)``0 -ominIndex`1`n`(S)->Index`xIndexedAggregate&(S,Index,Entry)``0 -ominIndex`1`x`(_$)->Index`cIndexedAggregate(Index,Entry)`has(Index,OrderedSet)`706073 -ominPoints3D`0`n`()->Integer`dPlot3D``706289 -ominPoints`0`n`()->Integer`dPlot``706365 -ominPoints`0`x`()->Integer`pGraphicsDefaults``706438 -ominPoints`1`x`(Integer)->Integer`pGraphicsDefaults``706512 -ominPol`2`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``706583 -ominPol`3`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``706618 -ominPoly`1`n`(Kernel(F))->SparseUnivariatePolynomial(F)`pAlgebraicFunction(R,F)`has(R,RetractableTo(Integer))`706653 -ominPoly`1`x`(Kernel(_$))->SparseUnivariatePolynomial(_$)`cExpressionSpace`has(_$,Ring)`706723 -ominRowIndex`1`x`(_$)->Integer`cRectangularMatrixCategory(m,n,R,Row,Col)``706792 -ominRowIndex`1`x`(_$)->Integer`cTwoDimensionalArrayCategory(R,Row,Col)``706882 -omin`0`x`()->_$`cFloatingPointSystem`AND(not(has(_$,ATTRIBUTE(arbitraryExponent))),not(has(_$,ATTRIBUTE(arbitraryPrecision))))`706970 -omin`0`x`()->_$`dSingleInteger``707033 +omerge!`3`x`((S,S)->Boolean,_$,_$)->_$`cExtensibleLinearAggregate(S)``854495 +omerge`3`x`((S,S)->Boolean,_$,_$)->_$`cFiniteLinearAggregate(S)``854596 +omergeDifference`2`x`(List(S),List(S))->List(S)`pMergeThing(S)``855227 +omergeFactors`2`n`(Factored(R),Factored(R))->Factored(R)`pFactoredFunctionUtilities(R)``855411 +omesh?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``855733 +omesh`1`x`(List(List(Point(R))))->_$`cThreeSpaceCategory(R)``855947 +omesh`1`x`(_$)->List(List(Point(R)))`cThreeSpaceCategory(R)``856171 +omesh`3`x`(List(List(Point(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``856433 +omesh`4`x`(_$,List(List(List(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``857176 +omesh`4`x`(_$,List(List(List(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty)->_$`cThreeSpaceCategory(R)``858170 +omesh`4`x`(_$,List(List(Point(R))),Boolean,Boolean)->_$`cThreeSpaceCategory(R)``858783 +omesh`4`x`(_$,List(List(Point(R))),List(SubSpaceComponentProperty),SubSpaceComponentProperty)->_$`cThreeSpaceCategory(R)``859560 +omeshFun2Var`5`n`((DoubleFloat,DoubleFloat)->DoubleFloat,Union((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat,"undefined"),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``859935 +omeshPar1Var`6`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``859996 +omeshPar2Var`4`n`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``860060 +omeshPar2Var`5`n`(ThreeSpace(DoubleFloat),(DoubleFloat,DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``860117 +omeshPar2Var`7`n`((DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,Union((DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat,"undefined"),Segment(DoubleFloat),Segment(DoubleFloat),List(DrawOption))->ThreeSpace(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``860179 +omessage`1`n`(String)->_$`dOutputForm``860248 +omessagePrint`1`n`(String)->Void`dOutputForm``860333 +omiddle`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``860473 +omidpoint`1`x`(Record(left:Fraction(Integer),right:Fraction(Integer)))->Fraction(Integer)`pRealZeroPackage(Pol)``860545 +omidpoints`1`x`(List(Record(left:Fraction(Integer),right:Fraction(Integer))))->List(Fraction(Integer))`pRealZeroPackage(Pol)``860622 +omightHaveRoots`2`x`(ThePolDom,_$)->Boolean`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``860727 +omin`0`x`()->_$`cFloatingPointSystem`AND(not(has(_$,ATTRIBUTE(arbitraryExponent))),not(has(_$,ATTRIBUTE(arbitraryPrecision))))`860832 +omin`0`x`()->_$`dSingleInteger``860895 omin`1`n`(A)->S`xFiniteSetAggregate&(A,S)``0 -omin`1`x`(_$)->S`cFiniteSetAggregate(S)`has(S,OrderedSet)`707090 -omin`1`x`(_$)->S`cOrderedMultisetAggregate(S)``707163 +omin`1`x`(_$)->S`cFiniteSetAggregate(S)`has(S,OrderedSet)`860952 +omin`1`x`(_$)->S`cOrderedMultisetAggregate(S)``861025 omin`2`n`(S,S)->S`xOrderedSet&(S)``0 -omin`2`x`(_$,_$)->_$`cOrderedSet``707247 -omindegTerm`1`x`(_$)->Record(k:OrderedFreeMonoid(vl),c:R)`cXFreeAlgebra(vl,R)``707341 -omindeg`1`n`(_$)->E`dXPolynomialRing(R,E)``707418 -omindeg`1`x`(_$)->OrderedFreeMonoid(vl)`cXFreeAlgebra(vl,R)``707576 +omin`2`x`(_$,_$)->_$`cOrderedSet``861109 +ominColIndex`1`x`(_$)->Integer`cRectangularMatrixCategory(m,n,R,Row,Col)``861203 +ominColIndex`1`x`(_$)->Integer`cTwoDimensionalArrayCategory(R,Row,Col)``861296 +omindeg`1`n`(_$)->E`dXPolynomialRing(R,E)``861497 +omindeg`1`x`(_$)->OrderedFreeMonoid(vl)`cXFreeAlgebra(vl,R)``861655 +omindegTerm`1`x`(_$)->Record(k:OrderedFreeMonoid(vl),c:R)`cXFreeAlgebra(vl,R)``861751 +ominGbasis`1`n`(List(Dpol))->List(Dpol)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``861828 +ominimalForm`1`x`(PolyRing)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``861866 +ominimalForm`2`x`(PolyRing,ProjPt)->PolyRing`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``861953 +ominimalForm`3`x`(PolyRing,ProjPt,Integer)->PolyRing`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``862037 ominimalPolynomial`1`n`(S)->SparseUnivariatePolynomial(F)`xFiniteAlgebraicExtensionField&(S,F)``0 ominimalPolynomial`1`n`(S)->SparseUnivariatePolynomial(R)`xComplexCategory&(S,R)``0 ominimalPolynomial`1`n`(S)->UP`xFramedAlgebra&(S,R,UP)``0 -ominimalPolynomial`1`n`(Vector(GF))->SparseUnivariatePolynomial(GF)`pInnerNormalBasisFieldFunctions(GF)``707672 -ominimalPolynomial`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)``707791 -ominimalPolynomial`1`x`(_$)->UP`cFiniteRankAlgebra(R,UP)`has(R,Field)`707912 +ominimalPolynomial`1`n`(Vector(GF))->SparseUnivariatePolynomial(GF)`pInnerNormalBasisFieldFunctions(GF)``862121 +ominimalPolynomial`1`x`(_$)->SparseUnivariatePolynomial(F)`cFiniteAlgebraicExtensionField(F)``862240 +ominimalPolynomial`1`x`(_$)->UP`cFiniteRankAlgebra(R,UP)`has(R,Field)`862361 ominimalPolynomial`2`n`(S,PositiveInteger)->SparseUnivariatePolynomial(S)`xFiniteAlgebraicExtensionField&(S,F)``0 -ominimalPolynomial`2`x`(_$,PositiveInteger)->SparseUnivariatePolynomial(_$)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`707991 -ominimize`1`n`(_$)->_$`dFractionalIdeal(R,F,UP,A)``708150 +ominimalPolynomial`2`x`(_$,PositiveInteger)->SparseUnivariatePolynomial(_$)`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`862440 +ominimize`1`n`(_$)->_$`dFractionalIdeal(R,F,UP,A)``862599 ominimumDegree`1`n`(S)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 -ominimumDegree`1`x`(_$)->E`cFiniteAbelianMonoidRing(R,E)``708226 -ominimumDegree`1`x`(_$)->NonNegativeInteger`cMonogenicLinearOperator(R)``708349 -ominimumDegree`1`x`(_$)->NonNegativeInteger`cUnivariateSkewPolynomialCategory(R)``708498 +ominimumDegree`1`x`(_$)->E`cFiniteAbelianMonoidRing(R,E)``862675 +ominimumDegree`1`x`(_$)->NonNegativeInteger`cMonogenicLinearOperator(R)``862798 +ominimumDegree`1`x`(_$)->NonNegativeInteger`cUnivariateSkewPolynomialCategory(R)``862947 ominimumDegree`2`n`(S,List(SingletonAsOrderedSet))->List(NonNegativeInteger)`xUnivariatePolynomialCategory&(S,R)``0 ominimumDegree`2`n`(S,SingletonAsOrderedSet)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 -ominimumDegree`2`x`(_$,List(VarSet))->List(NonNegativeInteger)`cPolynomialCategory(R,E,VarSet)``708646 -ominimumDegree`2`x`(_$,VarSet)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``708804 -ominimumExponent`0`x`()->Integer`dMachineFloat``708976 -ominimumExponent`1`x`(Integer)->Integer`dMachineFloat``709050 -ominordet`1`x`(M)->R`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``709134 -ominordet`1`x`(_$)->R`cMatrixCategory(R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`709258 -ominordet`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`709382 -ominrank`1`n`(List(Record(rank:NonNegativeInteger,eqns:List(Record(det:GR,rows:List(Integer),cols:List(Integer))),fgb:List(GR))))->NonNegativeInteger`pParametricLinearEquations(R,Var,Expon,GR)``709470 -ominset`1`n`(List(List(GR)))->List(List(GR))`pParametricLinearEquations(R,Var,Expon,GR)``709552 -ominus!`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``709701 -ominus!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``709852 -ominusInfinity`0`x`()->OrderedCompletion(Integer)`pInfinity``710055 -ominusInfinity`0`x`()->_$`dOrderedCompletion(R)``710108 -omirror`1`n`(_$)->_$`dLieExponentials(VarSet,R,Order)``710157 -omirror`1`n`(_$)->_$`dMagma(VarSet)``710255 -omirror`1`n`(_$)->_$`dOrderedFreeMonoid(S)``710527 -omirror`1`x`(_$)->_$`cFreeLieAlgebra(VarSet,R)``710590 -omirror`1`x`(_$)->_$`cXFreeAlgebra(vl,R)``710704 -omix`1`n`(List(Record(den:Integer,gcdnum:Integer)))->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``710804 -omkAnswer`3`n`(F,List(Record(scalar:Fraction(Integer),coeff:SparseUnivariatePolynomial(F),logand:SparseUnivariatePolynomial(F))),List(Record(integrand:F,intvar:F)))->_$`dIntegrationResult(F)``710839 -omkIntegral`1`n`(UPUP)->Record(coef:Fraction(UP),poly:UPUP)`pChangeOfVariable(F,UP,UPUP)``711005 -omkPrim`2`n`(F,Symbol)->F`pIntegrationTools(R,F)`AND(has(R,GcdDomain),has(F,ElementaryFunctionCategory))`711270 -omkcomm`1`x`(Integer)->_$`dCommutator``711391 -omkcomm`2`x`(_$,_$)->_$`dCommutator``711431 -omodTree`2`x`(R,List(R))->List(R)`pCRApackage(R)``711475 -omodifyPointData`3`x`(_$,NonNegativeInteger,Point(DoubleFloat))->Void`dThreeDimensionalViewport``711520 -omodifyPointData`3`x`(_$,NonNegativeInteger,Point(R))->_$`cThreeSpaceCategory(R)``711787 -omodifyPoint`3`n`(_$,List(NonNegativeInteger),NonNegativeInteger)->_$`dSubSpace(n,R)``712023 -omodifyPoint`3`n`(_$,List(NonNegativeInteger),Point(R))->_$`dSubSpace(n,R)``712532 -omodifyPoint`3`n`(_$,NonNegativeInteger,Point(R))->_$`dSubSpace(n,R)``713009 -omodularFactor`1`n`(UP)->Record(prime:Integer,factors:List(UP))`pGaloisGroupFactorizer(UP)``713324 -omodularGcdPrimitive`1`n`(List(BP))->BP`pInnerModularGcd(R,BP,pMod,nextMod)``713822 -omodularGcd`1`n`(List(BP))->BP`pInnerModularGcd(R,BP,pMod,nextMod)``713956 -omoduleSum`2`n`(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)),Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)))->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pIntegralBasisTools(R,UP,F)``714072 -omodule`1`n`(FractionalIdeal(R,F,UP,A))->_$`dFramedModule(R,F,UP,A,ibasis)`has(A,RetractableTo(F))`714981 -omodule`1`n`(Vector(A))->_$`dFramedModule(R,F,UP,A,ibasis)``715057 -omoduloP`1`x`(_$)->Integer`cPAdicIntegerCategory(p)``715159 -omodulus`0`n`()->Rep`dModMonic(R,Rep)``715222 -omodulus`0`x`()->Integer`cPAdicIntegerCategory(p)``715260 -omodulus`1`n`(_$)->Mod`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``715315 -omodulus`1`n`(_$)->Mod`dModularField(R,Mod,reduction,merge,exactQuo)``715354 -omodulus`1`n`(_$)->Mod`dModularRing(R,Mod,reduction,merge,exactQuo)``715393 -omoebiusMu`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``715432 -omoebius`4`n`(F,F,F,F)->_$`dMoebiusTransform(F)``715708 +ominimumDegree`2`x`(_$,List(VarSet))->List(NonNegativeInteger)`cPolynomialCategory(R,E,VarSet)``863095 +ominimumDegree`2`x`(_$,VarSet)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``863253 +ominimumExponent`0`x`()->Integer`dMachineFloat``863425 +ominimumExponent`1`x`(Integer)->Integer`dMachineFloat``863499 +ominIndex`1`n`(A)->Integer`xLazyStreamAggregate&(A,S)``0 +ominIndex`1`n`(S)->Index`xIndexedAggregate&(S,Index,Entry)``0 +ominIndex`1`x`(_$)->Index`cIndexedAggregate(Index,Entry)`has(Index,OrderedSet)`863583 +ominordet`1`x`(M)->R`pMatrixLinearAlgebraFunctions(R,Row,Col,M)``863803 +ominordet`1`x`(_$)->R`cMatrixCategory(R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`863927 +ominordet`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)`has(R,ATTRIBUTE(commutative("*")))`864166 +ominPoints`0`n`()->Integer`dPlot``864254 +ominPoints`0`x`()->Integer`pGraphicsDefaults``864327 +ominPoints`1`x`(Integer)->Integer`pGraphicsDefaults``864401 +ominPoints3D`0`n`()->Integer`dPlot3D``864472 +ominPol`2`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``864548 +ominPol`3`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(HomogeneousDistributedMultivariatePolynomial(lv,F)),OrderedVariableList(lv))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``864583 +ominPoly`1`n`(Kernel(F))->SparseUnivariatePolynomial(F)`pAlgebraicFunction(R,F)`has(R,RetractableTo(Integer))`864618 +ominPoly`1`x`(Kernel(_$))->SparseUnivariatePolynomial(_$)`cExpressionSpace`has(_$,Ring)`864688 +ominrank`1`n`(List(Record(rank:NonNegativeInteger,eqns:List(Record(det:GR,rows:List(Integer),cols:List(Integer))),fgb:List(GR))))->NonNegativeInteger`pParametricLinearEquations(R,Var,Expon,GR)``864757 +ominRowIndex`1`x`(_$)->Integer`cRectangularMatrixCategory(m,n,R,Row,Col)``864839 +ominRowIndex`1`x`(_$)->Integer`cTwoDimensionalArrayCategory(R,Row,Col)``864929 +ominset`1`n`(List(List(GR)))->List(List(GR))`pParametricLinearEquations(R,Var,Expon,GR)``865127 +ominus!`2`n`(Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``865276 +ominus!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``865427 +ominusInfinity`0`x`()->_$`dOrderedCompletion(R)``865630 +ominusInfinity`0`x`()->OrderedCompletion(Integer)`pInfinity``865679 +omirror`1`n`(_$)->_$`dLieExponentials(VarSet,R,Order)``865732 +omirror`1`n`(_$)->_$`dMagma(VarSet)``865830 +omirror`1`n`(_$)->_$`dOrderedFreeMonoid(S)``866073 +omirror`1`x`(_$)->_$`cFreeLieAlgebra(VarSet,R)``866228 +omirror`1`x`(_$)->_$`cXFreeAlgebra(vl,R)``866342 +omix`1`n`(List(Record(den:Integer,gcdnum:Integer)))->Integer`pPointsOfFiniteOrderTools(UP,UPUP)``866442 +omkAnswer`3`n`(F,List(Record(scalar:Fraction(Integer),coeff:SparseUnivariatePolynomial(F),logand:SparseUnivariatePolynomial(F))),List(Record(integrand:F,intvar:F)))->_$`dIntegrationResult(F)``866477 +omkcomm`1`x`(Integer)->_$`dCommutator``866643 +omkcomm`2`x`(_$,_$)->_$`dCommutator``866685 +omkIntegral`1`n`(UPUP)->Record(coef:Fraction(UP),poly:UPUP)`pChangeOfVariable(F,UP,UPUP)``866731 +omkPrim`2`n`(F,Symbol)->F`pIntegrationTools(R,F)`AND(has(R,GcdDomain),has(F,ElementaryFunctionCategory))`866996 +omodifyPoint`3`n`(_$,List(NonNegativeInteger),NonNegativeInteger)->_$`dSubSpace(n,R)``867117 +omodifyPoint`3`n`(_$,List(NonNegativeInteger),Point(R))->_$`dSubSpace(n,R)``867626 +omodifyPoint`3`n`(_$,NonNegativeInteger,Point(R))->_$`dSubSpace(n,R)``868103 +omodifyPointData`3`x`(_$,NonNegativeInteger,Point(DoubleFloat))->Void`dThreeDimensionalViewport``868418 +omodifyPointData`3`x`(_$,NonNegativeInteger,Point(R))->_$`cThreeSpaceCategory(R)``868685 +omodTree`2`x`(R,List(R))->List(R)`pCRApackage(R)``868921 +omodularFactor`1`n`(UP)->Record(prime:Integer,factors:List(UP))`pGaloisGroupFactorizer(UP)``868966 +omodularGcd`1`n`(List(BP))->BP`pInnerModularGcd(R,BP,pMod,nextMod)``869428 +omodularGcdPrimitive`1`n`(List(BP))->BP`pInnerModularGcd(R,BP,pMod,nextMod)``869544 +omodule`1`n`(FractionalIdeal(R,F,UP,A))->_$`dFramedModule(R,F,UP,A,ibasis)`has(A,RetractableTo(F))`869678 +omodule`1`n`(Vector(A))->_$`dFramedModule(R,F,UP,A,ibasis)``869754 +omoduleSum`2`n`(Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)),Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R)))->Record(basis:Matrix(R),basisDen:R,basisInv:Matrix(R))`pIntegralBasisTools(R,UP,F)``869856 +omoduloP`1`x`(_$)->Integer`cPAdicIntegerCategory(p)``870765 +omodulus`0`n`()->Rep`dModMonic(R,Rep)``870828 +omodulus`0`x`()->Integer`cPAdicIntegerCategory(p)``870870 +omodulus`1`n`(_$)->Mod`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``870925 +omodulus`1`n`(_$)->Mod`dModularField(R,Mod,reduction,merge,exactQuo)``870968 +omodulus`1`n`(_$)->Mod`dModularRing(R,Mod,reduction,merge,exactQuo)``871011 +omoebius`4`n`(F,F,F,F)->_$`dMoebiusTransform(F)``871054 +omoebiusMu`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``871134 omonic?`1`n`(S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -omonic?`1`n`(UP)->Boolean`pGaloisGroupPolynomialUtilities(R,UP)``715788 -omonic?`1`x`(_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``715891 -omonicCompleteDecompose`1`n`(UP)->List(UP)`pUnivariatePolynomialDecompositionPackage(R,UP)``716104 -omonicDecomposeIfCan`1`n`(UP)->Union(Record(left:UP,right:UP),"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``716311 -omonicDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariatePolynomialCategory(R)``716453 +omonic?`1`n`(UP)->Boolean`pGaloisGroupPolynomialUtilities(R,UP)``871410 +omonic?`1`x`(_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``871513 +omonicCompleteDecompose`1`n`(UP)->List(UP)`pUnivariatePolynomialDecompositionPackage(R,UP)``871726 +omonicDecomposeIfCan`1`n`(UP)->Union(Record(left:UP,right:UP),"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``871933 +omonicDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariatePolynomialCategory(R)``872075 omonicDivide`3`n`(S,S,VarSet)->Record(quotient:S,remainder:S)`xPolynomialCategory&(S,R,E,VarSet)``0 -omonicDivide`3`x`(_$,_$,VarSet)->Record(quotient:_$,remainder:_$)`cPolynomialCategory(R,E,VarSet)``716643 -omonicLeftDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,IntegralDomain)`716892 -omonicLeftDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,IntegralDomain)`717127 +omonicDivide`3`x`(_$,_$,VarSet)->Record(quotient:_$,remainder:_$)`cPolynomialCategory(R,E,VarSet)``872265 +omonicLeftDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,IntegralDomain)`872514 +omonicLeftDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,IntegralDomain)`872749 +omonicModulo`2`n`(_$,_$)->_$`dNewSparseUnivariatePolynomial(R)``873032 omonicModulo`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -omonicModulo`2`n`(_$,_$)->_$`dNewSparseUnivariatePolynomial(R)``717410 -omonicModulo`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``717641 -omonicRightDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,IntegralDomain)`717793 -omonicRightDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,IntegralDomain)`718030 -omonicRightFactorIfCan`2`n`(UP,NonNegativeInteger)->Union(UP,"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``718315 -omonomRDE`3`n`(Fraction(UP),Fraction(UP),(UP)->UP)->Union(Record(a:UP,b:Fraction(UP),c:Fraction(UP),t:UP),"failed")`pTranscendentalRischDE(F,UP)``718576 -omonomRDEsys`4`n`(Fraction(UP),Fraction(UP),Fraction(UP),(UP)->UP)->Union(Record(a:UP,b:Fraction(UP),h:UP,c1:Fraction(UP),c2:Fraction(UP),t:UP),"failed")`pTranscendentalRischDESystem(F,UP)``718909 -omonom`2`n`(A,Integer)->Stream(A)`pStreamTaylorSeriesOperations(A)``719326 -omonom`2`x`(Basis,R)->_$`cFreeModuleCat(R,Basis)``719423 -omonom`2`x`(OrderedFreeMonoid(vl),R)->_$`cXFreeAlgebra(vl,R)``719544 +omonicModulo`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``873263 +omonicRightDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,IntegralDomain)`873415 +omonicRightDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,IntegralDomain)`873652 +omonicRightFactorIfCan`2`n`(UP,NonNegativeInteger)->Union(UP,"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``873937 +omonom`2`n`(A,Integer)->Stream(A)`pStreamTaylorSeriesOperations(A)``874198 +omonom`2`x`(Basis,R)->_$`cFreeModuleCat(R,Basis)``874295 +omonom`2`x`(OrderedFreeMonoid(vl),R)->_$`cXFreeAlgebra(vl,R)``874416 +omonomial?`1`n`(_$)->Boolean`dInnerSparseUnivariatePowerSeries(Coef)``874513 +omonomial?`1`n`(_$)->Boolean`dLaurentPolynomial(R,UP)``874580 +omonomial?`1`n`(_$)->Boolean`dMonoidRing(R,M)``874625 omonomial?`1`n`(S)->Boolean`xAbelianMonoidRing&(S,R,E)``0 -omonomial?`1`n`(_$)->Boolean`dInnerSparseUnivariatePowerSeries(Coef)``719641 -omonomial?`1`n`(_$)->Boolean`dLaurentPolynomial(R,UP)``719708 -omonomial?`1`n`(_$)->Boolean`dMonoidRing(R,M)``719749 -omonomial?`1`x`(_$)->Boolean`cAbelianMonoidRing(R,E)``719816 -omonomial?`1`x`(_$)->Boolean`cFreeModuleCat(R,Basis)``719883 -omonomial?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``719970 -omonomialIntPoly`2`n`(UP,(UP)->UP)->Record(answer:UP,polypart:UP)`pTranscendentalIntegration(F,UP)``720043 -omonomialIntegrate`2`n`(Fraction(UP),(UP)->UP)->Record(ir:IntegrationResult(Fraction(UP)),specpart:Fraction(UP),polypart:UP)`pTranscendentalIntegration(F,UP)``720207 +omonomial?`1`x`(_$)->Boolean`cAbelianMonoidRing(R,E)``874692 +omonomial?`1`x`(_$)->Boolean`cFreeModuleCat(R,Basis)``874759 +omonomial?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``874846 omonomial`2`n`(Coef,Expon)->S`xUnivariatePowerSeriesCategory&(S,Coef,Expon)``0 omonomial`2`n`(R,E)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -omonomial`2`n`(R,Integer)->_$`dLaurentPolynomial(R,UP)``720429 -omonomial`2`n`(R,M)->_$`dMonoidRing(R,M)``720473 -omonomial`2`n`(R,ModuleMonomial(IS,E,ff))->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``720560 +omonomial`2`n`(R,Integer)->_$`dLaurentPolynomial(R,UP)``874919 +omonomial`2`n`(R,M)->_$`dMonoidRing(R,M)``874967 +omonomial`2`n`(R,ModuleMonomial(IS,E,ff))->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``875054 omonomial`2`n`(R,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 -omonomial`2`x`(A,S)->_$`cIndexedDirectProductCategory(A,S)``720604 -omonomial`2`x`(K,List(PositiveInteger))->_$`dCliffordAlgebra(n,K,Q)``720714 -omonomial`2`x`(R,E)->_$`cAbelianMonoidRing(R,E)``720823 -omonomial`2`x`(R,NonNegativeInteger)->_$`cMonogenicLinearOperator(R)``720920 -omonomial`2`x`(R,NonNegativeInteger)->_$`cUnivariateSkewPolynomialCategory(R)``721050 +omonomial2series`3`x`(List(_$),List(NonNegativeInteger),Integer)->_$`cLocalPowerSeriesCategory(K)``875102 +omonomial`2`x`(A,S)->_$`cIndexedDirectProductCategory(A,S)``875263 +omonomial`2`x`(K,List(PositiveInteger))->_$`dCliffordAlgebra(n,K,Q)``875373 +omonomial`2`x`(R,E)->_$`cAbelianMonoidRing(R,E)``875482 +omonomial`2`x`(R,NonNegativeInteger)->_$`cMonogenicLinearOperator(R)``875579 +omonomial`2`x`(R,NonNegativeInteger)->_$`cUnivariateSkewPolynomialCategory(R)``875709 omonomial`3`n`(S,List(SingletonAsOrderedSet),List(Expon))->S`xUnivariatePowerSeriesCategory&(S,Coef,Expon)``0 omonomial`3`n`(S,List(SingletonAsOrderedSet),List(NonNegativeInteger))->S`xUnivariatePolynomialCategory&(S,R)``0 omonomial`3`n`(S,List(VarSet),List(NonNegativeInteger))->S`xPolynomialCategory&(S,R,E,VarSet)``0 omonomial`3`n`(S,SingletonAsOrderedSet,Expon)->S`xUnivariatePowerSeriesCategory&(S,Coef,Expon)``0 omonomial`3`n`(S,SingletonAsOrderedSet,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 omonomial`3`n`(S,VarSet,NonNegativeInteger)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -omonomial`3`x`(_$,List(Var),List(Expon))->_$`cPowerSeriesCategory(Coef,Expon,Var)``721180 -omonomial`3`x`(_$,List(Var),List(NonNegativeInteger))->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``721282 -omonomial`3`x`(_$,List(VarSet),List(NonNegativeInteger))->_$`cPolynomialCategory(R,E,VarSet)``721394 -omonomial`3`x`(_$,Var,Expon)->_$`cPowerSeriesCategory(Coef,Expon,Var)``721473 -omonomial`3`x`(_$,Var,NonNegativeInteger)->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``721531 -omonomial`3`x`(_$,VarSet,NonNegativeInteger)->_$`cPolynomialCategory(R,E,VarSet)``721587 +omonomial`3`x`(_$,List(Var),List(Expon))->_$`cPowerSeriesCategory(Coef,Expon,Var)``875839 +omonomial`3`x`(_$,List(Var),List(NonNegativeInteger))->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``875941 +omonomial`3`x`(_$,List(VarSet),List(NonNegativeInteger))->_$`cPolynomialCategory(R,E,VarSet)``876053 +omonomial`3`x`(_$,Var,Expon)->_$`cPowerSeriesCategory(Coef,Expon,Var)``876132 +omonomial`3`x`(_$,Var,NonNegativeInteger)->_$`cMultivariateTaylorSeriesCategory(Coef,Var)``876190 +omonomial`3`x`(_$,VarSet,NonNegativeInteger)->_$`cPolynomialCategory(R,E,VarSet)``876246 +omonomialIntegrate`2`n`(Fraction(UP),(UP)->UP)->Record(ir:IntegrationResult(Fraction(UP)),specpart:Fraction(UP),polypart:UP)`pTranscendentalIntegration(F,UP)``876411 +omonomialIntPoly`2`n`(UP,(UP)->UP)->Record(answer:UP,polypart:UP)`pTranscendentalIntegration(F,UP)``876633 +omonomials`1`n`(_$)->List(_$)`dMonoidRing(R,M)``876797 omonomials`1`n`(S)->List(S)`xPolynomialCategory&(S,R,E,VarSet)``0 -omonomials`1`n`(_$)->List(_$)`dMonoidRing(R,M)``721752 -omonomials`1`x`(_$)->List(_$)`cFreeModuleCat(R,Basis)``721834 -omonomials`1`x`(_$)->List(_$)`cPolynomialCategory(R,E,VarSet)``721919 +omonomials`1`x`(_$)->List(_$)`cFreeModuleCat(R,Basis)``876879 +omonomials`1`x`(_$)->List(_$)`cPolynomialCategory(R,E,VarSet)``876964 +omonomials`1`x`(PolyRing)->List(PolyRing)`pPackageForPoly(R,PolyRing,E,dim)``0 +omonomRDE`3`n`(Fraction(UP),Fraction(UP),(UP)->UP)->Union(Record(a:UP,b:Fraction(UP),c:Fraction(UP),t:UP),"failed")`pTranscendentalRischDE(F,UP)``877146 +omonomRDEsys`4`n`(Fraction(UP),Fraction(UP),Fraction(UP),(UP)->UP)->Union(Record(a:UP,b:Fraction(UP),h:UP,c1:Fraction(UP),c2:Fraction(UP),t:UP),"failed")`pTranscendentalRischDESystem(F,UP)``877479 omore?`2`n`(A,NonNegativeInteger)->Boolean`xLazyStreamAggregate&(A,S)``0 omore?`2`n`(A,NonNegativeInteger)->Boolean`xUnaryRecursiveAggregate&(A,S)``0 omore?`2`n`(S,NonNegativeInteger)->Boolean`xAggregate&(S)``0 omore?`2`n`(S,NonNegativeInteger)->Boolean`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -omore?`2`n`(S,S)->Boolean`pUserDefinedPartialOrdering(S)`has(S,OrderedSet)`722101 -omore?`2`x`(_$,NonNegativeInteger)->Boolean`cAggregate``722310 -omoreAlgebraic?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``722391 -omoreAlgebraic?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``722698 -omorphism`1`n`((R)->R)->_$`dAutomorphism(R)``723005 -omorphism`1`n`((R,Integer)->R)->_$`dAutomorphism(R)``723086 -omorphism`2`n`((R)->R,(R)->R)->_$`dAutomorphism(R)``723168 -omove`3`n`(_$,NonNegativeInteger,NonNegativeInteger)->Void`dTwoDimensionalViewport``723296 -omove`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Void`dThreeDimensionalViewport``723546 -omovedPoints`1`x`(_$)->Set(S)`dPermutation(S)``723800 -omovedPoints`1`x`(_$)->Set(S)`dPermutationGroup(S)``723890 -ompsode`2`n`(List(Coef),List((List(UTS))->UTS))->List(UTS)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``723968 -omr`1`n`(List(List(List(S))))->Record(f1:List(S),f2:List(List(List(S))),f3:List(List(S)),f4:List(List(List(S))))`pTableauxBumpers(S)``724147 -omulmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``724322 -omultMonom`3`n`(R,E,_$)->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``724404 -omultiEuclideanTree`2`x`(List(R),R)->List(R)`pCRApackage(R)``724453 +omore?`2`n`(S,S)->Boolean`pUserDefinedPartialOrdering(S)`has(S,OrderedSet)`877896 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`cAggregate``878091 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`dArrayStack(S)``878172 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`dDequeue(S)``878271 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`dHeap(S)``878364 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`dQueue(S)``878451 +omore?`2`x`(_$,NonNegativeInteger)->Boolean`dStack(S)``878540 +omoreAlgebraic?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``878629 +omoreAlgebraic?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``878936 +omorphism`1`n`((R,Integer)->R)->_$`dAutomorphism(R)``879243 +omorphism`1`n`((R)->R)->_$`dAutomorphism(R)``879325 +omorphism`2`n`((R)->R,(R)->R)->_$`dAutomorphism(R)``879406 +omove`3`n`(_$,NonNegativeInteger,NonNegativeInteger)->Void`dTwoDimensionalViewport``879534 +omove`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Void`dThreeDimensionalViewport``879784 +omovedPoints`1`x`(_$)->Set(S)`dPermutationGroup(S)``880038 +omovedPoints`1`x`(_$)->Set(S)`dPermutation(S)``880117 +ompsode`2`n`(List(Coef),List((List(UTS))->UTS))->List(UTS)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``880341 +omr`1`n`(List(List(List(S))))->Record(f1:List(S),f2:List(List(List(S))),f3:List(List(S)),f4:List(List(List(S))))`pTableauxBumpers(S)``880520 +omulmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``880695 omultiEuclidean`2`n`(List(S),S)->Union(List(S),"failed")`xEuclideanDomain&(S)``0 -omultiEuclidean`2`x`(List(_$),_$)->Union(List(_$),"failed")`cEuclideanDomain``724509 -omultinomial`2`x`(I,List(I))->I`pIntegerCombinatoricFunctions(I)``724729 -omultiple?`1`n`(_$)->Boolean`dPattern(R)``724846 -omultiple`1`x`(F)->F`pFunctionSpaceAssertions(R,F)``724991 -omultiple`1`x`(Symbol)->Expression(Integer)`pPatternMatchAssertions``725297 -omultiplyCoefficients`2`n`((Integer)->Coef,_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)``725567 -omultiplyCoefficients`2`x`((Integer)->Coef,_$)->_$`cUnivariateLaurentSeriesCategory(Coef)``725734 -omultiplyCoefficients`2`x`((Integer)->Coef,_$)->_$`cUnivariateTaylorSeriesCategory(Coef)``725950 -omultiplyExponents`2`x`(_$,Fraction(Integer))->_$`cUnivariatePuiseuxSeriesCategory(Coef)``726174 -omultiplyExponents`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``726309 -omultiplyExponents`2`x`(_$,PositiveInteger)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``726479 -omultisect`3`n`(Integer,Integer,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``726606 -omultisect`3`n`(Integer,Integer,_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``726728 -omultiset`0`x`()->_$`dMultiset(S)``726873 -omultiset`1`x`(List(S))->_$`dMultiset(S)``726954 -omultiset`1`x`(S)->_$`dMultiset(S)``727030 -omultivariate`2`n`(Fraction(SparseUnivariatePolynomial(F)),V)->F`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``727100 -omultivariate`2`x`(Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(R)))),Symbol)->Fraction(Polynomial(R))`pRationalFunction(R)``727203 -omultivariate`2`x`(SparseUnivariatePolynomial(R),VarSet)->_$`cPolynomialCategory(R,E,VarSet)``727306 -omultivariate`2`x`(SparseUnivariatePolynomial(_$),VarSet)->_$`cPolynomialCategory(R,E,VarSet)``727440 -omultivariate`3`n`(SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F))),Kernel(F),F)->F`pGenusZeroIntegration(R,F,L)``727574 -omusserTrials`0`n`()->PositiveInteger`pGaloisGroupFactorizer(UP)``727626 -omusserTrials`1`n`(PositiveInteger)->PositiveInteger`pGaloisGroupFactorizer(UP)``727727 +omultiEuclidean`2`x`(List(_$),_$)->Union(List(_$),"failed")`cEuclideanDomain``880777 +omultiEuclideanTree`2`x`(List(R),R)->List(R)`pCRApackage(R)``880997 +omultinomial`2`x`(I,List(I))->I`pIntegerCombinatoricFunctions(I)``881053 +omultiple?`1`n`(_$)->Boolean`dPattern(R)``881170 +omultiple`1`x`(F)->F`pFunctionSpaceAssertions(R,F)``881315 +omultiple`1`x`(Symbol)->Expression(Integer)`pPatternMatchAssertions``881621 +omultiplicity`1`x`(List(List(PolyRing)))->NonNegativeInteger`pNewtonPolygon(K,PolyRing,E,dim)``0 +omultiplicity`2`x`(PolyRing,ProjPt)->NonNegativeInteger`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``881891 +omultiplicity`3`x`(PolyRing,ProjPt,Integer)->NonNegativeInteger`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``881977 +omultiplyCoefficients`2`n`((Integer)->Coef,_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)``882063 +omultiplyCoefficients`2`x`((Integer)->Coef,_$)->_$`cUnivariateLaurentSeriesCategory(Coef)``882230 +omultiplyCoefficients`2`x`((Integer)->Coef,_$)->_$`cUnivariateTaylorSeriesCategory(Coef)``882446 +omultiplyExponents`2`x`(_$,Fraction(Integer))->_$`cUnivariatePuiseuxSeriesCategory(Coef)``882670 +omultiplyExponents`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``882805 +omultiplyExponents`2`x`(_$,PositiveInteger)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``882975 +omultisect`3`n`(Integer,Integer,_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``883102 +omultisect`3`n`(Integer,Integer,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``883247 +omultisect`3`x`(Integer,Integer,_$)->_$`dUnivariateFormalPowerSeries(Coef)``0 +omultisect`3`x`(Integer,Integer,_$)->_$`dUnivariateTaylorSeriesCZero(Coef,var)``883369 +omultiServ`1`x`(SExpression)->Void`pAxiomServer``0 +omultiset`0`x`()->_$`dMultiset(S)``883514 +omultiset`1`x`(List(S))->_$`dMultiset(S)``883595 +omultiset`1`x`(S)->_$`dMultiset(S)``883671 +omultivariate`2`n`(Fraction(SparseUnivariatePolynomial(F)),V)->F`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``883741 +omultivariate`2`x`(Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(R)))),Symbol)->Fraction(Polynomial(R))`pRationalFunction(R)``883844 +omultivariate`2`x`(SparseUnivariatePolynomial(R),VarSet)->_$`cPolynomialCategory(R,E,VarSet)``883947 +omultivariate`2`x`(SparseUnivariatePolynomial(_$),VarSet)->_$`cPolynomialCategory(R,E,VarSet)``884081 +omultivariate`3`n`(SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F))),Kernel(F),F)->F`pGenusZeroIntegration(R,F,L)``884215 +omultMonom`3`n`(R,E,_$)->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``884267 +omultV`1`x`(_$)->NonNegativeInteger`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``884320 +oMusser`1`x`(PolK)->Factored(PolK)`pFiniteFieldSquareFreeDecomposition(K,PolK)``0 +omusserTrials`0`n`()->PositiveInteger`pGaloisGroupFactorizer(UP)``884395 +omusserTrials`1`n`(PositiveInteger)->PositiveInteger`pGaloisGroupFactorizer(UP)``884496 omvar`1`n`(S)->V`xRecursivePolynomialCategory&(S,R,E,V)``0 omvar`1`n`(S)->V`xTriangularSetCategory&(S,R,E,V,P)``0 -omvar`1`x`(_$)->V`cRecursivePolynomialCategory(R,E,V)``727866 -omvar`1`x`(_$)->VarSet`cPolynomialSetCategory(R,E,VarSet,P)``728089 -omyDegree`3`n`(SparseUnivariatePolynomial(P),List(OV),NonNegativeInteger)->List(NonNegativeInteger)`pMultivariateSquareFree(E,OV,R,P)``728249 -oname`1`n`(_$)->Symbol`dFunctionCalled(f)``728288 -oname`1`n`(_$)->Symbol`dKernel(S)``728329 -oname`1`n`(_$)->Symbol`dRuleCalled(f)``728391 -oname`1`x`(_$)->Name`cFileCategory(Name,S)``728432 -oname`1`x`(_$)->String`cFileNameCategory``728502 -oname`1`x`(_$)->Symbol`dBasicOperator``728564 -oname`1`x`(_$)->_$`dSymbol``728618 +omvar`1`x`(_$)->VarSet`cPolynomialSetCategory(R,E,VarSet,P)``884635 +omvar`1`x`(_$)->V`cRecursivePolynomialCategory(R,E,V)``884795 +omyDegree`3`n`(SparseUnivariatePolynomial(P),List(OV),NonNegativeInteger)->List(NonNegativeInteger)`pMultivariateSquareFree(E,OV,R,P)``885018 +oname`1`n`(_$)->Symbol`dFunctionCalled(f)``885057 +oname`1`n`(_$)->Symbol`dKernel(S)``885098 +oname`1`n`(_$)->Symbol`dRuleCalled(f)``885160 +oname`1`x`(_$)->_$`dSymbol``885201 +oname`1`x`(_$)->Name`cFileCategory(Name,S)``885261 +oname`1`x`(_$)->String`cFileNameCategory``885331 +oname`1`x`(_$)->Symbol`dBasicOperator``885393 onand`2`n`(S,S)->S`xBitAggregate&(S)``0 -onand`2`x`(_$,_$)->_$`cBitAggregate``728678 -onand`2`x`(_$,_$)->_$`dBoolean``728785 -onary?`1`x`(_$)->Boolean`dBasicOperator``728866 +onand`2`x`(_$,_$)->_$`cBitAggregate``885447 +onand`2`x`(_$,_$)->_$`dBoolean``885548 +onary?`1`x`(_$)->Boolean`dBasicOperator``885629 oncols`1`n`(S)->NonNegativeInteger`xRectangularMatrixCategory&(S,m,n,R,Row,Col)``0 -oncols`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)``728930 -oncols`1`x`(_$)->NonNegativeInteger`cTwoDimensionalArrayCategory(R,Row,Col)``729007 +oncols`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)``885693 +oncols`1`x`(_$)->NonNegativeInteger`cTwoDimensionalArrayCategory(R,Row,Col)``885770 +onegAndPosEdge`2`x`(PolyRing,List(List(PolyRing)))->List(List(PolyRing))`pNewtonPolygon(K,PolyRing,E,dim)``0 onegative?`1`n`(S)->Boolean`xOrderedRing&(S)``0 -onegative?`1`x`(_$)->Boolean`cIntervalCategory(R)``729082 -onegative?`1`x`(_$)->Boolean`cOrderedRing``729213 +onegative?`1`x`(_$)->Boolean`cIntervalCategory(R)``885949 +onegative?`1`x`(_$)->Boolean`cOrderedRing``886080 onegative?`2`n`(ThePols,S)->Boolean`xRealRootCharacterizationCategory&(S,TheField,ThePols)``0 -onegative?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``729288 -oneglist`1`x`(List(R1))->List(R1)`pExpertSystemToolsPackage1(R1)``729390 -onewLine`0`x`()->String`pDisplayPackage``729471 -onewReduc`0`n`()->Void`pFunctionSpaceReduce(R,F)``729531 -onewSubProgram`1`x`(Symbol)->Void`dTheSymbolTable``729570 -onewTypeLists`1`x`(_$)->SExpression`dSymbolTable``729677 -onew`0`n`()->_$`dPatternMatchListResult(R,S,L)``729721 -onew`0`n`()->_$`dPatternMatchResult(R,S)``729775 -onew`0`n`()->_$`dSubSpace(n,R)``729829 -onew`0`n`()->_$`dSubSpaceComponentProperty``729863 -onew`0`x`()->_$`dScriptFormulaFormat``729897 -onew`0`x`()->_$`dSymbol``730072 -onew`0`x`()->_$`dTexFormat``730140 -onew`1`x`(_$)->_$`dSymbol``730311 +onegative?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``886155 +oneglist`1`x`(List(R1))->List(R1)`pExpertSystemToolsPackage1(R1)``886257 +onew`0`n`()->_$`dPatternMatchListResult(R,S,L)``886338 +onew`0`n`()->_$`dPatternMatchResult(R,S)``886392 +onew`0`n`()->_$`dSubSpaceComponentProperty``886446 +onew`0`n`()->_$`dSubSpace(n,R)``886484 +onew`0`x`()->_$`dScriptFormulaFormat``886522 +onew`0`x`()->_$`dSymbol``886697 +onew`0`x`()->_$`dTexFormat``886765 +onew`1`x`(_$)->_$`dSymbol``886936 onew`2`n`(NonNegativeInteger,S)->A`xListAggregate&(A,S)``0 -onew`2`x`(NonNegativeInteger,S)->_$`cLinearAggregate(S)``730388 -onew`3`x`(NonNegativeInteger,NonNegativeInteger,R)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``730461 -onew`3`x`(String,String,String)->_$`cFileNameCategory``730557 -onextColeman`3`x`(List(Integer),List(Integer),Matrix(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``730873 -onextIrreduciblePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``731206 +onew`2`x`(NonNegativeInteger,S)->_$`cLinearAggregate(S)``887013 +onew`3`x`(NonNegativeInteger,NonNegativeInteger,R)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``887086 +onew`3`x`(String,String,String)->_$`cFileNameCategory``887279 +onewElement`2`x`(SparseUnivariatePolynomial(_$),Symbol)->_$`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +onewElement`3`x`(SparseUnivariatePolynomial(_$),_$,Symbol)->_$`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +onewElement`5`x`(SparseUnivariatePolynomial(_$),SparseUnivariatePolynomial(_$),PositiveInteger,_$,Symbol)->_$`dPseudoAlgebraicClosureOfRationalNumber``0 +onewLine`0`x`()->String`pDisplayPackage``887595 +onewReduc`0`n`()->Void`pFunctionSpaceReduce(R,F)``887655 +onewSubProgram`1`x`(Symbol)->Void`dTheSymbolTable``887694 +onewton`1`n`(List(F))->SparseUnivariatePolynomial(F)`pNewtonInterpolation(F)``887801 +onewtonPolygon`4`x`(PolyRing,Integer,Integer,Union("left","center","right","vertical","horizontal"))->List(List(PolyRing))`pNewtonPolygon(K,PolyRing,E,dim)``0 +onewtonPolySlope`1`x`(DistributedMultivariatePolynomial(construct('X,'Y),K))->List(List(NonNegativeInteger))`pBlowUpPackage(K,symb,PolyRing,E,BLMET)``0 +onewTypeLists`1`x`(_$)->SExpression`dSymbolTable``888159 +onext`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``888207 +onextColeman`3`x`(List(Integer),List(Integer),Matrix(Integer))->Matrix(Integer)`pSymmetricGroupCombinatoricFunctions``888437 +onextIrreduciblePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``888760 onextItem`1`n`(A)->Union(A,"failed")`xQuotientFieldCategory&(A,S)``0 onextItem`1`n`(S)->Union(S,"failed")`xFiniteFieldCategory&(S)``0 onextItem`1`n`(S)->Union(S,"failed")`xIntegerNumberSystem&(S)``0 onextItem`1`n`(S)->Union(S,"failed")`xUnivariatePolynomialCategory&(S,R)``0 -onextItem`1`x`(_$)->Union(_$,"failed")`cStepThrough``731913 -onextLatticePermutation`3`x`(List(Integer),List(Integer),Boolean)->List(Integer)`pSymmetricGroupCombinatoricFunctions``732000 -onextNormalPoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``732442 -onextNormalPrimitivePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``733278 -onextPartition`3`x`(List(Integer),Vector(Integer),Integer)->Vector(Integer)`pSymmetricGroupCombinatoricFunctions``734272 -onextPartition`3`x`(Vector(Integer),Vector(Integer),Integer)->Vector(Integer)`pSymmetricGroupCombinatoricFunctions``734678 -onextPrime`1`x`(I)->I`pIntegerPrimesPackage(I)``735084 -onextPrimitiveNormalPoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``735168 -onextPrimitivePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``736229 -onextSublist`2`n`(Integer,Integer)->List(List(Integer))`pParametricLinearEquations(R,Var,Expon,GR)``737053 -onextSubsetGray`2`n`(Vector(Vector(Integer)),PositiveInteger)->Vector(Vector(Integer))`pGrayCode``737148 -onext`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``738197 -onextsousResultant2`4`n`(polR,polR,polR,R)->polR`pPseudoRemainderSequence(R,polR)``738423 -onextsubResultant2`4`x`(_$,_$,_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`738691 -onilFactor`2`x`(R,Integer)->_$`dFactored(R)``738943 -onil`0`x`()->_$`dList(S)``739097 -onlde`1`n`(Stream(Stream(A)))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Algebra(Fraction(Integer)))`739141 -onoKaratsuba`2`x`(U,U)->U`pUnivariatePolynomialMultiplicationPackage(R,U)``739439 -onoLinearFactor?`1`n`(UP)->Boolean`pBrillhartTests(UP)``739538 +onextItem`1`x`(_$)->Union(_$,"failed")`cStepThrough``889467 +onextLatticePermutation`3`x`(List(Integer),List(Integer),Boolean)->List(Integer)`pSymmetricGroupCombinatoricFunctions``889554 +onextNormalPoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``889995 +onextNormalPrimitivePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``890826 +onextPartition`3`x`(List(Integer),Vector(Integer),Integer)->Vector(Integer)`pSymmetricGroupCombinatoricFunctions``891809 +onextPartition`3`x`(Vector(Integer),Vector(Integer),Integer)->Vector(Integer)`pSymmetricGroupCombinatoricFunctions``892197 +onextPrime`1`x`(I)->I`pIntegerPrimesPackage(I)``892585 +onextPrimitiveNormalPoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``892669 +onextPrimitivePoly`1`n`(SparseUnivariatePolynomial(GF))->Union(SparseUnivariatePolynomial(GF),"failed")`pFiniteFieldPolynomialPackage(GF)``893719 +onextsousResultant2`4`n`(polR,polR,polR,R)->polR`pPseudoRemainderSequence(R,polR)``894537 +onextSublist`2`n`(Integer,Integer)->List(List(Integer))`pParametricLinearEquations(R,Var,Expon,GR)``894805 +onextsubResultant2`4`x`(_$,_$,_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`894900 +onextSubsetGray`2`n`(Vector(Vector(Integer)),PositiveInteger)->Vector(Vector(Integer))`pGrayCode``895142 +onil`0`x`()->_$`dList(S)``896196 +onilFactor`2`x`(R,Integer)->_$`dFactored(R)``896240 +onlde`1`n`(Stream(Stream(A)))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Algebra(Fraction(Integer)))`896502 onode?`2`n`(A,A)->Boolean`xBinaryRecursiveAggregate&(A,S)``0 onode?`2`n`(A,A)->Boolean`xLazyStreamAggregate&(A,S)``0 onode?`2`n`(A,A)->Boolean`xUnaryRecursiveAggregate&(A,S)``0 -onode?`2`x`(_$,_$)->Boolean`cRecursiveAggregate(S)`has(S,SetCategory)`739781 -onodeOf?`2`n`(SplittingNode(V,C),_$)->Boolean`dSplittingTree(V,C)``739912 -onode`3`x`(_$,S,_$)->_$`cBinaryTreeCategory(S)``740025 +onode?`2`x`(_$,_$)->Boolean`cRecursiveAggregate(S)`has(S,SetCategory)`896798 +onode`3`x`(_$,S,_$)->_$`cBinaryTreeCategory(S)``896929 +onodeOf?`2`n`(SplittingNode(V,C),_$)->Boolean`dSplittingTree(V,C)``897083 onodes`1`n`(A)->List(A)`xBinaryRecursiveAggregate&(A,S)``0 onodes`1`n`(A)->List(A)`xLazyStreamAggregate&(A,S)``0 onodes`1`n`(A)->List(A)`xUnaryRecursiveAggregate&(A,S)``0 -onodes`1`x`(_$)->List(_$)`cRecursiveAggregate(S)``740168 -ononLinearPart`1`x`(List(Expression(DoubleFloat)))->List(Expression(DoubleFloat))`pe04AgentsPackage``740249 -ononQsign`1`n`(R)->Union(Integer,"failed")`pToolsForSign(R)``740342 -ononSingularModel`1`n`(Symbol)->List(Polynomial(F))`xFunctionFieldCategory&(S,F,UP,UPUP)``740382 -ononSingularModel`1`x`(Symbol)->List(Polynomial(F))`cFunctionFieldCategory(F,UP,UPUP)`has(F,Field)`740509 -ononcommutativeJordanAlgebra?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``740636 -ononcommutativeJordanAlgebra?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``740737 +onodes`1`x`(_$)->List(_$)`cRecursiveAggregate(S)``897196 +onoKaratsuba`2`x`(U,U)->U`pUnivariatePolynomialMultiplicationPackage(R,U)``897277 +onoLinearFactor?`1`n`(UP)->Boolean`pBrillhartTests(UP)``897376 +ononcommutativeJordanAlgebra?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``897619 +ononcommutativeJordanAlgebra?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``897720 +ononLinearPart`1`x`(List(Expression(DoubleFloat)))->List(Expression(DoubleFloat))`pe04AgentsPackage``897821 +ononQsign`1`n`(R)->Union(Integer,"failed")`pToolsForSign(R)``897906 +ononSingularModel`1`n`(Symbol)->List(Polynomial(F))`xFunctionFieldCategory&(S,F,UP,UPUP)``897946 +ononSingularModel`1`x`(Symbol)->List(Polynomial(F))`cFunctionFieldCategory(F,UP,UPUP)`has(F,Field)`898073 onor`2`n`(S,S)->S`xBitAggregate&(S)``0 -onor`2`x`(_$,_$)->_$`cBitAggregate``740838 -onor`2`x`(_$,_$)->_$`dBoolean``740943 -onormDeriv2`2`n`(SparseUnivariatePolynomial(R),Integer)->SparseUnivariatePolynomial(R)`pMultivariateSquareFree(E,OV,R,P)``741022 -onormFactors`1`n`(ExtP)->List(ExtP)`pNormRetractPackage(F,ExtF,SUEx,ExtP,n)``741063 -onormInvertible?`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pNormalizationPackage(R,E,V,P,TS)``741106 +onor`2`x`(_$,_$)->_$`cBitAggregate``898200 +onor`2`x`(_$,_$)->_$`dBoolean``898299 +onorm`1`n`(_$)->F`dFractionalIdeal(R,F,UP,A)``898378 +onorm`1`n`(_$)->F`dFramedModule(R,F,UP,A,ibasis)``898440 onorm`1`n`(S)->F`xFiniteAlgebraicExtensionField&(S,F)``0 onorm`1`n`(S)->R`xComplexCategory&(S,R)``0 onorm`1`n`(S)->R`xMonogenicAlgebra&(S,R,UP)``0 onorm`1`n`(S)->R`xOctonionCategory&(S,R)``0 onorm`1`n`(S)->R`xQuaternionCategory&(S,R)``0 onorm`1`n`(S)->S`xRealNumberSystem&(S)``0 -onorm`1`n`(UP)->R`pComplexRootFindingPackage(R,UP)``741220 -onorm`1`n`(_$)->F`dFractionalIdeal(R,F,UP,A)``741351 -onorm`1`n`(_$)->F`dFramedModule(R,F,UP,A,ibasis)``741413 -onorm`1`x`(PolE)->PolR`pNormInMonogenicAlgebra(R,PolR,E,PolE)``741476 -onorm`1`x`(_$)->F`cFiniteAlgebraicExtensionField(F)``741594 -onorm`1`x`(_$)->R`cComplexCategory(R)``741736 -onorm`1`x`(_$)->R`cFiniteRankAlgebra(R,UP)``741797 -onorm`1`x`(_$)->R`cOctonionCategory(R)``741912 -onorm`1`x`(_$)->R`cQuaternionCategory(R)``742022 -onorm`1`x`(_$)->_$`cRealNumberSystem``742118 +onorm`1`n`(UP)->R`pComplexRootFindingPackage(R,UP)``898503 +onorm`1`x`(_$)->_$`cRealNumberSystem``898615 +onorm`1`x`(_$)->F`cFiniteAlgebraicExtensionField(F)``898672 +onorm`1`x`(PolE)->PolR`pNormInMonogenicAlgebra(R,PolR,E,PolE)``898814 +onorm`1`x`(_$)->R`cComplexCategory(R)``898932 +onorm`1`x`(_$)->R`cFiniteRankAlgebra(R,UP)``898993 +onorm`1`x`(_$)->R`cOctonionCategory(R)``899108 +onorm`1`x`(_$)->R`cQuaternionCategory(R)``899218 +onorm`2`n`(_$,Kernel(_$))->_$`dInnerAlgebraicNumber``899314 +onorm`2`n`(_$,List(Kernel(_$)))->_$`dInnerAlgebraicNumber``899450 +onorm`2`n`(SparseUnivariatePolynomial(_$),Kernel(_$))->SparseUnivariatePolynomial(_$)`dInnerAlgebraicNumber``899587 +onorm`2`n`(SparseUnivariatePolynomial(_$),List(Kernel(_$)))->SparseUnivariatePolynomial(_$)`dInnerAlgebraicNumber``899717 onorm`2`n`(S,PositiveInteger)->S`xFiniteAlgebraicExtensionField&(S,F)``0 -onorm`2`n`(SparseUnivariatePolynomial(_$),Kernel(_$))->SparseUnivariatePolynomial(_$)`dInnerAlgebraicNumber``742175 -onorm`2`n`(SparseUnivariatePolynomial(_$),List(Kernel(_$)))->SparseUnivariatePolynomial(_$)`dInnerAlgebraicNumber``742305 -onorm`2`n`(UP,PositiveInteger)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``742436 -onorm`2`n`(Vector(GF),PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``742517 -onorm`2`n`(_$,Kernel(_$))->_$`dInnerAlgebraicNumber``742614 -onorm`2`n`(_$,List(Kernel(_$)))->_$`dInnerAlgebraicNumber``742750 -onorm`2`x`(SparseUnivariatePolynomial(_$),Kernel(_$))->SparseUnivariatePolynomial(_$)`dAlgebraicNumber``742887 -onorm`2`x`(SparseUnivariatePolynomial(_$),List(Kernel(_$)))->SparseUnivariatePolynomial(_$)`dAlgebraicNumber``743017 -onorm`2`x`(_$,Kernel(_$))->_$`dAlgebraicNumber``743148 -onorm`2`x`(_$,List(Kernel(_$)))->_$`dAlgebraicNumber``743284 -onorm`2`x`(_$,PositiveInteger)->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`743421 -onormal01`0`n`()->Float`pRandomFloatDistributions``743724 +onorm`2`n`(UP,PositiveInteger)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``899848 +onorm`2`n`(Vector(GF),PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``899929 +onorm`2`x`(_$,Kernel(_$))->_$`dAlgebraicNumber``900026 +onorm`2`x`(_$,List(Kernel(_$)))->_$`dAlgebraicNumber``900162 +onorm`2`x`(_$,PositiveInteger)->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`900299 +onorm`2`x`(SparseUnivariatePolynomial(_$),Kernel(_$))->SparseUnivariatePolynomial(_$)`dAlgebraicNumber``900606 +onorm`2`x`(SparseUnivariatePolynomial(_$),List(Kernel(_$)))->SparseUnivariatePolynomial(_$)`dAlgebraicNumber``900736 +onormal01`0`n`()->Float`pRandomFloatDistributions``900867 onormal?`1`n`(S)->Boolean`xFiniteAlgebraicExtensionField&(S,F)``0 -onormal?`1`n`(SparseUnivariatePolynomial(GF))->Boolean`pFiniteFieldPolynomialPackage(GF)``743763 -onormal?`1`n`(Vector(GF))->Boolean`pInnerNormalBasisFieldFunctions(GF)``743928 -onormal?`1`x`(_$)->Boolean`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`744027 -onormalDenom`2`n`(Fraction(UP),(UP)->UP)->UP`pMonomialExtensionTools(F,UP)``744312 -onormalDeriv`2`n`(SparseUnivariatePolynomial(P),Integer)->SparseUnivariatePolynomial(P)`pFactoringUtilities(E,OV,R,P)``744447 -onormalElement`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`744548 -onormalElement`1`n`(PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``744998 -onormalForm`2`x`(Dpol,List(Dpol))->Dpol`pGroebnerPackage(Dom,Expon,VarSet,Dpol)`has(Dom,Field)`745109 -onormalForm`3`n`(Matrix(K),Automorphism(K),(K)->K)->Record(R:Matrix(K),A:Matrix(K),Ainv:Matrix(K))`pPseudoLinearNormalForm(K)``745284 -onormal`2`n`(Float,Float)->()->Float`pRandomFloatDistributions``745532 -onormalise`1`x`(Matrix(Expression(Integer)))->Matrix(Expression(Integer))`pRadicalEigenPackage``745574 +onormal?`1`n`(SparseUnivariatePolynomial(GF))->Boolean`pFiniteFieldPolynomialPackage(GF)``900906 +onormal?`1`n`(Vector(GF))->Boolean`pInnerNormalBasisFieldFunctions(GF)``901071 +onormal?`1`x`(_$)->Boolean`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`901170 +onormal`2`n`(Float,Float)->()->Float`pRandomFloatDistributions``901455 +onormalDenom`2`n`(Fraction(UP),(UP)->UP)->UP`pMonomialExtensionTools(F,UP)``901497 +onormalDeriv`2`n`(SparseUnivariatePolynomial(P),Integer)->SparseUnivariatePolynomial(P)`pFactoringUtilities(E,OV,R,P)``901632 +onormalElement`0`x`()->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`901733 +onormalElement`1`n`(PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``902183 +onormalForm`2`x`(Dpol,List(Dpol))->Dpol`pGroebnerPackage(Dom,Expon,VarSet,Dpol)`has(Dom,Field)`902294 +onormalForm`3`n`(Matrix(K),Automorphism(K),(K)->K)->Record(R:Matrix(K),A:Matrix(K),Ainv:Matrix(K))`pPseudoLinearNormalForm(K)``902469 +onormalise`1`x`(Matrix(Expression(Integer)))->Matrix(Expression(Integer))`pRadicalEigenPackage``902717 +onormalize`1`x`(_$)->_$`dFloat``902882 +onormalize`1`x`(F)->F`pElementaryFunctionStructurePackage(R,F)``902951 +onormalize`2`x`(F,Symbol)->F`pElementaryFunctionStructurePackage(R,F)``903071 +onormalize`2`x`(P,TS)->List(Record(val:P,tower:TS))`pNormalizationPackage(R,E,V,P,TS)``903215 onormalizeAtInfinity`1`n`(Vector(S))->Vector(S)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -onormalizeAtInfinity`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``745739 -onormalizeIfCan`1`n`(ST)->ST`pLazardSetSolvingPackage(R,E,V,P,TS,ST)``745811 -onormalize`1`x`(F)->F`pElementaryFunctionStructurePackage(R,F)``745943 -onormalize`1`x`(_$)->_$`dFloat``746063 -onormalize`2`x`(F,Symbol)->F`pElementaryFunctionStructurePackage(R,F)``746132 -onormalize`2`x`(P,TS)->List(Record(val:P,tower:TS))`pNormalizationPackage(R,E,V,P,TS)``746276 +onormalizeAtInfinity`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``903328 onormalized?`1`n`(S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -onormalized?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``746389 +onormalized?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``903400 onormalized?`2`n`(P,S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 onormalized?`2`n`(S,List(S))->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 onormalized?`2`n`(S,S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -onormalized?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``746610 -onormalized?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``746834 -onormalized?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``747003 -onormalizedAssociate`2`x`(P,TS)->P`pNormalizationPackage(R,E,V,P,TS)``747187 -onormalizedDivide`2`n`(R,R)->Record(quotient:R,remainder:R)`pModularHermitianRowReduction(R)``747518 -onormalizedDivide`2`x`(R,R)->Record(quotient:R,remainder:R)`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,EuclideanDomain)`747720 +onormalized?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``903622 +onormalized?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``903806 +onormalized?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``903975 +onormalizedAssociate`2`x`(P,TS)->P`pNormalizationPackage(R,E,V,P,TS)``904199 +onormalizedDivide`2`n`(R,R)->Record(quotient:R,remainder:R)`pModularHermitianRowReduction(R)``904530 +onormalizedDivide`2`x`(R,R)->Record(quotient:R,remainder:R)`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,EuclideanDomain)`904732 +onormalizeIfCan`1`n`(ST)->ST`pLazardSetSolvingPackage(R,E,V,P,TS,ST)``904934 +onormDeriv2`2`n`(SparseUnivariatePolynomial(R),Integer)->SparseUnivariatePolynomial(R)`pMultivariateSquareFree(E,OV,R,P)``905066 +onormFactors`1`n`(ExtP)->List(ExtP)`pNormRetractPackage(F,ExtF,SUEx,ExtP,n)``905107 +onormInvertible?`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pNormalizationPackage(R,E,V,P,TS)``905150 +oNot`1`n`(_$)->_$`dIndexedBits(mn)``905264 +onot`1`n`(_$)->_$`dOutputForm``905333 onot`1`n`(S)->S`xBitAggregate&(S)``0 -onot`1`n`(_$)->_$`dOutputForm``747922 -onot`1`x`(_$)->_$`cBitAggregate``747978 -onot`1`x`(_$)->_$`dBoolean``748064 -onot`1`x`(_$)->_$`dSingleInteger``748118 -onotelem`1`n`(_$)->List(Record(integrand:F,intvar:F))`dIntegrationResult(F)``748212 -onpcoef`3`n`(SparseUnivariatePolynomial(P),List(BP),List(P))->Record(deter:List(SparseUnivariatePolynomial(P)),dterm:List(List(Record(expt:NonNegativeInteger,pcoef:P))),nfacts:List(BP),nlead:List(P))`pNPCoef(BP,E,OV,R,P)``748295 +onot`1`x`(_$)->_$`cBitAggregate``905389 +onot`1`x`(_$)->_$`dBoolean``905469 +onot`1`x`(_$)->_$`dSingleInteger``905523 +oNot`1`x`(_$)->_$`dSingleInteger``905611 +oNOT`1`x`(_$)->_$`dSwitch``905699 +oNOT`1`x`(Union(I:Expression(Integer),F:Expression(Float),CF:Expression(Complex(Float)),switch:_$))->_$`dSwitch``905788 +onotelem`1`n`(_$)->List(Record(integrand:F,intvar:F))`dIntegrationResult(F)``905877 +onpcoef`3`n`(SparseUnivariatePolynomial(P),List(BP),List(P))->Record(deter:List(SparseUnivariatePolynomial(P)),dterm:List(List(Record(expt:NonNegativeInteger,pcoef:P))),nfacts:List(BP),nlead:List(P))`pNPCoef(BP,E,OV,R,P)``905960 onrows`1`n`(S)->NonNegativeInteger`xRectangularMatrixCategory&(S,m,n,R,Row,Col)``0 -onrows`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)``748330 -onrows`1`x`(_$)->NonNegativeInteger`cTwoDimensionalArrayCategory(R,Row,Col)``748404 -onsqfree`3`n`(SparseUnivariatePolynomial(P),List(OV),List(List(R)))->Record(unitPart:P,suPart:List(Record(factor:SparseUnivariatePolynomial(P),exponent:Integer)))`pMultivariateSquareFree(E,OV,R,P)``748476 -onthCoef`2`x`(_$,Integer)->E`cFreeAbelianMonoidCategory(S,E)``748514 -onthExpon`2`n`(_$,Integer)->E`dListMonoidOps(S,E,un)``748598 -onthExpon`2`n`(_$,Integer)->Integer`dFreeGroup(S)``748684 -onthExpon`2`n`(_$,Integer)->NonNegativeInteger`dFreeMonoid(S)``748770 -onthExpon`2`n`(_$,Integer)->NonNegativeInteger`dOrderedFreeMonoid(S)``748856 -onthExponent`2`x`(_$,Integer)->Integer`dFactored(R)``748949 -onthFactor`2`n`(_$,Integer)->S`dFreeGroup(S)``749165 -onthFactor`2`n`(_$,Integer)->S`dFreeMonoid(S)``749250 -onthFactor`2`n`(_$,Integer)->S`dListMonoidOps(S,E,un)``749335 -onthFactor`2`n`(_$,Integer)->S`dOrderedFreeMonoid(S)``749420 -onthFactor`2`x`(_$,Integer)->R`dFactored(R)``749512 -onthFactor`2`x`(_$,Integer)->S`cFreeAbelianMonoidCategory(S,E)``749793 -onthFlag`2`x`(_$,Integer)->Union("nil","sqfr","irred","prime")`dFactored(R)``749874 -onthFractionalTerm`2`x`(_$,Integer)->_$`dPartialFraction(R)``750098 -onthRootIfCan`2`x`(K,NonNegativeInteger)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``750267 -onthRoot`2`n`(Factored(M),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:M,radicand:List(M))`pFactoredFunctions(M)``750380 +onrows`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)``905995 +onrows`1`x`(_$)->NonNegativeInteger`cTwoDimensionalArrayCategory(R,Row,Col)``906069 +onsqfree`3`n`(SparseUnivariatePolynomial(P),List(OV),List(List(R)))->Record(unitPart:P,suPart:List(Record(factor:SparseUnivariatePolynomial(P),exponent:Integer)))`pMultivariateSquareFree(E,OV,R,P)``906245 +onthCoef`2`x`(_$,Integer)->E`cFreeAbelianMonoidCategory(S,E)``906283 +onthExpon`2`n`(_$,Integer)->E`dListMonoidOps(S,E,un)``906367 +onthExpon`2`n`(_$,Integer)->Integer`dFreeGroup(S)``906453 +onthExpon`2`n`(_$,Integer)->NonNegativeInteger`dFreeMonoid(S)``906539 +onthExpon`2`n`(_$,Integer)->NonNegativeInteger`dOrderedFreeMonoid(S)``906625 +onthExponent`2`x`(_$,Integer)->Integer`dFactored(R)``906831 +onthFactor`2`n`(_$,Integer)->S`dFreeGroup(S)``907170 +onthFactor`2`n`(_$,Integer)->S`dFreeMonoid(S)``907255 +onthFactor`2`n`(_$,Integer)->S`dListMonoidOps(S,E,un)``907340 +onthFactor`2`n`(_$,Integer)->S`dOrderedFreeMonoid(S)``907425 +onthFactor`2`x`(_$,Integer)->R`dFactored(R)``907631 +onthFactor`2`x`(_$,Integer)->S`cFreeAbelianMonoidCategory(S,E)``908055 +onthFlag`2`x`(_$,Integer)->Union("nil","sqfr","irred","prime")`dFactored(R)``908136 +onthFractionalTerm`2`x`(_$,Integer)->_$`dPartialFraction(R)``908479 +onthr`2`n`(P,NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:P,radicand:List(P))`pPolynomialRoots(E,V,R,P,F)``908832 +onthRoot`2`n`(Factored(M),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:M,radicand:List(M))`pFactoredFunctions(M)``908890 onthRoot`2`n`(S,Integer)->S`xRadicalCategory&(S)``0 onthRoot`2`n`(S,Integer)->S`xRealClosedField&(S)``0 -onthRoot`2`x`(_$,Integer)->_$`cRadicalCategory``750687 -onthr`2`n`(P,NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:P,radicand:List(P))`pPolynomialRoots(E,V,R,P,F)``750757 -onull?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``750815 -onullSpace`1`n`(M)->List(Col)`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(Col,ATTRIBUTE(shallowlyMutable))`750896 -onullSpace`1`n`(M)->List(Col)`pInnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2)`has(Col2,ATTRIBUTE(shallowlyMutable))`750982 -onullSpace`1`x`(M)->List(Col)`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`751068 -onullSpace`1`x`(_$)->List(Col)`cMatrixCategory(R,Row,Col)`has(R,IntegralDomain)`751154 -onullSpace`1`x`(_$)->List(Col)`cRectangularMatrixCategory(m,n,R,Row,Col)`has(R,IntegralDomain)`751240 -onull`1`x`(_$)->Boolean`dList(S)``751327 -onullary?`1`x`(_$)->Boolean`dBasicOperator``751391 -onullary`1`x`(A)->()->A`pMappingPackage1(A)``751449 -onullity`1`n`(M)->NonNegativeInteger`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``751533 -onullity`1`x`(M)->NonNegativeInteger`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`751666 -onullity`1`x`(_$)->NonNegativeInteger`cMatrixCategory(R,Row,Col)`has(R,IntegralDomain)`751799 -onullity`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)`has(R,IntegralDomain)`751932 -onumFunEvals3D`0`n`()->Integer`dPlot3D``752065 -onumFunEvals`0`n`()->Integer`dPlot``752134 -onumber?`1`x`(_$)->Boolean`dExpression(R)`has(R,IntegralDomain)`752200 -onumberOfChildren`1`n`(_$)->NonNegativeInteger`dSubSpace(n,R)``752255 -onumberOfComponents`0`n`()->NonNegativeInteger`xFunctionFieldCategory&(S,F,UP,UPUP)``752303 -onumberOfComponents`0`x`()->NonNegativeInteger`cFunctionFieldCategory(F,UP,UPUP)``752395 -onumberOfComponents`1`x`(_$)->NonNegativeInteger`cThreeSpaceCategory(R)``752487 -onumberOfComposites`1`x`(_$)->NonNegativeInteger`cThreeSpaceCategory(R)``752682 -onumberOfComputedEntries`1`x`(_$)->NonNegativeInteger`cLazyStreamAggregate(S)``753148 -onumberOfCycles`1`x`(_$)->NonNegativeInteger`dPermutation(S)``753327 -onumberOfDivisors`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``753429 -onumberOfFactors`1`n`(List(Record(factor:UP,degree:Integer)))->NonNegativeInteger`pGaloisGroupFactorizer(UP)``753622 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+oOMunhandledSymbol`2`x`(String,String)->Exit`pOpenMathPackage``929418 +oOMUnknownCD?`1`x`(_$)->Boolean`dOpenMathErrorKind``929583 +oOMUnknownSymbol?`1`x`(_$)->Boolean`dOpenMathErrorKind``929676 +oOMwrite`1`x`(Expression(R))->String`pExpressionToOpenMath(R)``0 +oOMwrite`1`x`(_$)->String`cOpenMath``929770 +oOMwrite`2`x`(_$,Boolean)->String`cOpenMath``929887 +oOMwrite`2`x`(Expression(R),Boolean)->String`pExpressionToOpenMath(R)``0 +oOMwrite`2`x`(OpenMathDevice,Expression(R))->Void`pExpressionToOpenMath(R)``0 +oOMwrite`2`x`(OpenMathDevice,_$)->Void`cOpenMath``930132 +oOMwrite`3`x`(OpenMathDevice,_$,Boolean)->Void`cOpenMath``930282 +oOMwrite`3`x`(OpenMathDevice,Expression(R),Boolean)->Void`pExpressionToOpenMath(R)``0 oone?`1`n`(S)->Boolean`xMonadWithUnit&(S)``0 oone?`1`n`(S)->Boolean`xMonoid&(S)``0 oone?`1`n`(S)->Boolean`xQuaternionCategory&(S,R)``0 -oone?`1`x`(_$)->Boolean`cMonadWithUnit``762085 -oone?`1`x`(_$)->Boolean`cMonoid``762145 -oone?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``762200 -ooneDimensionalArray`1`x`(List(S))->_$`dOneDimensionalArray(S)``762306 -ooneDimensionalArray`2`x`(NonNegativeInteger,S)->_$`dOneDimensionalArray(S)``762393 -oop`1`n`(P)->_$`dOppositeMonogenicLinearOperator(P,R)``762492 -oopen?`1`n`(_$)->Boolean`dTubePlot(Curve)``762565 -oopen`1`x`(Name)->_$`cFileCategory(Name,S)``762640 -oopen`2`x`(Name,String)->_$`cFileCategory(Name,S)``762704 -ooperation`1`x`(_$)->Union(Null:"null",Assignment:"assignment",Conditional:"conditional",Return:"return",Block:"block",Comment:"comment",Call:"call",For:"for",While:"while",Repeat:"repeat",Goto:"goto",Continue:"continue",ArrayAssignment:"arrayAssignment",Save:"save",Stop:"stop",Common:"common",Print:"print")`dFortranCode``762820 -ooperator`1`n`(BasicOperator)->BasicOperator`pAlgebraicFunction(R,F)``762906 -ooperator`1`n`(BasicOperator)->BasicOperator`pCombinatorialFunction(R,F)``763138 -ooperator`1`n`(BasicOperator)->BasicOperator`pElementaryFunction(R,F)``763308 -ooperator`1`n`(BasicOperator)->BasicOperator`pFunctionalSpecialFunction(R,F)``763398 -ooperator`1`n`(BasicOperator)->BasicOperator`pLiouvillianFunction(R,F)``763570 -ooperator`1`n`(BasicOperator)->BasicOperator`xExpressionSpace&(S)``763649 +oone?`1`x`(_$)->Boolean`cMonadWithUnit``930531 +oone?`1`x`(_$)->Boolean`cMonoid``930591 +oone`1`x`(Boolean)->_$`dGuessOption``930646 +oone?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``930771 +oone`1`x`(List(GuessOption))->Boolean`dGuessOptionFunctions0``930877 +ooneDimensionalArray`1`x`(List(S))->_$`dOneDimensionalArray(S)``930967 +ooneDimensionalArray`2`x`(NonNegativeInteger,S)->_$`dOneDimensionalArray(S)``931144 +oop`1`n`(P)->_$`dOppositeMonogenicLinearOperator(P,R)``931314 +oopen?`1`n`(_$)->Boolean`dTubePlot(Curve)``931387 +oopen`1`x`(Name)->_$`cFileCategory(Name,S)``931462 +oopen`2`x`(Name,String)->_$`cFileCategory(Name,S)``931526 +ooperation`1`x`(_$)->Union(Null:"null",Assignment:"assignment",Conditional:"conditional",Return:"return",Block:"block",Comment:"comment",Call:"call",For:"for",While:"while",Repeat:"repeat",Goto:"goto",Continue:"continue",ArrayAssignment:"arrayAssignment",Save:"save",Stop:"stop",Common:"common",Print:"print")`dFortranCode``931642 +ooperator`1`n`(BasicOperator)->BasicOperator`pAlgebraicFunction(R,F)``931728 +ooperator`1`n`(BasicOperator)->BasicOperator`pCombinatorialFunction(R,F)``931960 +ooperator`1`n`(BasicOperator)->BasicOperator`pElementaryFunction(R,F)``932130 +ooperator`1`n`(BasicOperator)->BasicOperator`pFunctionalSpecialFunction(R,F)``932220 +ooperator`1`n`(BasicOperator)->BasicOperator`pLiouvillianFunction(R,F)``932392 +ooperator`1`n`(BasicOperator)->BasicOperator`xExpressionSpace&(S)``932471 ooperator`1`n`(BasicOperator)->BasicOperator`xFunctionSpace&(S,R)``0 -ooperator`1`n`(Symbol)->BasicOperator`pCommonOperators``763761 -ooperator`1`n`(_$)->BasicOperator`dKernel(S)``763939 -ooperator`1`x`(BasicOperator)->BasicOperator`cExpressionSpace``764006 -ooperator`1`x`(Symbol)->_$`dBasicOperator``764118 -ooperator`2`x`(Symbol,NonNegativeInteger)->_$`dBasicOperator``764198 +ooperator`1`n`(_$)->BasicOperator`dKernel(S)``932583 +ooperator`1`n`(Symbol)->BasicOperator`pCommonOperators``932650 +ooperator`1`x`(BasicOperator)->BasicOperator`cExpressionSpace``932828 +ooperator`1`x`(Symbol)->_$`dBasicOperator``932940 +ooperator`2`x`(Symbol,NonNegativeInteger)->_$`dBasicOperator``933020 ooperators`1`n`(S)->List(BasicOperator)`xExpressionSpace&(S)``0 -ooperators`1`x`(_$)->List(BasicOperator)`cExpressionSpace``764275 +ooperators`1`x`(_$)->List(BasicOperator)`cExpressionSpace``933097 oopeval`2`n`(BasicOperator,R)->R`dOperator(R)``0 -oopeval`2`x`(BasicOperator,M)->M`dModuleOperator(R,M)``764392 -ooptAttributes`1`x`(Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat))))->List(String)`pe04AgentsPackage``764445 -ooptimize`1`x`(NumericalOptimizationProblem)->Result`pAnnaNumericalOptimizationPackage``764553 -ooptimize`2`x`(Expression(Float),List(Float))->Result`pAnnaNumericalOptimizationPackage``764939 -ooptimize`2`x`(List(Expression(Float)),List(Float))->Result`pAnnaNumericalOptimizationPackage``765438 -ooptimize`2`x`(NumericalOptimizationProblem,RoutinesTable)->Result`pAnnaNumericalOptimizationPackage``765989 -ooptimize`4`x`(Expression(Float),List(Float),List(OrderedCompletion(Float)),List(OrderedCompletion(Float)))->Result`pAnnaNumericalOptimizationPackage``766430 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-oor`2`x`(_$,_$)->_$`cBitAggregate``770178 -oor`2`x`(_$,_$)->_$`dBoolean``770278 -oorbit`2`x`(_$,List(S))->Set(List(S))`dPermutationGroup(S)``770372 -oorbit`2`x`(_$,S)->Set(S)`cPermutationCategory(S)``770579 -oorbit`2`x`(_$,S)->Set(S)`dPermutationGroup(S)``770768 -oorbit`2`x`(_$,Set(S))->Set(Set(S))`dPermutationGroup(S)``770958 -oorbits`1`x`(_$)->Set(Set(S))`dPermutationGroup(S)``771063 -oord`1`x`(_$)->Integer`dCharacter``771198 +oopeval`2`x`(BasicOperator,M)->M`dModuleOperator(R,M)``933214 +ooptAttributes`1`x`(Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat))))->List(String)`pe04AgentsPackage``933267 +ooptimize`1`x`(NumericalOptimizationProblem)->Result`pAnnaNumericalOptimizationPackage``933375 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-oplot`5`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat))->_$`dPlot3D``803152 -oplot`5`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot``803334 -oplot`8`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``803592 -oplus!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``803660 -oplusInfinity`0`x`()->OrderedCompletion(Integer)`pInfinity``803854 -oplusInfinity`0`x`()->_$`dOrderedCompletion(R)``803906 -oplus`2`n`(_$,_$)->_$`dListMonoidOps(S,E,un)``803954 -oplus`2`x`(_$,_$)->_$`dThreeDimensionalMatrix(R)`has(R,Ring)`804074 -oplus`3`n`(S,E,_$)->_$`dListMonoidOps(S,E,un)``804174 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+oplot`5`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat))->_$`dPlot3D``977275 +oplot`5`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot``977457 +oplot`8`n`((DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``977715 +oplotPolar`1`n`((DoubleFloat)->DoubleFloat)->_$`dPlot``977787 +oplotPolar`2`n`((DoubleFloat)->DoubleFloat,Segment(DoubleFloat))->_$`dPlot``978009 +oplotPolar`2`n`(S,Symbol)->Plot`pPlotFunctions1(S)``978226 +oplotPolar`3`n`(S,Symbol,Segment(DoubleFloat))->Plot`pPlotFunctions1(S)``978345 +oplus`2`n`(_$,_$)->_$`dListMonoidOps(S,E,un)``978465 +oplus`2`x`(_$,_$)->_$`dThreeDimensionalMatrix(R)`has(R,Ring)`978585 +oplus!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``978685 +oplus`3`n`(S,E,_$)->_$`dListMonoidOps(S,E,un)``978879 +oplusInfinity`0`x`()->_$`dOrderedCompletion(R)``979008 +oplusInfinity`0`x`()->OrderedCompletion(Integer)`pInfinity``979056 +opmComplexintegrate`2`n`(F,Symbol)->Union(Record(special:F,integrand:F),"failed")`pPatternMatchIntegration(R,F)`AND(has(R,ConvertibleTo(Pattern(Integer))),has(R,PatternMatchable(Integer)),has(F,LiouvillianFunctionCategory))`979108 +opmintegrate`2`n`(F,Symbol)->Union(Record(special:F,integrand:F),"failed")`pPatternMatchIntegration(R,F)`AND(has(R,ConvertibleTo(Pattern(Integer))),has(R,PatternMatchable(Integer)),has(F,LiouvillianFunctionCategory))`979327 +opmintegrate`4`n`(F,Symbol,OrderedCompletion(F),OrderedCompletion(F))->Union(F,"failed")`pPatternMatchIntegration(R,F)`AND(has(R,ConvertibleTo(Pattern(Integer))),has(R,PatternMatchable(Integer)),has(F,SpecialFunctionCategory))`979461 +opo`1`n`(_$)->P`dOppositeMonogenicLinearOperator(P,R)``979618 +opoint?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``979691 +opoint`1`x`(List(R))->_$`cPointCategory(R)``979855 +opoint`1`x`(Point(R))->_$`cThreeSpaceCategory(R)``979968 +opoint`1`x`(_$)->Point(R)`cThreeSpaceCategory(R)``980088 +opoint`2`x`(_$,List(R))->_$`cThreeSpaceCategory(R)``980268 +opoint`2`x`(_$,NonNegativeInteger)->_$`cThreeSpaceCategory(R)``980524 +opoint`2`x`(_$,Point(R))->_$`cThreeSpaceCategory(R)``980688 +opoint`3`n`(_$,Point(DoubleFloat),Palette)->Void`dGraphImage``980932 +opoint`4`n`(DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat)->Point(DoubleFloat)`pTubePlotTools``981288 +opointColor`1`x`(Float)->_$`dDrawOption``981533 +opointColor`1`x`(Palette)->_$`dDrawOption``981676 +opointColorDefault`0`x`()->Palette`pViewDefaultsPackage``981847 +opointColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``981935 +opointColorPalette`2`n`(List(DrawOption),Palette)->Palette`pDrawOptionFunctions0``982045 +opointData`1`n`(_$)->List(Point(R))`dSubSpace(n,R)``982273 +opointDominateBy`1`x`(Places(K))->ProjectivePlane(K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``982393 +opointDominateBy`1`x`(PlacesOverPseudoAlgebraicClosureOfFiniteField(K))->ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``982490 +opointDominateBy`1`x`(Plc)->ProjPt`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``982587 +opointDominateBy`1`x`(Plc)->ProjPt`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``982684 +opointInIdeal?`2`x`(List(PolyRing),ProjPt)->Boolean`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``982781 +opointLists`1`n`(_$)->List(List(Point(DoubleFloat)))`dGraphImage``982899 +opointPlot`2`n`((DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``983061 +opointPlot`2`n`((DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat))->_$`dPlot``983248 +opointPlot`4`n`((DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot``983415 +opointPlot`5`n`((DoubleFloat)->Point(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``983692 +opoints`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``983753 +opointSizeDefault`0`x`()->PositiveInteger`pViewDefaultsPackage``984021 +opointSizeDefault`1`x`(PositiveInteger)->PositiveInteger`pViewDefaultsPackage``984111 +opointToPlace`2`x`(ProjPt,PolyRing)->Plc`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``984211 +opointV`1`x`(_$)->ProjPt`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``984372 +opointValue`1`x`(_$)->List(K)`cAffineSpaceCategory(K)``984428 +opointValue`1`x`(_$)->List(K)`cProjectiveSpaceCategory(K)``984556 +opoisson`1`n`(RationalNumber)->()->Integer`pRandomIntegerDistributions``984684 +opol`1`n`(Vector(GF))->SparseUnivariatePolynomial(GF)`pInnerNormalBasisFieldFunctions(GF)``984723 +opolar`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``984835 opolarCoordinates`1`n`(S)->Record(r:R,phi:R)`xComplexCategory&(S,R)``0 -opolarCoordinates`1`x`(_$)->Record(r:R,phi:R)`cComplexCategory(R)`AND(has(R,RealNumberSystem),has(R,TranscendentalFunctionCategory))`809525 -opolar`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``809640 -opole?`1`n`(_$)->Boolean`dInnerTaylorSeries(Coef)``809854 -opole?`1`x`(_$)->Boolean`cPowerSeriesCategory(Coef,Expon,Var)``809993 -opolyPart`1`x`(_$)->UP`dFullPartialFractionExpansion(F,UP)``810068 -opolyRDE`5`n`(UP,UP,UP,Integer,(UP)->UP)->Union(ans:Record(ans:UP,nosol:Boolean),eq:Record(b:UP,c:UP,m:Integer,alpha:UP,beta:UP))`pTranscendentalRischDE(F,UP)``810135 -opolyRicDE`2`n`(L,(UP)->List(F))->List(Record(poly:UP,eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``810703 -opolyRicDE`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F))->List(Record(poly:UP,eq:LinearOrdinaryDifferentialOperator2(UP,Fraction(UP))))`pRationalRicDE(F,UP)``811108 -opolygamma`2`n`(F,F)->F`pFunctionalSpecialFunction(R,F)``811527 -opolygamma`2`x`(NonNegativeInteger,Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``811622 -opolygamma`2`x`(NonNegativeInteger,DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``811706 -opolygamma`2`x`(_$,_$)->_$`cSpecialFunctionCategory``811790 -opolygon?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``811928 -opolygon`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``812078 -opolygon`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``812270 -opolygon`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``812499 -opolygon`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``812865 -opolynomialZeros`3`x`(Polynomial(Fraction(Integer)),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pExpertSystemContinuityPackage``813040 -opolynomial`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`cMultivariateTaylorSeriesCategory(Coef,Var)``813284 -opolynomial`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`cUnivariateTaylorSeriesCategory(Coef)``813407 -opolynomial`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Polynomial(Coef)`cMultivariateTaylorSeriesCategory(Coef,Var)``813530 -opolynomial`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Polynomial(Coef)`cUnivariateTaylorSeriesCategory(Coef)``813682 -opolyred`1`n`(UPUP)->UPUP`pPointsOfFiniteOrderTools(UP,UPUP)``813834 +opolarCoordinates`1`x`(_$)->Record(r:R,phi:R)`cComplexCategory(R)`AND(has(R,RealNumberSystem),has(R,TranscendentalFunctionCategory))`985049 +opolCase`3`n`(Z,NonNegativeInteger,List(Z))->Boolean`pLeadingCoefDetermination(OV,E,Z,P)``985164 +opole?`1`n`(_$)->Boolean`dInnerTaylorSeries(Coef)``985642 +opole?`1`x`(_$)->Boolean`cPowerSeriesCategory(Coef,Expon,Var)``985781 +oPollardSmallFactor`1`n`(I)->Union(I,"failed")`pIntegerFactorizationPackage(I)``985856 +opolygamma`2`n`(F,F)->F`pFunctionalSpecialFunction(R,F)``985952 +opolygamma`2`x`(_$,_$)->_$`cSpecialFunctionCategory``986047 +opolygamma`2`x`(NonNegativeInteger,Complex(DoubleFloat))->Complex(DoubleFloat)`pDoubleFloatSpecialFunctions``986185 +opolygamma`2`x`(NonNegativeInteger,DoubleFloat)->DoubleFloat`pDoubleFloatSpecialFunctions``986269 +opolygon?`1`x`(_$)->Boolean`cThreeSpaceCategory(R)``986353 +opolygon`1`x`(List(Point(R)))->_$`cThreeSpaceCategory(R)``986503 +opolygon`1`x`(_$)->List(Point(R))`cThreeSpaceCategory(R)``986695 +opolygon`2`x`(_$,List(List(R)))->_$`cThreeSpaceCategory(R)``986924 +opolygon`2`x`(_$,List(Point(R)))->_$`cThreeSpaceCategory(R)``987290 +opolynomial`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`cMultivariateTaylorSeriesCategory(Coef,Var)``987465 +opolynomial`2`x`(_$,NonNegativeInteger)->Polynomial(Coef)`cUnivariateTaylorSeriesCategory(Coef)``987588 +opolynomial`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Polynomial(Coef)`cMultivariateTaylorSeriesCategory(Coef,Var)``987711 +opolynomial`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Polynomial(Coef)`cUnivariateTaylorSeriesCategory(Coef)``987863 +opolynomialZeros`3`x`(Polynomial(Fraction(Integer)),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pExpertSystemContinuityPackage``988015 +opolyPart`1`x`(_$)->UP`dFullPartialFractionExpansion(F,UP)``988259 +opolyRDE`5`n`(UP,UP,UP,Integer,(UP)->UP)->Union(ans:Record(ans:UP,nosol:Boolean),eq:Record(b:UP,c:UP,m:Integer,alpha:UP,beta:UP))`pTranscendentalRischDE(F,UP)``988326 +opolyred`1`n`(UPUP)->UPUP`pPointsOfFiniteOrderTools(UP,UPUP)``988894 +opolyRicDE`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F))->List(Record(poly:UP,eq:LinearOrdinaryDifferentialOperator2(UP,Fraction(UP))))`pRationalRicDE(F,UP)``988933 +opolyRicDE`2`n`(L,(UP)->List(F))->List(Record(poly:UP,eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``989350 +opolyRing2UPUP`1`x`(PolyRing)->SparseUnivariatePolynomial(SparseUnivariatePolynomial(K))`pAffineAlgebraicSetComputeWithResultant(K,symb,PolyRing,E,ProjPt)``0 +opolyRingToBlUpRing`2`x`(PolyRing,BLMET)->DistributedMultivariatePolynomial(construct('X,'Y),K)`pBlowUpPackage(K,symb,PolyRing,E,BLMET)``0 opomopo!`4`n`(S,R,E,S)->S`xFiniteAbelianMonoidRing&(S,R,E)``0 -opomopo!`4`x`(_$,R,E,_$)->_$`cFiniteAbelianMonoidRing(R,E)``813873 -opop!`1`x`(_$)->S`cStackAggregate(S)``814038 -opopFortranOutputStack`0`x`()->Void`pFortranOutputStackPackage``814258 -oposition!`2`x`(_$,SingleInteger)->SingleInteger`dBinaryFile``814326 -oposition`1`x`(_$)->NonNegativeInteger`cCachableSet``814402 -oposition`1`x`(_$)->SingleInteger`dBinaryFile``814481 -oposition`2`n`((S)->Boolean,A)->Integer`xFiniteLinearAggregate&(A,S)``0 -oposition`2`n`((S)->Boolean,A)->Integer`xListAggregate&(A,S)``0 -oposition`2`n`((S)->Boolean,A)->Integer`xOneDimensionalArrayAggregate&(A,S)``0 +opomopo!`4`x`(_$,R,E,_$)->_$`cFiniteAbelianMonoidRing(R,E)``989755 +opop!`1`x`(_$)->S`cStackAggregate(S)``989920 +opop!`1`x`(_$)->S`dArrayStack(S)``990273 +opop!`1`x`(_$)->S`dDequeue(S)``990377 +opop!`1`x`(_$)->S`dStack(S)``990475 +opopFortranOutputStack`0`x`()->Void`pFortranOutputStackPackage``990569 +oposExpnPart`1`x`(_$)->_$`cLocalPowerSeriesCategory(K)``990637 +oposition`1`x`(_$)->NonNegativeInteger`cCachableSet``990733 +oposition`1`x`(_$)->SingleInteger`dBinaryFile``990812 oposition`2`n`(S,A)->Integer`xFiniteLinearAggregate&(A,S)``0 oposition`2`n`(S,A)->Integer`xListAggregate&(A,S)``0 oposition`2`n`(S,A)->Integer`xOneDimensionalArrayAggregate&(A,S)``0 -oposition`2`x`((S)->Boolean,_$)->Integer`cFiniteLinearAggregate(S)``814563 -oposition`2`x`(S,_$)->Integer`cFiniteLinearAggregate(S)`has(S,SetCategory)`814768 +oposition`2`n`((S)->Boolean,A)->Integer`xFiniteLinearAggregate&(A,S)``0 +oposition`2`n`((S)->Boolean,A)->Integer`xListAggregate&(A,S)``0 +oposition`2`n`((S)->Boolean,A)->Integer`xOneDimensionalArrayAggregate&(A,S)``0 +oposition`2`x`((S)->Boolean,_$)->Integer`cFiniteLinearAggregate(S)``990894 +oposition!`2`x`(_$,SingleInteger)->SingleInteger`dBinaryFile``991099 +oposition`2`x`(S,_$)->Integer`cFiniteLinearAggregate(S)`has(S,SetCategory)`991175 oposition`3`n`(S,A,Integer)->Integer`xFiniteLinearAggregate&(A,S)``0 oposition`3`n`(S,A,Integer)->Integer`xListAggregate&(A,S)``0 oposition`3`n`(S,A,Integer)->Integer`xOneDimensionalArrayAggregate&(A,S)``0 -oposition`3`x`(CharacterClass,_$,Integer)->Integer`cStringAggregate``814927 -oposition`3`x`(S,_$,Integer)->Integer`cFiniteLinearAggregate(S)`has(S,SetCategory)`815078 -oposition`3`x`(_$,_$,Integer)->Integer`cStringAggregate``815291 +oposition`3`x`(CharacterClass,_$,Integer)->Integer`cStringAggregate``991334 +oposition`3`x`(_$,_$,Integer)->Integer`cStringAggregate``991485 +oposition`3`x`(S,_$,Integer)->Integer`cFiniteLinearAggregate(S)`has(S,SetCategory)`991652 opositive?`1`n`(S)->Boolean`xIntegerNumberSystem&(S)``0 opositive?`1`n`(S)->Boolean`xOrderedRing&(S)``0 -opositive?`1`x`(_$)->Boolean`cIntervalCategory(R)``815458 -opositive?`1`x`(_$)->Boolean`cOrderedRing``815589 +opositive?`1`x`(_$)->Boolean`cIntervalCategory(R)``991865 +opositive?`1`x`(_$)->Boolean`cOrderedRing``991996 opositive?`2`n`(ThePols,S)->Boolean`xRealRootCharacterizationCategory&(S,TheField,ThePols)``0 -opositive?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``815667 -opositiveRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``815769 -opositiveSolve`1`x`(List(Polynomial(R)))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``815894 -opositiveSolve`1`x`(RegularChain(R,ls))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``815988 -opositiveSolve`2`x`(List(Polynomial(R)),Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``816114 -opositiveSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``816208 +opositive?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``992074 +opositiveRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``992176 +opositiveSolve`1`x`(List(Polynomial(R)))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``992301 +opositiveSolve`1`x`(RegularChain(R,ls))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``992395 +opositiveSolve`2`x`(List(Polynomial(R)),Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``992521 +opositiveSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``992615 opossiblyInfinite?`1`n`(A)->Boolean`xLazyStreamAggregate&(A,S)``0 opossiblyInfinite?`1`n`(A)->Boolean`xStreamAggregate&(A,S)``0 -opossiblyInfinite?`1`x`(_$)->Boolean`cStreamAggregate(S)``817062 -opossiblyNewVariety?`2`n`(List(P),List(List(P)))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``817276 -opostfix`2`n`(_$,_$)->_$`dOutputForm``817460 -opow`0`n`()->PrimitiveArray(_$)`dModMonic(R,Rep)``817536 -opower!`5`n`(Matrix(R),Matrix(R),Matrix(R),Matrix(R),NonNegativeInteger)->Matrix(R)`pStorageEfficientMatrixOperations(R)``817570 -opowerAssociative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``817859 -opowerSum`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``817965 -opower`2`n`(A,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Field)`818053 -opowern`2`n`(Fraction(Integer),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Algebra(Fraction(Integer)))`818144 -opowers`1`n`(List(Integer))->List(List(Integer))`dPartition``818224 +opossiblyInfinite?`1`x`(_$)->Boolean`cStreamAggregate(S)``993431 +opossiblyNewVariety?`2`n`(List(P),List(List(P)))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``993649 +opostfix`2`n`(_$,_$)->_$`dOutputForm``993833 +opow`0`n`()->PrimitiveArray(_$)`dModMonic(R,Rep)``993909 +opower`2`n`(A,Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Field)`993947 +opower!`5`n`(Matrix(R),Matrix(R),Matrix(R),Matrix(R),NonNegativeInteger)->Matrix(R)`pStorageEfficientMatrixOperations(R)``994038 +opowerAssociative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``994327 +opowern`2`n`(Fraction(Integer),Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)`has(A,Algebra(Fraction(Integer)))`994433 +opowers`1`n`(List(Integer))->List(List(Integer))`dPartition``994513 +opowerSum`1`x`(Integer)->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``994807 opowmod`3`n`(S,S,S)->S`xIntegerNumberSystem&(S)``0 -opowmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``818518 +opowmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``994895 opquo`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -opquo`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``818601 +opquo`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``994978 opquo`3`n`(S,S,V)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -opquo`3`x`(_$,_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``818780 -opr2dmp`1`n`(Polynomial(R))->GR`pParametricLinearEquations(R,Var,Expon,GR)``818949 -oprecision`0`x`()->PositiveInteger`cFloatingPointSystem``819008 -oprecision`0`x`()->PositiveInteger`dMachineFloat``819072 -oprecision`1`x`(PositiveInteger)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`819140 -oprecision`1`x`(PositiveInteger)->PositiveInteger`dMachineFloat``819225 -opredicate`1`n`(Pattern(R))->(D)->Boolean`pPatternFunctions1(R,D)``819303 -opredicates`1`n`(_$)->List(Any)`dPattern(R)``819456 +opquo`3`x`(_$,_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``995157 +opr2dmp`1`n`(Polynomial(R))->GR`pParametricLinearEquations(R,Var,Expon,GR)``995326 +oprecision`0`x`()->PositiveInteger`cFloatingPointSystem``995385 +oprecision`0`x`()->PositiveInteger`dMachineFloat``995449 +oprecision`1`x`(PositiveInteger)->PositiveInteger`cFloatingPointSystem`has(_$,ATTRIBUTE(arbitraryPrecision))`995517 +oprecision`1`x`(PositiveInteger)->PositiveInteger`dMachineFloat``995602 +opredicate`1`n`(Pattern(R))->(D)->Boolean`pPatternFunctions1(R,D)``995680 +opredicates`1`n`(_$)->List(Any)`dPattern(R)``995833 +oprefix`2`n`(_$,List(_$))->_$`dOutputForm``995973 oprefix?`2`n`(S,S)->Boolean`xStringAggregate&(S)``0 -oprefix?`2`x`(_$,_$)->Boolean`cStringAggregate``819596 -oprefixRagits`1`x`(_$)->List(Integer)`dRadixExpansion(bb)``819837 -oprefix`2`n`(_$,List(_$))->_$`dOutputForm``820054 +oprefix?`2`x`(_$,_$)->Boolean`cStringAggregate``996122 +oprefixRagits`1`x`(_$)->List(Integer)`dRadixExpansion(bb)``996381 oprem`2`n`(S,S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oprem`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``820203 +oprem`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)``996598 oprem`3`n`(S,S,V)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oprem`3`x`(_$,_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``820383 -oprepareDecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(Record(eq:List(P),tower:TS,ineq:List(P)))`pQuasiComponentPackage(R,E,V,P,TS)``820553 -oprepareDecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(Record(eq:List(P),tower:TS,ineq:List(P)))`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``820694 -oprepareSubResAlgo`3`x`(P,P,TS)->List(Record(val:List(P),tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``820835 -opreprocess`3`x`(List(P),Boolean,Boolean)->Record(val:List(P),towers:List(_$))`dRegularTriangularSet(R,E,V,P)``820964 -opreprocess`3`x`(List(P),Boolean,Boolean)->Record(val:List(P),towers:List(_$))`dSquareFreeRegularTriangularSet(R,E,V,P)``821087 -opresub`2`n`(_$,_$)->_$`dOutputForm``821210 -opresuper`2`n`(_$,_$)->_$`dOutputForm``821294 -oprevPrime`1`x`(I)->I`pIntegerPrimesPackage(I)``821382 -oprevious`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``821466 -oprimPartElseUnitCanonical!`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oprimPartElseUnitCanonical!`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`821653 -oprimPartElseUnitCanonical`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oprimPartElseUnitCanonical`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`821779 -oprimaryDecomp`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->List(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))`pIdealDecompositionPackage(vl,nv)``821959 +oprem`3`x`(_$,_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``996778 +oprepareDecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(Record(eq:List(P),tower:TS,ineq:List(P)))`pQuasiComponentPackage(R,E,V,P,TS)``996948 +oprepareDecompose`4`x`(List(P),List(TS),Boolean,Boolean)->List(Record(eq:List(P),tower:TS,ineq:List(P)))`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``997089 +oprepareSubResAlgo`3`x`(P,P,TS)->List(Record(val:List(P),tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``997230 +opreprocess`3`x`(List(P),Boolean,Boolean)->Record(val:List(P),towers:List(_$))`dRegularTriangularSet(R,E,V,P)``997359 +opreprocess`3`x`(List(P),Boolean,Boolean)->Record(val:List(P),towers:List(_$))`dSquareFreeRegularTriangularSet(R,E,V,P)``997482 +opresub`2`n`(_$,_$)->_$`dOutputForm``997605 +opresuper`2`n`(_$,_$)->_$`dOutputForm``997689 +oprevious`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``997777 +opreviousTower`1`x`(_$)->_$`cPseudoAlgebraicClosureOfPerfectFieldCategory``997968 +oprevPrime`1`x`(I)->I`pIntegerPrimesPackage(I)``998073 +oprimaryDecomp`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->List(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))`pIdealDecompositionPackage(vl,nv)``998157 +oprime`1`n`(_$)->_$`dOutputForm``998273 oprime?`1`n`(S)->Boolean`xField&(S)``0 oprime?`1`n`(S)->Boolean`xIntegerNumberSystem&(S)``0 oprime?`1`n`(S)->Boolean`xUniqueFactorizationDomain&(S)``0 -oprime?`1`x`(Complex(Integer))->Boolean`pGaussianFactorizationPackage``822075 -oprime?`1`x`(I)->Boolean`pIntegerPrimesPackage(I)``822156 -oprime?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``823294 -oprime?`1`x`(_$)->Boolean`cUniqueFactorizationDomain``823356 -oprimeFactor`2`x`(R,Integer)->_$`dFactored(R)``823520 +oprime?`1`x`(_$)->Boolean`cUniqueFactorizationDomain``998365 +oprime?`1`x`(Complex(Integer))->Boolean`pGaussianFactorizationPackage``998529 +oprime?`1`x`(I)->Boolean`pIntegerPrimesPackage(I)``998610 +oprime?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``999748 +oprime`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``999810 +oprimeFactor`2`x`(R,Integer)->_$`dFactored(R)``999892 oprimeFrobenius`1`n`(S)->S`xFieldOfPrimeCharacteristic&(S)``0 -oprimeFrobenius`1`x`(_$)->_$`cFieldOfPrimeCharacteristic``823670 +oprimeFrobenius`1`x`(_$)->_$`cFieldOfPrimeCharacteristic``1000136 oprimeFrobenius`2`n`(S,NonNegativeInteger)->S`xFieldOfPrimeCharacteristic&(S)``0 -oprimeFrobenius`2`x`(_$,NonNegativeInteger)->_$`cFieldOfPrimeCharacteristic``823762 -oprime`1`n`(_$)->_$`dOutputForm``823861 -oprime`2`n`(_$,NonNegativeInteger)->_$`dOutputForm``823953 -oprimes`2`x`(I,I)->List(I)`pIntegerPrimesPackage(I)``824035 -oprimextendedint`4`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),Fraction(UP))->Union(Record(answer:Fraction(UP),a0:F),Record(ratpart:Fraction(UP),coeff:Fraction(UP)),"failed")`pTranscendentalIntegration(F,UP)``824125 -oprimextintfrac`3`n`(Fraction(UP),(UP)->UP,Fraction(UP))->Union(Record(ratpart:Fraction(UP),coeff:Fraction(UP)),"failed")`pTranscendentalIntegration(F,UP)``824481 -oprimintegrate`3`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"))->Record(answer:IntegrationResult(Fraction(UP)),a0:F)`pTranscendentalIntegration(F,UP)``824732 -oprimintfldpoly`3`n`(UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),F)->Union(UP,"failed")`pTranscendentalIntegration(F,UP)``824944 +oprimeFrobenius`2`x`(_$,NonNegativeInteger)->_$`cFieldOfPrimeCharacteristic``1000226 +oprimes`2`x`(I,I)->List(I)`pIntegerPrimesPackage(I)``1000325 +oprimextendedint`4`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),Fraction(UP))->Union(Record(answer:Fraction(UP),a0:F),Record(ratpart:Fraction(UP),coeff:Fraction(UP)),"failed")`pTranscendentalIntegration(F,UP)``1000415 +oprimextintfrac`3`n`(Fraction(UP),(UP)->UP,Fraction(UP))->Union(Record(ratpart:Fraction(UP),coeff:Fraction(UP)),"failed")`pTranscendentalIntegration(F,UP)``1000771 +oprimintegrate`3`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"))->Record(answer:IntegrationResult(Fraction(UP)),a0:F)`pTranscendentalIntegration(F,UP)``1001022 +oprimintfldpoly`3`n`(UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),F)->Union(UP,"failed")`pTranscendentalIntegration(F,UP)``1001234 oprimitive?`1`n`(S)->Boolean`xFiniteFieldCategory&(S)``0 -oprimitive?`1`n`(SparseUnivariatePolynomial(GF))->Boolean`pFiniteFieldPolynomialPackage(GF)``825148 -oprimitive?`1`x`(_$)->Boolean`cFiniteFieldCategory``825297 -oprimitiveElement`0`x`()->_$`cFiniteFieldCategory``825541 -oprimitiveElement`1`x`(List(F))->Record(primelt:F,poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pFunctionSpacePrimitiveElement(R,F)``825741 -oprimitiveElement`2`n`(List(Polynomial(F)),List(Symbol))->Record(coef:List(Integer),poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``826021 -oprimitiveElement`2`x`(F,F)->Record(primelt:F,pol1:SparseUnivariatePolynomial(F),pol2:SparseUnivariatePolynomial(F),prim:SparseUnivariatePolynomial(F))`pFunctionSpacePrimitiveElement(R,F)`has(F,AlgebraicallyClosedField)`826464 -oprimitiveElement`3`n`(List(Polynomial(F)),List(Symbol),Symbol)->Record(coef:List(Integer),poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``826818 -oprimitiveElement`4`n`(Polynomial(F),Symbol,Polynomial(F),Symbol)->Record(coef1:Integer,coef2:Integer,prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``827266 +oprimitive?`1`n`(SparseUnivariatePolynomial(GF))->Boolean`pFiniteFieldPolynomialPackage(GF)``1001438 +oprimitive?`1`x`(_$)->Boolean`cFiniteFieldCategory``1001587 +oprimitiveElement`0`x`()->_$`cFiniteFieldCategory``1001835 +oprimitiveElement`1`x`(List(F))->Record(primelt:F,poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pFunctionSpacePrimitiveElement(R,F)``1002035 +oprimitiveElement`2`n`(List(Polynomial(F)),List(Symbol))->Record(coef:List(Integer),poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``1002315 +oprimitiveElement`2`x`(F,F)->Record(primelt:F,pol1:SparseUnivariatePolynomial(F),pol2:SparseUnivariatePolynomial(F),prim:SparseUnivariatePolynomial(F))`pFunctionSpacePrimitiveElement(R,F)`has(F,AlgebraicallyClosedField)`1002758 +oprimitiveElement`3`n`(List(Polynomial(F)),List(Symbol),Symbol)->Record(coef:List(Integer),poly:List(SparseUnivariatePolynomial(F)),prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``1003112 +oprimitiveElement`4`n`(Polynomial(F),Symbol,Polynomial(F),Symbol)->Record(coef1:Integer,coef2:Integer,prim:SparseUnivariatePolynomial(F))`pPrimitiveElement(F)``1003560 oprimitiveMonomials`1`n`(S)->List(S)`xPolynomialCategory&(S,R,E,VarSet)``0 -oprimitiveMonomials`1`x`(_$)->List(_$)`cPolynomialCategory(R,E,VarSet)``827646 -oprimitivePart!`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oprimitivePart!`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`827845 +oprimitiveMonomials`1`x`(_$)->List(_$)`cPolynomialCategory(R,E,VarSet)``1003940 oprimitivePart`1`n`(S)->S`xFiniteAbelianMonoidRing&(S,R,E)``0 oprimitivePart`1`n`(S)->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 oprimitivePart`1`n`(S)->S`xPolynomialCategory&(S,R,E,VarSet)``0 +oprimitivePart!`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 oprimitivePart`1`n`(S)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 -oprimitivePart`1`x`(_$)->_$`cFiniteAbelianMonoidRing(R,E)`has(R,GcdDomain)`827934 -oprimitivePart`1`x`(_$)->_$`cFunctionFieldCategory(F,UP,UPUP)``828057 -oprimitivePart`1`x`(_$)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`828180 -oprimitivePart`1`x`(_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,GcdDomain)`828304 +oprimitivePart`1`x`(_$)->_$`cFiniteAbelianMonoidRing(R,E)`has(R,GcdDomain)`1004143 +oprimitivePart`1`x`(_$)->_$`cFunctionFieldCategory(F,UP,UPUP)``1004266 +oprimitivePart`1`x`(_$)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1004389 +oprimitivePart!`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,GcdDomain)`1004513 +oprimitivePart`1`x`(_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,GcdDomain)`1004602 oprimitivePart`2`n`(S,VarSet)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -oprimitivePart`2`n`(UP,R)->UP`pSubResultantPackage(R,UP)`has(R,EuclideanDomain)`828435 -oprimitivePart`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`828634 -oprimlimintfrac`3`n`(Fraction(UP),(UP)->UP,List(Fraction(UP)))->Union(Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),"failed")`pTranscendentalIntegration(F,UP)``828800 -oprimlimitedint`4`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),List(Fraction(UP)))->Union(Record(answer:Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),a0:F),"failed")`pTranscendentalIntegration(F,UP)``829014 -oprinb`1`n`(Integer)->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``829397 +oprimitivePart`2`n`(UP,R)->UP`pSubResultantPackage(R,UP)`has(R,EuclideanDomain)`1004733 +oprimitivePart`2`x`(_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1004932 +oprimlimintfrac`3`n`(Fraction(UP),(UP)->UP,List(Fraction(UP)))->Union(Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),"failed")`pTranscendentalIntegration(F,UP)``1005098 +oprimlimitedint`4`n`(Fraction(UP),(UP)->UP,(F)->Union(Record(ratpart:F,coeff:F),"failed"),List(Fraction(UP)))->Union(Record(answer:Record(mainpart:Fraction(UP),limitedlogs:List(Record(coeff:Fraction(UP),logand:Fraction(UP)))),a0:F),"failed")`pTranscendentalIntegration(F,UP)``1005312 +oprimPartElseUnitCanonical`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +oprimPartElseUnitCanonical!`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +oprimPartElseUnitCanonical!`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1005695 +oprimPartElseUnitCanonical`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1005821 +oprinb`1`n`(Integer)->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1006001 oprincipal?`1`n`(S)->Boolean`xFiniteDivisorCategory&(S,F,UP,UPUP,R)``0 -oprincipal?`1`x`(_$)->Boolean`cFiniteDivisorCategory(F,UP,UPUP,R)``829431 +oprincipal?`1`x`(_$)->Boolean`cFiniteDivisorCategory(F,UP,UPUP,R)``1006035 oprincipalIdeal`1`n`(List(S))->Record(coef:List(S),generator:S)`xEuclideanDomain&(S)``0 -oprincipalIdeal`1`x`(List(_$))->Record(coef:List(_$),generator:_$)`cPrincipalIdealDomain``829511 -oprindINFO`6`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol),Dpol,Dpol,Integer,Integer,Integer)->Integer`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``829737 -oprinpolINFO`1`n`(List(Dpol))->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``829775 -oprinshINFO`1`n`(Dpol)->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``829815 -oprintCode`1`x`(_$)->Void`dFortranCode``829854 -oprintHeader`0`x`()->Void`dTheSymbolTable``829922 -oprintHeader`1`x`(Symbol)->Void`dTheSymbolTable``830070 -oprintHeader`2`x`(Symbol,_$)->Void`dTheSymbolTable``830216 -oprintInfo!`2`n`(String,String)->Void`pTabulatedComputationPackage(Key,Entry)``830368 +oprincipalIdeal`1`x`(List(_$))->Record(coef:List(_$),generator:_$)`cPrincipalIdealDomain``1006115 +oprindINFO`6`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol),Dpol,Dpol,Integer,Integer,Integer)->Integer`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1006341 +oprinpolINFO`1`n`(List(Dpol))->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1006379 +oprinshINFO`1`n`(Dpol)->Void`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1006419 +oprint`1`n`(_$)->Void`dOutputForm``1006458 +oprint`1`x`(OutputForm)->Void`pPrintPackage``1006507 +oprintCode`1`x`(_$)->Void`dFortranCode``1006618 +oprintHeader`0`x`()->Void`dTheSymbolTable``1006686 +oprintHeader`1`x`(Symbol)->Void`dTheSymbolTable``1006834 +oprintHeader`2`x`(Symbol,_$)->Void`dTheSymbolTable``1006980 +oprintInfo`0`x`()->Boolean`cLocalPowerSeriesCategory(K)``1007132 +oprintInfo`0`x`()->Boolean`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``1007187 +oprintInfo`1`x`(Boolean)->Boolean`cLocalPowerSeriesCategory(K)``1007242 +oprintInfo`1`x`(Boolean)->Boolean`pLocalParametrizationOfSimplePointPackage(K,symb,PolyRing,E,ProjPt,PCS,Plc)``1007398 +oprintInfo`1`x`(List(Boolean))->Void`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``1007554 +oprintInfo!`2`n`(String,String)->Void`pTabulatedComputationPackage(Key,Entry)``1007671 oprintInfo`2`x`(List(Record(val:List(P),tower:TS)),NonNegativeInteger)->Void`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 oprintInfo`2`x`(List(Record(val:List(P),tower:TS)),NonNegativeInteger)->Void`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oprintStatement`1`x`(List(OutputForm))->_$`dFortranCode``830613 -oprintStats!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``830692 -oprintTypes`1`x`(Symbol)->Void`dTheSymbolTable``830744 -oprintTypes`1`x`(_$)->Void`dSymbolTable``830865 -oprint`1`n`(_$)->Void`dOutputForm``830986 -oprint`1`x`(OutputForm)->Void`pPrintPackage``831035 -oprintingInfo?`0`n`()->Boolean`pTabulatedComputationPackage(Key,Entry)``831146 -oprobablyZeroDim?`1`n`(List(P))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``831267 -oproblemPoints`3`x`(Expression(DoubleFloat),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pExpertSystemContinuityPackage``831457 -oproblemPoints`3`x`(Expression(DoubleFloat),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pd01AgentsPackage``831675 -oprocessTemplate`1`x`(FileName)->FileName`dFortranTemplate``831883 -oprocessTemplate`2`x`(FileName,FileName)->FileName`dFortranTemplate``832010 -oprod`1`n`(_$)->_$`dOutputForm``832122 -oprod`2`n`(_$,_$)->_$`dOutputForm``832210 -oprod`3`n`(_$,_$,_$)->_$`dOutputForm``832336 -oproduct`2`n`(F,SegmentBinding(F))->F`pCombinatorialFunction(R,F)``832502 -oproduct`2`n`(F,Symbol)->F`pCombinatorialFunction(R,F)``832610 -oproduct`2`x`(_$,SegmentBinding(_$))->_$`cCombinatorialOpsCategory``832766 -oproduct`2`x`(_$,Symbol)->_$`cCombinatorialOpsCategory``832874 -oproduct`2`x`(_$,_$)->_$`cGradedAlgebra(R,E)``833030 -oproduct`2`x`(_$,_$)->_$`dCartesianTensor(minix,dim,R)``833492 -oproduct`3`n`(_$,_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)``833769 -oprolateSpheroidal`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``833879 -oprologue`1`x`(_$)->List(String)`dScriptFormulaFormat``834227 -oprologue`1`x`(_$)->List(String)`dTexFormat``834315 -oproperties`1`x`(_$)->AssociationList(String,None)`dBasicOperator``834395 -oproperty`2`x`(_$,String)->Union(None,"failed")`dBasicOperator``834496 +oprintingInfo?`0`n`()->Boolean`pTabulatedComputationPackage(Key,Entry)``1007916 +oprintStatement`1`x`(List(OutputForm))->_$`dFortranCode``1008037 +oprintStats!`0`n`()->Void`pTabulatedComputationPackage(Key,Entry)``1008116 +oprintTypes`1`x`(Symbol)->Void`dTheSymbolTable``1008168 +oprintTypes`1`x`(_$)->Void`dSymbolTable``1008289 +oprobablyZeroDim?`1`n`(List(P))->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``1008410 +oproblemPoints`3`x`(Expression(DoubleFloat),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pd01AgentsPackage``1008600 +oproblemPoints`3`x`(Expression(DoubleFloat),Symbol,Segment(OrderedCompletion(DoubleFloat)))->List(DoubleFloat)`pExpertSystemContinuityPackage``1008808 +oprocessTemplate`1`x`(FileName)->FileName`dFortranTemplate``1009026 +oprocessTemplate`2`x`(FileName,FileName)->FileName`dFortranTemplate``1009153 +oprod`1`n`(_$)->_$`dOutputForm``1009265 +oprod`2`n`(_$,_$)->_$`dOutputForm``1009353 +oprod`3`n`(_$,_$,_$)->_$`dOutputForm``1009479 +oproduct`2`n`(F,SegmentBinding(F))->F`pCombinatorialFunction(R,F)``1009645 +oproduct`2`n`(F,Symbol)->F`pCombinatorialFunction(R,F)``1009753 +oproduct`2`x`(_$,_$)->_$`cGradedAlgebra(R,E)``1009909 +oproduct`2`x`(_$,_$)->_$`dCartesianTensor(minix,dim,R)``1010371 +oproduct`2`x`(_$,SegmentBinding(_$))->_$`cCombinatorialOpsCategory``1011003 +oproduct`2`x`(_$,Symbol)->_$`cCombinatorialOpsCategory``1011111 +oproduct`3`n`(_$,_$,NonNegativeInteger)->_$`dXPBWPolynomial(VarSet,R)``1011267 +oprojectivePoint`1`x`(List(K))->_$`cProjectiveSpaceCategory(K)``1011377 +oprojectivePoint`1`x`(List(K))->ProjectivePlane(K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +oprojectivePoint`1`x`(List(PseudoAlgebraicClosureOfFiniteField(K)))->ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +oprolateSpheroidal`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``1011446 +oprologue`1`x`(_$)->List(String)`dScriptFormulaFormat``1011794 +oprologue`1`x`(_$)->List(String)`dTexFormat``1011882 +oproperties`1`x`(_$)->AssociationList(String,None)`dBasicOperator``1011962 +oproperty`2`x`(_$,String)->Union(None,"failed")`dBasicOperator``1012063 +opseudoDivide`2`n`(polR,polR)->Record(coef:R,quotient:polR,remainder:polR)`pPseudoRemainderSequence(R,polR)``1012192 opseudoDivide`2`n`(S,S)->Record(coef:R,quotient:S,remainder:S)`xUnivariatePolynomialCategory&(S,R)``0 opseudoDivide`2`n`(S,S)->Record(quotient:S,remainder:S)`xRecursivePolynomialCategory&(S,R,E,V)``0 -opseudoDivide`2`n`(polR,polR)->Record(coef:R,quotient:polR,remainder:polR)`pPseudoRemainderSequence(R,polR)``834625 -opseudoDivide`2`x`(_$,_$)->Record(coef:R,quotient:_$,remainder:_$)`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`834741 -opseudoDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cRecursivePolynomialCategory(R,E,V)``834940 +opseudoDivide`2`x`(_$,_$)->Record(coef:R,quotient:_$,remainder:_$)`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`1012308 +opseudoDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cRecursivePolynomialCategory(R,E,V)``1012507 opseudoQuotient`2`n`(S,S)->S`xUnivariatePolynomialCategory&(S,R)``0 -opseudoQuotient`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`835188 -opseudoRemainder`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)``835382 -opsolve`1`n`(Matrix(GR))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``835621 -opsolve`2`n`(Matrix(GR),List(GR))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``835750 -opsolve`2`n`(Matrix(GR),List(Symbol))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``835902 -opsolve`2`n`(Matrix(GR),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``836055 -opsolve`2`n`(Matrix(GR),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``836203 -opsolve`3`n`(Matrix(GR),List(GR),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``836432 -opsolve`3`n`(Matrix(GR),List(GR),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``836607 -opsolve`3`n`(Matrix(GR),List(Symbol),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``836847 -opsolve`3`n`(Matrix(GR),List(Symbol),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``837023 -opsolve`3`n`(Matrix(GR),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``837264 -opsolve`4`n`(Matrix(GR),List(GR),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``837474 -opsolve`4`n`(Matrix(GR),List(Symbol),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``837730 -optFunc`4`n`((DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->(DoubleFloat,DoubleFloat)->Point(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``837994 -optree`1`x`(S)->_$`dPendantTree(S)``838093 -optree`2`x`(_$,_$)->_$`dPendantTree(S)``838140 -opuiseux`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``838181 -opuiseux`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``838364 -opuiseux`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``838434 -opuiseux`2`x`(FE,Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``838548 -opuiseux`2`x`(Fraction(Integer),ULS)->_$`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``838792 -opuiseux`3`x`(FE,Equation(FE),Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``838847 -opuiseux`4`x`((Fraction(Integer))->FE,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``839019 -opuiseux`5`x`(FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``839261 -opureLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``839499 +opseudoQuotient`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`1012755 +opseudoRemainder`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)``1012949 +opsolve`1`n`(Matrix(GR))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1013188 +opsolve`2`n`(Matrix(GR),List(GR))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1013317 +opsolve`2`n`(Matrix(GR),List(Symbol))->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1013469 +opsolve`2`n`(Matrix(GR),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1013622 +opsolve`2`n`(Matrix(GR),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1013770 +opsolve`3`n`(Matrix(GR),List(GR),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1013999 +opsolve`3`n`(Matrix(GR),List(GR),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1014174 +opsolve`3`n`(Matrix(GR),List(Symbol),PositiveInteger)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1014414 +opsolve`3`n`(Matrix(GR),List(Symbol),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1014590 +opsolve`3`n`(Matrix(GR),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1014831 +opsolve`4`n`(Matrix(GR),List(GR),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1015041 +opsolve`4`n`(Matrix(GR),List(Symbol),PositiveInteger,String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1015297 +optFunc`4`n`((DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat)->DoubleFloat,(DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->(DoubleFloat,DoubleFloat)->Point(DoubleFloat)`pMeshCreationRoutinesForThreeDimensions``1015561 +opToDmp`1`n`(Polynomial(R))->DistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``1015660 +opToHdmp`1`n`(Polynomial(R))->HomogeneousDistributedMultivariatePolynomial(lv,R)`pPolToPol(lv,R)``1015746 +optree`1`x`(S)->_$`dPendantTree(S)``1015834 +optree`2`x`(_$,_$)->_$`dPendantTree(S)``1015938 +opuiseux`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1016094 +opuiseux`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1016281 +opuiseux`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1016351 +opuiseux`2`x`(FE,Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1016465 +opuiseux`2`x`(Fraction(Integer),ULS)->_$`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``1016713 +opuiseux`3`x`(FE,Equation(FE),Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1016768 +opuiseux`4`x`((Fraction(Integer))->FE,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1016940 +opuiseux`5`x`(FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1017182 +opureLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``1017420 opurelyAlgebraic?`1`n`(S)->Boolean`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -opurelyAlgebraic?`1`x`(_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``839638 +opurelyAlgebraic?`1`x`(_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``1017559 opurelyAlgebraic?`2`n`(P,S)->Boolean`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -opurelyAlgebraic?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``839981 +opurelyAlgebraic?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``1017882 opurelyAlgebraicLeadingMonomial?`2`n`(P,S)->Boolean`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -opurelyAlgebraicLeadingMonomial?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``840123 +opurelyAlgebraicLeadingMonomial?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``1018024 opurelyTranscendental?`2`n`(P,S)->Boolean`xRegularTriangularSetCategory&(S,R,E,V,P)``0 -opurelyTranscendental?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``840321 -opush!`2`x`(S,_$)->S`cStackAggregate(S)``840471 -opushFortranOutputStack`1`x`(FileName)->Void`pFortranOutputStackPackage``840735 -opushFortranOutputStack`1`x`(String)->Void`pFortranOutputStackPackage``840821 -opushdown`2`n`(PPR,List(OV))->PPR`pPushVariables(R,E,OV,PPR)``840907 -opushdown`2`n`(PPR,OV)->PPR`pPushVariables(R,E,OV,PPR)``840954 -opushdown`2`x`(PRF,OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``841000 -opushdterm`2`x`(SparseUnivariatePolynomial(PRF),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``841152 -opushucoef`2`x`(SparseUnivariatePolynomial(Polynomial(R)),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``841307 -opushuconst`2`x`(Fraction(Polynomial(R)),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``841457 -opushup`2`n`(PPR,List(OV))->PPR`pPushVariables(R,E,OV,PPR)``841595 -opushup`2`n`(PPR,OV)->PPR`pPushVariables(R,E,OV,PPR)``841640 -opushup`2`x`(PRF,OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``841684 -oputColorInfo`2`n`(List(List(Point(DoubleFloat))),List(Palette))->List(List(Point(DoubleFloat)))`dGraphImage``841844 -oputGraph`3`n`(_$,GraphImage,PositiveInteger)->Void`dTwoDimensionalViewport``842050 -oqPot`2`n`(Vector(GF),Integer)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``842497 +opurelyTranscendental?`2`x`(P,_$)->Boolean`cRegularTriangularSetCategory(R,E,V,P)``1018222 +opush!`2`x`(S,_$)->S`cStackAggregate(S)``1018372 +opush!`2`x`(S,_$)->S`dArrayStack(S)``1018773 +opush!`2`x`(S,_$)->S`dDequeue(S)``1018883 +opush!`2`x`(S,_$)->S`dStack(S)``1018982 +opushdown`2`n`(PPR,List(OV))->PPR`pPushVariables(R,E,OV,PPR)``1019082 +opushdown`2`n`(PPR,OV)->PPR`pPushVariables(R,E,OV,PPR)``1019129 +opushdown`2`x`(PRF,OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1019175 +opushdterm`2`x`(SparseUnivariatePolynomial(PRF),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1019327 +opushFortranOutputStack`1`x`(FileName)->Void`pFortranOutputStackPackage``1019482 +opushFortranOutputStack`1`x`(String)->Void`pFortranOutputStackPackage``1019568 +opushucoef`2`x`(SparseUnivariatePolynomial(Polynomial(R)),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1019654 +opushuconst`2`x`(Fraction(Polynomial(R)),OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1019804 +opushup`2`n`(PPR,List(OV))->PPR`pPushVariables(R,E,OV,PPR)``1019942 +opushup`2`n`(PPR,OV)->PPR`pPushVariables(R,E,OV,PPR)``1019987 +opushup`2`x`(PRF,OV)->PRF`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1020031 +oputColorInfo`2`n`(List(List(Point(DoubleFloat))),List(Palette))->List(List(Point(DoubleFloat)))`dGraphImage``1020191 +oputGraph`3`n`(_$,GraphImage,PositiveInteger)->Void`dTwoDimensionalViewport``1020397 oqelt`2`n`(S,Dom)->Im`xEltableAggregate&(S,Dom,Im)``0 -oqelt`2`x`(_$,Dom)->Im`cEltableAggregate(Dom,Im)``842716 -oqelt`3`x`(_$,Integer,Integer)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``843087 -oqelt`3`x`(_$,Integer,Integer)->R`cTwoDimensionalArrayCategory(R,Row,Col)``843285 -oqfactor`1`n`(UP)->Union(Factored(SparseUnivariatePolynomial(Fraction(Integer))),"failed")`pFunctionSpaceUnivariatePolynomialFactor(R,F,UP)``843461 -oqinterval`2`x`(R,R)->_$`cIntervalCategory(R)``843573 -oqqq`3`n`(NonNegativeInteger,TaylorSeries(R),Stream(TaylorSeries(R)))->(Stream(TaylorSeries(R)))->Stream(TaylorSeries(R))`pWeierstrassPreparation(R)``843715 -oqroot`2`n`(Fraction(Integer),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:F,radicand:F)`pPolynomialRoots(E,V,R,P,F)``843765 +oqelt`2`x`(_$,Dom)->Im`cEltableAggregate(Dom,Im)``1020844 +oqelt`3`x`(_$,Integer,Integer)->R`cRectangularMatrixCategory(m,n,R,Row,Col)``1021215 +oqelt`3`x`(_$,Integer,Integer)->R`cTwoDimensionalArrayCategory(R,Row,Col)``1021417 +oqfactor`1`n`(UP)->Union(Factored(SparseUnivariatePolynomial(Fraction(Integer))),"failed")`pFunctionSpaceUnivariatePolynomialFactor(R,F,UP)``1021746 +oqinterval`2`x`(R,R)->_$`cIntervalCategory(R)``1021858 +oqPot`2`n`(Vector(GF),Integer)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``1022000 +oqqq`3`n`(NonNegativeInteger,TaylorSeries(R),Stream(TaylorSeries(R)))->(Stream(TaylorSeries(R)))->Stream(TaylorSeries(R))`pWeierstrassPreparation(R)``1022219 +oqroot`2`n`(Fraction(Integer),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:F,radicand:F)`pPolynomialRoots(E,V,R,P,F)``1022269 oqsetelt!`3`n`(S,Dom,Im)->Im`xEltableAggregate&(S,Dom,Im)``0 -oqsetelt!`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)`has(_$,ATTRIBUTE(shallowlyMutable))`843862 -oqsetelt!`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``844118 -oquadratic?`1`x`(Expression(DoubleFloat))->Boolean`pe04AgentsPackage``844301 -oquadraticForm`1`x`(SquareMatrix(n,K))->_$`dQuadraticForm(n,K)``844380 -oquadraticNorm`1`n`(UP)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``844480 -oquadratic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``844566 -oquadratic`3`n`(F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``844607 -oquartic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``844656 -oquartic`5`n`(F,F,F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``844695 -oquasiAlgebraicSet`2`n`(List(Dpoly),Dpoly)->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``844750 +oqsetelt!`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)`has(_$,ATTRIBUTE(shallowlyMutable))`1022366 +oqsetelt!`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``1022622 +oqShiftAction`4`x`(D,NonNegativeInteger,NonNegativeInteger,V)->D`pFractionFreeFastGaussian(D,V)``1022973 +oqShiftC`2`x`(D,NonNegativeInteger)->List(D)`pFractionFreeFastGaussian(D,V)``1023222 +oquadratic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``1023550 +oquadratic?`1`x`(Expression(DoubleFloat))->Boolean`pe04AgentsPackage``1023591 +oquadratic`3`n`(F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``1023670 +oquadraticBezier`3`x`(List(R),List(R),List(R))->(R)->List(R)`pBezier(R)``1023719 +oquadraticForm`1`x`(SquareMatrix(n,K))->_$`dQuadraticForm(n,K)``1024475 +oquadraticNorm`1`n`(UP)->F`pGaloisGroupFactorizationUtilities(R,UP,F)``1024575 +oquadTransform`3`x`(DistributedMultivariatePolynomial(construct('X,'Y),K),NonNegativeInteger,BLMET)->DistributedMultivariatePolynomial(construct('X,'Y),K)`pBlowUpPackage(K,symb,PolyRing,E,BLMET)``1024661 +oquartic`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``1024969 +oquartic`5`n`(F,F,F,F,F)->List(F)`pPolynomialSolveByFormulas(UP,F)``1025008 +oquasiAlgebraicSet`2`n`(List(Dpoly),Dpoly)->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``1025063 oquasiComponent`1`n`(S)->Record(close:List(P),open:List(P))`xTriangularSetCategory&(S,R,E,V,P)``0 -oquasiComponent`1`x`(_$)->Record(close:List(P),open:List(P))`cTriangularSetCategory(R,E,V,P)``844953 +oquasiComponent`1`x`(_$)->Record(close:List(P),open:List(P))`cTriangularSetCategory(R,E,V,P)``1025266 oquasiMonic?`1`n`(S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -oquasiMonic?`1`x`(_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``845159 -oquasiMonicPolynomials`1`n`(List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``845374 -oquasiRegular?`1`n`(_$)->Boolean`dXPolynomialRing(R,E)``845570 -oquasiRegular?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``845651 -oquasiRegular`1`n`(_$)->_$`dXPolynomialRing(R,E)``845732 -oquasiRegular`1`x`(_$)->_$`cXFreeAlgebra(vl,R)``845803 -oquatern`4`x`(R,R,R,R)->_$`cQuaternionCategory(R)``845874 -oqueue`1`x`(List(S))->_$`dQueue(S)``845949 -oquickSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``846109 -oquoByVar`1`x`(_$)->_$`cUnivariateTaylorSeriesCategory(Coef)``846234 +oquasiMonic?`1`x`(_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``1025472 +oquasiMonicPolynomials`1`n`(List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``1025687 +oquasiRegular?`1`n`(_$)->Boolean`dXPolynomialRing(R,E)``1025883 +oquasiRegular`1`n`(_$)->_$`dXPolynomialRing(R,E)``1025964 +oquasiRegular?`1`x`(_$)->Boolean`cXFreeAlgebra(vl,R)``1026035 +oquasiRegular`1`x`(_$)->_$`cXFreeAlgebra(vl,R)``1026115 +oquatern`4`x`(R,R,R,R)->_$`cQuaternionCategory(R)``1026186 +oqueue`1`x`(List(S))->_$`dQueue(S)``1026261 +oquickSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``1026523 +oquo`2`n`(_$,_$)->_$`dOutputForm``1026648 oquo`2`n`(S,S)->S`xComplexCategory&(S,R)``0 oquo`2`n`(S,S)->S`xEuclideanDomain&(S)``0 -oquo`2`n`(_$,_$)->_$`dOutputForm``846503 -oquo`2`x`(_$,_$)->_$`cEuclideanDomain``846560 -oquo`2`x`(_$,_$)->_$`dNonNegativeInteger``846671 -oquote`0`x`()->_$`dCharacter``846768 -oquote`1`n`(_$)->_$`dOutputForm``846839 -oquoted?`1`n`(_$)->Boolean`dPattern(R)``846909 -oquotedOperators`1`x`(_$)->List(Symbol)`dRewriteRule(Base,R,F)``847000 -oquotientByP`1`x`(_$)->_$`cPAdicIntegerCategory(p)``847227 -oquotient`2`x`(_$,DPoly)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``847302 -oquotient`2`x`(_$,_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``847455 -orCoord`1`n`(Point(R))->R`pPointPackage(R)``847560 -oradPoly`1`n`(UPUP)->Union(Record(radicand:Fraction(UP),deg:NonNegativeInteger),"failed")`pChangeOfVariable(F,UP,UPUP)``847831 -oradicalEigenvalues`1`x`(Matrix(Fraction(Polynomial(Integer))))->List(Expression(Integer))`pRadicalEigenPackage``847960 -oradicalEigenvector`2`x`(Expression(Integer),Matrix(Fraction(Polynomial(Integer))))->List(Matrix(Expression(Integer)))`pRadicalEigenPackage``848114 -oradicalEigenvectors`1`x`(Matrix(Fraction(Polynomial(Integer))))->List(Record(radval:Expression(Integer),radmult:Integer,radvect:List(Matrix(Expression(Integer)))))`pRadicalEigenPackage``848314 -oradicalOfLeftTraceForm`0`x`()->List(A)`pAlgebraPackage(R,A)``848495 -oradicalRoots`2`x`(Fraction(Polynomial(R)),Symbol)->List(Expression(R))`pRadicalSolvePackage(R)``848733 -oradicalRoots`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Expression(R)))`pRadicalSolvePackage(R)``848887 -oradicalSimplify`1`n`(QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pQuasiAlgebraicSet2(vl,nv)``849067 -oradicalSolve`1`x`(Equation(Fraction(Polynomial(R))))->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``849385 -oradicalSolve`1`x`(Fraction(Polynomial(R)))->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``849582 -oradicalSolve`1`x`(List(Equation(Fraction(Polynomial(R)))))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``849748 -oradicalSolve`1`x`(List(Fraction(Polynomial(R))))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``849959 -oradicalSolve`2`x`(Equation(Fraction(Polynomial(R))),Symbol)->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``850150 -oradicalSolve`2`x`(Fraction(Polynomial(R)),Symbol)->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``850321 -oradicalSolve`2`x`(List(Equation(Fraction(Polynomial(R)))),List(Symbol))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``850516 -oradicalSolve`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``850715 -oradical`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pIdealDecompositionPackage(vl,nv)``850948 -oradix`2`x`(Fraction(Integer),Integer)->Any`pRadixUtilities``851016 -oraisePolynomial`1`n`(SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(P)`pFactoringUtilities(E,OV,R,P)``851100 -oramified?`1`x`(F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``851262 -oramified?`1`x`(UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``851329 -oramifiedAtInfinity?`0`x`()->Boolean`cFunctionFieldCategory(F,UP,UPUP)``851399 -oran`1`n`(Integer)->R`pFactoringUtilities(E,OV,R,P)``851466 -orandnum`0`x`()->Integer`pRandomNumberSource``851569 -orandnum`1`x`(Integer)->Integer`pRandomNumberSource``851634 -orandomLC`2`n`(NonNegativeInteger,Vector(A))->A`dFractionalIdeal(R,F,UP,A)``851702 -orandomR`0`n`()->R`pGeneralPolynomialGcdPackage(E,OV,R,P)``851765 -orandomR`0`n`()->R`pPolynomialFactorizationByRecursion(R,E,VarSet,S)``851821 -orandomR`0`n`()->R`pPolynomialFactorizationByRecursionUnivariate(R,S)``851881 +oquo`2`x`(_$,_$)->_$`cEuclideanDomain``1026705 +oquo`2`x`(_$,_$)->_$`dNonNegativeInteger``1026816 +oquoByVar`1`x`(_$)->_$`cUnivariateTaylorSeriesCategory(Coef)``1026913 +oquote`0`x`()->_$`dCharacter``1027182 +oquote`1`n`(_$)->_$`dOutputForm``1027288 +oquoted?`1`n`(_$)->Boolean`dPattern(R)``1027358 +oquotedOperators`1`x`(_$)->List(Symbol)`dRewriteRule(Base,R,F)``1027449 +oquotient`2`x`(_$,DPoly)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1027676 +oquotient`2`x`(_$,_$)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1027829 +oquotientByP`1`x`(_$)->_$`cPAdicIntegerCategory(p)``1027934 +oquotValuation`1`x`(_$)->Integer`cBlowUpMethodCategory``0 +oquotVecSpaceBasis`2`x`(List(List(K)),List(List(K)))->List(List(K))`pLinesOpPack(K)``1028009 +oradical`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pIdealDecompositionPackage(vl,nv)``1028345 +oradicalEigenvalues`1`x`(Matrix(Fraction(Polynomial(Integer))))->List(Expression(Integer))`pRadicalEigenPackage``1028413 +oradicalEigenvector`2`x`(Expression(Integer),Matrix(Fraction(Polynomial(Integer))))->List(Matrix(Expression(Integer)))`pRadicalEigenPackage``1028567 +oradicalEigenvectors`1`x`(Matrix(Fraction(Polynomial(Integer))))->List(Record(radval:Expression(Integer),radmult:Integer,radvect:List(Matrix(Expression(Integer)))))`pRadicalEigenPackage``1028767 +oradicalOfLeftTraceForm`0`x`()->List(A)`pAlgebraPackage(R,A)``1028948 +oradicalRoots`2`x`(Fraction(Polynomial(R)),Symbol)->List(Expression(R))`pRadicalSolvePackage(R)``1029186 +oradicalRoots`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Expression(R)))`pRadicalSolvePackage(R)``1029499 +oradicalSimplify`1`n`(QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->QuasiAlgebraicSet(Fraction(Integer),OrderedVariableList(vl),DirectProduct(nv,NonNegativeInteger),DistributedMultivariatePolynomial(vl,Fraction(Integer)))`pQuasiAlgebraicSet2(vl,nv)``1029951 +oradicalSolve`1`x`(Equation(Fraction(Polynomial(R))))->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``1030269 +oradicalSolve`1`x`(Fraction(Polynomial(R)))->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``1030602 +oradicalSolve`1`x`(List(Equation(Fraction(Polynomial(R)))))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``1030923 +oradicalSolve`1`x`(List(Fraction(Polynomial(R))))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``1031372 +oradicalSolve`2`x`(Equation(Fraction(Polynomial(R))),Symbol)->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``1031818 +oradicalSolve`2`x`(Fraction(Polynomial(R)),Symbol)->List(Equation(Expression(R)))`pRadicalSolvePackage(R)``1032150 +oradicalSolve`2`x`(List(Equation(Fraction(Polynomial(R)))),List(Symbol))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``1032518 +oradicalSolve`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Equation(Expression(R))))`pRadicalSolvePackage(R)``1032979 +oradix`2`x`(Fraction(Integer),Integer)->Any`pRadixUtilities``1033498 +oradPoly`1`n`(UPUP)->Union(Record(radicand:Fraction(UP),deg:NonNegativeInteger),"failed")`pChangeOfVariable(F,UP,UPUP)``1033582 +oraisePolynomial`1`n`(SparseUnivariatePolynomial(R))->SparseUnivariatePolynomial(P)`pFactoringUtilities(E,OV,R,P)``1033711 +oramified?`1`x`(F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1033873 +oramified?`1`x`(UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1033940 +oramifiedAtInfinity?`0`x`()->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1034010 +oramifMult`1`x`(_$)->Integer`cBlowUpMethodCategory``0 +oran`1`n`(Integer)->R`pFactoringUtilities(E,OV,R,P)``1034077 +orandnum`0`x`()->Integer`pRandomNumberSource``1034180 +orandnum`1`x`(Integer)->Integer`pRandomNumberSource``1034245 orandom`0`n`()->A`xFiniteSetAggregate&(A,S)``0 orandom`0`n`()->A`xQuotientFieldCategory&(A,S)``0 orandom`0`n`()->S`xMonogenicAlgebra&(S,R,UP)``0 -orandom`0`x`()->_$`cFinite``851943 -orandom`0`x`()->_$`cIntegerNumberSystem``852005 -orandom`0`x`()->_$`cQuotientFieldCategory(S)`has(S,IntegerNumberSystem)`852054 -orandom`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``852104 -orandom`1`n`(PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``852234 -orandom`1`x`(_$)->Permutation(S)`dPermutationGroup(S)``852318 -orandom`1`x`(_$)->_$`cIntegerNumberSystem``852456 -orandom`1`x`(_$)->_$`dInteger``852527 -orandom`1`x`(_$)->_$`dNonNegativeInteger``852598 -orandom`2`n`(PositiveInteger,PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``852669 -orandom`2`x`(_$,Integer)->Permutation(S)`dPermutationGroup(S)``852845 -orangeIsFinite`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")`pd01AgentsPackage``852953 -orangePascalTriangle`0`n`()->NonNegativeInteger`pGaloisGroupUtilities(R)``853053 -orangePascalTriangle`1`n`(NonNegativeInteger)->NonNegativeInteger`pGaloisGroupUtilities(R)``853133 -orange`1`x`(List(Segment(Float)))->_$`dDrawOption``853252 -orange`1`x`(List(Segment(Fraction(Integer))))->_$`dDrawOption``853377 -oranges`1`n`(_$)->List(Segment(Float))`dGraphImage``853502 -oranges`1`x`(List(Segment(Float)))->_$`dDrawOption``853670 -oranges`2`n`(List(DrawOption),List(Segment(Float)))->List(Segment(Float))`pDrawOptionFunctions0``853802 -oranges`2`n`(_$,List(Segment(Float)))->List(Segment(Float))`dGraphImage``854008 +orandom`0`x`()->_$`cFinite``1034313 +orandom`0`x`()->_$`cIntegerNumberSystem``1034375 +orandom`0`x`()->_$`cQuotientFieldCategory(S)`has(S,IntegerNumberSystem)`1034424 +orandom`1`n`(PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``1034474 +orandom`1`n`(PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``1034605 +orandom`1`x`(_$)->_$`cIntegerNumberSystem``1034689 +orandom`1`x`(_$)->_$`dInteger``1034760 +orandom`1`x`(_$)->_$`dNonNegativeInteger``1034831 +orandom`1`x`(_$)->Permutation(S)`dPermutationGroup(S)``1034902 +orandom`2`n`(PositiveInteger,PositiveInteger)->SparseUnivariatePolynomial(GF)`pFiniteFieldPolynomialPackage(GF)``1035049 +orandom`2`x`(_$,Integer)->Permutation(S)`dPermutationGroup(S)``1035226 +orandomLC`2`n`(NonNegativeInteger,Vector(A))->A`dFractionalIdeal(R,F,UP,A)``1035335 +orandomR`0`n`()->R`pGeneralPolynomialGcdPackage(E,OV,R,P)``1035398 +orandomR`0`n`()->R`pPolynomialFactorizationByRecursion(R,E,VarSet,S)``1035454 +orandomR`0`n`()->R`pPolynomialFactorizationByRecursionUnivariate(R,S)``1035514 +orange`1`x`(List(Segment(Float)))->_$`dDrawOption``1035576 +orange`1`x`(List(Segment(Fraction(Integer))))->_$`dDrawOption``1035701 +orangeIsFinite`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")`pd01AgentsPackage``1035826 +orangePascalTriangle`0`n`()->NonNegativeInteger`pGaloisGroupUtilities(R)``1035926 +orangePascalTriangle`1`n`(NonNegativeInteger)->NonNegativeInteger`pGaloisGroupUtilities(R)``1036006 +oranges`1`n`(_$)->List(Segment(Float))`dGraphImage``1036125 +oranges`1`x`(List(Segment(Float)))->_$`dDrawOption``1036293 +oranges`2`n`(List(DrawOption),List(Segment(Float)))->List(Segment(Float))`pDrawOptionFunctions0``1036425 +oranges`2`n`(_$,List(Segment(Float)))->List(Segment(Float))`dGraphImage``1036631 orank`0`n`()->PositiveInteger`xComplexCategory&(S,R)``0 -orank`0`x`()->PositiveInteger`cFiniteRankAlgebra(R,UP)``854262 -orank`0`x`()->PositiveInteger`cFiniteRankNonAssociativeAlgebra(R)``854316 -orank`1`n`(M)->NonNegativeInteger`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``854389 -orank`1`x`(M)->NonNegativeInteger`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`854452 -orank`1`x`(_$)->NonNegativeInteger`cMatrixCategory(R,Row,Col)`has(R,IntegralDomain)`854515 -orank`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)`has(R,IntegralDomain)`854578 -orank`1`x`(_$)->NonNegativeInteger`dCartesianTensor(minix,dim,R)``854641 -orank`2`x`(M,Col)->NonNegativeInteger`pLinearSystemMatrixPackage(F,Row,Col,M)``854784 -orank`2`x`(Matrix(F),Vector(F))->NonNegativeInteger`pLinearSystemMatrixPackage1(F)``854900 -orarrow`2`n`(_$,_$)->_$`dOutputForm``855016 -oratDenom`1`x`(F)->F`pAlgebraicManipulations(R,F)``855090 -oratDenom`2`x`(F,F)->F`pAlgebraicManipulations(R,F)``855228 -oratDenom`2`x`(F,List(F))->F`pAlgebraicManipulations(R,F)``855346 -oratDenom`2`x`(F,List(Kernel(F)))->F`pAlgebraicManipulations(R,F)``855485 -oratDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),Fraction(UP))->Record(particular:Union(Fraction(UP),"failed"),basis:List(Fraction(UP)))`pRationalLODE(F,UP)``855616 -oratDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),List(Fraction(UP)))->Record(basis:List(Fraction(UP)),mat:Matrix(F))`pRationalLODE(F,UP)``855938 -oratDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),Fraction(UP))->Record(particular:Union(Fraction(UP),"failed"),basis:List(Fraction(UP)))`pRationalLODE(F,UP)``856186 -oratDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),List(Fraction(UP)))->Record(basis:List(Fraction(UP)),mat:Matrix(F))`pRationalLODE(F,UP)``856508 -oratPoly`1`x`(F)->SparseUnivariatePolynomial(F)`pAlgebraicManipulations(R,F)``856756 +orank`0`x`()->PositiveInteger`cFiniteRankAlgebra(R,UP)``1036885 +orank`0`x`()->PositiveInteger`cFiniteRankNonAssociativeAlgebra(R)``1036939 +orank`1`n`(M)->NonNegativeInteger`pInnerMatrixLinearAlgebraFunctions(R,Row,Col,M)``1037012 +orank`1`x`(M)->NonNegativeInteger`pMatrixLinearAlgebraFunctions(R,Row,Col,M)`has(R,IntegralDomain)`1037075 +orank`1`x`(_$)->NonNegativeInteger`cMatrixCategory(R,Row,Col)`has(R,IntegralDomain)`1037138 +orank`1`x`(_$)->NonNegativeInteger`cRectangularMatrixCategory(m,n,R,Row,Col)`has(R,IntegralDomain)`1037289 +orank`1`x`(_$)->NonNegativeInteger`dCartesianTensor(minix,dim,R)``1037352 +orank`2`x`(Matrix(F),Vector(F))->NonNegativeInteger`pLinearSystemMatrixPackage1(F)``1037642 +orank`2`x`(M,Col)->NonNegativeInteger`pLinearSystemMatrixPackage(F,Row,Col,M)``1037758 +orarrow`2`n`(_$,_$)->_$`dOutputForm``1037874 +oratDenom`1`x`(F)->F`pAlgebraicManipulations(R,F)``1037948 +oratDenom`2`x`(F,F)->F`pAlgebraicManipulations(R,F)``1038086 +oratDenom`2`x`(F,List(F))->F`pAlgebraicManipulations(R,F)``1038204 +oratDenom`2`x`(F,List(Kernel(F)))->F`pAlgebraicManipulations(R,F)``1038343 +oratDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),Fraction(UP))->Record(particular:Union(Fraction(UP),"failed"),basis:List(Fraction(UP)))`pRationalLODE(F,UP)``1038474 +oratDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),List(Fraction(UP)))->Record(basis:List(Fraction(UP)),mat:Matrix(F))`pRationalLODE(F,UP)``1038796 +oratDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),Fraction(UP))->Record(particular:Union(Fraction(UP),"failed"),basis:List(Fraction(UP)))`pRationalLODE(F,UP)``1039044 +oratDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),List(Fraction(UP)))->Record(basis:List(Fraction(UP)),mat:Matrix(F))`pRationalLODE(F,UP)``1039366 orational?`1`n`(S)->Boolean`xComplexCategory&(S,R)``0 orational?`1`n`(S)->Boolean`xIntegerNumberSystem&(S)``0 orational?`1`n`(S)->Boolean`xOctonionCategory&(S,R)``0 orational?`1`n`(S)->Boolean`xQuaternionCategory&(S,R)``0 -orational?`1`x`(S)->Boolean`pRationalRetractions(S)``856884 -orational?`1`x`(_$)->Boolean`cComplexCategory(R)`has(R,IntegerNumberSystem)`856991 -orational?`1`x`(_$)->Boolean`cIntegerNumberSystem``857058 -orational?`1`x`(_$)->Boolean`cOctonionCategory(R)`has(R,IntegerNumberSystem)`857159 -orational?`1`x`(_$)->Boolean`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`857275 -orational?`1`x`(_$)->Boolean`dFactored(R)`has(R,IntegerNumberSystem)`857471 -orational?`1`x`(_$)->Boolean`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`857591 -orational?`1`x`(_$)->Boolean`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`857665 -orationalApproximation`2`x`(_$,NonNegativeInteger)->Fraction(Integer)`dDoubleFloat``857739 -orationalApproximation`2`x`(_$,NonNegativeInteger)->Fraction(Integer)`dFloat``857877 -orationalApproximation`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Fraction(Integer)`dDoubleFloat``858015 -orationalApproximation`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Fraction(Integer)`dFloat``858197 -orationalFunction`2`x`(_$,Integer)->Fraction(Polynomial(Coef))`cUnivariateLaurentSeriesCategory(Coef)`has(Coef,IntegralDomain)`858377 -orationalFunction`3`x`(_$,Integer,Integer)->Fraction(Polynomial(Coef))`cUnivariateLaurentSeriesCategory(Coef)`has(Coef,IntegralDomain)`858520 -orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xComplexCategory&(S,R)``0 -orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xIntegerNumberSystem&(S)``0 -orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xOctonionCategory&(S,R)``0 -orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xQuaternionCategory&(S,R)``0 -orationalIfCan`1`x`(S)->Union(Fraction(Integer),"failed")`pRationalRetractions(S)``858685 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cComplexCategory(R)`has(R,IntegerNumberSystem)`858804 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cIntegerNumberSystem``858926 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cOctonionCategory(R)`has(R,IntegerNumberSystem)`859031 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`859146 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dFactored(R)`has(R,IntegerNumberSystem)`859371 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`859481 -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`859593 -orationalPoint?`2`n`(F,F)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``859706 -orationalPoint?`2`x`(F,F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``859788 -orationalPoints`0`n`()->List(List(F))`xFunctionFieldCategory&(S,F,UP,UPUP)``859870 -orationalPoints`0`x`()->List(List(F))`cFunctionFieldCategory(F,UP,UPUP)`has(F,Finite)`859953 -orationalPower`1`x`(_$)->Fraction(Integer)`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``860036 orational`1`n`(S)->Fraction(Integer)`xComplexCategory&(S,R)``0 orational`1`n`(S)->Fraction(Integer)`xIntegerNumberSystem&(S)``0 orational`1`n`(S)->Fraction(Integer)`xOctonionCategory&(S,R)``0 orational`1`n`(S)->Fraction(Integer)`xQuaternionCategory&(S,R)``0 -orational`1`x`(S)->Fraction(Integer)`pRationalRetractions(S)``860134 -orational`1`x`(_$)->Fraction(Integer)`cComplexCategory(R)`has(R,IntegerNumberSystem)`860243 -orational`1`x`(_$)->Fraction(Integer)`cIntegerNumberSystem``860353 -orational`1`x`(_$)->Fraction(Integer)`cOctonionCategory(R)`has(R,IntegerNumberSystem)`860441 -orational`1`x`(_$)->Fraction(Integer)`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`860561 -orational`1`x`(_$)->Fraction(Integer)`dFactored(R)`has(R,IntegerNumberSystem)`860772 -orational`1`x`(_$)->Fraction(Integer)`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`860932 -orational`1`x`(_$)->Fraction(Integer)`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`861049 -oratpart`1`n`(_$)->F`dIntegrationResult(F)``861164 -oravel`1`x`(_$)->List(R)`dCartesianTensor(minix,dim,R)``861241 -ordHack1`3`n`(Vector(S),Vector(Integer),Integer)->()->S`pRandomDistributions(S)``861362 -ordregime`1`n`(String)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``861409 -oread!`1`x`(_$)->S`cFileCategory(Name,S)``861482 -oreadIfCan!`1`x`(_$)->Union(S,"failed")`dFile(S)``861646 -oreadIfCan!`1`x`(_$)->Union(SingleInteger,"failed")`dBinaryFile``861841 -oreadIfCan!`1`x`(_$)->Union(String,"failed")`dTextFile``862036 -oreadLine!`1`x`(_$)->String`dTextFile``862249 -oreadLineIfCan!`1`x`(_$)->Union(String,"failed")`dTextFile``862343 -oreadable?`1`x`(_$)->Boolean`cFileNameCategory``862560 -oreal?`1`x`(F)->Boolean`pComplexTrigonometricManipulations(R,F)``862651 -oreal?`1`x`(F)->Boolean`pTrigonometricManipulations(R,F)``862716 -oreal?`1`x`(_$)->Boolean`dFortranScalarType``862781 -orealEigenvalues`2`x`(Matrix(Fraction(Integer)),Par)->List(Par)`pNumericRealEigenPackage(Par)``862867 -orealEigenvectors`2`x`(Matrix(Fraction(Integer)),Par)->List(Record(outval:Par,outmult:Integer,outvect:List(Matrix(Par))))`pNumericRealEigenPackage(Par)``863096 -orealElementary`1`x`(F)->F`pElementaryFunctionStructurePackage(R,F)``863395 -orealElementary`2`x`(F,Symbol)->F`pElementaryFunctionStructurePackage(R,F)``863551 -orealRoots`2`x`(Fraction(Polynomial(Integer)),Par)->List(Par)`pFloatingRealPackage(Par)``863745 -orealRoots`3`x`(List(Fraction(Polynomial(Integer))),List(Symbol),Par)->List(List(Par))`pFloatingRealPackage(Par)``863864 -orealSolve`1`x`(List(Polynomial(R)))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``864189 -orealSolve`1`x`(RegularChain(R,ls))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``864282 -orealSolve`2`x`(List(Polynomial(R)),Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``864562 -orealSolve`3`n`(List(Polynomial(Integer)),List(Symbol),Float)->List(List(Float))`pRealSolvePackage``864664 -orealSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``864880 -orealSolve`4`x`(List(Polynomial(R)),Boolean,Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``864992 -orealZeros`1`x`(Pol)->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``865910 -orealZeros`1`x`(Pol)->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``866041 -orealZeros`2`x`(Pol,Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``866172 -orealZeros`2`x`(Pol,Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``866333 -orealZeros`2`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``866494 -orealZeros`2`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``866690 -orealZeros`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``866886 -orealZeros`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``867115 -oreal`1`x`(F)->Expression(R)`pComplexTrigonometricManipulations(R,F)``867344 -oreal`1`x`(F)->F`pTrigonometricManipulations(R,F)``867438 -oreal`1`x`(_$)->R`cComplexCategory(R)``867532 -oreal`1`x`(_$)->R`cOctonionCategory(R)``867585 -oreal`1`x`(_$)->R`cQuaternionCategory(R)``867648 -orecip`0`n`()->_$`dMoebiusTransform(F)``867717 +orational?`1`x`(_$)->Boolean`cAffineSpaceCategory(K)``1039614 +orational?`1`x`(_$)->Boolean`cComplexCategory(R)`has(R,IntegerNumberSystem)`1039724 +orational?`1`x`(_$)->Boolean`cIntegerNumberSystem``1039791 +orational?`1`x`(_$)->Boolean`cOctonionCategory(R)`has(R,IntegerNumberSystem)`1039892 +orational?`1`x`(_$)->Boolean`cProjectiveSpaceCategory(K)``1040008 +orational?`1`x`(_$)->Boolean`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`1040118 +orational?`1`x`(_$)->Boolean`dFactored(R)`has(R,IntegerNumberSystem)`1040314 +orational?`1`x`(_$)->Boolean`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`1040434 +orational?`1`x`(_$)->Boolean`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`1040508 +orational`1`x`(_$)->Fraction(Integer)`cComplexCategory(R)`has(R,IntegerNumberSystem)`1040582 +orational`1`x`(_$)->Fraction(Integer)`cIntegerNumberSystem``1040692 +orational`1`x`(_$)->Fraction(Integer)`cOctonionCategory(R)`has(R,IntegerNumberSystem)`1040780 +orational`1`x`(_$)->Fraction(Integer)`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`1040900 +orational`1`x`(_$)->Fraction(Integer)`dFactored(R)`has(R,IntegerNumberSystem)`1041111 +orational`1`x`(_$)->Fraction(Integer)`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`1041271 +orational`1`x`(_$)->Fraction(Integer)`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`1041388 +orational?`1`x`(S)->Boolean`pRationalRetractions(S)``1041503 +orational`1`x`(S)->Fraction(Integer)`pRationalRetractions(S)``1041610 +orational?`2`x`(_$,NonNegativeInteger)->Boolean`cAffineSpaceCategory(K)``1041719 +orational?`2`x`(_$,NonNegativeInteger)->Boolean`cProjectiveSpaceCategory(K)``1041803 +orationalApproximation`2`x`(_$,NonNegativeInteger)->Fraction(Integer)`dDoubleFloat``1041887 +orationalApproximation`2`x`(_$,NonNegativeInteger)->Fraction(Integer)`dFloat``1042025 +orationalApproximation`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Fraction(Integer)`dDoubleFloat``1042163 +orationalApproximation`3`x`(_$,NonNegativeInteger,NonNegativeInteger)->Fraction(Integer)`dFloat``1042345 +orationalFunction`2`x`(_$,Integer)->Fraction(Polynomial(Coef))`cUnivariateLaurentSeriesCategory(Coef)`has(Coef,IntegralDomain)`1042525 +orationalFunction`3`x`(_$,Integer,Integer)->Fraction(Polynomial(Coef))`cUnivariateLaurentSeriesCategory(Coef)`has(Coef,IntegralDomain)`1042668 +orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xComplexCategory&(S,R)``0 +orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xIntegerNumberSystem&(S)``0 +orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xOctonionCategory&(S,R)``0 +orationalIfCan`1`n`(S)->Union(Fraction(Integer),"failed")`xQuaternionCategory&(S,R)``0 +orationalIfCan`1`x`(S)->Union(Fraction(Integer),"failed")`pRationalRetractions(S)``1042833 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cComplexCategory(R)`has(R,IntegerNumberSystem)`1042952 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cIntegerNumberSystem``1043074 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cOctonionCategory(R)`has(R,IntegerNumberSystem)`1043179 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cQuaternionCategory(R)`has(R,IntegerNumberSystem)`1043294 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dFactored(R)`has(R,IntegerNumberSystem)`1043523 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dOnePointCompletion(R)`has(R,IntegerNumberSystem)`1043633 +orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`dOrderedCompletion(R)`has(R,IntegerNumberSystem)`1043745 +orationalPlaces`0`x`()->List(Places(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``1043858 +orationalPlaces`0`x`()->List(PlacesOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``1043980 +orationalPlaces`0`x`()->List(Plc)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)`has(K,Finite)`1044102 +orationalPoint?`2`n`(F,F)->Boolean`xFunctionFieldCategory&(S,F,UP,UPUP)``1044224 +orationalPoint?`2`x`(F,F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1044788 +orationalPoints`0`n`()->List(List(F))`xFunctionFieldCategory&(S,F,UP,UPUP)``1045352 +orationalPoints`0`x`()->List(List(F))`cFunctionFieldCategory(F,UP,UPUP)`has(F,Finite)`1045442 +orationalPoints`0`x`()->List(ProjectivePlane(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +orationalPoints`0`x`()->List(ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +orationalPoints`0`x`()->List(ProjPt)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)`has(K,Finite)`0 +orationalPoints`2`x`(PolyRing,PositiveInteger)->List(ProjPt)`pProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt)``1045532 +orationalPower`1`x`(_$)->Fraction(Integer)`cUnivariatePuiseuxSeriesConstructorCategory(Coef,ULS)``1045807 +oratpart`1`n`(_$)->F`dIntegrationResult(F)``1045905 +oratPoly`1`x`(F)->SparseUnivariatePolynomial(F)`pAlgebraicManipulations(R,F)``1045982 +oravel`1`x`(_$)->List(R)`dCartesianTensor(minix,dim,R)``1046110 +orCoord`1`n`(Point(R))->R`pPointPackage(R)``1046401 +ordHack1`3`n`(Vector(S),Vector(Integer),Integer)->()->S`pRandomDistributions(S)``1046672 +ordregime`1`n`(String)->List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))))`pParametricLinearEquations(R,Var,Expon,GR)``1046719 +oread!`1`x`(_$)->S`cFileCategory(Name,S)``1046792 +oreadable?`1`x`(_$)->Boolean`cFileNameCategory``1046956 +oreadIfCan!`1`x`(_$)->Union(S,"failed")`dFile(S)``1047047 +oreadIfCan!`1`x`(_$)->Union(SingleInteger,"failed")`dBinaryFile``1047242 +oreadIfCan!`1`x`(_$)->Union(String,"failed")`dTextFile``1047437 +oreadLine!`1`x`(_$)->String`dTextFile``1047650 +oreadLineIfCan!`1`x`(_$)->Union(String,"failed")`dTextFile``1047744 +oreal?`1`x`(_$)->Boolean`dFortranScalarType``1047961 +oreal?`1`x`(F)->Boolean`pComplexTrigonometricManipulations(R,F)``1048047 +oreal?`1`x`(F)->Boolean`pTrigonometricManipulations(R,F)``1048112 +oreal`1`x`(F)->Expression(R)`pComplexTrigonometricManipulations(R,F)``1048177 +oreal`1`x`(F)->F`pTrigonometricManipulations(R,F)``1048271 +oreal`1`x`(_$)->R`cComplexCategory(R)``1048365 +oreal`1`x`(_$)->R`cOctonionCategory(R)``1048418 +oreal`1`x`(_$)->R`cQuaternionCategory(R)``1048481 +orealEigenvalues`2`x`(Matrix(Fraction(Integer)),Par)->List(Par)`pNumericRealEigenPackage(Par)``1048550 +orealEigenvectors`2`x`(Matrix(Fraction(Integer)),Par)->List(Record(outval:Par,outmult:Integer,outvect:List(Matrix(Par))))`pNumericRealEigenPackage(Par)``1048779 +orealElementary`1`x`(F)->F`pElementaryFunctionStructurePackage(R,F)``1049078 +orealElementary`2`x`(F,Symbol)->F`pElementaryFunctionStructurePackage(R,F)``1049234 +orealRoots`2`x`(Fraction(Polynomial(Integer)),Par)->List(Par)`pFloatingRealPackage(Par)``1049428 +orealRoots`3`x`(List(Fraction(Polynomial(Integer))),List(Symbol),Par)->List(List(Par))`pFloatingRealPackage(Par)``1049547 +orealSolve`1`x`(List(Polynomial(R)))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1049872 +orealSolve`1`x`(RegularChain(R,ls))->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1049965 +orealSolve`2`x`(List(Polynomial(R)),Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1050245 +orealSolve`3`n`(List(Polynomial(Integer)),List(Symbol),Float)->List(List(Float))`pRealSolvePackage``1050347 +orealSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1050959 +orealSolve`4`x`(List(Polynomial(R)),Boolean,Boolean,Boolean)->List(List(RealClosure(Fraction(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1051071 +orealZeros`1`x`(Pol)->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``1051941 +orealZeros`1`x`(Pol)->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``1052072 +orealZeros`2`x`(Pol,Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``1052203 +orealZeros`2`x`(Pol,Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``1052364 +orealZeros`2`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``1052525 +orealZeros`2`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``1052721 +orealZeros`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackage(Pol)``1052917 +orealZeros`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->List(Record(left:Fraction(Integer),right:Fraction(Integer)))`pRealZeroPackageQ(Pol)``1053146 +orecip`0`n`()->_$`dMoebiusTransform(F)``1053375 +orecip`1`n`(_$)->_$`dMoebiusTransform(F)``1053479 +orecip`1`n`(Stream(A))->Union(Stream(A),"failed")`pStreamTaylorSeriesOperations(A)``1053523 orecip`1`n`(S)->Union(S,"failed")`xComplexCategory&(S,R)``0 orecip`1`n`(S)->Union(S,"failed")`xFiniteRankNonAssociativeAlgebra&(S,R)``0 orecip`1`n`(S)->Union(S,"failed")`xGroup&(S)``0 orecip`1`n`(S)->Union(S,"failed")`xIntegralDomain&(S)``0 orecip`1`n`(S)->Union(S,"failed")`xMonogenicAlgebra&(S,R,UP)``0 orecip`1`n`(S)->Union(S,"failed")`xMonoid&(S)``0 -orecip`1`n`(Stream(A))->Union(Stream(A),"failed")`pStreamTaylorSeriesOperations(A)``867821 -orecip`1`n`(_$)->Union(_$,"failed")`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``867924 -orecip`1`n`(_$)->Union(_$,"failed")`dModularRing(R,Mod,reduction,merge,exactQuo)``867961 -orecip`1`n`(_$)->_$`dMoebiusTransform(F)``867998 -orecip`1`x`(_$)->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`868042 -orecip`1`x`(_$)->Union(_$,"failed")`cMonadWithUnit``868275 -orecip`1`x`(_$)->Union(_$,"failed")`cMonoid``868477 -orecip`1`x`(_$)->Union(_$,"failed")`dCliffordAlgebra(n,K,Q)``868617 +orecip`1`n`(_$)->Union(_$,"failed")`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``1053626 +orecip`1`n`(_$)->Union(_$,"failed")`dModularRing(R,Mod,reduction,merge,exactQuo)``1053667 +orecip`1`x`(_$)->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1053708 +orecip`1`x`(_$)->Union(_$,"failed")`cMonadWithUnit``1053941 +orecip`1`x`(_$)->Union(_$,"failed")`cMonoid``1054143 +orecip`1`x`(_$)->Union(_$,"failed")`dCliffordAlgebra(n,K,Q)``1054283 orecip`2`n`(ThePols,S)->Union(ThePols,"failed")`xRealRootCharacterizationCategory&(S,TheField,ThePols)``0 -orecip`2`x`(P,TS)->Record(num:P,den:P)`pNormalizationPackage(R,E,V,P,TS)``868731 -orecip`2`x`(ThePols,_$)->Union(ThePols,"failed")`cRealRootCharacterizationCategory(TheField,ThePols)``868934 -oreciprocalPolynomial`1`n`(UP)->UP`pComplexRootFindingPackage(R,UP)``869026 -orecolor`2`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),(DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->(DoubleFloat,DoubleFloat)->Point(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``869196 -orecoverAfterFail`3`x`(_$,String,Integer)->Union(String,"failed")`dRoutinesTable``869294 -orectangularMatrix`1`n`(Matrix(R))->_$`dRectangularMatrix(m,n,R)``869408 -orecur`1`x`((NonNegativeInteger,A)->A)->(NonNegativeInteger,A)->A`pMappingPackage1(A)``869533 -orecur`3`n`((NonNegativeInteger,A)->A,NonNegativeInteger,A)->A`pMappingPackageInternalHacks1(A)``869652 -oredPo`2`n`(Dpol,List(Dpol))->Record(poly:Dpol,mult:Dom)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``869723 -oredPol`2`n`(Dpol,List(Dpol))->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``869757 -ored`0`x`()->_$`dColor``869792 -oredmat`2`n`(Matrix(GR),List(GR))->Matrix(GR)`pParametricLinearEquations(R,Var,Expon,GR)``869865 -oredpps`2`n`(Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R))))),List(GR))->Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))`pParametricLinearEquations(R,Var,Expon,GR)``870004 -oreduceBasisAtInfinity`1`n`(Vector(S))->Vector(S)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -oreduceBasisAtInfinity`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``870120 -oreduceByQuasiMonic`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 -oreduceByQuasiMonic`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``870284 -oreduceLODE`2`n`(LO,A)->Record(mat:Matrix(L),vec:Vector(F))`pReduceLODE(F,L,UP,A,LO)``870427 -oreduce`1`n`(FPol)->_$`dResidueRing(F,Expon,VarSet,FPol,LFPol)``870782 +orecip`2`x`(P,TS)->Record(num:P,den:P)`pNormalizationPackage(R,E,V,P,TS)``1054397 +orecip`2`x`(ThePols,_$)->Union(ThePols,"failed")`cRealRootCharacterizationCategory(TheField,ThePols)``1054600 +oreciprocalPolynomial`1`n`(UP)->UP`pComplexRootFindingPackage(R,UP)``1054692 +orecolor`2`x`((DoubleFloat,DoubleFloat)->Point(DoubleFloat),(DoubleFloat,DoubleFloat,DoubleFloat)->DoubleFloat)->(DoubleFloat,DoubleFloat)->Point(DoubleFloat)`pTopLevelDrawFunctionsForCompiledFunctions``1054862 +orecoverAfterFail`3`x`(_$,String,Integer)->Union(String,"failed")`dRoutinesTable``1054960 +orectangularMatrix`1`n`(Matrix(R))->_$`dRectangularMatrix(m,n,R)``1055074 +orecur`1`x`((NonNegativeInteger,A)->A)->(NonNegativeInteger,A)->A`pMappingPackage1(A)``1055199 +orecur`3`n`((NonNegativeInteger,A)->A,NonNegativeInteger,A)->A`pMappingPackageInternalHacks1(A)``1055318 +ored`0`x`()->_$`dColor``1055389 +oredmat`2`n`(Matrix(GR),List(GR))->Matrix(GR)`pParametricLinearEquations(R,Var,Expon,GR)``1055462 +oredPo`2`n`(Dpol,List(Dpol))->Record(poly:Dpol,mult:Dom)`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1055601 +oredPol`2`n`(Dpol,List(Dpol))->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1055635 +oredpps`2`n`(Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R))))),List(GR))->Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R)))))`pParametricLinearEquations(R,Var,Expon,GR)``1055670 +oreduce`1`n`(_$)->_$`dInnerAlgebraicNumber``1055786 +oreduce`1`n`(FPol)->_$`dResidueRing(F,Expon,VarSet,FPol,LFPol)``1055915 oreduce`1`n`(Fraction(SparseUnivariatePolynomial(R)))->Union(S,"failed")`xComplexCategory&(S,R)``0 oreduce`1`n`(Fraction(UP))->Union(S,"failed")`xMonogenicAlgebra&(S,R,UP)``0 -oreduce`1`n`(Rep)->_$`dModMonic(R,Rep)``870869 +oreduce`1`n`(Rep)->_$`dModMonic(R,Rep)``1056002 +oreduce`1`n`(SparseUnivariatePolynomial(R1))->Record(pol:SparseUnivariatePolynomial(R1),deg:PositiveInteger)`pDegreeReductionPackage(R1,R2)``1056044 oreduce`1`n`(SparseUnivariatePolynomial(R))->S`xComplexCategory&(S,R)``0 -oreduce`1`n`(SparseUnivariatePolynomial(R1))->Record(pol:SparseUnivariatePolynomial(R1),deg:PositiveInteger)`pDegreeReductionPackage(R1,R2)``870907 oreduce`1`n`(UP)->S`xMonogenicAlgebra&(S,R,UP)``0 -oreduce`1`n`(_$)->_$`dInnerAlgebraicNumber``870947 -oreduce`1`x`(Fraction(UP))->Union(_$,"failed")`cMonogenicAlgebra(R,UP)`has(R,Field)`871076 -oreduce`1`x`(UP)->_$`cMonogenicAlgebra(R,UP)``871160 -oreduce`1`x`(_$)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``871313 -oreduce`1`x`(_$)->_$`dAlgebraicNumber``871444 -oreduce`1`x`(_$)->_$`dExpression(R)`has(R,IntegralDomain)`871573 +oreduce`1`x`(_$)->_$`cFiniteDivisorCategory(F,UP,UPUP,R)``1056084 +oreduce`1`x`(_$)->_$`dAlgebraicNumber``1056215 +oreduce`1`x`(_$)->_$`dExpression(R)`has(R,IntegralDomain)`1056344 +oreduce`1`x`(Fraction(UP))->Union(_$,"failed")`cMonogenicAlgebra(R,UP)`has(R,Field)`1056476 +oreduce`1`x`(List(_$))->Divisor(_$)`cPlacesCategory(K,PCS)``0 +oreduce`1`x`(SparseUnivariatePolynomial(_$))->_$`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +oreduce`1`x`(UP)->_$`cMonogenicAlgebra(R,UP)``1056560 oreduce`2`n`((P,P)->P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 +oreduce`2`n`(R,Mod)->_$`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``1056713 +oreduce`2`n`(R,Mod)->_$`dModularField(R,Mod,reduction,merge,exactQuo)``1056759 +oreduce`2`n`(R,Mod)->_$`dModularRing(R,Mod,reduction,merge,exactQuo)``1056805 oreduce`2`n`((S,S)->S,A)->S`xCollection&(A,S)``0 oreduce`2`n`((S,S)->S,A)->S`xListAggregate&(A,S)``0 oreduce`2`n`((S,S)->S,A)->S`xOneDimensionalArrayAggregate&(A,S)``0 -oreduce`2`n`(R,Mod)->_$`dEuclideanModularRing(S,R,Mod,reduction,merge,exactQuo)``871705 -oreduce`2`n`(R,Mod)->_$`dModularField(R,Mod,reduction,merge,exactQuo)``871747 -oreduce`2`n`(R,Mod)->_$`dModularRing(R,Mod,reduction,merge,exactQuo)``871789 -oreduce`2`x`((S,S)->S,_$)->S`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`871831 +oreduce`2`x`((S,S)->S,_$)->S`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`1056851 oreduce`3`n`((P,P)->P,S,P)->P`xTriangularSetCategory&(S,R,E,V,P)``0 oreduce`3`n`((S,S)->S,A,S)->S`xCollection&(A,S)``0 oreduce`3`n`((S,S)->S,A,S)->S`xListAggregate&(A,S)``0 oreduce`3`n`((S,S)->S,A,S)->S`xOneDimensionalArrayAggregate&(A,S)``0 -oreduce`3`x`((A,B)->B,DirectProduct(dim,A),B)->B`pDirectProductFunctions2(dim,A,B)``872247 -oreduce`3`x`((A,B)->B,List(A),B)->B`pListFunctions2(A,B)``872421 -oreduce`3`x`((A,B)->B,OneDimensionalArray(A),B)->B`pOneDimensionalArrayFunctions2(A,B)``872802 -oreduce`3`x`((A,B)->B,PrimitiveArray(A),B)->B`pPrimitiveArrayFunctions2(A,B)``873150 -oreduce`3`x`((A,B)->B,Vector(A),B)->B`pVectorFunctions2(A,B)``873492 -oreduce`3`x`((R1,R2)->R2,M1,R2)->R2`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``873666 -oreduce`3`x`((R1,R2)->R2,M1,R2)->R2`pRectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2)``873803 -oreduce`3`x`((S,R)->R,A,R)->R`pFiniteLinearAggregateFunctions2(S,A,R,B)``873946 -oreduce`3`x`((S,R)->R,A,R)->R`pFiniteSetAggregateFunctions2(S,A,R,B)``874282 -oreduce`3`x`((S,S)->S,_$,S)->S`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`874610 -oreduce`3`x`(B,(A,B)->B,Stream(A))->B`pStreamFunctions2(A,B)``875053 +oreduce`3`x`((A,B)->B,DirectProduct(dim,A),B)->B`pDirectProductFunctions2(dim,A,B)``1057457 +oreduce`3`x`((A,B)->B,List(A),B)->B`pListFunctions2(A,B)``1057631 +oreduce`3`x`((A,B)->B,OneDimensionalArray(A),B)->B`pOneDimensionalArrayFunctions2(A,B)``1058012 +oreduce`3`x`((A,B)->B,PrimitiveArray(A),B)->B`pPrimitiveArrayFunctions2(A,B)``1058678 +oreduce`3`x`((A,B)->B,Vector(A),B)->B`pVectorFunctions2(A,B)``1059333 +oreduce`3`x`(B,(A,B)->B,Stream(A))->B`pStreamFunctions2(A,B)``1059507 +oreduce`3`x`((R1,R2)->R2,M1,R2)->R2`pMatrixCategoryFunctions2(R1,Row1,Col1,M1,R2,Row2,Col2,M2)``1060071 +oreduce`3`x`((R1,R2)->R2,M1,R2)->R2`pRectangularMatrixCategoryFunctions2(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2)``1060208 +oreduce`3`x`((S,R)->R,A,R)->R`pFiniteLinearAggregateFunctions2(S,A,R,B)``1060351 +oreduce`3`x`((S,R)->R,A,R)->R`pFiniteSetAggregateFunctions2(S,A,R,B)``1060691 +oreduce`3`x`((S,S)->S,_$,S)->S`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`1061023 oreduce`4`n`((P,P)->P,S,P,P)->P`xTriangularSetCategory&(S,R,E,V,P)``0 +oreduce`4`n`(P,S,(P,P)->P,(P,P)->Boolean)->P`xTriangularSetCategory&(S,R,E,V,P)``0 oreduce`4`n`((S,S)->S,A,S,S)->S`xCollection&(A,S)``0 oreduce`4`n`((S,S)->S,A,S,S)->S`xListAggregate&(A,S)``0 oreduce`4`n`((S,S)->S,A,S,S)->S`xOneDimensionalArrayAggregate&(A,S)``0 -oreduce`4`n`(P,S,(P,P)->P,(P,P)->Boolean)->P`xTriangularSetCategory&(S,R,E,V,P)``0 -oreduce`4`x`((S,S)->S,_$,S,S)->S`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`875277 -oreduce`4`x`(P,_$,(P,P)->P,(P,P)->Boolean)->P`cTriangularSetCategory(R,E,V,P)``875715 +oreduce`4`x`(P,_$,(P,P)->P,(P,P)->Boolean)->P`cTriangularSetCategory(R,E,V,P)``1061466 +oreduce`4`x`((S,S)->S,_$,S,S)->S`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`1062200 +oreduceBasisAtInfinity`1`n`(Vector(S))->Vector(S)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 +oreduceBasisAtInfinity`1`x`(Vector(_$))->Vector(_$)`cFunctionFieldCategory(F,UP,UPUP)``1062638 +oreduceByQuasiMonic`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 +oreduceByQuasiMonic`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``1062802 oreduced?`2`n`(S,List(S))->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 oreduced?`2`n`(S,S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -oreduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``876449 -oreduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``876612 +oreduced?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``1062945 +oreduced?`2`x`(_$,List(_$))->Boolean`cRecursivePolynomialCategory(R,E,V)``1063060 oreduced?`3`n`(P,S,(P,P)->Boolean)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -oreduced?`3`x`(P,_$,(P,P)->Boolean)->Boolean`cTriangularSetCategory(R,E,V,P)``876727 -oreducedContinuedFraction`2`x`(R,Stream(R))->_$`dContinuedFraction(R)``877012 -oreducedDiscriminant`1`n`(UP)->R`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``877330 -oreducedForm`1`x`(_$)->_$`dContinuedFraction(R)``877382 -oreducedQPowers`1`n`(SparseUnivariatePolynomial(GF))->PrimitiveArray(SparseUnivariatePolynomial(GF))`pFiniteFieldPolynomialPackage(GF)``877634 +oreduced?`3`x`(P,_$,(P,P)->Boolean)->Boolean`cTriangularSetCategory(R,E,V,P)``1063223 +oreducedContinuedFraction`2`x`(R,Stream(R))->_$`dContinuedFraction(R)``1063507 +oreducedDiscriminant`1`n`(UP)->R`pPAdicWildFunctionFieldIntegralBasis(K,R,UP,F)``1063825 +oreducedForm`1`x`(_$)->_$`dContinuedFraction(R)``1063877 +oreducedQPowers`1`n`(SparseUnivariatePolynomial(GF))->PrimitiveArray(SparseUnivariatePolynomial(GF))`pFiniteFieldPolynomialPackage(GF)``1064129 oreducedSystem`1`n`(Matrix(A))->Matrix(Integer)`xQuotientFieldCategory&(A,S)``0 oreducedSystem`1`n`(Matrix(A))->Matrix(S)`xQuotientFieldCategory&(A,S)``0 oreducedSystem`1`n`(Matrix(S))->Matrix(Integer)`xComplexCategory&(S,R)``0 @@ -6876,7 +7678,7 @@ oreducedSystem`1`n`(Matrix(S))->Matrix(R)`xDirectProductCategory&(S,dim,R)``0 oreducedSystem`1`n`(Matrix(S))->Matrix(R)`xFullyLinearlyExplicitRingOver&(S,R)``0 oreducedSystem`1`n`(Matrix(S))->Matrix(R)`xPolynomialCategory&(S,R,E,VarSet)``0 oreducedSystem`1`n`(Matrix(S))->Matrix(R)`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -oreducedSystem`1`x`(Matrix(_$))->Matrix(R)`cLinearlyExplicitRingOver(R)``877805 +oreducedSystem`1`x`(Matrix(_$))->Matrix(R)`cLinearlyExplicitRingOver(R)``1064300 oreducedSystem`2`n`(Matrix(A),Vector(A))->Record(mat:Matrix(Integer),vec:Vector(Integer))`xQuotientFieldCategory&(A,S)``0 oreducedSystem`2`n`(Matrix(A),Vector(A))->Record(mat:Matrix(S),vec:Vector(S))`xQuotientFieldCategory&(A,S)``0 oreducedSystem`2`n`(Matrix(S),Vector(S))->Record(mat:Matrix(Integer),vec:Vector(Integer))`xComplexCategory&(S,R)``0 @@ -6889,186 +7691,306 @@ oreducedSystem`2`n`(Matrix(S),Vector(S))->Record(mat:Matrix(R),vec:Vector(R))`xD oreducedSystem`2`n`(Matrix(S),Vector(S))->Record(mat:Matrix(R),vec:Vector(R))`xFullyLinearlyExplicitRingOver&(S,R)``0 oreducedSystem`2`n`(Matrix(S),Vector(S))->Record(mat:Matrix(R),vec:Vector(R))`xPolynomialCategory&(S,R,E,VarSet)``0 oreducedSystem`2`n`(Matrix(S),Vector(S))->Record(mat:Matrix(R),vec:Vector(R))`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -oreducedSystem`2`x`(Matrix(_$),Vector(_$))->Record(mat:Matrix(R),vec:Vector(R))`cLinearlyExplicitRingOver(R)``877943 -oreduction`2`n`(BP,R)->BP`pGenExEuclid(R,BP)``878108 -oreduction`2`n`(BP,R)->BP`pInnerModularGcd(R,BP,pMod,nextMod)``878278 -oreduction`2`n`(TP,RP)->TP`pGeneralHenselPackage(RP,TP)``878388 +oreducedSystem`2`x`(Matrix(_$),Vector(_$))->Record(mat:Matrix(R),vec:Vector(R))`cLinearlyExplicitRingOver(R)``1064438 +oreduceLineOverLine`3`x`(List(K),List(K),K)->List(K)`pLinesOpPack(K)``1064603 +oreduceLODE`2`n`(LO,A)->Record(mat:Matrix(L),vec:Vector(F))`pReduceLODE(F,L,UP,A,LO)``1064755 +oReduceOrder`2`n`(L,F)->L`pReductionOfOrder(F,L)``1065110 +oReduceOrder`2`n`(L,List(F))->Record(eq:L,op:List(F))`pReductionOfOrder(F,L)``1065316 +oreduceRow`1`x`(List(List(K)))->List(List(K))`pLinesOpPack(K)``1065613 +oreduceRowOnList`2`x`(List(K),List(List(K)))->List(List(K))`pLinesOpPack(K)``1065806 +oreduction`2`n`(BP,R)->BP`pGenExEuclid(R,BP)``1066012 +oreduction`2`n`(BP,R)->BP`pInnerModularGcd(R,BP,pMod,nextMod)``1066186 +oreduction`2`n`(TP,RP)->TP`pGeneralHenselPackage(RP,TP)``1066296 +oreductum`1`n`(_$)->_$`dAntiSymm(R,lVar)``1066389 +oreductum`1`n`(_$)->_$`dDeRhamComplex(CoefRing,listIndVar)``1066574 +oreductum`1`n`(_$)->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``1066755 +oreductum`1`n`(_$)->_$`dLaurentPolynomial(R,UP)``1066799 +oreductum`1`n`(_$)->_$`dMonoidRing(R,M)`has(M,OrderedSet)`1066843 +oreductum`1`n`(_$)->_$`dXPolynomialRing(R,E)``1066909 oreductum`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 oreductum`1`n`(S)->S`xUnivariatePowerSeriesCategory&(S,Coef,Expon)``0 -oreductum`1`n`(_$)->_$`dAntiSymm(R,lVar)``878481 -oreductum`1`n`(_$)->_$`dDeRhamComplex(CoefRing,listIndVar)``878666 -oreductum`1`n`(_$)->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``878847 -oreductum`1`n`(_$)->_$`dLaurentPolynomial(R,UP)``878887 -oreductum`1`n`(_$)->_$`dMonoidRing(R,M)`has(M,OrderedSet)`878927 -oreductum`1`n`(_$)->_$`dXPolynomialRing(R,E)``878993 -oreductum`1`x`(_$)->_$`cAbelianMonoidRing(R,E)``879102 -oreductum`1`x`(_$)->_$`cFreeModuleCat(R,Basis)``879213 -oreductum`1`x`(_$)->_$`cIndexedDirectProductCategory(A,S)``879280 -oreductum`1`x`(_$)->_$`cMonogenicLinearOperator(R)``879447 -oreductum`1`x`(_$)->_$`cUnivariateSkewPolynomialCategory(R)``879571 +oreductum`1`x`(_$)->_$`cAbelianMonoidRing(R,E)``1067018 +oreductum`1`x`(_$)->_$`cFreeModuleCat(R,Basis)``1067129 +oreductum`1`x`(_$)->_$`cIndexedDirectProductCategory(A,S)``1067196 +oreductum`1`x`(_$)->_$`cMonogenicLinearOperator(R)``1067363 +oreductum`1`x`(_$)->_$`cUnivariateSkewPolynomialCategory(R)``1067487 +oreductum`1`x`(_$)->_$`dDivisor(S)``0 oreductum`2`n`(S,V)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oreductum`2`x`(_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``879695 -oref`1`n`(S)->_$`dReference(S)``879865 -orefine`1`n`(_$)->_$`dPlot3D``879940 -orefine`1`n`(_$)->_$`dPlot``879978 -orefine`1`x`(_$)->_$`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``880045 -orefine`2`n`(Factored(R),(R)->Factored(R))->Factored(R)`pFactoredFunctionUtilities(R)``880128 -orefine`2`n`(_$,DoubleFloat)->_$`dPlaneAlgebraicCurvePlot``880542 -orefine`2`n`(_$,Segment(DoubleFloat))->_$`dPlot3D``880586 -orefine`2`n`(_$,Segment(DoubleFloat))->_$`dPlot``880628 -orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->Record(left:Fraction(Integer),right:Fraction(Integer))`pRealZeroPackage(Pol)``880670 -orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->Record(left:Fraction(Integer),right:Fraction(Integer))`pRealZeroPackageQ(Pol)``880853 -orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Record(left:Fraction(Integer),right:Fraction(Integer)))->Union(Record(left:Fraction(Integer),right:Fraction(Integer)),"failed")`pRealZeroPackage(Pol)``881036 -orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Record(left:Fraction(Integer),right:Fraction(Integer)))->Union(Record(left:Fraction(Integer),right:Fraction(Integer)),"failed")`pRealZeroPackageQ(Pol)``881344 -oregime`7`n`(Record(det:GR,rows:List(Integer),cols:List(Integer)),Matrix(GR),List(Fraction(Polynomial(R))),List(List(GR)),NonNegativeInteger,NonNegativeInteger,Integer)->Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R))))))`pParametricLinearEquations(R,Var,Expon,GR)``881652 -oregion`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``882510 +oreductum`2`x`(_$,V)->_$`cRecursivePolynomialCategory(R,E,V)``1067611 +oref`1`n`(S)->_$`dReference(S)``1067781 +orefine`1`n`(_$)->_$`dPlot3D``1067856 +orefine`1`n`(_$)->_$`dPlot``1067898 +orefine`1`x`(_$)->_$`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``1067965 +orefine`2`n`(_$,DoubleFloat)->_$`dPlaneAlgebraicCurvePlot``1068048 +orefine`2`n`(Factored(R),(R)->Factored(R))->Factored(R)`pFactoredFunctionUtilities(R)``1068266 +orefine`2`n`(_$,Segment(DoubleFloat))->_$`dPlot3D``1068680 +orefine`2`n`(_$,Segment(DoubleFloat))->_$`dPlot``1068726 +orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->Record(left:Fraction(Integer),right:Fraction(Integer))`pRealZeroPackage(Pol)``1068772 +orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Fraction(Integer))->Record(left:Fraction(Integer),right:Fraction(Integer))`pRealZeroPackageQ(Pol)``1068955 +orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Record(left:Fraction(Integer),right:Fraction(Integer)))->Union(Record(left:Fraction(Integer),right:Fraction(Integer)),"failed")`pRealZeroPackage(Pol)``1069138 +orefine`3`x`(Pol,Record(left:Fraction(Integer),right:Fraction(Integer)),Record(left:Fraction(Integer),right:Fraction(Integer)))->Union(Record(left:Fraction(Integer),right:Fraction(Integer)),"failed")`pRealZeroPackageQ(Pol)``1069446 +oregime`7`n`(Record(det:GR,rows:List(Integer),cols:List(Integer)),Matrix(GR),List(Fraction(Polynomial(R))),List(List(GR)),NonNegativeInteger,NonNegativeInteger,Integer)->Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R))))))`pParametricLinearEquations(R,Var,Expon,GR)``1069754 +oregion`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``1070612 oregularRepresentation`1`n`(S)->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 -oregularRepresentation`1`x`(_$)->Matrix(R)`cFramedAlgebra(R,UP)``882790 +oregularRepresentation`1`x`(_$)->Matrix(R)`cFramedAlgebra(R,UP)``1070892 oregularRepresentation`2`n`(S,Vector(S))->Matrix(R)`xFiniteRankAlgebra&(S,R,UP)``0 oregularRepresentation`2`n`(S,Vector(S))->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 -oregularRepresentation`2`x`(_$,Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``882942 -oreindex`2`x`(_$,List(Integer))->_$`dCartesianTensor(minix,dim,R)``883116 -orelationsIdeal`1`x`(List(DPoly))->SuchThat(List(Polynomial(F)),List(Equation(Polynomial(F))))`dPolynomialIdeals(F,Expon,VarSet,DPoly)`has(VarSet,ConvertibleTo(Symbol))`883390 -orelativeApprox`2`x`(_$,_$)->Fraction(Integer)`dRealClosure(TheField)``883502 -orelativeApprox`3`x`(ThePolDom,_$,TheField)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``883640 -orelativeApprox`3`x`(ThePols,_$,TheField)->TheField`cRealRootCharacterizationCategory(TheField,ThePols)``883781 -orelerror`2`x`(_$,_$)->Integer`dFloat``883913 +oregularRepresentation`2`x`(_$,Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``1071044 +oreindex`2`x`(_$,List(Integer))->_$`dCartesianTensor(minix,dim,R)``1071218 +orelationsIdeal`1`x`(List(DPoly))->SuchThat(List(Polynomial(F)),List(Equation(Polynomial(F))))`dPolynomialIdeals(F,Expon,VarSet,DPoly)`has(VarSet,ConvertibleTo(Symbol))`1071784 +orelativeApprox`2`x`(_$,_$)->Fraction(Integer)`dRealClosure(TheField)``1071896 +orelativeApprox`3`x`(ThePolDom,_$,TheField)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``1072034 +orelativeApprox`3`x`(ThePols,_$,TheField)->TheField`cRealRootCharacterizationCategory(TheField,ThePols)``1072175 +orelerror`2`x`(_$,_$)->Integer`dFloat``1072307 +orem`2`n`(_$,_$)->_$`dOutputForm``1072425 orem`2`n`(S,S)->S`xComplexCategory&(S,R)``0 orem`2`n`(S,S)->S`xEuclideanDomain&(S)``0 -orem`2`n`(_$,_$)->_$`dOutputForm``884031 -orem`2`x`(_$,_$)->_$`cEuclideanDomain``884088 -orem`2`x`(_$,_$)->_$`dNonNegativeInteger``884200 +orem`2`x`(_$,_$)->_$`cEuclideanDomain``1072482 +orem`2`x`(_$,_$)->_$`dNonNegativeInteger``1072594 oremainder`2`n`(P,S)->Record(rnum:R,polnum:P,den:R)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -oremainder`2`x`(P,_$)->Record(rnum:R,polnum:P,den:R)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`884270 -oremove!`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->S`xTableAggregate&(S,Key,Entry)``0 -oremove!`2`n`((S)->Boolean,A)->A`xDictionary&(A,S)``0 -oremove!`2`n`((S)->Boolean,A)->A`xExtensibleLinearAggregate&(A,S)``0 -oremove!`2`n`((S)->Boolean,A)->A`xListAggregate&(A,S)``0 +oremainder`2`x`(P,_$)->Record(rnum:R,polnum:P,den:R)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`1072664 +oRemainderList`1`n`(_$)->List(Record(k:Symbol,c:_$))`dXPolynomial(R)``0 +oRemainderList`1`n`(_$)->List(Record(k:VarSet,c:_$))`dXRecursivePolynomial(VarSet,R)``1073044 oremove!`2`n`(Key,S)->Union(Entry,"failed")`xTableAggregate&(S,Key,Entry)``0 +oremove!`2`n`((Record(key:Key,entry:Entry))->Boolean,S)->S`xTableAggregate&(S,Key,Entry)``0 oremove!`2`n`(Record(key:Key,entry:Entry),S)->S`xTableAggregate&(S,Key,Entry)``0 +oremove`2`n`(S,A)->A`xCollection&(A,S)``0 oremove!`2`n`(S,A)->A`xDictionary&(A,S)``0 +oremove`2`n`(S,A)->A`xExtensibleLinearAggregate&(A,S)``0 oremove!`2`n`(S,A)->A`xExtensibleLinearAggregate&(A,S)``0 oremove!`2`n`(S,A)->A`xListAggregate&(A,S)``0 -oremove!`2`n`(SplittingNode(V,C),_$)->_$`dSplittingTree(V,C)``884650 -oremove!`2`x`((S)->Boolean,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`884722 -oremove!`2`x`((S)->Boolean,_$)->_$`cExtensibleLinearAggregate(S)``884880 -oremove!`2`x`(Key,_$)->Union(Entry,"failed")`cKeyedDictionary(Key,Entry)``885018 -oremove!`2`x`(S,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`885224 -oremove!`2`x`(S,_$)->_$`cExtensibleLinearAggregate(S)`has(S,SetCategory)`885367 -oremove!`3`x`((S)->Boolean,_$,Integer)->_$`dMultiset(S)``885453 -oremove!`3`x`(S,_$,Integer)->_$`dMultiset(S)``885752 -oremoveConstantTerm`2`n`(F,Symbol)->F`pIntegrationTools(R,F)`has(R,IntegralDomain)`886003 -oremoveCosSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``886115 -oremoveCoshSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``886294 -oremoveDuplicates!`1`n`(A)->A`xListAggregate&(A,S)``0 -oremoveDuplicates!`1`x`(_$)->_$`cExtensibleLinearAggregate(S)`has(S,SetCategory)`886477 -oremoveDuplicates!`1`x`(_$)->_$`cMultiDictionary(S)``886560 +oremove`2`n`((S)->Boolean,A)->A`xCollection&(A,S)``0 +oremove!`2`n`((S)->Boolean,A)->A`xDictionary&(A,S)``0 +oremove`2`n`((S)->Boolean,A)->A`xExtensibleLinearAggregate&(A,S)``0 +oremove!`2`n`((S)->Boolean,A)->A`xExtensibleLinearAggregate&(A,S)``0 +oremove!`2`n`((S)->Boolean,A)->A`xListAggregate&(A,S)``0 +oremove!`2`n`(SplittingNode(V,C),_$)->_$`dSplittingTree(V,C)``1073132 +oremove`2`n`(SplittingNode(V,C),_$)->_$`dSplittingTree(V,C)``1073204 +oremove!`2`x`(Key,_$)->Union(Entry,"failed")`cKeyedDictionary(Key,Entry)``1073427 +oremove`2`x`((S)->Boolean,_$)->_$`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`1073633 +oremove!`2`x`((S)->Boolean,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`1073890 +oremove!`2`x`((S)->Boolean,_$)->_$`cExtensibleLinearAggregate(S)``1074048 +oremove`2`x`((S)->Boolean,_$)->_$`cLazyStreamAggregate(S)``1074186 +oremove`2`x`(S,_$)->_$`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`1074591 +oremove!`2`x`(S,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`1074824 +oremove!`2`x`(S,_$)->_$`cExtensibleLinearAggregate(S)`has(S,SetCategory)`1074967 +oremove`3`x`((S)->Boolean,_$,Integer)->_$`dMultiset(S)``1075053 +oremove!`3`x`((S)->Boolean,_$,Integer)->_$`dMultiset(S)``1075337 +oremove`3`x`(S,_$,Integer)->_$`dMultiset(S)``1075636 +oremove!`3`x`(S,_$,Integer)->_$`dMultiset(S)``1075872 +oremoveConjugate`1`x`(List(_$))->List(_$)`cAffineSpaceCategory(K)``1076123 +oremoveConjugate`1`x`(List(_$))->List(_$)`cProjectiveSpaceCategory(K)``1076261 +oremoveConjugate`2`x`(List(_$),NonNegativeInteger)->List(_$)`cAffineSpaceCategory(K)``1076399 +oremoveConjugate`2`x`(List(_$),NonNegativeInteger)->List(_$)`cProjectiveSpaceCategory(K)``1076553 +oremoveConstantTerm`2`n`(F,Symbol)->F`pIntegrationTools(R,F)`has(R,IntegralDomain)`1076707 +oremoveCoshSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``1076819 +oremoveCosSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``1077002 oremoveDuplicates`1`n`(A)->A`xCollection&(A,S)``0 oremoveDuplicates`1`n`(A)->A`xExtensibleLinearAggregate&(A,S)``0 -oremoveDuplicates`1`x`(_$)->_$`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`886662 -oremoveIrreducibleRedundantFactors`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`886752 -oremoveRedundantFactorsInContents`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`887131 -oremoveRedundantFactorsInPols`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`887554 -oremoveRedundantFactors`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``887957 -oremoveRedundantFactors`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``888770 -oremoveRedundantFactors`2`n`(List(P),P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``889136 -oremoveRedundantFactors`2`n`(P,P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``889503 -oremoveRedundantFactors`3`n`(List(P),List(P),(List(P))->List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``889636 -oremoveRoughlyRedundantFactorsInContents`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`889902 -oremoveRoughlyRedundantFactorsInPol`2`n`(P,List(P))->P`pPolynomialSetUtilitiesPackage(R,E,V,P)``890320 -oremoveRoughlyRedundantFactorsInPols`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``890486 -oremoveRoughlyRedundantFactorsInPols`3`n`(List(P),List(P),Boolean)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``890831 -oremoveSinSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``891148 -oremoveSinhSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``891327 -oremoveSquaresIfCan`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``891510 -oremoveSuperfluousCases`1`x`(List(Record(val:List(P),tower:TS)))->List(Record(val:List(P),tower:TS))`pQuasiComponentPackage(R,E,V,P,TS)``891724 -oremoveSuperfluousCases`1`x`(List(Record(val:List(P),tower:TS)))->List(Record(val:List(P),tower:TS))`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``891830 -oremoveSuperfluousQuasiComponents`1`x`(List(TS))->List(TS)`pQuasiComponentPackage(R,E,V,P,TS)``891936 -oremoveSuperfluousQuasiComponents`1`x`(List(TS))->List(TS)`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``892146 +oremoveDuplicates!`1`n`(A)->A`xListAggregate&(A,S)``0 +oremoveDuplicates`1`x`(_$)->_$`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`1077181 +oremoveDuplicates!`1`x`(_$)->_$`cExtensibleLinearAggregate(S)`has(S,SetCategory)`1077271 +oremoveDuplicates!`1`x`(_$)->_$`cMultiDictionary(S)``1077354 +oremoveFirstZeroes`1`x`(_$)->_$`cLocalPowerSeriesCategory(K)``0 +oremoveIrreducibleRedundantFactors`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`1077456 +oremoveRedundantFactors`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1077835 +oremoveRedundantFactors`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1078648 +oremoveRedundantFactors`2`n`(List(P),P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1079014 +oremoveRedundantFactors`2`n`(P,P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1079381 +oremoveRedundantFactors`3`n`(List(P),List(P),(List(P))->List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1079514 +oremoveRedundantFactorsInContents`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`1079780 +oremoveRedundantFactorsInPols`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`1080203 +oremoveRoughlyRedundantFactorsInContents`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`1080606 +oremoveRoughlyRedundantFactorsInPol`2`n`(P,List(P))->P`pPolynomialSetUtilitiesPackage(R,E,V,P)``1081024 +oremoveRoughlyRedundantFactorsInPols`2`n`(List(P),List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1081190 +oremoveRoughlyRedundantFactorsInPols`3`n`(List(P),List(P),Boolean)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1081535 +oremoveSinhSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``1081852 +oremoveSinSq`1`x`(F)->F`pTranscendentalManipulations(R,F)``1082035 +oremoveSquaresIfCan`1`n`(List(P))->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1082214 +oremoveSuperfluousCases`1`x`(List(Record(val:List(P),tower:TS)))->List(Record(val:List(P),tower:TS))`pQuasiComponentPackage(R,E,V,P,TS)``1082428 +oremoveSuperfluousCases`1`x`(List(Record(val:List(P),tower:TS)))->List(Record(val:List(P),tower:TS))`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1082534 +oremoveSuperfluousQuasiComponents`1`x`(List(TS))->List(TS)`pQuasiComponentPackage(R,E,V,P,TS)``1082640 +oremoveSuperfluousQuasiComponents`1`x`(List(TS))->List(TS)`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1082850 oremoveZero`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 -oremoveZero`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``892356 +oremoveZero`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``1083060 oremoveZeroes`1`n`(_$)->_$`dBalancedPAdicRational(p)``0 +oremoveZeroes`1`n`(_$)->_$`dPAdicRationalConstructor(p,PADIC)``1083381 oremoveZeroes`1`n`(_$)->_$`dPAdicRational(p)``0 -oremoveZeroes`1`n`(_$)->_$`dPAdicRationalConstructor(p,PADIC)``892677 -oremoveZeroes`1`x`(_$)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``893241 +oremoveZeroes`1`x`(_$)->_$`cLocalPowerSeriesCategory(K)``1083945 +oremoveZeroes`1`x`(_$)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1084011 oremoveZeroes`2`n`(Integer,_$)->_$`dBalancedPAdicRational(p)``0 +oremoveZeroes`2`n`(Integer,_$)->_$`dPAdicRationalConstructor(p,PADIC)``1084554 oremoveZeroes`2`n`(Integer,_$)->_$`dPAdicRational(p)``0 -oremoveZeroes`2`n`(Integer,_$)->_$`dPAdicRationalConstructor(p,PADIC)``893780 -oremoveZeroes`2`x`(Integer,_$)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``893894 -oremove`2`n`((S)->Boolean,A)->A`xCollection&(A,S)``0 -oremove`2`n`((S)->Boolean,A)->A`xExtensibleLinearAggregate&(A,S)``0 -oremove`2`n`(S,A)->A`xCollection&(A,S)``0 -oremove`2`n`(S,A)->A`xExtensibleLinearAggregate&(A,S)``0 -oremove`2`n`(SplittingNode(V,C),_$)->_$`dSplittingTree(V,C)``894360 -oremove`2`x`((S)->Boolean,_$)->_$`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`894583 -oremove`2`x`((S)->Boolean,_$)->_$`cLazyStreamAggregate(S)``894836 -oremove`2`x`(S,_$)->_$`cCollection(S)`AND(has(_$,ATTRIBUTE(finiteAggregate)),has(S,SetCategory))`895034 -oremove`3`x`((S)->Boolean,_$,Integer)->_$`dMultiset(S)``895263 -oremove`3`x`(S,_$,Integer)->_$`dMultiset(S)``895547 -orename!`2`x`(_$,OutputForm)->_$`cRealClosedField``895783 -orename`2`x`(_$,OutputForm)->_$`cRealClosedField``895867 -oreopen!`2`x`(_$,String)->_$`cFileCategory(Name,S)``895945 -oreorder`2`n`(_$,List(Integer))->_$`dDistributedMultivariatePolynomial(vl,R)``896137 -oreorder`2`n`(_$,List(Integer))->_$`dGeneralDistributedMultivariatePolynomial(vl,R,E)``896281 -oreorder`2`n`(_$,List(Integer))->_$`dHomogeneousDistributedMultivariatePolynomial(vl,R)``896425 -orepSq`2`n`(Vector(GF),NonNegativeInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``896569 -orepeatUntilLoop`2`x`(Switch,_$)->_$`dFortranCode``896702 -orepeating?`2`x`(List(S),_$)->Boolean`dStream(S)`has(S,SetCategory)`896783 -orepeating`1`x`(List(S))->_$`dStream(S)``896920 -oreplaceKthElement`3`n`(_$,PositiveInteger,PositiveInteger)->Union(_$,"failed")`dSetOfMIntegersInOneToN(m,n)``897004 -oreplace`3`x`(_$,UniversalSegment(Integer),_$)->_$`cStringAggregate``897203 -orepresentationType`0`x`()->Union("prime","polynomial","normal","cyclic")`cFiniteFieldCategory``897331 -orepresents`1`n`(Vector(F))->S`xFiniteAlgebraicExtensionField&(S,F)``0 +oremoveZeroes`2`x`(Integer,_$)->_$`cLocalPowerSeriesCategory(K)``1084668 +oremoveZeroes`2`x`(Integer,_$)->_$`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1084766 +orename!`2`x`(_$,OutputForm)->_$`cRealClosedField``1085232 +orename`2`x`(_$,OutputForm)->_$`cRealClosedField``1085316 +oreopen!`2`x`(_$,String)->_$`cFileCategory(Name,S)``1085394 +oreorder`2`n`(_$,List(Integer))->_$`dDistributedMultivariatePolynomial(vl,R)``1085586 +oreorder`2`n`(_$,List(Integer))->_$`dGeneralDistributedMultivariatePolynomial(vl,R,E)``1085730 +oreorder`2`n`(_$,List(Integer))->_$`dHomogeneousDistributedMultivariatePolynomial(vl,R)``1085874 +orepeating`1`x`(List(S))->_$`dStream(S)``1086018 +orepeating?`2`x`(List(S),_$)->Boolean`dStream(S)`has(S,SetCategory)`1086178 +orepeatUntilLoop`2`x`(Switch,_$)->_$`dFortranCode``1086465 +oreplace`3`x`(_$,UniversalSegment(Integer),_$)->_$`cStringAggregate``1086546 +oreplaceDiffs`3`x`(F,BasicOperator,Symbol)->F`pExpressionSolve(R,F,UTSF,UTSSUPF)``0 +oreplaceKthElement`3`n`(_$,PositiveInteger,PositiveInteger)->Union(_$,"failed")`dSetOfMIntegersInOneToN(m,n)``1086674 +oreplaceVarByOne`2`x`(PolyRing,Integer)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``1086873 +oreplaceVarByZero`2`x`(PolyRing,Integer)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``1086983 +orepresentationType`0`x`()->Union("prime","polynomial","normal","cyclic")`cFiniteFieldCategory``1087095 orepresents`1`n`(Vector(Fraction(UP)))->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 +orepresents`1`n`(Vector(F))->S`xFiniteAlgebraicExtensionField&(S,F)``0 orepresents`1`n`(Vector(R))->S`xFramedAlgebra&(S,R,UP)``0 orepresents`1`n`(Vector(R))->S`xFramedNonAssociativeAlgebra&(S,R)``0 -orepresents`1`x`(Vector(F))->_$`cFiniteAlgebraicExtensionField(F)``897488 -orepresents`1`x`(Vector(R))->_$`cFramedAlgebra(R,UP)``897638 -orepresents`1`x`(Vector(R))->_$`cFramedNonAssociativeAlgebra(R)``897790 +orepresents`1`x`(Vector(F))->_$`cFiniteAlgebraicExtensionField(F)``1087252 +orepresents`1`x`(Vector(R))->_$`cFramedAlgebra(R,UP)``1087402 +orepresents`1`x`(Vector(R))->_$`cFramedNonAssociativeAlgebra(R)``1087554 orepresents`2`n`(Vector(Fraction(UP)),Vector(S))->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 orepresents`2`n`(Vector(R),Vector(S))->S`xFiniteRankAlgebra&(S,R,UP)``0 orepresents`2`n`(Vector(R),Vector(S))->S`xFiniteRankNonAssociativeAlgebra&(S,R)``0 orepresents`2`n`(Vector(R),Vector(S))->S`xFramedAlgebra&(S,R,UP)``0 orepresents`2`n`(Vector(R),Vector(S))->S`xFramedNonAssociativeAlgebra&(S,R)``0 orepresents`2`n`(Vector(UP),UP)->S`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -orepresents`2`x`(Vector(R),Vector(_$))->_$`cFiniteRankAlgebra(R,UP)``897959 -orepresents`2`x`(Vector(R),Vector(_$))->_$`cFiniteRankNonAssociativeAlgebra(R)``898053 -orepresents`2`x`(Vector(UP),UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``898172 -orepresents`2`x`(Vector(UP),UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``898274 -oreseed`1`x`(Integer)->Void`pRandomNumberSource``898376 -oresetAttributeButtons`0`x`()->Void`dAttributeButtons``898450 -oresetBadValues`1`n`(_$)->_$`dPattern(R)``898538 -oresetNew`0`x`()->Void`dSymbol``898698 -oresetVariableOrder`0`x`()->Void`pUserDefinedVariableOrdering``898825 -oreset`1`n`(_$)->Void`dTwoDimensionalViewport``898949 -oreset`1`x`(_$)->Void`dThreeDimensionalViewport``899165 -oreshape`2`x`(List(S),PR)->PS`pMPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS)``899385 -oreshape`2`x`(List(T),CartesianTensor(minix,dim,S))->CartesianTensor(minix,dim,T)`pCartesianTensorFunctions2(minix,dim,S,T)``899428 -oresize`3`n`(_$,PositiveInteger,PositiveInteger)->Void`dTwoDimensionalViewport``899550 -oresize`3`x`(_$,PositiveInteger,PositiveInteger)->Void`dThreeDimensionalViewport``899799 +orepresents`2`x`(Vector(R),Vector(_$))->_$`cFiniteRankAlgebra(R,UP)``1087723 +orepresents`2`x`(Vector(R),Vector(_$))->_$`cFiniteRankNonAssociativeAlgebra(R)``1087813 +orepresents`2`x`(Vector(UP),UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``1087932 +orepresents`2`x`(Vector(UP),UP)->_$`cFunctionFieldCategory(F,UP,UPUP)``1088034 +orepSq`2`n`(Vector(GF),NonNegativeInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``1088136 +oreseed`1`x`(Integer)->Void`pRandomNumberSource``1088269 +oreset`0`x`()->Void`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +oreset`1`n`(_$)->Void`dTwoDimensionalViewport``1088343 +oreset`1`x`(_$)->Void`dThreeDimensionalViewport``1088559 +oresetAttributeButtons`0`x`()->Void`dAttributeButtons``1088779 +oresetBadValues`1`n`(_$)->_$`dPattern(R)``1088867 +oresetNew`0`x`()->Void`dSymbol``1089027 +oresetVariableOrder`0`x`()->Void`pUserDefinedVariableOrdering``1089154 +oreshape`2`x`(List(S),PR)->PS`pMPolyCatFunctions2(VarSet,E1,E2,R,S,PR,PS)``1089278 +oreshape`2`x`(List(T),CartesianTensor(minix,dim,S))->CartesianTensor(minix,dim,T)`pCartesianTensorFunctions2(minix,dim,S,T)``1089321 +oresize`3`n`(_$,PositiveInteger,PositiveInteger)->Void`dTwoDimensionalViewport``1089443 +oresize`3`x`(_$,PositiveInteger,PositiveInteger)->Void`dThreeDimensionalViewport``1089692 orest`1`n`(A)->A`xLazyStreamAggregate&(A,S)``0 orest`1`n`(A)->A`xUnaryRecursiveAggregate&(A,S)``0 +orest`1`n`(_$)->_$`dMagma(VarSet)``1089945 +orest`1`n`(_$)->_$`dOrderedFreeMonoid(S)``1090074 +orest`1`n`(_$)->_$`dPoincareBirkhoffWittLyndonBasis(VarSet)``1090228 orest`1`n`(S)->Union(S,"failed")`xTriangularSetCategory&(S,R,E,V,P)``0 -orest`1`n`(_$)->_$`dMagma(VarSet)``900052 -orest`1`n`(_$)->_$`dOrderedFreeMonoid(S)``900210 -orest`1`n`(_$)->_$`dPoincareBirkhoffWittLyndonBasis(VarSet)``900274 -orest`1`x`(_$)->Union(_$,"failed")`cTriangularSetCategory(R,E,V,P)``900351 -orest`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``900547 +orest`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``1090305 +orest`1`x`(_$)->Union(_$,"failed")`cTriangularSetCategory(R,E,V,P)``1090445 orest`2`n`(A,NonNegativeInteger)->A`xLazyStreamAggregate&(A,S)``0 orest`2`n`(A,NonNegativeInteger)->A`xUnaryRecursiveAggregate&(A,S)``0 -orest`2`x`(_$,NonNegativeInteger)->_$`cUnaryRecursiveAggregate(S)``900687 -orestorePrecision`0`x`()->Void`pNAGLinkSupportPackage``900830 -oresult`1`n`(_$)->List(Record(val:V,tower:C))`dSplittingTree(V,C)``900879 -oresultantEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``901130 -oresultantEuclideannaif`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``901269 -oresultantReduitEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultantReduit:R)`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`901443 -oresultantReduit`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`901630 -oresultant`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)``901755 -oresultant`2`x`(_$,_$)->R`cUnivariatePolynomialCategory(R)`has(R,CommutativeRing)`901865 -oresultant`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`901960 +orest`2`x`(_$,NonNegativeInteger)->_$`cUnaryRecursiveAggregate(S)``1090641 +orestorePrecision`0`x`()->Void`pNAGLinkSupportPackage``1090788 +oresult`1`n`(_$)->List(Record(val:V,tower:C))`dSplittingTree(V,C)``1090837 +oresultant`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)``1091088 +oresultant`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1091198 +oresultant`2`x`(_$,_$)->R`cUnivariatePolynomialCategory(R)`has(R,CommutativeRing)`1091453 oresultant`3`n`(S,S,VarSet)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -oresultant`3`x`(_$,_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,CommutativeRing)`902215 -oresultantnaif`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)``902352 +oresultant`3`x`(_$,_$,VarSet)->_$`cPolynomialCategory(R,E,VarSet)`has(R,CommutativeRing)`1091548 +oresultantEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``1091685 +oresultantEuclideannaif`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``1091824 +oresultantnaif`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)``1091998 +oresultantReduit`2`n`(polR,polR)->R`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`1092163 +oresultantReduitEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,resultantReduit:R)`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`1092288 +oretract`1`n`(A)->Fraction(Integer)`xFullyRetractableTo&(A,S)``0 +oretract`1`n`(A)->Fraction(Integer)`xQuotientFieldCategory&(A,S)``0 +oretract`1`n`(A)->Integer`xFullyRetractableTo&(A,S)``0 +oretract`1`n`(A)->Integer`xQuotientFieldCategory&(A,S)``0 +oretract`1`n`(A)->S`xDifferentialVariableCategory&(A,S)``0 +oretract`1`n`(A)->S`xFullyRetractableTo&(A,S)``0 +oretract`1`n`(A)->S`xQuotientFieldCategory&(A,S)``0 +oretract`1`n`(A)->S`xRetractableTo&(A,S)``0 +oretract`1`n`(A)->Symbol`xQuotientFieldCategory&(A,S)``0 +oretract`1`n`(Polynomial(Fraction(Integer)))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(Polynomial(Integer))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(Polynomial(R))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(S)->Fraction(Integer)`xComplexCategory&(S,R)``0 +oretract`1`n`(S)->Fraction(Integer)`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->Fraction(Integer)`xMonogenicAlgebra&(S,R,UP)``0 +oretract`1`n`(S)->Fraction(Integer)`xOctonionCategory&(S,R)``0 +oretract`1`n`(S)->Fraction(Integer)`xPolynomialCategory&(S,R,E,VarSet)``0 +oretract`1`n`(S)->Fraction(Integer)`xQuaternionCategory&(S,R)``0 +oretract`1`n`(S)->Fraction(Integer)`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(S)->Fraction(Integer)`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +oretract`1`n`(S)->Fraction(Integer)`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 +oretract`1`n`(S)->Fraction(Integer)`xUnivariatePolynomialCategory&(S,R)``0 +oretract`1`n`(S)->Fraction(Polynomial(R))`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->Integer`xComplexCategory&(S,R)``0 +oretract`1`n`(S)->Integer`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->Integer`xIntegerNumberSystem&(S)``0 +oretract`1`n`(S)->Integer`xMonogenicAlgebra&(S,R,UP)``0 +oretract`1`n`(S)->Integer`xOctonionCategory&(S,R)``0 +oretract`1`n`(S)->Integer`xPolynomialCategory&(S,R,E,VarSet)``0 +oretract`1`n`(S)->Integer`xQuaternionCategory&(S,R)``0 +oretract`1`n`(S)->Integer`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(S)->Integer`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +oretract`1`n`(S)->Integer`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 +oretract`1`n`(S)->Integer`xUnivariatePolynomialCategory&(S,R)``0 +oretract`1`n`(S)->Kernel(S)`xExpressionSpace&(S)``0 +oretract`1`n`(S)->Kernel(S)`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->Polynomial(R)`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->R`xComplexCategory&(S,R)``0 +oretract`1`n`(S)->R`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->R`xMonogenicAlgebra&(S,R,UP)``0 +oretract`1`n`(S)->R`xOctonionCategory&(S,R)``0 +oretract`1`n`(S)->R`xPolynomialCategory&(S,R,E,VarSet)``0 +oretract`1`n`(S)->R`xQuaternionCategory&(S,R)``0 +oretract`1`n`(S)->R`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`n`(S)->R`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 +oretract`1`n`(S)->R`xUnivariatePolynomialCategory&(S,R)``0 +oretract`1`n`(S)->SingletonAsOrderedSet`xUnivariatePolynomialCategory&(S,R)``0 +oretract`1`n`(S)->Symbol`xFunctionSpace&(S,R)``0 +oretract`1`n`(S)->Symbol`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 +oretract`1`n`(S)->ULS`xUnivariatePuiseuxSeriesConstructorCategory&(S,Coef,ULS)``0 +oretract`1`n`(S)->UTS`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 +oretract`1`n`(S)->VarSet`xPolynomialCategory&(S,R,E,VarSet)``0 +oretract`1`n`(S)->V`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretract`1`x`(Any)->S`pAnyFunctions1(S)``1092475 +oretract`1`x`(Expression(Float))->_$`cFortranFunctionCategory``1092639 +oretract`1`x`(Expression(Float))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1092763 +oretract`1`x`(Expression(Integer))->_$`cFortranFunctionCategory``1093036 +oretract`1`x`(Expression(Integer))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1093160 +oretract`1`x`(Expression(R))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1093433 +oretract`1`x`(_$)->Fraction(MyUnivariatePolynomial(q,R))`dMyExpression(q,R)``0 +oretract`1`x`(Fraction(Polynomial(Float)))->_$`cFortranFunctionCategory``1093706 +oretract`1`x`(Fraction(Polynomial(Float)))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1093830 +oretract`1`x`(Fraction(Polynomial(Integer)))->_$`cFortranFunctionCategory``1094103 +oretract`1`x`(Fraction(Polynomial(Integer)))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1094227 +oretract`1`x`(List(P))->_$`cPolynomialSetCategory(R,E,VarSet,P)``1094500 +oretract`1`x`(Matrix(Expression(Float)))->_$`cFortranMatrixFunctionCategory``1094680 +oretract`1`x`(Matrix(Expression(Integer)))->_$`cFortranMatrixFunctionCategory``1094804 +oretract`1`x`(Matrix(Fraction(Polynomial(Float))))->_$`cFortranMatrixFunctionCategory``1094928 +oretract`1`x`(Matrix(Fraction(Polynomial(Integer))))->_$`cFortranMatrixFunctionCategory``1095052 +oretract`1`x`(Matrix(Polynomial(Float)))->_$`cFortranMatrixFunctionCategory``1095176 +oretract`1`x`(Matrix(Polynomial(Integer)))->_$`cFortranMatrixFunctionCategory``1095300 +oretract`1`x`(Polynomial(Float))->_$`cFortranFunctionCategory``1095424 +oretract`1`x`(Polynomial(Float))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1095548 +oretract`1`x`(Polynomial(Fraction(Integer)))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`1095821 +oretract`1`x`(Polynomial(Integer))->_$`cFortranFunctionCategory``1096009 +oretract`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`1096133 +oretract`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`1096321 +oretract`1`x`(Polynomial(Integer))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1096509 +oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)),not(has(R,QuotientFieldCategory(Integer))))`1096782 +oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,IntegerNumberSystem)))`1096970 +oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,Algebra(Integer))))`1097158 +oretract`1`x`(_$)->Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat)`dNumericalPDEProblem``1097346 +oretract`1`x`(_$)->Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat)`dNumericalODEProblem``1097389 +oretract`1`x`(_$)->S`cRetractableTo(S)``1097432 +oretract`1`x`(Symbol)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1097567 +oretract`1`x`(_$)->Union(nia:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),mdnia:Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat))`dNumericalIntegrationProblem``1097786 +oretract`1`x`(_$)->Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))`dNumericalOptimizationProblem``1097829 +oretract`1`x`(UnivariateFormalPowerSeries(F))->_$`dNottinghamGroup(F)``0 +oretract`1`x`(Vector(Expression(Float)))->_$`cFortranVectorFunctionCategory``1097872 +oretract`1`x`(Vector(Expression(Integer)))->_$`cFortranVectorFunctionCategory``1097996 +oretract`1`x`(Vector(Fraction(Polynomial(Float))))->_$`cFortranVectorFunctionCategory``1098120 +oretract`1`x`(Vector(Fraction(Polynomial(Integer))))->_$`cFortranVectorFunctionCategory``1098244 +oretract`1`x`(Vector(Polynomial(Float)))->_$`cFortranVectorFunctionCategory``1098368 +oretract`1`x`(Vector(Polynomial(Integer)))->_$`cFortranVectorFunctionCategory``1098492 +oretractable?`1`n`(_$)->Boolean`dAntiSymm(R,lVar)``1098616 +oretractable?`1`n`(_$)->Boolean`dDeRhamComplex(CoefRing,listIndVar)``1098722 +oretractable?`1`n`(_$)->Boolean`dLyndonWord(VarSet)``1098849 +oretractable?`1`n`(_$)->Boolean`dMagma(VarSet)``1098944 +oretractable?`1`n`(_$)->Boolean`dPoincareBirkhoffWittLyndonBasis(VarSet)``1099039 +oretractable?`1`x`(Any)->Boolean`pAnyFunctions1(S)``1099135 oretractIfCan`1`n`(A)->Union(Fraction(Integer),"failed")`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 oretractIfCan`1`n`(A)->Union(Fraction(Integer),"failed")`xFullyRetractableTo&(A,S)``0 oretractIfCan`1`n`(A)->Union(Fraction(Integer),"failed")`xQuotientFieldCategory&(A,S)``0 @@ -7082,7 +8004,7 @@ oretractIfCan`1`n`(A)->Union(S,"failed")`xFullyRetractableTo&(A,S)``0 oretractIfCan`1`n`(A)->Union(S,"failed")`xQuotientFieldCategory&(A,S)``0 oretractIfCan`1`n`(A)->Union(Symbol,"failed")`xQuotientFieldCategory&(A,S)``0 oretractIfCan`1`n`(A)->Union(V,"failed")`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -oretractIfCan`1`n`(ExtP)->Union(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),"failed")`pNormRetractPackage(F,ExtF,SUEx,ExtP,n)``902517 +oretractIfCan`1`n`(ExtP)->Union(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),"failed")`pNormRetractPackage(F,ExtF,SUEx,ExtP,n)``1099233 oretractIfCan`1`n`(List(P))->Union(S,"failed")`xTriangularSetCategory&(S,R,E,V,P)``0 oretractIfCan`1`n`(Polynomial(Fraction(Integer)))->Union(S,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 oretractIfCan`1`n`(Polynomial(Integer))->Union(S,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 @@ -7129,2255 +8051,2338 @@ oretractIfCan`1`n`(S)->Union(Symbol,"failed")`xFunctionSpace&(S,R)``0 oretractIfCan`1`n`(S)->Union(Symbol,"failed")`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 oretractIfCan`1`n`(S)->Union(ULS,"failed")`xUnivariatePuiseuxSeriesConstructorCategory&(S,Coef,ULS)``0 oretractIfCan`1`n`(S)->Union(UTS,"failed")`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 -oretractIfCan`1`n`(S)->Union(V,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 oretractIfCan`1`n`(S)->Union(VarSet,"failed")`xPolynomialCategory&(S,R,E,VarSet)``0 -oretractIfCan`1`x`(Any)->Union(S,"failed")`pAnyFunctions1(S)``902561 -oretractIfCan`1`x`(Expression(Float))->Union(_$,"failed")`cFortranFunctionCategory``902727 -oretractIfCan`1`x`(Expression(Float))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`902856 -oretractIfCan`1`x`(Expression(Integer))->Union(_$,"failed")`cFortranFunctionCategory``903198 -oretractIfCan`1`x`(Expression(Integer))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`903327 -oretractIfCan`1`x`(Expression(R))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)``903669 -oretractIfCan`1`x`(Fraction(Polynomial(Float)))->Union(_$,"failed")`cFortranFunctionCategory``904011 -oretractIfCan`1`x`(Fraction(Polynomial(Float)))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`904140 -oretractIfCan`1`x`(Fraction(Polynomial(Integer)))->Union(_$,"failed")`cFortranFunctionCategory``904482 -oretractIfCan`1`x`(Fraction(Polynomial(Integer)))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`904611 -oretractIfCan`1`x`(List(P))->Union(_$,"failed")`cPolynomialSetCategory(R,E,VarSet,P)``904953 -oretractIfCan`1`x`(Matrix(Expression(Float)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905146 -oretractIfCan`1`x`(Matrix(Expression(Integer)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905275 -oretractIfCan`1`x`(Matrix(Fraction(Polynomial(Float))))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905404 -oretractIfCan`1`x`(Matrix(Fraction(Polynomial(Integer))))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905533 -oretractIfCan`1`x`(Matrix(Polynomial(Float)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905662 -oretractIfCan`1`x`(Matrix(Polynomial(Integer)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``905791 -oretractIfCan`1`x`(Polynomial(Float))->Union(_$,"failed")`cFortranFunctionCategory``905920 -oretractIfCan`1`x`(Polynomial(Float))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`906049 -oretractIfCan`1`x`(Polynomial(Fraction(Integer)))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`906391 -oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cFortranFunctionCategory``906539 -oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`906668 -oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`906816 -oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`906964 -oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)),not(has(R,QuotientFieldCategory(Integer))))`907306 -oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,IntegerNumberSystem)))`907454 -oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,Algebra(Integer))))`907602 -oretractIfCan`1`x`(Symbol)->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)``907750 -oretractIfCan`1`x`(Vector(Expression(Float)))->Union(_$,"failed")`cFortranVectorFunctionCategory``908024 -oretractIfCan`1`x`(Vector(Expression(Integer)))->Union(_$,"failed")`cFortranVectorFunctionCategory``908153 -oretractIfCan`1`x`(Vector(Fraction(Polynomial(Float))))->Union(_$,"failed")`cFortranVectorFunctionCategory``908282 -oretractIfCan`1`x`(Vector(Fraction(Polynomial(Integer))))->Union(_$,"failed")`cFortranVectorFunctionCategory``908411 -oretractIfCan`1`x`(Vector(Polynomial(Float)))->Union(_$,"failed")`cFortranVectorFunctionCategory``908540 -oretractIfCan`1`x`(Vector(Polynomial(Integer)))->Union(_$,"failed")`cFortranVectorFunctionCategory``908669 -oretractIfCan`1`x`(_$)->Union(S,"failed")`cRetractableTo(S)``908798 -oretract`1`n`(A)->Fraction(Integer)`xFullyRetractableTo&(A,S)``0 -oretract`1`n`(A)->Fraction(Integer)`xQuotientFieldCategory&(A,S)``0 -oretract`1`n`(A)->Integer`xFullyRetractableTo&(A,S)``0 -oretract`1`n`(A)->Integer`xQuotientFieldCategory&(A,S)``0 -oretract`1`n`(A)->S`xDifferentialVariableCategory&(A,S)``0 -oretract`1`n`(A)->S`xFullyRetractableTo&(A,S)``0 -oretract`1`n`(A)->S`xQuotientFieldCategory&(A,S)``0 -oretract`1`n`(A)->S`xRetractableTo&(A,S)``0 -oretract`1`n`(A)->Symbol`xQuotientFieldCategory&(A,S)``0 -oretract`1`n`(Polynomial(Fraction(Integer)))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(Polynomial(Integer))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(Polynomial(R))->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(S)->Fraction(Integer)`xComplexCategory&(S,R)``0 -oretract`1`n`(S)->Fraction(Integer)`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->Fraction(Integer)`xMonogenicAlgebra&(S,R,UP)``0 -oretract`1`n`(S)->Fraction(Integer)`xOctonionCategory&(S,R)``0 -oretract`1`n`(S)->Fraction(Integer)`xPolynomialCategory&(S,R,E,VarSet)``0 -oretract`1`n`(S)->Fraction(Integer)`xQuaternionCategory&(S,R)``0 -oretract`1`n`(S)->Fraction(Integer)`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(S)->Fraction(Integer)`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -oretract`1`n`(S)->Fraction(Integer)`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 -oretract`1`n`(S)->Fraction(Integer)`xUnivariatePolynomialCategory&(S,R)``0 -oretract`1`n`(S)->Fraction(Polynomial(R))`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->Integer`xComplexCategory&(S,R)``0 -oretract`1`n`(S)->Integer`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->Integer`xIntegerNumberSystem&(S)``0 -oretract`1`n`(S)->Integer`xMonogenicAlgebra&(S,R,UP)``0 -oretract`1`n`(S)->Integer`xOctonionCategory&(S,R)``0 -oretract`1`n`(S)->Integer`xPolynomialCategory&(S,R,E,VarSet)``0 -oretract`1`n`(S)->Integer`xQuaternionCategory&(S,R)``0 -oretract`1`n`(S)->Integer`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(S)->Integer`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -oretract`1`n`(S)->Integer`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 -oretract`1`n`(S)->Integer`xUnivariatePolynomialCategory&(S,R)``0 -oretract`1`n`(S)->Kernel(S)`xExpressionSpace&(S)``0 -oretract`1`n`(S)->Kernel(S)`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->Polynomial(R)`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->R`xComplexCategory&(S,R)``0 -oretract`1`n`(S)->R`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->R`xMonogenicAlgebra&(S,R,UP)``0 -oretract`1`n`(S)->R`xOctonionCategory&(S,R)``0 -oretract`1`n`(S)->R`xPolynomialCategory&(S,R,E,VarSet)``0 -oretract`1`n`(S)->R`xQuaternionCategory&(S,R)``0 -oretract`1`n`(S)->R`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(S)->R`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -oretract`1`n`(S)->R`xUnivariatePolynomialCategory&(S,R)``0 -oretract`1`n`(S)->SingletonAsOrderedSet`xUnivariatePolynomialCategory&(S,R)``0 -oretract`1`n`(S)->Symbol`xFunctionSpace&(S,R)``0 -oretract`1`n`(S)->Symbol`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 -oretract`1`n`(S)->ULS`xUnivariatePuiseuxSeriesConstructorCategory&(S,Coef,ULS)``0 -oretract`1`n`(S)->UTS`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 -oretract`1`n`(S)->V`xRecursivePolynomialCategory&(S,R,E,V)``0 -oretract`1`n`(S)->VarSet`xPolynomialCategory&(S,R,E,VarSet)``0 -oretract`1`x`(Any)->S`pAnyFunctions1(S)``908948 -oretract`1`x`(Expression(Float))->_$`cFortranFunctionCategory``909112 -oretract`1`x`(Expression(Float))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`909236 -oretract`1`x`(Expression(Integer))->_$`cFortranFunctionCategory``909565 -oretract`1`x`(Expression(Integer))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`909689 -oretract`1`x`(Expression(R))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``910018 -oretract`1`x`(Fraction(Polynomial(Float)))->_$`cFortranFunctionCategory``910347 -oretract`1`x`(Fraction(Polynomial(Float)))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`910471 -oretract`1`x`(Fraction(Polynomial(Integer)))->_$`cFortranFunctionCategory``910800 -oretract`1`x`(Fraction(Polynomial(Integer)))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`910924 -oretract`1`x`(List(P))->_$`cPolynomialSetCategory(R,E,VarSet,P)``911253 -oretract`1`x`(Matrix(Expression(Float)))->_$`cFortranMatrixFunctionCategory``911433 -oretract`1`x`(Matrix(Expression(Integer)))->_$`cFortranMatrixFunctionCategory``911557 -oretract`1`x`(Matrix(Fraction(Polynomial(Float))))->_$`cFortranMatrixFunctionCategory``911681 -oretract`1`x`(Matrix(Fraction(Polynomial(Integer))))->_$`cFortranMatrixFunctionCategory``911805 -oretract`1`x`(Matrix(Polynomial(Float)))->_$`cFortranMatrixFunctionCategory``911929 -oretract`1`x`(Matrix(Polynomial(Integer)))->_$`cFortranMatrixFunctionCategory``912053 -oretract`1`x`(Polynomial(Float))->_$`cFortranFunctionCategory``912177 -oretract`1`x`(Polynomial(Float))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`912301 -oretract`1`x`(Polynomial(Fraction(Integer)))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`912630 -oretract`1`x`(Polynomial(Integer))->_$`cFortranFunctionCategory``912818 -oretract`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`912942 -oretract`1`x`(Polynomial(Integer))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`913130 -oretract`1`x`(Polynomial(Integer))->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`913318 -oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)),not(has(R,QuotientFieldCategory(Integer))))`913647 -oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,IntegerNumberSystem)))`913835 -oretract`1`x`(Polynomial(R))->_$`cRecursivePolynomialCategory(R,E,V)`AND(has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,Algebra(Integer))))`914023 -oretract`1`x`(Symbol)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``914211 -oretract`1`x`(Vector(Expression(Float)))->_$`cFortranVectorFunctionCategory``914472 -oretract`1`x`(Vector(Expression(Integer)))->_$`cFortranVectorFunctionCategory``914596 -oretract`1`x`(Vector(Fraction(Polynomial(Float))))->_$`cFortranVectorFunctionCategory``914720 -oretract`1`x`(Vector(Fraction(Polynomial(Integer))))->_$`cFortranVectorFunctionCategory``914844 -oretract`1`x`(Vector(Polynomial(Float)))->_$`cFortranVectorFunctionCategory``914968 -oretract`1`x`(Vector(Polynomial(Integer)))->_$`cFortranVectorFunctionCategory``915092 -oretract`1`x`(_$)->Record(pde:List(Expression(DoubleFloat)),constraints:List(Record(start:DoubleFloat,finish:DoubleFloat,grid:NonNegativeInteger,boundaryType:Integer,dStart:Matrix(DoubleFloat),dFinish:Matrix(DoubleFloat))),f:List(List(Expression(DoubleFloat))),st:String,tol:DoubleFloat)`dNumericalPDEProblem``915216 -oretract`1`x`(_$)->Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat)`dNumericalODEProblem``915257 -oretract`1`x`(_$)->S`cRetractableTo(S)``915298 -oretract`1`x`(_$)->Union(nia:Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat),mdnia:Record(fn:Expression(DoubleFloat),range:List(Segment(OrderedCompletion(DoubleFloat))),abserr:DoubleFloat,relerr:DoubleFloat))`dNumericalIntegrationProblem``915433 -oretract`1`x`(_$)->Union(noa:Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))),lsa:Record(lfn:List(Expression(DoubleFloat)),init:List(DoubleFloat)))`dNumericalOptimizationProblem``915474 -oretractable?`1`n`(_$)->Boolean`dAntiSymm(R,lVar)``915515 -oretractable?`1`n`(_$)->Boolean`dDeRhamComplex(CoefRing,listIndVar)``915621 -oretractable?`1`n`(_$)->Boolean`dLyndonWord(VarSet)``915748 -oretractable?`1`n`(_$)->Boolean`dMagma(VarSet)``915843 -oretractable?`1`n`(_$)->Boolean`dPoincareBirkhoffWittLyndonBasis(VarSet)``915938 -oretractable?`1`x`(Any)->Boolean`pAnyFunctions1(S)``916034 -oreturnType!`1`x`(Union(fst:FortranScalarType,void:"void"))->Void`dTheSymbolTable``916132 -oreturnType!`2`x`(Symbol,Union(fst:FortranScalarType,void:"void"))->Void`dTheSymbolTable``916256 -oreturnType!`3`x`(Symbol,Union(fst:FortranScalarType,void:"void"),_$)->Void`dTheSymbolTable``916382 -oreturnTypeOf`2`x`(Symbol,_$)->Union(fst:FortranScalarType,void:"void")`dTheSymbolTable``916514 -oreturns`0`x`()->_$`dFortranCode``916602 -oreturns`1`x`(Expression(Complex(Float)))->_$`dFortranCode``916682 -oreturns`1`x`(Expression(Float))->_$`dFortranCode``916785 -oreturns`1`x`(Expression(Integer))->_$`dFortranCode``916888 -oreturns`1`x`(Expression(MachineComplex))->_$`dFortranCode``916991 -oreturns`1`x`(Expression(MachineFloat))->_$`dFortranCode``917094 -oreturns`1`x`(Expression(MachineInteger))->_$`dFortranCode``917197 +oretractIfCan`1`n`(S)->Union(V,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 +oretractIfCan`1`x`(Any)->Union(S,"failed")`pAnyFunctions1(S)``1099277 +oretractIfCan`1`x`(Expression(Float))->Union(_$,"failed")`cFortranFunctionCategory``1099443 +oretractIfCan`1`x`(Expression(Float))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1099572 +oretractIfCan`1`x`(Expression(Integer))->Union(_$,"failed")`cFortranFunctionCategory``1099858 +oretractIfCan`1`x`(Expression(Integer))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1099987 +oretractIfCan`1`x`(Expression(R))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1100273 +oretractIfCan`1`x`(Fraction(Polynomial(Float)))->Union(_$,"failed")`cFortranFunctionCategory``1100559 +oretractIfCan`1`x`(Fraction(Polynomial(Float)))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1100688 +oretractIfCan`1`x`(Fraction(Polynomial(Integer)))->Union(_$,"failed")`cFortranFunctionCategory``1100974 +oretractIfCan`1`x`(Fraction(Polynomial(Integer)))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1101103 +oretractIfCan`1`x`(List(P))->Union(_$,"failed")`cPolynomialSetCategory(R,E,VarSet,P)``1101389 +oretractIfCan`1`x`(Matrix(Expression(Float)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1101582 +oretractIfCan`1`x`(Matrix(Expression(Integer)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1101711 +oretractIfCan`1`x`(Matrix(Fraction(Polynomial(Float))))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1101840 +oretractIfCan`1`x`(Matrix(Fraction(Polynomial(Integer))))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1101969 +oretractIfCan`1`x`(Matrix(Polynomial(Float)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1102098 +oretractIfCan`1`x`(Matrix(Polynomial(Integer)))->Union(_$,"failed")`cFortranMatrixFunctionCategory``1102227 +oretractIfCan`1`x`(Polynomial(Float))->Union(_$,"failed")`cFortranFunctionCategory``1102356 +oretractIfCan`1`x`(Polynomial(Float))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Float))`1102485 +oretractIfCan`1`x`(Polynomial(Fraction(Integer)))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`1102771 +oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cFortranFunctionCategory``1102919 +oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)))`1103048 +oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))))`1103196 +oretractIfCan`1`x`(Polynomial(Integer))->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)`has(R,RetractableTo(Integer))`1103344 +oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Fraction(Integer))),has(V,ConvertibleTo(Symbol)),not(has(R,QuotientFieldCategory(Integer))))`1103630 +oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(R,Algebra(Integer)),has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,IntegerNumberSystem)))`1103778 +oretractIfCan`1`x`(Polynomial(R))->Union(_$,"failed")`cRecursivePolynomialCategory(R,E,V)`AND(has(V,ConvertibleTo(Symbol)),not(has(R,Algebra(Fraction(Integer)))),not(has(R,Algebra(Integer))))`1103926 +oretractIfCan`1`x`(Symbol)->Union(_$,"failed")`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1104074 +oretractIfCan`1`x`(_$)->Union(S,"failed")`cRetractableTo(S)``1104306 +oretractIfCan`1`x`(Vector(Expression(Float)))->Union(_$,"failed")`cFortranVectorFunctionCategory``1104456 +oretractIfCan`1`x`(Vector(Expression(Integer)))->Union(_$,"failed")`cFortranVectorFunctionCategory``1104585 +oretractIfCan`1`x`(Vector(Fraction(Polynomial(Float))))->Union(_$,"failed")`cFortranVectorFunctionCategory``1104714 +oretractIfCan`1`x`(Vector(Fraction(Polynomial(Integer))))->Union(_$,"failed")`cFortranVectorFunctionCategory``1104843 +oretractIfCan`1`x`(Vector(Polynomial(Float)))->Union(_$,"failed")`cFortranVectorFunctionCategory``1104972 +oretractIfCan`1`x`(Vector(Polynomial(Integer)))->Union(_$,"failed")`cFortranVectorFunctionCategory``1105101 +oretractToGrn`1`x`(_$)->PseudoAlgebraicClosureOfRationalNumber`dPseudoAlgebraicClosureOfAlgExtOfRationalNumber(downLevel)``0 +oreturns`0`x`()->_$`dFortranCode``1105230 +oreturns`1`x`(Expression(Complex(Float)))->_$`dFortranCode``1105310 +oreturns`1`x`(Expression(Float))->_$`dFortranCode``1105413 +oreturns`1`x`(Expression(Integer))->_$`dFortranCode``1105516 +oreturns`1`x`(Expression(MachineComplex))->_$`dFortranCode``1105619 +oreturns`1`x`(Expression(MachineFloat))->_$`dFortranCode``1105722 +oreturns`1`x`(Expression(MachineInteger))->_$`dFortranCode``1105825 +oreturnType!`1`x`(Union(fst:FortranScalarType,void:"void"))->Void`dTheSymbolTable``1105928 +oreturnType!`2`x`(Symbol,Union(fst:FortranScalarType,void:"void"))->Void`dTheSymbolTable``1106052 +oreturnType!`3`x`(Symbol,Union(fst:FortranScalarType,void:"void"),_$)->Void`dTheSymbolTable``1106178 +oreturnTypeOf`2`x`(Symbol,_$)->Union(fst:FortranScalarType,void:"void")`dTheSymbolTable``1106310 +oreverse`1`n`(A)->A`xFiniteLinearAggregate&(A,S)``0 oreverse!`1`n`(A)->A`xListAggregate&(A,S)``0 oreverse!`1`n`(A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -oreverse!`1`n`(_$)->_$`dListMonoidOps(S,E,un)``917300 -oreverse!`1`x`(_$)->_$`cDequeueAggregate(S)``917410 -oreverse!`1`x`(_$)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`917583 -oreverseLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``917662 -oreverse`1`n`(A)->A`xFiniteLinearAggregate&(A,S)``0 -oreverse`1`n`(UP)->UP`pGaloisGroupPolynomialUtilities(R,UP)``917858 -oreverse`1`n`(_$)->_$`dListMonoidOps(S,E,un)``917927 -oreverse`1`x`(_$)->_$`cFiniteLinearAggregate(S)``918146 -orevert`1`n`(Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``918231 -orevert`1`n`(_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``918409 +oreverse!`1`n`(_$)->_$`dListMonoidOps(S,E,un)``1106398 +oreverse`1`n`(_$)->_$`dListMonoidOps(S,E,un)``1106508 +oreverse`1`n`(UP)->UP`pGaloisGroupPolynomialUtilities(R,UP)``1106727 +oreverse!`1`x`(_$)->_$`cDequeueAggregate(S)``1106796 +oreverse!`1`x`(_$)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1106969 +oreverse`1`x`(_$)->_$`cFiniteLinearAggregate(S)``1107048 +oreverse!`1`x`(_$)->_$`dDequeue(S)``1107133 +oreverseLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``1107235 +orevert`1`n`(_$)->_$`dUnivariateTaylorSeries(Coef,var,cen)``1107431 +orevert`1`n`(Stream(A))->Stream(A)`pStreamTaylorSeriesOperations(A)``1107617 +orevert`1`x`(_$)->_$`dUnivariateFormalPowerSeries(Coef)``0 +orevert`1`x`(_$)->_$`dUnivariateTaylorSeriesCZero(Coef,var)``1107795 orewriteIdealWithHeadRemainder`2`n`(List(P),S)->List(P)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -orewriteIdealWithHeadRemainder`2`x`(List(P),_$)->List(P)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`918595 -orewriteIdealWithQuasiMonicGenerators`3`n`(List(P),(P,P)->Boolean,(P,P)->P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``918999 +orewriteIdealWithHeadRemainder`2`x`(List(P),_$)->List(P)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`1107981 +orewriteIdealWithQuasiMonicGenerators`3`n`(List(P),(P,P)->Boolean,(P,P)->P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1108385 orewriteIdealWithRemainder`2`n`(List(P),S)->List(P)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -orewriteIdealWithRemainder`2`x`(List(P),_$)->List(P)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`919494 -orewriteSetByReducingWithParticularGenerators`4`n`(List(P),(P)->Boolean,(P,P)->Boolean,(P,P)->P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``919866 +orewriteIdealWithRemainder`2`x`(List(P),_$)->List(P)`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`1108880 +orewriteSetByReducingWithParticularGenerators`4`n`(List(P),(P)->Boolean,(P,P)->Boolean,(P,P)->P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1109252 orewriteSetWithReduction`4`n`(List(P),S,(P,P)->P,(P,P)->Boolean)->List(P)`xTriangularSetCategory&(S,R,E,V,P)``0 -orewriteSetWithReduction`4`x`(List(P),_$,(P,P)->P,(P,P)->Boolean)->List(P)`cTriangularSetCategory(R,E,V,P)``920489 -orhs`1`n`(_$)->S2`dSuchThat(S1,S2)``921571 -orhs`1`x`(_$)->F`dRewriteRule(Base,R,F)``921627 -orhs`1`x`(_$)->S`dEquation(S)``921698 -oricDsolve`1`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`921773 -oricDsolve`1`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`921887 -oricDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`922001 -oricDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->List(F))->List(Fraction(UP))`pRationalRicDE(F,UP)``922222 -oricDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`922389 -oricDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F))->List(Fraction(UP))`pRationalRicDE(F,UP)``922610 -oricDsolve`3`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->List(F),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)``922777 -oricDsolve`3`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)``923051 -oridHack1`4`n`(Integer,Integer,Integer,Integer)->Integer`pRandomIntegerDistributions``923325 -orightAlternative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``923377 -orightAlternative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``923602 +orewriteSetWithReduction`4`x`(List(P),_$,(P,P)->P,(P,P)->Boolean)->List(P)`cTriangularSetCategory(R,E,V,P)``1109875 +oRF2UTS`1`n`(Fraction(UP))->UTS`pUTSodetools(F,UP,L,UTS)`has(F,IntegralDomain)`1110957 +orhs`1`n`(_$)->S2`dSuchThat(S1,S2)``1111019 +orhs`1`x`(_$)->F`dRewriteRule(Base,R,F)``1111075 +orhs`1`x`(_$)->S`dEquation(S)``1111146 +oricDsolve`1`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`1111221 +oricDsolve`1`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`1111335 +oricDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`1111449 +oricDsolve`2`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->List(F))->List(Fraction(UP))`pRationalRicDE(F,UP)``1111670 +oricDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)`has(F,AlgebraicallyClosedField)`1111837 +oricDsolve`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F))->List(Fraction(UP))`pRationalRicDE(F,UP)``1112058 +oricDsolve`3`n`(LinearOrdinaryDifferentialOperator1(Fraction(UP)),(UP)->List(F),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)``1112225 +oricDsolve`3`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->List(F),(UP)->Factored(UP))->List(Fraction(UP))`pRationalRicDE(F,UP)``1112499 +oridHack1`4`n`(Integer,Integer,Integer,Integer)->Integer`pRandomIntegerDistributions``1112773 +oright`1`n`(_$)->_$`dLyndonWord(VarSet)``1112825 +oright`1`n`(_$)->_$`dMagma(VarSet)``1112949 +oright`1`n`(_$)->_$`dOutputForm``1113073 +oright`1`x`(_$)->_$`cBinaryRecursiveAggregate(S)``1113142 +oright`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``1113190 +oright`2`n`(_$,Integer)->_$`dOutputForm``1113266 +orightAlternative?`0`n`()->Boolean`xFiniteRankNonAssociativeAlgebra&(S,R)``1113355 +orightAlternative?`0`x`()->Boolean`cFiniteRankNonAssociativeAlgebra(R)``1113584 orightCharacteristicPolynomial`1`n`(S)->SparseUnivariatePolynomial(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 -orightCharacteristicPolynomial`1`x`(_$)->SparseUnivariatePolynomial(R)`cFiniteRankNonAssociativeAlgebra(R)``923827 -orightDiscriminant`0`n`()->R`xFramedNonAssociativeAlgebra&(S,R)``923987 -orightDiscriminant`0`x`()->R`cFramedNonAssociativeAlgebra(R)``924358 +orightCharacteristicPolynomial`1`x`(_$)->SparseUnivariatePolynomial(R)`cFiniteRankNonAssociativeAlgebra(R)``1113813 +orightDiscriminant`0`n`()->R`xFramedNonAssociativeAlgebra&(S,R)``1113973 +orightDiscriminant`0`x`()->R`cFramedNonAssociativeAlgebra(R)``1114348 orightDiscriminant`1`n`(Vector(S))->R`xFiniteRankNonAssociativeAlgebra&(S,R)``0 orightDiscriminant`1`n`(Vector(S))->R`xFramedNonAssociativeAlgebra&(S,R)``0 -orightDiscriminant`1`x`(Vector(_$))->R`cFiniteRankNonAssociativeAlgebra(R)``924729 -orightDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`925041 -orightDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,Field)`925249 +orightDiscriminant`1`x`(Vector(_$))->R`cFiniteRankNonAssociativeAlgebra(R)``1114723 +orightDivide`2`x`(_$,_$)->Record(quotient:_$,remainder:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1115047 +orightDivide`3`n`(C,C,Automorphism(R))->Record(quotient:C,remainder:C)`pUnivariateSkewPolynomialCategoryOps(R,C)`has(R,Field)`1115255 orightExactQuotient`2`n`(S,S)->Union(S,"failed")`xUnivariateSkewPolynomialCategory&(S,R)``0 -orightExactQuotient`2`x`(_$,_$)->Union(_$,"failed")`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`925505 +orightExactQuotient`2`x`(_$,_$)->Union(_$,"failed")`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1115511 orightExtendedGcd`2`n`(S,S)->Record(coef1:S,coef2:S,generator:S)`xUnivariateSkewPolynomialCategory&(S,R)``0 -orightExtendedGcd`2`x`(_$,_$)->Record(coef1:_$,coef2:_$,generator:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`925615 -orightFactorCandidate`2`x`(UP,NonNegativeInteger)->UP`pPolynomialDecomposition(UP,F)``925731 -orightFactorIfCan`3`n`(UP,NonNegativeInteger,R)->Union(UP,"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``925787 +orightExtendedGcd`2`x`(_$,_$)->Record(coef1:_$,coef2:_$,generator:_$)`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1115621 +orightFactorCandidate`2`x`(UP,NonNegativeInteger)->UP`pPolynomialDecomposition(UP,F)``1115737 +orightFactorIfCan`3`n`(UP,NonNegativeInteger,R)->Union(UP,"failed")`pUnivariatePolynomialDecompositionPackage(R,UP)``1115793 orightGcd`2`n`(S,S)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 -orightGcd`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`926075 +orightGcd`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1116081 orightLcm`2`n`(S,S)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 -orightLcm`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`926315 +orightLcm`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1116321 orightMinimalPolynomial`1`n`(S)->SparseUnivariatePolynomial(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 -orightMinimalPolynomial`1`x`(_$)->SparseUnivariatePolynomial(R)`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`926516 -orightMult`2`n`(_$,S)->_$`dListMonoidOps(S,E,un)``926752 +orightMinimalPolynomial`1`x`(_$)->SparseUnivariatePolynomial(R)`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1116522 +orightMult`2`n`(_$,S)->_$`dListMonoidOps(S,E,un)``1116762 orightNorm`1`n`(S)->R`xFiniteRankNonAssociativeAlgebra&(S,R)``0 -orightNorm`1`x`(_$)->R`cFiniteRankNonAssociativeAlgebra(R)``926881 -orightOne`1`x`(_$)->Union(_$,"failed")`dEquation(S)`has(S,Group)`926981 -orightOne`1`x`(_$)->Union(_$,"failed")`dEquation(S)`has(S,Monoid)`927040 +orightNorm`1`x`(_$)->R`cFiniteRankNonAssociativeAlgebra(R)``1116891 +orightOne`1`x`(_$)->Union(_$,"failed")`dEquation(S)`has(S,Group)`1116991 +orightOne`1`x`(_$)->Union(_$,"failed")`dEquation(S)`has(S,Monoid)`1117050 orightPower`2`n`(S,NonNegativeInteger)->S`xMonadWithUnit&(S)``0 orightPower`2`n`(S,PositiveInteger)->S`xMonad&(S)``0 orightPower`2`n`(S,PositiveInteger)->S`xMonadWithUnit&(S)``0 -orightPower`2`x`(_$,NonNegativeInteger)->_$`cMonadWithUnit``927099 -orightPower`2`x`(_$,PositiveInteger)->_$`cMonad``927294 +orightPower`2`x`(_$,NonNegativeInteger)->_$`cMonadWithUnit``1117109 +orightPower`2`x`(_$,PositiveInteger)->_$`cMonad``1117304 orightQuotient`2`n`(S,S)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 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+orightRankPolynomial`0`x`()->SparseUnivariatePolynomial(Polynomial(R))`cFramedNonAssociativeAlgebra(R)`has(R,Field)`1118194 orightRecip`1`n`(S)->Union(S,"failed")`xFiniteRankNonAssociativeAlgebra&(S,R)``0 -orightRecip`1`x`(_$)->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`928425 -orightRecip`1`x`(_$)->Union(_$,"failed")`cMonadWithUnit``928647 +orightRecip`1`x`(_$)->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1118435 +orightRecip`1`x`(_$)->Union(_$,"failed")`cMonadWithUnit``1118657 orightRegularRepresentation`1`n`(S)->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``0 -orightRegularRepresentation`1`x`(_$)->Matrix(R)`cFramedNonAssociativeAlgebra(R)``928838 +orightRegularRepresentation`1`x`(_$)->Matrix(R)`cFramedNonAssociativeAlgebra(R)``1118848 orightRegularRepresentation`2`n`(S,Vector(S))->Matrix(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 orightRegularRepresentation`2`n`(S,Vector(S))->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``0 -orightRegularRepresentation`2`x`(_$,Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``929012 +orightRegularRepresentation`2`x`(_$,Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``1119022 orightRemainder`2`n`(S,S)->S`xUnivariateSkewPolynomialCategory&(S,R)``0 -orightRemainder`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`929221 -orightScalarTimes!`3`n`(Matrix(R),Matrix(R),R)->Matrix(R)`pStorageEfficientMatrixOperations(R)``929415 -orightTraceMatrix`0`n`()->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``929610 -orightTraceMatrix`0`x`()->Matrix(R)`cFramedNonAssociativeAlgebra(R)``929898 +orightRemainder`2`x`(_$,_$)->_$`cUnivariateSkewPolynomialCategory(R)`has(R,Field)`1119231 +orightScalarTimes!`3`n`(Matrix(R),Matrix(R),R)->Matrix(R)`pStorageEfficientMatrixOperations(R)``1119425 +orightTrace`1`n`(S)->R`xFiniteRankNonAssociativeAlgebra&(S,R)``0 +orightTrace`1`x`(_$)->R`cFiniteRankNonAssociativeAlgebra(R)``1119620 +orightTraceMatrix`0`n`()->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``1119715 +orightTraceMatrix`0`x`()->Matrix(R)`cFramedNonAssociativeAlgebra(R)``1120003 orightTraceMatrix`1`n`(Vector(S))->Matrix(R)`xFiniteRankNonAssociativeAlgebra&(S,R)``0 orightTraceMatrix`1`n`(Vector(S))->Matrix(R)`xFramedNonAssociativeAlgebra&(S,R)``0 -orightTraceMatrix`1`x`(Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``930186 -orightTrace`1`n`(S)->R`xFiniteRankNonAssociativeAlgebra&(S,R)``0 -orightTrace`1`x`(_$)->R`cFiniteRankNonAssociativeAlgebra(R)``930400 -orightTrim`2`x`(_$,Character)->_$`cStringAggregate``930495 -orightTrim`2`x`(_$,CharacterClass)->_$`cStringAggregate``930672 +orightTraceMatrix`1`x`(Vector(_$))->Matrix(R)`cFiniteRankNonAssociativeAlgebra(R)``1120291 +orightTrim`2`x`(_$,CharacterClass)->_$`cStringAggregate``1120505 +orightTrim`2`x`(_$,Character)->_$`cStringAggregate``1120703 orightUnit`0`n`()->Union(S,"failed")`xFramedNonAssociativeAlgebra&(S,R)``0 -orightUnit`0`x`()->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`930870 +orightUnit`0`x`()->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1120880 +orightUnits`0`n`()->Union(Record(particular:_$,basis:List(_$)),"failed")`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``1121007 orightUnits`0`n`()->Union(Record(particular:S,basis:List(S)),"failed")`xFramedNonAssociativeAlgebra&(S,R)``0 -orightUnits`0`n`()->Union(Record(particular:_$,basis:List(_$)),"failed")`dGenericNonAssociativeAlgebra(R,n,ls,gamma)``930997 -orightUnits`0`x`()->Union(Record(particular:_$,basis:List(_$)),"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`931122 -orightZero`1`x`(_$)->_$`dEquation(S)`has(S,AbelianGroup)`931248 -oright`1`n`(_$)->_$`dLyndonWord(VarSet)``931307 -oright`1`n`(_$)->_$`dMagma(VarSet)``931465 -oright`1`n`(_$)->_$`dOutputForm``931618 -oright`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``931687 -oright`1`x`(_$)->_$`cBinaryRecursiveAggregate(S)``931763 -oright`2`n`(_$,Integer)->_$`dOutputForm``931811 -orischDE`6`n`(Integer,F,F,Symbol,(F,List(F))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed"),(F,F)->Union(Record(ratpart:F,coeff:F),"failed"))->Record(ans:F,right:F,sol?:Boolean)`pElementaryRischDE(R,F)``931900 -orischDEsys`7`n`(Integer,F,F,F,Symbol,(F,List(F))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed"),(F,F)->Union(Record(ratpart:F,coeff:F),"failed"))->Union(List(F),"failed")`pElementaryRischDESystem(R,F)``932279 -orischNormalize`2`x`(F,Symbol)->Record(func:F,kers:List(Kernel(F)),vals:List(F))`pElementaryFunctionStructurePackage(R,F)``932615 -ork4`5`x`(Vector(Float),Integer,Float,Float,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``932834 -ork4`9`x`(Vector(Float),Integer,Float,Float,(Vector(Float),Vector(Float),Float)->Void,Vector(Float),Vector(Float),Vector(Float),Vector(Float))->Void`pNumericalOrdinaryDifferentialEquations``933487 -ork4a`8`x`(Vector(Float),Integer,Float,Float,Float,Float,Integer,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``933750 -ork4f`6`x`(Vector(Float),Integer,Float,Float,Integer,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``934087 -ork4qc`14`x`(Vector(Float),Integer,Float,Record(try:Float,did:Float,next:Float),Float,Vector(Float),(Vector(Float),Vector(Float),Float)->Void,Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float),Vector(Float))->Void`pNumericalOrdinaryDifferentialEquations``934593 -ork4qc`7`x`(Vector(Float),Integer,Float,Record(try:Float,did:Float,next:Float),Float,Vector(Float),(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``935106 -oroman`1`x`(Integer)->_$`dRomanNumeral``935584 -oroman`1`x`(Symbol)->_$`dRomanNumeral``935645 -oromberg`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``935713 -orombergo`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``936413 -oroot?`1`n`(_$)->Boolean`dSubSpace(n,R)``937107 -orootBound`1`n`(UP)->Integer`pGaloisGroupFactorizationUtilities(R,UP,F)``937144 -orootKerSimp`3`x`(BasicOperator,F,NonNegativeInteger)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`937241 -orootNormalize`2`x`(F,Kernel(F))->F`pElementaryFunctionStructurePackage(R,F)``937312 -orootOfIrreduciblePoly`1`x`(SparseUnivariatePolynomial(GF))->F`pFiniteFieldPolynomialPackage2(F,GF)``937519 +orightUnits`0`x`()->Union(Record(particular:_$,basis:List(_$)),"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1121132 +orightZero`1`x`(_$)->_$`dEquation(S)`has(S,AbelianGroup)`1121258 +orischDE`6`n`(Integer,F,F,Symbol,(F,List(F))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed"),(F,F)->Union(Record(ratpart:F,coeff:F),"failed"))->Record(ans:F,right:F,sol?:Boolean)`pElementaryRischDE(R,F)``1121317 +orischDEsys`7`n`(Integer,F,F,F,Symbol,(F,List(F))->Union(Record(mainpart:F,limitedlogs:List(Record(coeff:F,logand:F))),"failed"),(F,F)->Union(Record(ratpart:F,coeff:F),"failed"))->Union(List(F),"failed")`pElementaryRischDESystem(R,F)``1121696 +orischNormalize`2`x`(F,Symbol)->Record(func:F,kers:List(Kernel(F)),vals:List(F))`pElementaryFunctionStructurePackage(R,F)``1122032 +oRittWuCompare`2`n`(S,S)->Union(Boolean,"failed")`xRecursivePolynomialCategory&(S,R,E,V)``0 +oRittWuCompare`2`x`(_$,_$)->Union(Boolean,"failed")`cRecursivePolynomialCategory(R,E,V)``1122251 +ork4`5`x`(Vector(Float),Integer,Float,Float,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``1122512 +ork4`9`x`(Vector(Float),Integer,Float,Float,(Vector(Float),Vector(Float),Float)->Void,Vector(Float),Vector(Float),Vector(Float),Vector(Float))->Void`pNumericalOrdinaryDifferentialEquations``1123180 +ork4a`8`x`(Vector(Float),Integer,Float,Float,Float,Float,Integer,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``1123443 +ork4f`6`x`(Vector(Float),Integer,Float,Float,Integer,(Vector(Float),Vector(Float),Float)->Void)->Void`pNumericalOrdinaryDifferentialEquations``1123795 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+orootOf`2`n`(S,Symbol)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 orootOf`2`n`(ThePols,PositiveInteger)->Union(S,"failed")`xRealRootCharacterizationCategory&(S,TheField,ThePols)``0 -orootOf`2`x`(SparseUnivariatePolynomial(_$),PositiveInteger)->Union(_$,"failed")`cRealClosedField``938201 -orootOf`2`x`(SparseUnivariatePolynomial(_$),Symbol)->_$`cAlgebraicallyClosedField``938321 -orootOf`2`x`(ThePols,PositiveInteger)->Union(_$,"failed")`cRealRootCharacterizationCategory(TheField,ThePols)``938437 -orootOf`2`x`(_$,Symbol)->_$`cAlgebraicallyClosedFunctionSpace(R)``938535 +orootOf`2`x`(SparseUnivariatePolynomial(_$),PositiveInteger)->Union(_$,"failed")`cRealClosedField``1128220 +orootOf`2`x`(SparseUnivariatePolynomial(_$),Symbol)->_$`cAlgebraicallyClosedField``1128340 +orootOf`2`x`(_$,Symbol)->_$`cAlgebraicallyClosedFunctionSpace(R)``1128601 +orootOf`2`x`(ThePols,PositiveInteger)->Union(_$,"failed")`cRealRootCharacterizationCategory(TheField,ThePols)``1128716 orootOf`3`n`(SparseUnivariatePolynomial(S),PositiveInteger,OutputForm)->Union(S,"failed")`xRealClosedField&(S)``0 -orootOf`3`x`(SparseUnivariatePolynomial(_$),PositiveInteger,OutputForm)->Union(_$,"failed")`cRealClosedField``938650 -orootPoly`2`n`(Fraction(UP),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:Fraction(UP),radicand:UP)`pChangeOfVariable(F,UP,UPUP)``938778 -orootPower`1`x`(F)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`938955 -orootProduct`1`x`(F)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`939113 -orootRadius`1`n`(UP)->R`pComplexRootFindingPackage(R,UP)``939348 -orootRadius`2`n`(UP,R)->R`pComplexRootFindingPackage(R,UP)``939563 -orootSimp`1`x`(F)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`939688 -orootSplit`1`x`(F)->F`pAlgebraicManipulations(R,F)``939920 -oroot`1`n`(_$)->_$`dOutputForm``940150 -oroot`2`n`(_$,_$)->_$`dOutputForm``940225 -oroot`2`x`(SparseUnivariatePolynomial(Integer),Integer)->_$`cPAdicIntegerCategory(p)``940308 +orootOf`3`x`(SparseUnivariatePolynomial(_$),PositiveInteger,OutputForm)->Union(_$,"failed")`cRealClosedField``1128814 +orootOfIrreduciblePoly`1`x`(SparseUnivariatePolynomial(GF))->F`pFiniteFieldPolynomialPackage2(F,GF)``1128942 +orootPoly`2`n`(Fraction(UP),NonNegativeInteger)->Record(exponent:NonNegativeInteger,coef:Fraction(UP),radicand:UP)`pChangeOfVariable(F,UP,UPUP)``1129195 +orootPower`1`x`(F)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`1129372 +orootProduct`1`x`(F)->F`pAlgebraicManipulations(R,F)`AND(has(R,GcdDomain),has(R,OrderedSet),has(R,RetractableTo(Integer)),has(F,FunctionSpace(R)))`1129530 +orootRadius`1`n`(UP)->R`pComplexRootFindingPackage(R,UP)``1129765 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+osatisfy?`2`n`(List(D),Pattern(R))->Boolean`pPatternFunctions1(R,D)``1152402 +osatisfy?`2`n`(_$,Pattern(R))->Union(Boolean,"failed")`dPatternMatchResult(R,S)``1152543 +osaturate`2`x`(_$,DPoly)->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1152777 +osaturate`3`x`(_$,DPoly,List(VarSet))->_$`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1152924 +osave`0`x`()->_$`dFortranCode``1153091 +osay`1`x`(List(String))->Void`pDisplayPackage``1153158 +osay`1`x`(String)->Void`pDisplayPackage``1153223 +osayLength`1`x`(List(String))->Integer`pDisplayPackage``1153279 +osayLength`1`x`(String)->Integer`pDisplayPackage``1153370 +osbt`2`x`(_$,_$)->_$`cLocalPowerSeriesCategory(K)``0 +oscalarMatrix`1`x`(R)->_$`cSquareMatrixCategory(ndim,R,Row,Col)``1153452 oscalarMatrix`2`n`(NonNegativeInteger,R)->S`xMatrixCategory&(S,R,Row,Col)``0 -oscalarMatrix`2`x`(NonNegativeInteger,R)->_$`cMatrixCategory(R,Row,Col)``961384 -oscalarTypeOf`1`x`(_$)->Union(fst:FortranScalarType,void:"void")`dFortranType``961518 -oscaleRoots`2`n`(UP,R)->UP`pGaloisGroupPolynomialUtilities(R,UP)``961590 -oscale`1`n`(F)->_$`dMoebiusTransform(F)``961693 -oscale`2`n`(_$,F)->_$`dMoebiusTransform(F)``961798 -oscale`4`n`(_$,PositiveInteger,Float,Float)->Void`dTwoDimensionalViewport``961898 -oscanOneDimSubspaces`2`x`(List(Vector(R)),Integer)->Vector(R)`pRepresentationPackage2(R)`AND(has(R,Field),has(R,Finite))`962215 -oscan`3`x`((A,B)->B,DirectProduct(dim,A),B)->DirectProduct(dim,B)`pDirectProductFunctions2(dim,A,B)``962907 -oscan`3`x`((A,B)->B,List(A),B)->List(B)`pListFunctions2(A,B)``963144 -oscan`3`x`((A,B)->B,OneDimensionalArray(A),B)->OneDimensionalArray(B)`pOneDimensionalArrayFunctions2(A,B)``963549 -oscan`3`x`((A,B)->B,PrimitiveArray(A),B)->PrimitiveArray(B)`pPrimitiveArrayFunctions2(A,B)``963865 -oscan`3`x`((A,B)->B,Vector(A),B)->Vector(B)`pVectorFunctions2(A,B)``964175 -oscan`3`x`((S,R)->R,A,R)->B`pFiniteLinearAggregateFunctions2(S,A,R,B)``964412 -oscan`3`x`((S,R)->R,A,R)->B`pFiniteSetAggregateFunctions2(S,A,R,B)``964721 -oscan`3`x`(B,(A,B)->B,Stream(A))->Stream(B)`pStreamFunctions2(A,B)``965030 -oschema`2`n`(polR,polR)->List(NonNegativeInteger)`pPseudoRemainderSequence(R,polR)``965213 -oschwerpunkt`1`n`(UP)->Complex(R)`pComplexRootFindingPackage(R,UP)``965352 -oscreenResolution3D`0`n`()->Integer`dPlot3D``965612 -oscreenResolution`0`n`()->Integer`dPlot``965693 -oscreenResolution`0`x`()->Integer`pGraphicsDefaults``965756 -oscreenResolution`1`x`(Integer)->Integer`pGraphicsDefaults``965829 -oscript`2`x`(_$,List(List(OutputForm)))->_$`dSymbol``965903 -oscript`2`x`(_$,Record(sub:List(OutputForm),sup:List(OutputForm),presup:List(OutputForm),presub:List(OutputForm),args:List(OutputForm)))->_$`dSymbol``966248 -oscripted?`1`x`(_$)->Boolean`dSymbol``966445 -oscripts`1`x`(_$)->Record(sub:List(OutputForm),sup:List(OutputForm),presup:List(OutputForm),presub:List(OutputForm),args:List(OutputForm))`dSymbol``966527 -oscripts`2`n`(_$,List(_$))->_$`dOutputForm``966589 -osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pExpertSystemContinuityPackage``966727 -osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pExpertSystemToolsPackage``966837 -osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pd01AgentsPackage``966926 -ose2rfi`1`n`(List(Symbol))->List(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``967023 -osearch`2`x`(Key,_$)->Union(Entry,"failed")`cKeyedDictionary(Key,Entry)``967082 -osec2cos`1`x`(F)->F`pTranscendentalManipulations(R,F)``967304 -osecIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``967402 -osec`1`n`(F)->F`pElementaryFunction(R,F)``967489 +oscalarMatrix`2`x`(NonNegativeInteger,R)->_$`cMatrixCategory(R,Row,Col)``1153582 +oscalarTypeOf`1`x`(_$)->Union(fst:FortranScalarType,void:"void")`dFortranType``1153799 +oscale`1`n`(F)->_$`dMoebiusTransform(F)``1153871 +oscale`2`n`(_$,F)->_$`dMoebiusTransform(F)``1153976 +oscale`3`x`(R,R,R)->_$`dDenavitHartenbergMatrix(R)``1154066 +oscale`4`n`(_$,PositiveInteger,Float,Float)->Void`dTwoDimensionalViewport``1154183 +oscaleRoots`2`n`(UP,R)->UP`pGaloisGroupPolynomialUtilities(R,UP)``1154500 +oscan`3`x`((A,B)->B,DirectProduct(dim,A),B)->DirectProduct(dim,B)`pDirectProductFunctions2(dim,A,B)``1154603 +oscan`3`x`((A,B)->B,List(A),B)->List(B)`pListFunctions2(A,B)``1154840 +oscan`3`x`((A,B)->B,OneDimensionalArray(A),B)->OneDimensionalArray(B)`pOneDimensionalArrayFunctions2(A,B)``1155245 +oscan`3`x`((A,B)->B,PrimitiveArray(A),B)->PrimitiveArray(B)`pPrimitiveArrayFunctions2(A,B)``1155873 +oscan`3`x`((A,B)->B,Vector(A),B)->Vector(B)`pVectorFunctions2(A,B)``1156490 +oscan`3`x`(B,(A,B)->B,Stream(A))->Stream(B)`pStreamFunctions2(A,B)``1156727 +oscan`3`x`((S,R)->R,A,R)->B`pFiniteLinearAggregateFunctions2(S,A,R,B)``1157165 +oscan`3`x`((S,R)->R,A,R)->B`pFiniteSetAggregateFunctions2(S,A,R,B)``1157474 +oScanArabic`1`n`(String)->PositiveInteger`pNumberFormats``1157783 +oScanFloatIgnoreSpaces`1`n`(String)->Float`pNumberFormats``1157868 +oScanFloatIgnoreSpacesIfCan`1`n`(String)->Union(Float,"failed")`pNumberFormats``1158062 +oscanOneDimSubspaces`2`x`(List(Vector(R)),Integer)->Vector(R)`pRepresentationPackage2(R)`AND(has(R,Field),has(R,Finite))`1158190 +oScanRoman`1`n`(String)->PositiveInteger`pNumberFormats``1158889 +oschema`2`n`(polR,polR)->List(NonNegativeInteger)`pPseudoRemainderSequence(R,polR)``1158971 +oschwerpunkt`1`n`(UP)->Complex(R)`pComplexRootFindingPackage(R,UP)``1159110 +oscreenResolution`0`n`()->Integer`dPlot``1159365 +oscreenResolution`0`x`()->Integer`pGraphicsDefaults``1159428 +oscreenResolution`1`x`(Integer)->Integer`pGraphicsDefaults``1159501 +oscreenResolution3D`0`n`()->Integer`dPlot3D``1159575 +oscript`2`x`(_$,List(List(OutputForm)))->_$`dSymbol``1159656 +oscript`2`x`(_$,Record(sub:List(OutputForm),sup:List(OutputForm),presup:List(OutputForm),presub:List(OutputForm),args:List(OutputForm)))->_$`dSymbol``1160001 +oscripted?`1`x`(_$)->Boolean`dSymbol``1160198 +oscripts`1`x`(_$)->Record(sub:List(OutputForm),sup:List(OutputForm),presup:List(OutputForm),presub:List(OutputForm),args:List(OutputForm))`dSymbol``1160280 +oscripts`2`n`(_$,List(_$))->_$`dOutputForm``1160342 +osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pd01AgentsPackage``1160480 +osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pExpertSystemContinuityPackage``1160577 +osdf2lst`1`x`(Stream(DoubleFloat))->List(String)`pExpertSystemToolsPackage``1160687 +ose2rfi`1`n`(List(Symbol))->List(Fraction(Polynomial(R)))`pParametricLinearEquations(R,Var,Expon,GR)``1160776 +osearch`2`x`(Key,_$)->Union(Entry,"failed")`cKeyedDictionary(Key,Entry)``1160835 +osec`1`n`(F)->F`pElementaryFunction(R,F)``1161057 osec`1`n`(S)->S`xTrigonometricFunctionCategory&(S)``0 osec`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -osec`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``967550 -osec`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``967617 -osec`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``967684 -osec`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``967752 -osec`1`x`(_$)->_$`cTrigonometricFunctionCategory``967822 -osech2cosh`1`x`(F)->F`pTranscendentalManipulations(R,F)``967875 -osechIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``967977 -osech`1`n`(F)->F`pElementaryFunction(R,F)``968066 +osec`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1161118 +osec`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1161185 +osec`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1161252 +osec`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1161320 +osec`1`x`(_$)->_$`cTrigonometricFunctionCategory``1161390 +osec2cos`1`x`(F)->F`pTranscendentalManipulations(R,F)``1161443 +osech`1`n`(F)->F`pElementaryFunction(R,F)``1161541 osech`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 osech`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -osech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``968139 -osech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``968222 -osech`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``968305 -osech`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``968385 -osech`1`x`(_$)->_$`cHyperbolicFunctionCategory``968467 +osech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1161614 +osech`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1161697 +osech`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1161780 +osech`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1161860 +osech`1`x`(_$)->_$`cHyperbolicFunctionCategory``1161942 +osech2cosh`1`x`(F)->F`pTranscendentalManipulations(R,F)``1162007 +osechIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1162109 +osecIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1162198 osecond`1`n`(A)->S`xUnaryRecursiveAggregate&(A,S)``0 -osecond`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``968532 -oseed`0`x`()->Integer`pRandomNumberSource``968652 -osegment`1`x`(S)->_$`dUniversalSegment(S)``968705 -osegment`1`x`(_$)->Segment(S)`dSegmentBinding(S)``968787 -osegment`2`x`(S,S)->_$`cSegmentCategory(S)``968991 -oselect!`2`n`((S)->Boolean,A)->A`xDictionary&(A,S)``0 -oselect!`2`n`((S)->Boolean,A)->A`xListAggregate&(A,S)``0 -oselect!`2`x`((S)->Boolean,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`969075 -oselect!`2`x`((S)->Boolean,_$)->_$`cExtensibleLinearAggregate(S)``969236 -oselectAndPolynomials`2`n`(List((P)->Boolean),List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``969366 -oselectFiniteRoutines`1`x`(_$)->_$`dRoutinesTable``969678 -oselectIntegrationRoutines`1`x`(_$)->_$`dRoutinesTable``969813 -oselectMultiDimensionalRoutines`1`x`(_$)->_$`dRoutinesTable``969928 -oselectNonFiniteRoutines`1`x`(_$)->_$`dRoutinesTable``970084 -oselectODEIVPRoutines`1`x`(_$)->_$`dRoutinesTable``970227 -oselectOptimizationRoutines`1`x`(_$)->_$`dRoutinesTable``970354 -oselectOrPolynomials`2`n`(List((P)->Boolean),List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``970470 -oselectPDERoutines`1`x`(_$)->_$`dRoutinesTable``970780 -oselectPolynomials`2`n`((P)->Boolean,List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``970904 -oselectSumOfSquaresRoutines`1`x`(_$)->_$`dRoutinesTable``971170 +osecond`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``1162285 +oseed`0`x`()->Integer`pRandomNumberSource``1162409 +oSEGMENT`1`n`(_$)->_$`dOutputForm``1162462 +oSEGMENT`1`x`(S)->_$`dUniversalSegment(S)``1162524 +osegment`1`x`(S)->_$`dUniversalSegment(S)``1162610 +osegment`1`x`(_$)->Segment(S)`dSegmentBinding(S)``1162692 +oSEGMENT`2`n`(_$,_$)->_$`dOutputForm``1162896 +oSEGMENT`2`x`(S,S)->_$`cSegmentCategory(S)``1162962 +osegment`2`x`(S,S)->_$`cSegmentCategory(S)``1163044 +oselect`2`n`(_$,NonNegativeInteger)->S`dTuple(S)``1163128 oselect`2`n`((P)->Boolean,S)->S`xTriangularSetCategory&(S,R,E,V,P)``0 oselect`2`n`((S)->Boolean,A)->A`xCollection&(A,S)``0 +oselect!`2`n`((S)->Boolean,A)->A`xDictionary&(A,S)``0 oselect`2`n`((S)->Boolean,A)->A`xExtensibleLinearAggregate&(A,S)``0 +oselect!`2`n`((S)->Boolean,A)->A`xListAggregate&(A,S)``0 oselect`2`n`(S,V)->Union(P,"failed")`xTriangularSetCategory&(S,R,E,V,P)``0 -oselect`2`n`(_$,NonNegativeInteger)->S`dTuple(S)``971308 -oselect`2`x`((S)->Boolean,_$)->_$`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`971406 -oselect`2`x`((S)->Boolean,_$)->_$`cLazyStreamAggregate(S)``971650 -oselect`2`x`((S)->Boolean,_$)->_$`dInfiniteTuple(S)``971834 -oselect`2`x`(_$,V)->Union(P,"failed")`cTriangularSetCategory(R,E,V,P)``971900 -oselectfirst`1`n`(_$)->A`dProduct(A,B)``972038 -oselectsecond`1`n`(_$)->B`dProduct(A,B)``972081 -osemiDegreeSubResultantEuclidean`3`n`(polR,polR,NonNegativeInteger)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``972125 -osemiDiscriminantEuclidean`1`n`(polR)->Record(coef2:polR,discriminant:R)`pPseudoRemainderSequence(R,polR)``972388 -osemiIndiceSubResultantEuclidean`3`n`(polR,polR,NonNegativeInteger)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``972604 -osemiLastSubResultantEuclidean`2`n`(polR,polR)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``972891 -osemiResultantEuclidean1`2`n`(polR,polR)->Record(coef1:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``973148 -osemiResultantEuclidean2`2`n`(polR,polR)->Record(coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``973317 -osemiResultantEuclideannaif`2`n`(polR,polR)->Record(coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``973535 -osemiResultantReduitEuclidean`2`n`(polR,polR)->Record(coef2:polR,resultantReduit:R)`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`973714 -osemiSubResultantGcdEuclidean1`2`n`(polR,polR)->Record(coef1:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``973909 -osemiSubResultantGcdEuclidean2`2`n`(polR,polR)->Record(coef2:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``974189 -osemicolonSeparate`1`n`(List(_$))->_$`dOutputForm``974532 +oselect`2`x`((S)->Boolean,_$)->_$`cCollection(S)`has(_$,ATTRIBUTE(finiteAggregate))`1163428 +oselect!`2`x`((S)->Boolean,_$)->_$`cDictionaryOperations(S)`has(_$,ATTRIBUTE(finiteAggregate))`1163676 +oselect!`2`x`((S)->Boolean,_$)->_$`cExtensibleLinearAggregate(S)``1163837 +oselect`2`x`((S)->Boolean,_$)->_$`cLazyStreamAggregate(S)``1163967 +oselect`2`x`((S)->Boolean,_$)->_$`dInfiniteTuple(S)``1164306 +oselect`2`x`(_$,V)->Union(P,"failed")`cTriangularSetCategory(R,E,V,P)``1164372 +oselectAndPolynomials`2`n`(List((P)->Boolean),List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``1164510 +oselectFiniteRoutines`1`x`(_$)->_$`dRoutinesTable``1164822 +oselectfirst`1`n`(_$)->A`dProduct(A,B)``1164957 +oselectIntegrationRoutines`1`x`(_$)->_$`dRoutinesTable``1165004 +oselectMultiDimensionalRoutines`1`x`(_$)->_$`dRoutinesTable``1165119 +oselectNonFiniteRoutines`1`x`(_$)->_$`dRoutinesTable``1165275 +oselectODEIVPRoutines`1`x`(_$)->_$`dRoutinesTable``1165418 +oselectOptimizationRoutines`1`x`(_$)->_$`dRoutinesTable``1165545 +oselectOrPolynomials`2`n`(List((P)->Boolean),List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``1165661 +oselectPDERoutines`1`x`(_$)->_$`dRoutinesTable``1165971 +oselectPolynomials`2`n`((P)->Boolean,List(P))->Record(goodPols:List(P),badPols:List(P))`pPolynomialSetUtilitiesPackage(R,E,V,P)``1166095 +oselectsecond`1`n`(_$)->B`dProduct(A,B)``1166361 +oselectSumOfSquaresRoutines`1`x`(_$)->_$`dRoutinesTable``1166409 +osemicolonSeparate`1`n`(List(_$))->_$`dOutputForm``1166547 +osemiDegreeSubResultantEuclidean`3`n`(polR,polR,NonNegativeInteger)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``1166650 +osemiDiscriminantEuclidean`1`n`(polR)->Record(coef2:polR,discriminant:R)`pPseudoRemainderSequence(R,polR)``1166913 +osemiIndiceSubResultantEuclidean`3`n`(polR,polR,NonNegativeInteger)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``1167129 +osemiLastSubResultantEuclidean`2`n`(polR,polR)->Record(coef2:polR,subResultant:polR)`pPseudoRemainderSequence(R,polR)``1167416 +osemiResultantEuclidean1`2`n`(polR,polR)->Record(coef1:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``1167673 +osemiResultantEuclidean2`2`n`(polR,polR)->Record(coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``1167842 +osemiResultantEuclideannaif`2`n`(polR,polR)->Record(coef2:polR,resultant:R)`pPseudoRemainderSequence(R,polR)``1168060 +osemiResultantReduitEuclidean`2`n`(polR,polR)->Record(coef2:polR,resultantReduit:R)`pPseudoRemainderSequence(R,polR)`has(R,GcdDomain)`1168239 +osemiSubResultantGcdEuclidean1`2`n`(polR,polR)->Record(coef1:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``1168434 +osemiSubResultantGcdEuclidean2`2`n`(polR,polR)->Record(coef2:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``1168714 oseparant`1`n`(A)->A`xDifferentialPolynomialCategory&(A,R,S,V,E)``0 -oseparant`1`x`(_$)->_$`cDifferentialPolynomialCategory(R,S,V,E)``974635 -oseparateDegrees`1`x`(FP)->List(Record(deg:NonNegativeInteger,prod:FP))`pDistinctDegreeFactorize(F,FP)``974760 -oseparateFactors`1`x`(List(Record(deg:NonNegativeInteger,prod:FP)))->List(FP)`pDistinctDegreeFactorize(F,FP)``974912 -oseparateFactors`2`x`(List(Record(factor:U,degree:Integer)),Integer)->List(U)`pModularDistinctDegreeFactorizer(U)``975078 -oseparate`1`n`(Fraction(UP))->Record(polyPart:_$,fracPart:Fraction(UP))`dLaurentPolynomial(R,UP)`has(R,Field)`975262 -oseparate`1`n`(_$)->List(_$)`dSubSpace(n,R)``975302 +oseparant`1`x`(_$)->_$`cDifferentialPolynomialCategory(R,S,V,E)``1169057 +oseparate`1`n`(Fraction(UP))->Record(polyPart:_$,fracPart:Fraction(UP))`dLaurentPolynomial(R,UP)`has(R,Field)`1169182 +oseparate`1`n`(_$)->List(_$)`dSubSpace(n,R)``1169226 oseparate`2`n`(S,S)->Record(primePart:S,commonPart:S)`xUnivariatePolynomialCategory&(S,R)``0 -oseparate`2`x`(_$,_$)->Record(primePart:_$,commonPart:_$)`cUnivariatePolynomialCategory(R)`has(R,GcdDomain)`975468 -osequences`1`x`(List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``975605 -osequences`2`x`(List(Integer),List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``975813 -oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),Equation(F))->Any`pExpressionSpaceODESolver(R,F)``976178 -oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),F)->Any`pExpressionSpaceODESolver(R,F)``976425 -oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``976535 -oseriesSolve`4`x`(F,BasicOperator,Equation(F),Equation(F))->Any`pExpressionSpaceODESolver(R,F)``976958 -oseriesSolve`4`x`(F,BasicOperator,Equation(F),F)->Any`pExpressionSpaceODESolver(R,F)``977079 -oseriesSolve`4`x`(F,BasicOperator,Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``977198 -oseriesSolve`4`x`(List(Equation(F)),List(BasicOperator),Equation(F),List(Equation(F)))->Any`pExpressionSpaceODESolver(R,F)``977343 -oseriesSolve`4`x`(List(Equation(F)),List(BasicOperator),Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``977764 -oseriesSolve`4`x`(List(F),List(BasicOperator),Equation(F),List(Equation(F)))->Any`pExpressionSpaceODESolver(R,F)``977972 -oseriesSolve`4`x`(List(F),List(BasicOperator),Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``978200 -oseriesToOutputForm`5`n`(Stream(Record(k:Integer,c:Coef)),Reference(OrderedCompletion(Integer)),Symbol,Coef,Fraction(Integer))->OutputForm`dInnerSparseUnivariatePowerSeries(Coef)``978395 -oseries`1`n`(Stream(Coef))->_$`dInnerTaylorSeries(Coef)``978499 -oseries`1`n`(Stream(Record(k:Integer,c:Coef)))->_$`dInnerSparseUnivariatePowerSeries(Coef)``978929 -oseries`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``979128 -oseries`1`x`(Stream(Coef))->_$`cUnivariateTaylorSeriesCategory(Coef)``979309 -oseries`1`x`(Stream(Record(k:Integer,c:Coef)))->_$`cUnivariateLaurentSeriesCategory(Coef)``979407 -oseries`1`x`(Stream(Record(k:NonNegativeInteger,c:Coef)))->_$`cUnivariateTaylorSeriesCategory(Coef)``979606 -oseries`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``979805 -oseries`2`x`((Integer)->FE,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``979866 -oseries`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``979952 -oseries`2`x`(FE,Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``980057 -oseries`2`x`(NonNegativeInteger,Stream(Record(k:Fraction(Integer),c:Coef)))->_$`cUnivariatePuiseuxSeriesCategory(Coef)``980299 -oseries`3`x`((Integer)->FE,Equation(FE),UniversalSegment(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``980611 -oseries`3`x`(FE,Equation(FE),Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``980804 -oseries`3`x`(FE,Symbol,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``980967 -oseries`4`x`((Fraction(Integer))->FE,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``981051 -oseries`4`x`(FE,Symbol,Equation(FE),UniversalSegment(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``981291 -oseries`5`x`(FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``981476 -osetAdaptive3D`1`n`(Boolean)->Boolean`dPlot3D``981712 -osetAdaptive`1`n`(Boolean)->Boolean`dPlot``981831 -osetAttributeButtonStep`1`x`(Float)->Float`dAttributeButtons``981944 -osetButtonValue`2`x`(String,Float)->Float`dAttributeButtons``982151 -osetButtonValue`3`x`(String,String,Float)->Float`dAttributeButtons``982463 -osetClipValue`1`x`(DoubleFloat)->DoubleFloat`pDrawComplex``982818 -osetClosed`2`n`(_$,Boolean)->Boolean`dTubePlot(Curve)``982941 -osetColumn!`3`n`(S,Integer,Col)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -osetColumn!`3`x`(_$,Integer,Col)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``983115 -osetCondition!`2`n`(_$,C)->_$`dSplittingNode(V,C)``983201 -osetDifference`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`983363 -osetEmpty!`1`n`(_$)->_$`dSplittingNode(V,C)``983536 -osetEpilogue!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``983613 -osetEpilogue!`2`x`(_$,List(String))->List(String)`dTexFormat``983729 -osetErrorBound`1`n`(R)->R`pComplexRootFindingPackage(R,UP)``983837 -osetFieldInfo`2`n`(Vector(List(Record(value:GF,index:SingleInteger))),GF)->Void`pInnerNormalBasisFieldFunctions(GF)``984136 -osetFormula!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``984326 -osetImagSteps`1`x`(Integer)->Integer`pDrawComplex``984440 -osetIntersection`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`984591 -osetLabelValue`1`x`(SingleInteger)->SingleInteger`dFortranCode``984772 -osetLegalFortranSourceExtensions`1`x`(List(String))->List(String)`pFortranPackage``984856 -osetMaxPoints3D`1`n`(Integer)->Integer`dPlot3D``984921 -osetMaxPoints`1`n`(Integer)->Integer`dPlot``985010 -osetMinPoints3D`1`n`(Integer)->Integer`dPlot3D``985096 -osetMinPoints`1`n`(Integer)->Integer`dPlot``985185 -osetOfMinN`1`n`(List(PositiveInteger))->_$`dSetOfMIntegersInOneToN(m,n)``985271 -osetOrder`1`n`(List(S))->Void`pUserDefinedPartialOrdering(S)``985440 -osetOrder`2`n`(List(S),List(S))->Void`pUserDefinedPartialOrdering(S)``985803 -osetPoly`1`n`(Rep)->Rep`dModMonic(R,Rep)``986241 -osetPosition`2`x`(_$,NonNegativeInteger)->Void`cCachableSet``986280 -osetPredicates`2`n`(_$,List(Any))->_$`dPattern(R)``986359 -osetPrologue!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``986477 -osetPrologue!`2`x`(_$,List(String))->List(String)`dTexFormat``986593 -osetProperties`2`x`(_$,AssociationList(String,None))->_$`dBasicOperator``986701 -osetProperty`3`x`(_$,String,None)->_$`dBasicOperator``986867 -osetRealSteps`1`x`(Integer)->Integer`pDrawComplex``987062 -osetRow!`3`n`(S,Integer,Row)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -osetRow!`3`x`(_$,Integer,Row)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``987208 -osetScreenResolution3D`1`n`(Integer)->Integer`dPlot3D``987288 -osetScreenResolution`1`n`(Integer)->Integer`dPlot``987382 -osetStatus!`2`n`(_$,Boolean)->_$`dSplittingNode(V,C)``987458 -osetStatus`2`n`(_$,Union(Boolean,"failed"))->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``987614 -osetTex!`2`x`(_$,List(String))->List(String)`dTexFormat``987969 -osetTopPredicate`3`n`(_$,List(Symbol),Any)->_$`dPattern(R)``988067 -osetUnion`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`988202 -osetValue!`2`n`(_$,V)->_$`dSplittingNode(V,C)``988372 -osetVariableOrder`1`x`(List(Symbol))->Void`pUserDefinedVariableOrdering``988526 -osetVariableOrder`2`x`(List(Symbol),List(Symbol))->Void`pUserDefinedVariableOrdering``988665 +oseparate`2`x`(_$,_$)->Record(primePart:_$,commonPart:_$)`cUnivariatePolynomialCategory(R)`has(R,GcdDomain)`1169392 +oseparateDegrees`1`x`(FP)->List(Record(deg:NonNegativeInteger,prod:FP))`pDistinctDegreeFactorize(F,FP)``1169529 +oseparateFactors`1`x`(List(Record(deg:NonNegativeInteger,prod:FP)))->List(FP)`pDistinctDegreeFactorize(F,FP)``1169681 +oseparateFactors`2`x`(List(Record(factor:U,degree:Integer)),Integer)->List(U)`pModularDistinctDegreeFactorizer(U)``1169804 +osequences`1`x`(List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``1169941 +osequences`2`x`(List(Integer),List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``1170149 +oseries`1`n`(Stream(Coef))->_$`dInnerTaylorSeries(Coef)``1170514 +oseries`1`n`(Stream(Record(k:Integer,c:Coef)))->_$`dInnerSparseUnivariatePowerSeries(Coef)``1170944 +oseries`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1171143 +oseries`1`x`(Stream(Coef))->_$`cUnivariateTaylorSeriesCategory(Coef)``1171328 +oseries`1`x`(Stream(Record(k:Integer,c:Coef)))->_$`cUnivariateLaurentSeriesCategory(Coef)``1171426 +oseries`1`x`(Stream(Record(k:NonNegativeInteger,c:Coef)))->_$`cUnivariateTaylorSeriesCategory(Coef)``1171625 +oseries`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1171824 +oseries`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1171885 +oseries`2`x`(FE,Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1171990 +oseries`2`x`((Integer)->FE,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1172236 +oseries`2`x`(NonNegativeInteger,Stream(Record(k:Fraction(Integer),c:Coef)))->_$`cUnivariatePuiseuxSeriesCategory(Coef)``1172322 +oseries`3`x`(FE,Equation(FE),Fraction(Integer))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1172634 +oseries`3`x`(FE,Symbol,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1172797 +oseries`3`x`((Integer)->FE,Equation(FE),UniversalSegment(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1172881 +oseries`3`x`(Integer,K,_$)->_$`cLocalPowerSeriesCategory(K)``1173074 +oseries`4`x`(FE,Symbol,Equation(FE),UniversalSegment(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1173143 +oseries`4`x`((Fraction(Integer))->FE,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1173328 +oseries`5`x`(FE,Symbol,Equation(FE),UniversalSegment(Fraction(Integer)),Fraction(Integer))->Any`pGenerateUnivariatePowerSeries(R,FE)``1173568 +oseriesSolve`2`x`((UTSSUPF)->UTSSUPF,List(F))->UTSF`pTaylorSolve(F,UTSF,UTSSUPF)``0 +oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),Equation(F))->Any`pExpressionSpaceODESolver(R,F)``1173804 +oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),F)->Any`pExpressionSpaceODESolver(R,F)``1174055 +oseriesSolve`4`x`(Equation(F),BasicOperator,Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``1174165 +oseriesSolve`4`x`(F,BasicOperator,Equation(F),Equation(F))->Any`pExpressionSpaceODESolver(R,F)``1174588 +oseriesSolve`4`x`(F,BasicOperator,Equation(F),F)->Any`pExpressionSpaceODESolver(R,F)``1174709 +oseriesSolve`4`x`(F,BasicOperator,Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``1174828 +oseriesSolve`4`x`(F,BasicOperator,Symbol,List(F))->UTSF`pExpressionSolve(R,F,UTSF,UTSSUPF)``0 +oseriesSolve`4`x`(List(Equation(F)),List(BasicOperator),Equation(F),List(Equation(F)))->Any`pExpressionSpaceODESolver(R,F)``1174973 +oseriesSolve`4`x`(List(Equation(F)),List(BasicOperator),Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``1175398 +oseriesSolve`4`x`(List(F),List(BasicOperator),Equation(F),List(Equation(F)))->Any`pExpressionSpaceODESolver(R,F)``1175606 +oseriesSolve`4`x`(List(F),List(BasicOperator),Equation(F),List(F))->Any`pExpressionSpaceODESolver(R,F)``1175883 +oseriesToOutputForm`5`n`(Stream(Record(k:Integer,c:Coef)),Reference(OrderedCompletion(Integer)),Symbol,Coef,Fraction(Integer))->OutputForm`dInnerSparseUnivariatePowerSeries(Coef)``1176078 oset`0`n`()->A`xFiniteSetAggregate&(A,S)``0 -oset`0`x`()->_$`cSetAggregate(S)``988851 +oset`0`x`()->_$`cSetAggregate(S)``1176182 oset`1`n`(List(S))->A`xFiniteSetAggregate&(A,S)``0 -oset`1`x`(List(S))->_$`cSetAggregate(S)``988930 +oset`1`x`(List(S))->_$`cSetAggregate(S)``1176261 +osetAdaptive`1`n`(Boolean)->Boolean`dPlot``1176377 +osetAdaptive3D`1`n`(Boolean)->Boolean`dPlot3D``1176490 +osetAttributeButtonStep`1`x`(Float)->Float`dAttributeButtons``1176609 +osetButtonValue`2`x`(String,Float)->Float`dAttributeButtons``1176816 +osetButtonValue`3`x`(String,String,Float)->Float`dAttributeButtons``1177128 +osetchart!`2`x`(_$,BLMET)->BLMET`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 osetchildren!`2`n`(A,List(A))->A`xUnaryRecursiveAggregate&(A,S)``0 -osetchildren!`2`x`(_$,List(_$))->_$`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989046 -osetelt!`5`x`(_$,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger,R)->R`dThreeDimensionalMatrix(R)``989180 -osetelt`2`n`(_$,S)->S`dReference(S)``989326 +osetchildren!`2`x`(_$,List(_$))->_$`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1177483 +osetClipValue`1`x`(DoubleFloat)->DoubleFloat`pDrawComplex``1177617 +osetClosed`2`n`(_$,Boolean)->Boolean`dTubePlot(Curve)``1177740 +osetColumn!`3`n`(S,Integer,Col)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 +osetColumn!`3`x`(_$,Integer,Col)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``1177914 +osetCondition!`2`n`(_$,C)->_$`dSplittingNode(V,C)``1178269 +osetCurve`1`x`(DistributedMultivariatePolynomial(symb,K))->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +osetCurve`1`x`(DistributedMultivariatePolynomial(symb,K))->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +osetCurve`1`x`(PolyRing)->PolyRing`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``0 +osetcurve!`2`x`(_$,DistributedMultivariatePolynomial(construct('X,'Y),K))->DistributedMultivariatePolynomial(construct('X,'Y),K)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetDegree!`2`x`(_$,PositiveInteger)->Void`cPlacesCategory(K,PCS)``1178431 +osetDifference`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`1178481 +osetelt`2`n`(_$,S)->S`dReference(S)``1178654 osetelt`3`n`(A,"first",S)->S`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"first",S)->S`xUnaryRecursiveAggregate&(A,S)``0 +osetelt`3`n`(A,Integer,S)->S`xOneDimensionalArrayAggregate&(A,S)``0 +osetelt`3`n`(A,Integer,S)->S`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"last",S)->S`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"last",S)->S`xUnaryRecursiveAggregate&(A,S)``0 osetelt`3`n`(A,"left",A)->A`xBinaryRecursiveAggregate&(A,S)``0 osetelt`3`n`(A,"rest",A)->A`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"rest",A)->A`xUnaryRecursiveAggregate&(A,S)``0 osetelt`3`n`(A,"right",A)->A`xBinaryRecursiveAggregate&(A,S)``0 +osetelt`3`n`(A,UniversalSegment(Integer),S)->S`xOneDimensionalArrayAggregate&(A,S)``0 +osetelt`3`n`(A,UniversalSegment(Integer),S)->S`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"value",S)->S`xBinaryRecursiveAggregate&(A,S)``0 osetelt`3`n`(A,"value",S)->S`xRecursiveAggregate&(A,S)``0 osetelt`3`n`(A,"value",S)->S`xStreamAggregate&(A,S)``0 osetelt`3`n`(A,"value",S)->S`xUnaryRecursiveAggregate&(A,S)``0 -osetelt`3`n`(A,Integer,S)->S`xOneDimensionalArrayAggregate&(A,S)``0 -osetelt`3`n`(A,Integer,S)->S`xStreamAggregate&(A,S)``0 -osetelt`3`n`(A,UniversalSegment(Integer),S)->S`xOneDimensionalArrayAggregate&(A,S)``0 -osetelt`3`n`(A,UniversalSegment(Integer),S)->S`xStreamAggregate&(A,S)``0 -osetelt`3`x`(_$,"first",S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989408 -osetelt`3`x`(_$,"last",S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989561 -osetelt`3`x`(_$,"left",_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989711 -osetelt`3`x`(_$,"rest",_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989848 -osetelt`3`x`(_$,"right",_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`989998 -osetelt`3`x`(_$,"value",S)->S`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`990145 -osetelt`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)`has(_$,ATTRIBUTE(shallowlyMutable))`990284 -osetelt`3`x`(_$,Key,Entry)->Entry`cTableAggregate(Key,Entry)``990477 -osetelt`3`x`(_$,Symbol,Any)->Any`dLibrary``990648 -osetelt`3`x`(_$,UniversalSegment(Integer),S)->S`cLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`990775 +osetelt`3`x`(_$,Dom,Im)->Im`cEltableAggregate(Dom,Im)`has(_$,ATTRIBUTE(shallowlyMutable))`1178736 +osetelt`3`x`(_$,"first",S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1178929 +osetelt`3`x`(_$,Integer,K)->K`cAffineSpaceCategory(K)``1179082 +osetelt`3`x`(_$,Integer,K)->K`cProjectiveSpaceCategory(K)``1179145 +osetelt`3`x`(_$,Key,Entry)->Entry`cTableAggregate(Key,Entry)``1179208 +osetelt`3`x`(_$,"last",S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1179379 +osetelt`3`x`(_$,"left",_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1179529 +osetelt`3`x`(_$,"rest",_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1179666 +osetelt`3`x`(_$,"right",_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1179816 +osetelt`3`x`(_$,Symbol,Any)->Any`dLibrary``1179963 +osetelt`3`x`(_$,UniversalSegment(Integer),S)->S`cLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1180090 +osetelt`3`x`(_$,"value",S)->S`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1180492 osetelt`4`n`(S,Integer,Integer,R)->R`xMatrixCategory&(S,R,Row,Col)``0 osetelt`4`n`(S,List(Integer),List(Integer),S)->S`xMatrixCategory&(S,R,Row,Col)``0 -osetelt`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``991173 -osetelt`4`x`(_$,List(Integer),List(Integer),_$)->_$`cMatrixCategory(R,Row,Col)``991351 -osetfirst!`2`x`(_$,S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`991683 +osetelt`4`x`(_$,Integer,Integer,R)->R`cTwoDimensionalArrayCategory(R,Row,Col)``1180631 +osetelt`4`x`(_$,List(Integer),List(Integer),_$)->_$`cMatrixCategory(R,Row,Col)``1180975 +osetelt!`5`x`(_$,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger,R)->R`dThreeDimensionalMatrix(R)``1181492 +osetEmpty!`1`n`(_$)->_$`dSplittingNode(V,C)``1181638 +osetEpilogue!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``1181715 +osetEpilogue!`2`x`(_$,List(String))->List(String)`dTexFormat``1181831 +osetErrorBound`1`n`(R)->R`pComplexRootFindingPackage(R,UP)``1181939 +osetexcpDiv!`2`x`(_$,DIVISOR)->DIVISOR`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetFieldInfo`2`n`(Vector(List(Record(value:GF,index:SingleInteger))),GF)->Void`pInnerNormalBasisFieldFunctions(GF)``1182239 +osetfirst!`2`x`(_$,S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1182429 +osetFormula!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``1182518 +osetFoundPlacesToEmpty`0`x`()->List(_$)`cPlacesCategory(K,PCS)``1182632 +osetFoundZeroes`1`x`(List(K))->List(K)`pRootsFindingPackage(K)``1182725 +osetImagSteps`1`x`(Integer)->Integer`pDrawComplex``1182801 +osetIntersection`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`1182952 +osetLabelValue`1`x`(SingleInteger)->SingleInteger`dFortranCode``1183133 osetlast!`2`n`(A,S)->S`xUnaryRecursiveAggregate&(A,S)``0 -osetlast!`2`x`(_$,S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`991772 -osetleaves!`2`x`(_$,List(S))->_$`dBalancedBinaryTree(S)``991866 -osetleft!`2`x`(_$,_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`991981 -osetnext!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`992060 -osetprevious!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`992194 -osetref`2`n`(_$,S)->S`dReference(S)``992336 -osetrest!`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`992394 -osetrest!`3`x`(_$,Integer,_$)->_$`dStream(S)``992480 -osetright!`2`x`(_$,_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`992604 +osetlast!`2`x`(_$,S)->S`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1183217 +osetleaves!`2`x`(_$,List(S))->_$`dBalancedBinaryTree(S)``1183311 +osetleft!`2`x`(_$,_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1183561 +osetLegalFortranSourceExtensions`1`x`(List(String))->List(String)`pFortranPackage``1183640 +osetlocalParam!`2`x`(_$,List(PCS))->List(PCS)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetlocalPoint!`2`x`(_$,AffinePlane(K))->AffinePlane(K)`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetMaxPoints`1`n`(Integer)->Integer`dPlot``1183705 +osetMaxPoints3D`1`n`(Integer)->Integer`dPlot3D``1183791 +osetMinPoints`1`n`(Integer)->Integer`dPlot``1183880 +osetMinPoints3D`1`n`(Integer)->Integer`dPlot3D``1183966 +osetmult!`2`x`(_$,NonNegativeInteger)->NonNegativeInteger`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetnext!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1184055 +osetOfMinN`1`n`(List(PositiveInteger))->_$`dSetOfMIntegersInOneToN(m,n)``1184189 +osetOrder`1`n`(List(S))->Void`pUserDefinedPartialOrdering(S)``1184358 +osetOrder`2`n`(List(S),List(S))->Void`pUserDefinedPartialOrdering(S)``1184721 +osetParam!`2`x`(_$,List(PCS))->Void`cPlacesCategory(K,PCS)``1185159 +osetpoint!`2`x`(_$,ProjPt)->ProjPt`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetPoly`1`n`(Rep)->Rep`dModMonic(R,Rep)``1185249 +osetPosition`2`x`(_$,NonNegativeInteger)->Void`cCachableSet``1185292 +osetPredicates`2`n`(_$,List(Any))->_$`dPattern(R)``1185371 +osetprevious!`2`x`(_$,_$)->_$`cDoublyLinkedAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1185489 +osetPrologue!`2`x`(_$,List(String))->List(String)`dScriptFormulaFormat``1185631 +osetPrologue!`2`x`(_$,List(String))->List(String)`dTexFormat``1185747 +osetProperties`2`x`(_$,AssociationList(String,None))->_$`dBasicOperator``1185855 +osetProperty`3`x`(_$,String,None)->_$`dBasicOperator``1186021 +osetRealSteps`1`x`(Integer)->Integer`pDrawComplex``1186216 +osetref`2`n`(_$,S)->S`dReference(S)``1186362 +osetrest!`2`x`(_$,_$)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1186420 +osetrest!`3`x`(_$,Integer,_$)->_$`dStream(S)``1186506 +osetright!`2`x`(_$,_$)->_$`cBinaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1186844 +osetRow!`3`n`(S,Integer,Row)->S`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 +osetRow!`3`x`(_$,Integer,Row)->_$`cTwoDimensionalArrayCategory(R,Row,Col)``1186924 +osetScreenResolution`1`n`(Integer)->Integer`dPlot``1187266 +osetScreenResolution3D`1`n`(Integer)->Integer`dPlot3D``1187342 +osetSingularPoints`1`x`(List(ProjectivePlane(K)))->List(ProjectivePlane(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``0 +osetSingularPoints`1`x`(List(ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K)))->List(ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +osetSingularPoints`1`x`(List(ProjPt))->List(ProjPt)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``1187436 +osetStatus!`2`n`(_$,Boolean)->_$`dSplittingNode(V,C)``1187835 +osetStatus`2`n`(_$,Union(Boolean,"failed"))->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``1187991 osetsubMatrix!`4`n`(S,Integer,Integer,S)->S`xMatrixCategory&(S,R,Row,Col)``0 -osetsubMatrix!`4`x`(_$,Integer,Integer,_$)->_$`cMatrixCategory(R,Row,Col)``992684 +osetsubMatrix!`4`x`(_$,Integer,Integer,_$)->_$`cMatrixCategory(R,Row,Col)``1188346 +osetsubmult!`2`x`(_$,NonNegativeInteger)->NonNegativeInteger`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetsymbName!`2`x`(_$,Symbol)->Symbol`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osetTex!`2`x`(_$,List(String))->List(String)`dTexFormat``1188761 +osetTopPredicate`3`n`(_$,List(Symbol),Any)->_$`dPattern(R)``1188859 +osetTower!`1`x`(_$)->Void`cPseudoAlgebraicClosureOfPerfectFieldCategory``0 +osetUnion`2`x`(_$,_$)->_$`dList(S)`has(S,SetCategory)`1188994 osetvalue!`2`n`(A,S)->S`xUnaryRecursiveAggregate&(A,S)``0 -osetvalue!`2`x`(_$,S)->S`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`992906 -osh`2`x`(_$,NonNegativeInteger)->_$`cXFreeAlgebra(vl,R)`has(R,CommutativeRing)`992982 -osh`2`x`(_$,_$)->_$`cXFreeAlgebra(vl,R)`has(R,CommutativeRing)`993061 -oshade`1`n`(Point(R))->R`pPointPackage(R)``993190 -oshade`1`x`(_$)->Integer`dPalette``993519 -oshallowCopy`1`n`(_$)->_$`dSubSpace(n,R)``993601 -oshallowExpand`1`x`(_$)->OutputForm`dFreeNilpotentLie(n,class,R)``993644 -oshanksDiscLogAlgorithm`3`n`(M,M,NonNegativeInteger)->Union(NonNegativeInteger,"failed")`pDiscreteLogarithmPackage(M)``993691 -oshellSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``993970 +osetValue!`2`n`(_$,V)->_$`dSplittingNode(V,C)``1189164 +osetvalue!`2`x`(_$,S)->S`cRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1189318 +osetVariableOrder`1`x`(List(Symbol))->Void`pUserDefinedVariableOrdering``1189394 +osetVariableOrder`2`x`(List(Symbol),List(Symbol))->Void`pUserDefinedVariableOrdering``1189533 +oSFunction`1`x`(List(Integer))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``1189719 +osh`2`x`(_$,_$)->_$`cXFreeAlgebra(vl,R)`has(R,CommutativeRing)`1189880 +osh`2`x`(_$,NonNegativeInteger)->_$`cXFreeAlgebra(vl,R)`has(R,CommutativeRing)`1190009 +oshade`1`n`(Point(R))->R`pPointPackage(R)``1190088 +oshade`1`x`(_$)->Integer`dPalette``1190417 +oshallowCopy`1`n`(_$)->_$`dSubSpace(n,R)``1190499 +oshallowExpand`1`x`(_$)->OutputForm`dFreeNilpotentLie(n,class,R)``1190546 +oshanksDiscLogAlgorithm`3`n`(M,M,NonNegativeInteger)->Union(NonNegativeInteger,"failed")`pDiscreteLogarithmPackage(M)``1190595 +oshellSort`2`x`((S,S)->Boolean,V)->V`pFiniteLinearAggregateSort(S,V)``1190878 +oshift`1`n`(F)->_$`dMoebiusTransform(F)``1191003 +oshift`2`n`(_$,F)->_$`dMoebiusTransform(F)``1191108 +oshift`2`x`(_$,_$)->_$`cIntegerNumberSystem``1191198 +oshift`2`x`(_$,Integer)->_$`cLocalPowerSeriesCategory(K)``1191260 +oshift`2`x`(_$,Integer)->_$`dFloat``1191311 +oshift`2`x`(_$,Integer)->_$`dNonNegativeInteger``1191387 +oShiftAction`3`x`(NonNegativeInteger,NonNegativeInteger,V)->D`pFractionFreeFastGaussian(D,V)``1191447 +oShiftC`1`x`(NonNegativeInteger)->List(D)`pFractionFreeFastGaussian(D,V)``1191680 +oshiftHP`1`x`(List(GuessOption))->HPSPEC`pGuessUnivariatePolynomial(q)``1191991 +oshiftHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(AlgebraicNumber))->Stream(UnivariateFormalPowerSeries(AlgebraicNumber)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(A--lgebraicNumber))->AlgebraicNumber,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->SparseUnivariatePolynomial(AlgebraicNumber),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(AlgebraicNumber))`pGuessAlgebraicNumber``0 +oshiftHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Integer)))->Stream(UnivariateFormalPowerSeries(Fraction(Integer))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePoly--nomial(Integer))->Integer,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->SparseUnivariatePolynomial(Fraction(Integer)),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Integer))`pGuessInteger``0 +oshiftHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))->Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativ--eInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer)))->Polynomial(Integer),AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->SparseUnivariatePolynomial(Fraction(Polynomial(Integer))),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Polynomial(Integer)))`pGuessPolynomial``0 +oshiftHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F))->F,AF:(NonNegativeInteger,NonNegativeInteger,Univaria--teFormalPowerSeries(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(F))`pGuessFinite(F)``0 +oshiftHP`1`x`(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(EXPRR,Symbol)->Stream(EXPRR),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S))->S,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUn--ivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,EXPRR)->EXPRR,C:(NonNegativeInteger)->List(S))`pGuess(F,S,EXPRR,R,retract,coerce)``1192100 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->HPSPEC`pGuessUnivariatePolynomial(q)``1192209 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(AlgebraicNumber))->Stream(UnivariateFormalPowerSeries(AlgebraicNumber)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePo--lynomial(AlgebraicNumber))->AlgebraicNumber,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(AlgebraicNumber)))->SparseUnivariatePolynomial(AlgebraicNumber),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(AlgebraicNumber))`pGuessAlgebraicNumber`has(AlgebraicNumber,RetractableTo(Symbol))`0 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Integer)))->Stream(UnivariateFormalPowerSeries(Fraction(Integer))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer)))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUniv--ariatePolynomial(Integer))->Integer,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Integer))))->SparseUnivariatePolynomial(Fraction(Integer)),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Integer))`pGuessInteger`AND(has(Fraction(Integer),RetractableTo(Symbol)),has(Integer,RetractableTo(Symbol)))`0 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))))->Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer)))),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(--NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(Polynomial(Integer)))->Polynomial(Integer),AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))->SparseUnivariatePolynomial(Fraction(Polynomial(Integer))),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(Polynomial(Integer)))`pGuessPolynomial`AND(has(Fraction(Polynomial(Integer)),RetractableTo(Symbol)),--has(Polynomial(Integer),RetractableTo(Symbol)))`0 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(Expression(Integer),Symbol)->Stream(Expression(Integer)),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(F))->F,AF:(NonNegativeInteger,NonNegativeIntege--r,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,Expression(Integer))->Expression(Integer),C:(NonNegativeInteger)->List(F))`pGuessFinite(F)`has(F,RetractableTo(Symbol))`0 +oshiftHP`1`x`(Symbol)->(List(GuessOption))->Record(guessStream:(UnivariateFormalPowerSeries(F))->Stream(UnivariateFormalPowerSeries(F)),degreeStream:Stream(NonNegativeInteger),testStream:(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F)))->Stream(UnivariateFormalPowerSeries(SparseUnivariatePolynomial(F))),exprStream:(EXPRR,Symbol)->Stream(EXPRR),A:(NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial(S))->S,AF:(NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSerie--s(SparseUnivariatePolynomial(F)))->SparseUnivariatePolynomial(F),AX:(NonNegativeInteger,Symbol,EXPRR)->EXPRR,C:(NonNegativeInteger)->List(S))`pGuess(F,S,EXPRR,R,retract,coerce)`AND(has(F,RetractableTo(Symbol)),has(S,RetractableTo(Symbol)))`1192331 +oshiftInfoRec`3`x`(BasicOperator,Symbol,F)->Record(max:Union(Integer,"failed"),ord:Union(Integer,"failed"),ker:Kernel(F))`pRecurrenceOperator(R,F)`has(R,Ring)`0 oshiftLeft`2`n`(S,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 -oshiftLeft`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``994095 +oshiftLeft`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``1192453 oshiftRight`2`n`(S,NonNegativeInteger)->S`xUnivariatePolynomialCategory&(S,R)``0 -oshiftRight`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``994161 -oshiftRoots`2`n`(UP,R)->UP`pGaloisGroupPolynomialUtilities(R,UP)``994250 -oshift`1`n`(F)->_$`dMoebiusTransform(F)``994366 -oshift`2`n`(_$,F)->_$`dMoebiusTransform(F)``994471 -oshift`2`x`(_$,Integer)->_$`dFloat``994571 -oshift`2`x`(_$,Integer)->_$`dNonNegativeInteger``994647 -oshift`2`x`(_$,_$)->_$`cIntegerNumberSystem``994707 -oshowAll?`0`x`()->Boolean`dStream(S)`has(S,SetCategory)`994769 -oshowAllElements`1`x`(_$)->OutputForm`dStream(S)`has(S,SetCategory)`994868 -oshowArrayValues`1`x`(Boolean)->Boolean`dResult``994962 -oshowAttributes`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:--Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")),"failed")`dIntegrationFunctionsTable``995096 -oshowClipRegion`2`x`(_$,String)->Void`dThreeDimensionalViewport``995144 -oshowFortranOutputStack`0`x`()->Stack(String)`pFortranOutputStackPackage``995398 -oshowIntensityFunctions`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float),"failed")`dODEIntensityFunctionsTable``995470 -oshowRegion`2`x`(_$,String)->Void`dThreeDimensionalViewport``995576 -oshowScalarValues`1`x`(Boolean)->Boolean`dResult``995820 -oshowTheFTable`0`x`()->_$`dIntegrationFunctionsTable``995956 -oshowTheIFTable`0`x`()->_$`dODEIntensityFunctionsTable``996026 -oshowTheRoutinesTable`0`x`()->_$`dRoutinesTable``996107 -oshowTheSymbolTable`0`x`()->_$`dTheSymbolTable``996187 -oshowTypeInOutput`1`x`(Boolean)->String`dAny``996256 -oshow`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``996529 -oshrinkable`1`n`(Boolean)->Boolean`dIndexedFlexibleArray(S,mn)``996780 +oshiftRight`2`x`(_$,NonNegativeInteger)->_$`cUnivariatePolynomialCategory(R)``1192519 +oshiftRoots`2`n`(UP,R)->UP`pGaloisGroupPolynomialUtilities(R,UP)``1192608 +oshow`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``1192724 +oshowAll?`0`x`()->Boolean`dStream(S)`has(S,SetCategory)`1192975 +oshowAllElements`1`x`(_$)->OutputForm`dStream(S)`has(S,SetCategory)`1193074 +oshowArrayValues`1`x`(Boolean)->Boolean`dResult``1193350 +oshowAttributes`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(endPointContinuity:Union(continuous:"Continuous at the end points",lowerSingular:"There is a singularity at the lower end point",upperSingular:"There is a singularity at the upper end point",bothSingular:"There are singularities at both end points",notEvaluated:"End point continuity not yet evaluated"),singularitiesStream:Union(str:--Stream(DoubleFloat),notEvaluated:"Internal singularities not yet evaluated"),range:Union(finite:"The range is finite",lowerInfinite:"The bottom of range is infinite",upperInfinite:"The top of range is infinite",bothInfinite:"Both top and bottom points are infinite",notEvaluated:"Range not yet evaluated")),"failed")`dIntegrationFunctionsTable``1193484 +oshowClipRegion`2`x`(_$,String)->Void`dThreeDimensionalViewport``1193534 +oshowFortranOutputStack`0`x`()->Stack(String)`pFortranOutputStackPackage``1193788 +oshowIntensityFunctions`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Union(Record(stiffness:Float,stability:Float,expense:Float,accuracy:Float,intermediateResults:Float),"failed")`dODEIntensityFunctionsTable``1193860 +oshowRegion`2`x`(_$,String)->Void`dThreeDimensionalViewport``1193966 +oshowScalarValues`1`x`(Boolean)->Boolean`dResult``1194210 +oshowTheFTable`0`x`()->_$`dIntegrationFunctionsTable``1194346 +oshowTheIFTable`0`x`()->_$`dODEIntensityFunctionsTable``1194416 +oshowTheRoutinesTable`0`x`()->_$`dRoutinesTable``1194497 +oshowTheSymbolTable`0`x`()->_$`dTheSymbolTable``1194577 +oshowTypeInOutput`1`x`(Boolean)->String`dAny``1194646 +oshrinkable`1`n`(Boolean)->Boolean`dIndexedFlexibleArray(S,mn)``1194919 oshrinkable`1`x`(Boolean)->Boolean`dFlexibleArray(S)``0 -oshuffle`2`x`(List(Integer),List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``996900 -oshufflein`2`x`(List(Integer),Stream(List(Integer)))->Stream(List(Integer))`pPartitionsAndPermutations``997111 -osignAround`3`n`(UP,Integer,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``997261 -osignAround`3`n`(UP,R,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``997311 -osignAround`4`n`(UP,R,Integer,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``997361 -osign`1`n`(R)->Union(Integer,"failed")`pToolsForSign(R)``997415 +oshuffle`2`x`(List(Integer),List(Integer))->Stream(List(Integer))`pPartitionsAndPermutations``1195171 +oshufflein`2`x`(List(Integer),Stream(List(Integer)))->Stream(List(Integer))`pPartitionsAndPermutations``1195382 +oSi`1`n`(F)->F`pLiouvillianFunction(R,F)``1195532 +oSi`1`x`(_$)->_$`cLiouvillianFunctionCategory``1195585 +osign`1`n`(R)->Union(Integer,"failed")`pToolsForSign(R)``1195709 osign`1`n`(S)->Integer`xOrderedRing&(S)``0 -osign`1`x`(F)->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``997451 -osign`1`x`(Fraction(Polynomial(R)))->Union(Integer,"failed")`pRationalFunctionSign(R)``997532 -osign`1`x`(_$)->Integer`cOrderedRing``997612 -osign`1`x`(_$)->Integer`dPermutation(S)``997727 -osign`2`x`(ThePols,_$)->Integer`cRealRootCharacterizationCategory(TheField,ThePols)``997823 -osign`3`x`(F,Symbol,OrderedCompletion(F))->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``997915 -osign`3`x`(Fraction(Polynomial(R)),Symbol,OrderedCompletion(Fraction(Polynomial(R))))->Union(Integer,"failed")`pRationalFunctionSign(R)``998045 -osign`4`x`(F,Symbol,F,String)->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``998180 -osign`4`x`(Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R)),String)->Union(Integer,"failed")`pRationalFunctionSign(R)``998342 -osimpleBounds?`1`x`(List(Expression(DoubleFloat)))->Boolean`pe04AgentsPackage``998568 -osimplifyExp`1`x`(F)->F`pTranscendentalManipulations(R,F)``998667 -osimplifyLog`1`x`(F)->F`pTranscendentalManipulations(R,F)``998784 -osimplifyPower`2`x`(_$,Integer)->_$`dExpression(R)`has(R,IntegralDomain)`998995 -osimplify`1`n`(_$)->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`999054 -osimplify`1`x`(AlgebraicNumber)->Expression(Integer)`pSimplifyAlgebraicNumberConvertPackage``999358 -osimplify`1`x`(F)->F`pTranscendentalManipulations(R,F)``999422 -osimpson`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``999906 -osimpsono`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1000596 -osin2csc`1`x`(F)->F`pTranscendentalManipulations(R,F)``1001290 -osin?`1`n`(_$)->Boolean`dFourierComponent(E)``1001388 -osinIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1001473 -osin`1`n`(E)->_$`dFourierComponent(E)``1001560 -osin`1`n`(F)->F`pElementaryFunction(R,F)``1001626 +osign`1`x`(Fraction(Polynomial(R)))->Union(Integer,"failed")`pRationalFunctionSign(R)``1195745 +osign`1`x`(F)->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``1195825 +osign`1`x`(_$)->Integer`cOrderedRing``1195906 +osign`1`x`(_$)->Integer`dPermutation(S)``1196021 +osign`2`x`(ThePols,_$)->Integer`cRealRootCharacterizationCategory(TheField,ThePols)``1196117 +osign`3`x`(Fraction(Polynomial(R)),Symbol,OrderedCompletion(Fraction(Polynomial(R))))->Union(Integer,"failed")`pRationalFunctionSign(R)``1196209 +osign`3`x`(F,Symbol,OrderedCompletion(F))->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``1196344 +osign`4`x`(Fraction(Polynomial(R)),Symbol,Fraction(Polynomial(R)),String)->Union(Integer,"failed")`pRationalFunctionSign(R)``1196474 +osign`4`x`(F,Symbol,F,String)->Union(Integer,"failed")`pElementaryFunctionSign(R,F)``1196700 +osignAround`3`n`(UP,Integer,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``1196862 +osignAround`3`n`(UP,R,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``1196912 +osignAround`4`n`(UP,R,Integer,(R)->Union(Integer,"failed"))->Union(Integer,"failed")`pInnerPolySign(R,UP)``1196962 +osimpleBounds?`1`x`(List(Expression(DoubleFloat)))->Boolean`pe04AgentsPackage``1197016 +osimplify`1`n`(_$)->_$`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)`AND(has(R,CharacteristicZero),has(R,EuclideanDomain))`1197115 +osimplify`1`x`(AlgebraicNumber)->Expression(Integer)`pSimplifyAlgebraicNumberConvertPackage``1197419 +osimplify`1`x`(F)->F`pTranscendentalManipulations(R,F)``1197483 +osimplifyExp`1`x`(F)->F`pTranscendentalManipulations(R,F)``1197967 +osimplifyLog`1`x`(F)->F`pTranscendentalManipulations(R,F)``1198084 +osimplifyPower`2`x`(_$,Integer)->_$`dExpression(R)`has(R,IntegralDomain)`1198295 +osimpson`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1198356 +osimpsono`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1199046 +osin?`1`n`(_$)->Boolean`dFourierComponent(E)``1199740 +osin`1`n`(E)->_$`dFourierComponent(E)``1199825 +osin`1`n`(F)->F`pElementaryFunction(R,F)``1199891 osin`1`n`(S)->S`xComplexCategory&(S,R)``0 osin`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -osin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1001685 -osin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1001750 -osin`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1001815 -osin`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1001881 -osin`1`x`(_$)->_$`cTrigonometricFunctionCategory``1001949 -osin`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1002000 -osincos`1`n`(Stream(Coef))->Record(sin:Stream(Coef),cos:Stream(Coef))`pStreamTranscendentalFunctions(Coef)``1002067 -osingRicDE`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->Factored(UP))->List(Record(frac:Fraction(UP),eq:LinearOrdinaryDifferentialOperator2(UP,Fraction(UP))))`pRationalRicDE(F,UP)``1002169 -osingRicDE`3`n`(L,(UP,SparseUnivariatePolynomial(UP))->List(UP),(UP)->Factored(UP))->List(Record(frac:Fraction(UP),eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``1002654 -osingleFactorBound`1`n`(UP)->Integer`pGaloisGroupFactorizationUtilities(R,UP,F)``1003246 -osingleFactorBound`2`n`(UP,NonNegativeInteger)->Integer`pGaloisGroupFactorizationUtilities(R,UP,F)``1003436 -osingular?`1`x`(F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1003691 -osingular?`1`x`(UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1003758 -osingularAtInfinity?`0`x`()->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1003828 -osingularitiesOf`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Stream(DoubleFloat)`pd01AgentsPackage``1003909 -osingularitiesOf`3`x`(Expression(DoubleFloat),List(Symbol),Segment(OrderedCompletion(DoubleFloat)))->Stream(DoubleFloat)`pExpertSystemContinuityPackage``1004026 -osingularitiesOf`3`x`(Vector(Expression(DoubleFloat)),List(Symbol),Segment(OrderedCompletion(DoubleFloat)))->Stream(DoubleFloat)`pExpertSystemContinuityPackage``1004253 -osinh2csch`1`x`(F)->F`pTranscendentalManipulations(R,F)``1004480 -osinhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1004582 -osinh`1`n`(F)->F`pElementaryFunction(R,F)``1004671 +osin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1199950 +osin`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1200015 +osin`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1200080 +osin`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1200146 +osin`1`x`(_$)->_$`cTrigonometricFunctionCategory``1200214 +osin`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1200265 +osin2csc`1`x`(F)->F`pTranscendentalManipulations(R,F)``1200332 +osincos`1`n`(Stream(Coef))->Record(sin:Stream(Coef),cos:Stream(Coef))`pStreamTranscendentalFunctions(Coef)``1200430 +osingleFactorBound`1`n`(UP)->Integer`pGaloisGroupFactorizationUtilities(R,UP,F)``1200532 +osingleFactorBound`2`n`(UP,NonNegativeInteger)->Integer`pGaloisGroupFactorizationUtilities(R,UP,F)``1200722 +osingRicDE`2`n`(LinearOrdinaryDifferentialOperator2(UP,Fraction(UP)),(UP)->Factored(UP))->List(Record(frac:Fraction(UP),eq:LinearOrdinaryDifferentialOperator2(UP,Fraction(UP))))`pRationalRicDE(F,UP)``1200977 +osingRicDE`3`n`(L,(UP,SparseUnivariatePolynomial(UP))->List(UP),(UP)->Factored(UP))->List(Record(frac:Fraction(UP),eq:L))`pPrimitiveRatRicDE(F,UP,L,LQ)``1201462 +osingular?`1`x`(F)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1202054 +osingular?`1`x`(UP)->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1202121 +osingularAtInfinity?`0`x`()->Boolean`cFunctionFieldCategory(F,UP,UPUP)``1202191 +osingularitiesOf`1`x`(Record(var:Symbol,fn:Expression(DoubleFloat),range:Segment(OrderedCompletion(DoubleFloat)),abserr:DoubleFloat,relerr:DoubleFloat))->Stream(DoubleFloat)`pd01AgentsPackage``1202272 +osingularitiesOf`3`x`(Expression(DoubleFloat),List(Symbol),Segment(OrderedCompletion(DoubleFloat)))->Stream(DoubleFloat)`pExpertSystemContinuityPackage``1202389 +osingularitiesOf`3`x`(Vector(Expression(DoubleFloat)),List(Symbol),Segment(OrderedCompletion(DoubleFloat)))->Stream(DoubleFloat)`pExpertSystemContinuityPackage``1202616 +osingularPoints`0`x`()->List(ProjectivePlane(K))`pPackageForAlgebraicFunctionField(K,symb,BLMET)``1202843 +osingularPoints`0`x`()->List(ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``1203124 +osingularPoints`0`x`()->List(ProjPt)`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``1203405 +osingularPoints`1`x`(PolyRing)->List(ProjPt)`pProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt)``1203686 +osingularPointsWithRestriction`2`x`(PolyRing,List(PolyRing))->List(ProjPt)`pProjectiveAlgebraicSetPackage(K,symb,PolyRing,E,ProjPt)``1203745 +osinh`1`n`(F)->F`pElementaryFunction(R,F)``1203793 osinh`1`n`(S)->S`xComplexCategory&(S,R)``0 osinh`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 osinh`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -osinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1004742 -osinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1004823 -osinh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1004904 -osinh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1004982 -osinh`1`x`(_$)->_$`cHyperbolicFunctionCategory``1005062 -osinh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1005125 -osinhcosh`1`n`(Stream(Coef))->Record(sinh:Stream(Coef),cosh:Stream(Coef))`pStreamTranscendentalFunctions(Coef)``1005194 +osinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1203864 +osinh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1203945 +osinh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1204026 +osinh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1204104 +osinh`1`x`(_$)->_$`cHyperbolicFunctionCategory``1204184 +osinh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1204247 +osinh2csch`1`x`(F)->F`pTranscendentalManipulations(R,F)``1204316 +osinhcosh`1`n`(Stream(Coef))->Record(sinh:Stream(Coef),cosh:Stream(Coef))`pStreamTranscendentalFunctions(Coef)``1204418 +osinhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1204533 +osinIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1204622 +osize`0`n`()->NonNegativeInteger`xDirectProductCategory&(S,dim,R)``0 +osize`0`n`()->NonNegativeInteger`xFiniteAlgebraicExtensionField&(S,F)``0 +osize`0`n`()->NonNegativeInteger`xFiniteSetAggregate&(A,S)``0 +osize`0`n`()->NonNegativeInteger`xMonogenicAlgebra&(S,R,UP)``0 +osize`0`x`()->Integer`pRandomNumberSource``1204709 +osize`0`x`()->NonNegativeInteger`cFinite``1204773 +osize`1`n`(_$)->NonNegativeInteger`dFreeGroup(S)``1204837 +osize`1`n`(_$)->NonNegativeInteger`dFreeMonoid(S)``1204904 +osize`1`n`(_$)->NonNegativeInteger`dListMonoidOps(S,E,un)``1204971 +osize`1`n`(_$)->NonNegativeInteger`dOrderedFreeMonoid(S)``1205043 +osize`1`x`(_$)->NonNegativeInteger`cFreeAbelianMonoidCategory(S,E)``1205205 +osize`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``1205402 osize?`2`n`(A,NonNegativeInteger)->Boolean`xLazyStreamAggregate&(A,S)``0 osize?`2`n`(A,NonNegativeInteger)->Boolean`xUnaryRecursiveAggregate&(A,S)``0 osize?`2`n`(S,NonNegativeInteger)->Boolean`xAggregate&(S)``0 osize?`2`n`(S,NonNegativeInteger)->Boolean`xTwoDimensionalArrayCategory&(S,R,Row,Col)``0 -osize?`2`x`(_$,NonNegativeInteger)->Boolean`cAggregate``1005309 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`cAggregate``1205444 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`dArrayStack(S)``1205520 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`dDequeue(S)``1205619 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`dHeap(S)``1205712 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`dQueue(S)``1205799 +osize?`2`x`(_$,NonNegativeInteger)->Boolean`dStack(S)``1205888 osizeLess?`2`n`(S,S)->Boolean`xEuclideanDomain&(S)``0 -osizeLess?`2`x`(_$,_$)->Boolean`cEuclideanDomain``1005385 -osizeMultiplication`0`n`()->NonNegativeInteger`dFiniteFieldNormalBasisExtension(GF,extdeg)``1005539 -osizeMultiplication`0`n`()->NonNegativeInteger`dFiniteFieldNormalBasisExtensionByPolynomial(GF,uni)``1005719 -osizeMultiplication`0`x`()->NonNegativeInteger`dFiniteFieldNormalBasis(p,extdeg)``1005899 -osizeMultiplication`1`n`(Vector(List(Record(value:GF,index:SingleInteger))))->NonNegativeInteger`pFiniteFieldFunctions(GF)``1006079 -osizePascalTriangle`0`n`()->NonNegativeInteger`pGaloisGroupUtilities(R)``1006182 -osize`0`n`()->NonNegativeInteger`xDirectProductCategory&(S,dim,R)``0 -osize`0`n`()->NonNegativeInteger`xFiniteAlgebraicExtensionField&(S,F)``0 -osize`0`n`()->NonNegativeInteger`xFiniteSetAggregate&(A,S)``0 -osize`0`n`()->NonNegativeInteger`xMonogenicAlgebra&(S,R,UP)``0 -osize`0`x`()->Integer`pRandomNumberSource``1006278 -osize`0`x`()->NonNegativeInteger`cFinite``1006342 -osize`1`n`(_$)->NonNegativeInteger`dFreeGroup(S)``1006406 -osize`1`n`(_$)->NonNegativeInteger`dFreeMonoid(S)``1006473 -osize`1`n`(_$)->NonNegativeInteger`dListMonoidOps(S,E,un)``1006540 -osize`1`n`(_$)->NonNegativeInteger`dOrderedFreeMonoid(S)``1006612 -osize`1`x`(_$)->NonNegativeInteger`cFreeAbelianMonoidCategory(S,E)``1006679 -osize`1`x`(_$)->TheField`dRightOpenIntervalRootCharacterization(TheField,ThePolDom)``1006848 -oskewSFunction`2`x`(List(Integer),List(Integer))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``1006890 -oslash`2`n`(_$,_$)->_$`dOutputForm``1007080 -oslex`1`n`(List(S))->List(List(S))`pTableauxBumpers(S)``1007177 -osmith`1`x`(M)->M`pSmithNormalForm(R,Row,Col,M)``1007371 -osn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``1007448 -osncndn`2`n`(Stream(Coef),Coef)->List(Stream(Coef))`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``1007546 -osocf2socdf`1`x`(Segment(OrderedCompletion(Float)))->Segment(OrderedCompletion(DoubleFloat))`pExpertSystemToolsPackage``1007594 -osolid?`1`n`(_$)->Boolean`dSubSpaceComponentProperty``1007748 -osolid`2`n`(_$,Boolean)->Boolean`dSubSpaceComponentProperty``1007786 -osolve1`2`n`(SparseUnivariatePolynomial(K),Par)->List(F)`pInnerNumericEigenPackage(K,F,Par)``1007827 -osolveInField`1`n`(List(Polynomial(R)))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1008098 -osolveInField`2`n`(List(Polynomial(R)),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1008248 -osolveInField`3`n`(Matrix(LO),Vector(F),(LO,F)->Record(particular:Union(F,"failed"),basis:List(F)))->Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F)))`pSystemODESolver(F,LO)``1008395 -osolveLinearPolynomialEquationByFractions`2`n`(List(SparseUnivariatePolynomial(R)),SparseUnivariatePolynomial(R))->Union(List(SparseUnivariatePolynomial(R)),"failed")`pLinearPolynomialEquationByFractions(R)``1008816 -osolveLinearPolynomialEquationByRecursion`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`pPolynomialFactorizationByRecursion(R,E,VarSet,S)``1009065 -osolveLinearPolynomialEquationByRecursion`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`pPolynomialFactorizationByRecursionUnivariate(R,S)``1009486 -osolveLinearPolynomialEquation`2`n`(List(FPP),FPP)->Union(List(FPP),"failed")`pFiniteFieldSolveLinearPolynomialEquation(F,FP,FPP)``1009907 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+osizePascalTriangle`0`n`()->NonNegativeInteger`pGaloisGroupUtilities(R)``1206775 +oskewSFunction`2`x`(List(Integer),List(Integer))->SymmetricPolynomial(Fraction(Integer))`pCycleIndicators``1206871 +oslash`2`n`(_$,_$)->_$`dOutputForm``1207061 +oslex`1`n`(List(S))->List(List(S))`pTableauxBumpers(S)``1207158 +oslope`1`x`(List(PolyRing))->Record(height:Integer,base:Integer,quotient:Integer,reste:Integer,type:Union("left","center","right","vertical","horizontal"))`pNewtonPolygon(K,PolyRing,E,dim)``0 +oslope`2`x`(PolyRing,PolyRing)->Record(height:Integer,base:Integer,quotient:Integer,reste:Integer,type:Union("left","center","right","vertical","horizontal"))`pNewtonPolygon(K,PolyRing,E,dim)``0 +osmith`1`x`(M)->M`pSmithNormalForm(R,Row,Col,M)``1207315 +osn`2`n`(UTS,Coef)->UTS`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``1207392 +osncndn`2`n`(Stream(Coef),Coef)->List(Stream(Coef))`pEllipticFunctionsUnivariateTaylorSeries(Coef,UTS)``1207490 +osocf2socdf`1`x`(Segment(OrderedCompletion(Float)))->Segment(OrderedCompletion(DoubleFloat))`pExpertSystemToolsPackage``1207538 +osolid?`1`n`(_$)->Boolean`dSubSpaceComponentProperty``1207692 +osolid`2`n`(_$,Boolean)->Boolean`dSubSpaceComponentProperty``1207734 +osolve`10`x`(Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String,DoubleFloat)->Result`pAnnaPartialDifferentialEquationPackage``1207779 +osolve1`2`n`(SparseUnivariatePolynomial(K),Par)->List(F)`pInnerNumericEigenPackage(K,F,Par)``1209001 +osolve`1`n`(List(Polynomial(R)))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1209272 +osolve`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``1209452 +osolve`1`x`(Equation(Expression(R)))->List(Equation(Expression(R)))`pTransSolvePackage(R)``1209489 +osolve`1`x`(Equation(Fraction(Polynomial(R))))->List(Equation(Fraction(Polynomial(R))))`pSystemSolvePackage(R)``1209699 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+osolve`2`x`(Matrix(F),Vector(F))->Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F)))`pLinearSystemMatrixPackage1(F)``1215757 +osolve`2`x`(M,Col)->Record(particular:Union(Col,"failed"),basis:List(Col))`pLinearSystemMatrixPackage(F,Row,Col,M)``1215904 +osolve`2`x`(M,List(Col))->List(Record(particular:Union(Col,"failed"),basis:List(Col)))`pLinearSystemMatrixPackage(F,Row,Col,M)``1216051 +osolve`2`x`(NumericalODEProblem,RoutinesTable)->Result`pAnnaOrdinaryDifferentialEquationPackage``1216259 +osolve`2`x`(NumericalPDEProblem,RoutinesTable)->Result`pAnnaPartialDifferentialEquationPackage``1217502 +osolve`3`n`(Matrix(F),Vector(F),(LO,F)->Union(Record(particular:F,basis:List(F)),"failed"))->Union(Record(particular:Vector(F),basis:Matrix(F)),"failed")`pSystemODESolver(F,LO)``1218153 +osolve`3`x`(Equation(F),BasicOperator,Symbol)->Union(Record(particular:F,basis:List(F)),F,"failed")`pElementaryFunctionODESolver(R,F)``1218575 +osolve`3`x`(F,BasicOperator,Symbol)->Union(Record(particular:F,basis:List(F)),F,"failed")`pElementaryFunctionODESolver(R,F)``1219377 +osolve`3`x`(L,F,Symbol)->Union(Record(particular:F,basis:List(F)),"failed")`pElementaryFunctionLODESolver(R,F,L)``1220132 +osolve`3`x`(List(Equation(F)),List(BasicOperator),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1220707 +osolve`3`x`(List(F),List(BasicOperator),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1221127 +osolve`3`x`(Matrix(F),Vector(F),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1221547 +osolve`4`n`(F,F,BasicOperator,Symbol)->Union(F,"failed")`pNonLinearFirstOrderODESolver(R,F)``1221871 +osolve`4`x`(Equation(F),BasicOperator,Equation(F),List(F))->Union(F,"failed")`pElementaryFunctionODESolver(R,F)``1222124 +osolve`4`x`(F,BasicOperator,Equation(F),List(F))->Union(F,"failed")`pElementaryFunctionODESolver(R,F)``1222415 +osolve`4`x`(Vector(Expression(Float)),Float,Float,List(Float))->Result`pAnnaOrdinaryDifferentialEquationPackage``1222706 +osolve`5`x`(L,F,Symbol,F,List(F))->Union(F,"failed")`pElementaryFunctionLODESolver(R,F,L)``1223932 +osolve`5`x`(Vector(Expression(Float)),Float,Float,List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1224177 +osolve`6`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1225403 +osolve`6`x`(Vector(Expression(Float)),Float,Float,List(Float),List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1226783 +osolve`7`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1228134 +osolve`8`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float,Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1229649 +osolve`9`x`(Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String)->Result`pAnnaPartialDifferentialEquationPackage``1231238 +osolveid`3`n`(BP,R,Vector(List(BP)))->Union(List(BP),"failed")`pGenExEuclid(R,BP)``1232445 +osolveInField`1`n`(List(Polynomial(R)))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1232627 +osolveInField`2`n`(List(Polynomial(R)),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1232777 +osolveInField`3`n`(Matrix(LO),Vector(F),(LO,F)->Record(particular:Union(F,"failed"),basis:List(F)))->Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F)))`pSystemODESolver(F,LO)``1232924 +osolveLinear`2`n`(Vector(R),R)->Union(Vector(Fraction(S)),"failed")`pLinearDependence(S,R)`NOT(has(S,Field))`1233345 +osolveLinear`2`n`(Vector(R),R)->Union(Vector(S),"failed")`pLinearDependence(S,R)`has(S,Field)`1233548 +osolveLinearlyOverQ`2`x`(Vector(R),R)->Union(Vector(Fraction(Integer)),"failed")`pIntegerLinearDependence(R)``1233729 +osolveLinearPolynomialEquation`2`n`(List(FPP),FPP)->Union(List(FPP),"failed")`pFiniteFieldSolveLinearPolynomialEquation(F,FP,FPP)``1233922 +osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(CR)),SparseUnivariatePolynomial(CR))->Union(List(SparseUnivariatePolynomial(CR)),"failed")`pComplexIntegerSolveLinearPolynomialEquation(R,CR)``1234187 +osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(Integer)),SparseUnivariatePolynomial(Integer))->Union(List(SparseUnivariatePolynomial(Integer)),"failed")`pIntegerSolveLinearPolynomialEquation``1234512 osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`xComplexCategory&(S,R)``0 osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`xPolynomialCategory&(S,R,E,VarSet)``0 osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`xPolynomialFactorizationExplicit&(S)``0 osolveLinearPolynomialEquation`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`xUnivariatePolynomialCategory&(S,R)``0 -osolveLinearPolynomialEquation`2`x`(List(SparseUnivariatePolynomial(_$)),SparseUnivariatePolynomial(_$))->Union(List(SparseUnivariatePolynomial(_$)),"failed")`cPolynomialFactorizationExplicit``1010762 -osolveLinear`2`n`(Vector(R),R)->Union(Vector(Fraction(S)),"failed")`pLinearDependence(S,R)`NOT(has(S,Field))`1011027 -osolveLinear`2`n`(Vector(R),R)->Union(Vector(S),"failed")`pLinearDependence(S,R)`has(S,Field)`1011230 -osolveLinearlyOverQ`2`x`(Vector(R),R)->Union(Vector(Fraction(Integer)),"failed")`pIntegerLinearDependence(R)``1011411 -osolveRetract`2`n`(List(Polynomial(R)),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pRetractSolvePackage(Q,R)``1011604 -osolve`10`x`(Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String,DoubleFloat)->Result`pAnnaPartialDifferentialEquationPackage``1011859 -osolve`1`n`(List(Polynomial(R)))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1013081 -osolve`1`n`(UP)->List(F)`pPolynomialSolveByFormulas(UP,F)``1013261 -osolve`1`x`(Equation(Expression(R)))->List(Equation(Expression(R)))`pTransSolvePackage(R)``1013298 -osolve`1`x`(Equation(Fraction(Polynomial(R))))->List(Equation(Fraction(Polynomial(R))))`pSystemSolvePackage(R)``1013508 -osolve`1`x`(Expression(R))->List(Equation(Expression(R)))`pTransSolvePackage(R)``1013638 -osolve`1`x`(Fraction(Polynomial(R)))->List(Equation(Fraction(Polynomial(R))))`pSystemSolvePackage(R)``1013837 -osolve`1`x`(List(Equation(Fraction(Polynomial(R)))))->List(List(Equation(Fraction(Polynomial(R)))))`pSystemSolvePackage(R)``1013974 -osolve`1`x`(List(Fraction(Polynomial(R))))->List(List(Equation(Fraction(Polynomial(R)))))`pSystemSolvePackage(R)``1014127 -osolve`1`x`(NumericalODEProblem)->Result`pAnnaOrdinaryDifferentialEquationPackage``1014267 -osolve`1`x`(NumericalPDEProblem)->Result`pAnnaPartialDifferentialEquationPackage``1015454 -osolve`2`n`(List(Polynomial(R)),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pNonLinearSolvePackage(R)``1016087 -osolve`2`n`(Polynomial(Fraction(Integer)),Float)->List(Float)`pRealSolvePackage``1016264 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-osolve`2`x`(List(Equation(Fraction(Polynomial(Integer)))),Par)->List(List(Equation(Polynomial(Par))))`pFloatingRealPackage(Par)``1017697 -osolve`2`x`(List(Equation(Fraction(Polynomial(R)))),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pSystemSolvePackage(R)``1017908 -osolve`2`x`(List(Fraction(Polynomial(Integer))),Par)->List(List(Equation(Polynomial(Par))))`pFloatingRealPackage(Par)``1018061 -osolve`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pSystemSolvePackage(R)``1018282 -osolve`2`x`(List(List(F)),List(Vector(F)))->List(Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F))))`pLinearSystemMatrixPackage1(F)``1018422 -osolve`2`x`(List(List(F)),Vector(F))->Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F)))`pLinearSystemMatrixPackage1(F)``1018630 -osolve`2`x`(M,Col)->Record(particular:Union(Col,"failed"),basis:List(Col))`pLinearSystemMatrixPackage(F,Row,Col,M)``1018777 -osolve`2`x`(M,List(Col))->List(Record(particular:Union(Col,"failed"),basis:List(Col)))`pLinearSystemMatrixPackage(F,Row,Col,M)``1018924 -osolve`2`x`(Matrix(F),List(Vector(F)))->List(Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F))))`pLinearSystemMatrixPackage1(F)``1019132 -osolve`2`x`(Matrix(F),Symbol)->Union(List(Vector(F)),"failed")`pElementaryFunctionODESolver(R,F)``1019340 -osolve`2`x`(Matrix(F),Vector(F))->Record(particular:Union(Vector(F),"failed"),basis:List(Vector(F)))`pLinearSystemMatrixPackage1(F)``1019459 -osolve`2`x`(NumericalODEProblem,RoutinesTable)->Result`pAnnaOrdinaryDifferentialEquationPackage``1019606 -osolve`2`x`(NumericalPDEProblem,RoutinesTable)->Result`pAnnaPartialDifferentialEquationPackage``1020849 -osolve`3`n`(Matrix(F),Vector(F),(LO,F)->Union(Record(particular:F,basis:List(F)),"failed"))->Union(Record(particular:Vector(F),basis:Matrix(F)),"failed")`pSystemODESolver(F,LO)``1021500 -osolve`3`x`(Equation(F),BasicOperator,Symbol)->Union(Record(particular:F,basis:List(F)),F,"failed")`pElementaryFunctionODESolver(R,F)``1021922 -osolve`3`x`(F,BasicOperator,Symbol)->Union(Record(particular:F,basis:List(F)),F,"failed")`pElementaryFunctionODESolver(R,F)``1022724 -osolve`3`x`(L,F,Symbol)->Union(Record(particular:F,basis:List(F)),"failed")`pElementaryFunctionLODESolver(R,F,L)``1023479 -osolve`3`x`(List(Equation(F)),List(BasicOperator),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1024054 -osolve`3`x`(List(F),List(BasicOperator),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1024474 -osolve`3`x`(Matrix(F),Vector(F),Symbol)->Union(Record(particular:Vector(F),basis:List(Vector(F))),"failed")`pElementaryFunctionODESolver(R,F)``1024894 -osolve`4`n`(F,F,BasicOperator,Symbol)->Union(F,"failed")`pNonLinearFirstOrderODESolver(R,F)``1025218 -osolve`4`x`(Equation(F),BasicOperator,Equation(F),List(F))->Union(F,"failed")`pElementaryFunctionODESolver(R,F)``1025471 -osolve`4`x`(F,BasicOperator,Equation(F),List(F))->Union(F,"failed")`pElementaryFunctionODESolver(R,F)``1025762 -osolve`4`x`(Vector(Expression(Float)),Float,Float,List(Float))->Result`pAnnaOrdinaryDifferentialEquationPackage``1026053 -osolve`5`x`(L,F,Symbol,F,List(F))->Union(F,"failed")`pElementaryFunctionLODESolver(R,F,L)``1027279 -osolve`5`x`(Vector(Expression(Float)),Float,Float,List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1027524 -osolve`6`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1028750 -osolve`6`x`(Vector(Expression(Float)),Float,Float,List(Float),List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1030130 -osolve`7`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1031481 -osolve`8`x`(Vector(Expression(Float)),Float,Float,List(Float),Expression(Float),List(Float),Float,Float)->Result`pAnnaOrdinaryDifferentialEquationPackage``1032996 -osolve`9`x`(Float,Float,Float,Float,NonNegativeInteger,NonNegativeInteger,List(Expression(Float)),List(List(Expression(Float))),String)->Result`pAnnaPartialDifferentialEquationPackage``1034585 -osolveid`3`n`(BP,R,Vector(List(BP)))->Union(List(BP),"failed")`pGenExEuclid(R,BP)``1035792 -osomeBasis`0`x`()->Vector(_$)`cFiniteRankNonAssociativeAlgebra(R)``1035974 +osolveLinearPolynomialEquation`2`x`(List(SparseUnivariatePolynomial(_$)),SparseUnivariatePolynomial(_$))->Union(List(SparseUnivariatePolynomial(_$)),"failed")`cPolynomialFactorizationExplicit``1234777 +osolveLinearPolynomialEquationByFractions`2`n`(List(SparseUnivariatePolynomial(R)),SparseUnivariatePolynomial(R))->Union(List(SparseUnivariatePolynomial(R)),"failed")`pLinearPolynomialEquationByFractions(R)``1235042 +osolveLinearPolynomialEquationByRecursion`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`pPolynomialFactorizationByRecursion(R,E,VarSet,S)``1235291 +osolveLinearPolynomialEquationByRecursion`2`n`(List(SparseUnivariatePolynomial(S)),SparseUnivariatePolynomial(S))->Union(List(SparseUnivariatePolynomial(S)),"failed")`pPolynomialFactorizationByRecursionUnivariate(R,S)``1235712 +osolveRetract`2`n`(List(Polynomial(R)),List(Symbol))->List(List(Equation(Fraction(Polynomial(R)))))`pRetractSolvePackage(Q,R)``1236133 +osomeBasis`0`x`()->Vector(_$)`cFiniteRankNonAssociativeAlgebra(R)``1236388 +osort`1`n`(A)->A`xFiniteLinearAggregate&(A,S)``0 osort!`1`n`(A)->A`xFiniteLinearAggregate&(A,S)``0 osort!`1`n`(A)->A`xListAggregate&(A,S)``0 osort!`1`n`(A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -osort!`1`x`(_$)->_$`cFiniteLinearAggregate(S)`AND(has(_$,ATTRIBUTE(shallowlyMutable)),has(S,OrderedSet))`1036036 +osort!`1`x`(_$)->_$`cFiniteLinearAggregate(S)`AND(has(_$,ATTRIBUTE(shallowlyMutable)),has(S,OrderedSet))`1236450 +osort`1`x`(_$)->_$`cFiniteLinearAggregate(S)`has(S,OrderedSet)`1236528 +osort`1`x`(List(_$))->List(_$)`dPermutation(S)``1236667 +osort`2`n`((S,S)->Boolean,A)->A`xFiniteLinearAggregate&(A,S)``0 osort!`2`n`((S,S)->Boolean,A)->A`xFiniteLinearAggregate&(A,S)``0 osort!`2`n`((S,S)->Boolean,A)->A`xListAggregate&(A,S)``0 osort!`2`n`((S,S)->Boolean,A)->A`xOneDimensionalArrayAggregate&(A,S)``0 -osort!`2`x`((S,S)->Boolean,_$)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1036114 -osortConstraints`1`x`(Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))))->Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat)))`pe04AgentsPackage``1036197 -osort`1`n`(A)->A`xFiniteLinearAggregate&(A,S)``0 -osort`1`x`(List(_$))->List(_$)`dPermutation(S)``1036406 -osort`1`x`(_$)->_$`cFiniteLinearAggregate(S)`has(S,OrderedSet)`1036690 -osort`2`n`((S,S)->Boolean,A)->A`xFiniteLinearAggregate&(A,S)``0 osort`2`n`(S,VarSet)->Record(under:S,floor:S,upper:S)`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -osort`2`x`((S,S)->Boolean,_$)->_$`cFiniteLinearAggregate(S)``1036825 -osort`2`x`(_$,VarSet)->Record(under:_$,floor:_$,upper:_$)`cPolynomialSetCategory(R,E,VarSet,P)``1036927 +osort!`2`x`((S,S)->Boolean,_$)->_$`cFiniteLinearAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1236952 +osort`2`x`((S,S)->Boolean,_$)->_$`cFiniteLinearAggregate(S)``1237035 +osort`2`x`(_$,VarSet)->Record(under:_$,floor:_$,upper:_$)`cPolynomialSetCategory(R,E,VarSet,P)``1237137 +osortConstraints`1`x`(Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat))))->Record(fn:Expression(DoubleFloat),init:List(DoubleFloat),lb:List(OrderedCompletion(DoubleFloat)),cf:List(Expression(DoubleFloat)),ub:List(OrderedCompletion(DoubleFloat)))`pe04AgentsPackage``1237420 osorted?`1`n`(A)->Boolean`xFiniteLinearAggregate&(A,S)``0 osorted?`1`n`(A)->Boolean`xListAggregate&(A,S)``0 osorted?`1`n`(A)->Boolean`xOneDimensionalArrayAggregate&(A,S)``0 -osorted?`1`x`(_$)->Boolean`cFiniteLinearAggregate(S)`has(S,OrderedSet)`1037210 +osorted?`1`x`(_$)->Boolean`cFiniteLinearAggregate(S)`has(S,OrderedSet)`1237629 osorted?`2`n`((S,S)->Boolean,A)->Boolean`xFiniteLinearAggregate&(A,S)``0 osorted?`2`n`((S,S)->Boolean,A)->Boolean`xListAggregate&(A,S)``0 osorted?`2`n`((S,S)->Boolean,A)->Boolean`xOneDimensionalArrayAggregate&(A,S)``0 -osorted?`2`x`((S,S)->Boolean,_$)->Boolean`cFiniteLinearAggregate(S)``1037293 -ospace`0`x`()->_$`dCharacter``1037384 -ospace`1`n`(List(DrawOption))->ThreeSpace(DoubleFloat)`pDrawOptionFunctions0``1037436 -ospace`1`x`(ThreeSpace(DoubleFloat))->_$`dDrawOption``1037636 -osparsityIF`1`x`(Matrix(Expression(DoubleFloat)))->Float`pd02AgentsPackage``1037747 -ospecialTrigs`2`n`(F,List(Record(func:F,pole:Boolean)))->Union(F,"failed")`pElementaryFunction(R,F)``1037820 -ospherical`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``1037886 +osorted?`2`x`((S,S)->Boolean,_$)->Boolean`cFiniteLinearAggregate(S)``1237712 +ospace`0`x`()->_$`dCharacter``1237803 +ospace`1`n`(List(DrawOption))->ThreeSpace(DoubleFloat)`pDrawOptionFunctions0``1237890 +ospace`1`x`(ThreeSpace(DoubleFloat))->_$`dDrawOption``1238090 +osparsityIF`1`x`(Matrix(Expression(DoubleFloat)))->Float`pd02AgentsPackage``1238201 +ospecialTrigs`2`n`(F,List(Record(func:F,pole:Boolean)))->Union(F,"failed")`pElementaryFunction(R,F)``1238274 +ospherical`1`x`(Point(R))->Point(R)`pCoordinateSystems(R)``1238340 +osplit`1`x`(IntegrationResult(F))->IntegrationResult(F)`pIntegrationResultToFunction(R,F)``1238606 +osplit`1`x`(IntegrationResult(Fraction(Polynomial(R))))->IntegrationResult(Fraction(Polynomial(R)))`pIntegrationResultRFToFunction(R)``1238795 +osplit`1`x`(_$)->List(_$)`cDivisorCategory(S)``1238984 +osplit`1`x`(UP)->Factored(UP)`pAlgFactor(UP)``1239127 osplit!`2`n`(A,Integer)->A`xUnaryRecursiveAggregate&(A,S)``0 -osplit!`2`x`(_$,Integer)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1038152 -osplitConstant`2`n`(F,Symbol)->Record(const:F,nconst:F)`pPatternMatchIntegration(R,F)``1038419 -osplitDenominator`1`n`(B)->Record(num:A,den:R)`pInnerCommonDenominator(R,Q,A,B)``1038546 -osplitDenominator`1`x`(A)->Record(num:A,den:R)`pCommonDenominator(R,Q,A)``1038731 -osplitDenominator`1`x`(Matrix(Q))->Record(num:Matrix(R),den:R)`pMatrixCommonDenominator(R,Q)``1038916 -osplitDenominator`1`x`(UP)->Record(num:UP,den:R)`pUnivariatePolynomialCommonDenominator(R,Q,UP)``1039066 -osplitDenominator`2`n`(LQ,List(Fraction(UP)))->Record(eq:L,rh:List(Fraction(UP)))`pPrimitiveRatDE(F,UP,L,LQ)``1039220 -osplitLinear`1`x`(Expression(DoubleFloat))->Expression(DoubleFloat)`pe04AgentsPackage``1039434 -osplitNodeOf!`3`n`(_$,_$,List(SplittingNode(V,C)))->_$`dSplittingTree(V,C)``1039523 -osplitNodeOf!`4`n`(_$,_$,List(SplittingNode(V,C)),(C,C)->Boolean)->_$`dSplittingTree(V,C)``1039834 -osplitSquarefree`2`n`(UP,(UP)->UP)->Record(normal:Factored(UP),special:Factored(UP))`pMonomialExtensionTools(F,UP)``1040162 -osplit`1`x`(IntegrationResult(F))->IntegrationResult(F)`pIntegrationResultToFunction(R,F)``1040498 -osplit`1`x`(IntegrationResult(Fraction(Polynomial(R))))->IntegrationResult(Fraction(Polynomial(R)))`pIntegrationResultRFToFunction(R)``1040687 -osplit`1`x`(UP)->Factored(UP)`pAlgFactor(UP)``1040876 -osplit`2`n`(UP,(UP)->UP)->Record(normal:UP,special:UP)`pMonomialExtensionTools(F,UP)``1040967 -osplit`2`x`(List(Matrix(R)),Vector(R))->List(List(Matrix(R)))`pRepresentationPackage2(R)`has(R,Field)`1041233 -osplit`2`x`(List(Matrix(R)),Vector(Vector(R)))->List(List(Matrix(R)))`pRepresentationPackage2(R)`has(R,Field)`1042046 -osplit`2`x`(S,_$)->Record(less:_$,greater:_$)`dBinarySearchTree(S)``1042207 -osplit`2`x`(_$,Character)->List(_$)`cStringAggregate``1042367 -osplit`2`x`(_$,CharacterClass)->List(_$)`cStringAggregate``1042456 -osqfrFactor`2`x`(R,Integer)->_$`dFactored(R)``1042551 -osqfree`1`n`(GR)->GR`pParametricLinearEquations(R,Var,Expon,GR)``1042705 +osplit`2`n`(UP,(UP)->UP)->Record(normal:UP,special:UP)`pMonomialExtensionTools(F,UP)``1239218 +osplit`2`x`(_$,CharacterClass)->List(_$)`cStringAggregate``1239484 +osplit`2`x`(_$,Character)->List(_$)`cStringAggregate``1239579 +osplit!`2`x`(_$,Integer)->_$`cUnaryRecursiveAggregate(S)`has(_$,ATTRIBUTE(shallowlyMutable))`1239668 +osplit`2`x`(List(Matrix(R)),Vector(R))->List(List(Matrix(R)))`pRepresentationPackage2(R)`has(R,Field)`1239939 +osplit`2`x`(List(Matrix(R)),Vector(Vector(R)))->List(List(Matrix(R)))`pRepresentationPackage2(R)`has(R,Field)`1240766 +osplit`2`x`(S,_$)->Record(less:_$,greater:_$)`dBinarySearchTree(S)``1240921 +osplitConstant`2`n`(F,Symbol)->Record(const:F,nconst:F)`pPatternMatchIntegration(R,F)``1241203 +osplitDenominator`1`n`(B)->Record(num:A,den:R)`pInnerCommonDenominator(R,Q,A,B)``1241330 +osplitDenominator`1`x`(A)->Record(num:A,den:R)`pCommonDenominator(R,Q,A)``1241515 +osplitDenominator`1`x`(Matrix(Q))->Record(num:Matrix(R),den:R)`pMatrixCommonDenominator(R,Q)``1241700 +osplitDenominator`1`x`(UP)->Record(num:UP,den:R)`pUnivariatePolynomialCommonDenominator(R,Q,UP)``1241850 +osplitDenominator`2`n`(LQ,List(Fraction(UP)))->Record(eq:L,rh:List(Fraction(UP)))`pPrimitiveRatDE(F,UP,L,LQ)``1242004 +osplitLinear`1`x`(Expression(DoubleFloat))->Expression(DoubleFloat)`pe04AgentsPackage``1242218 +osplitNodeOf!`3`n`(_$,_$,List(SplittingNode(V,C)))->_$`dSplittingTree(V,C)``1242307 +osplitNodeOf!`4`n`(_$,_$,List(SplittingNode(V,C)),(C,C)->Boolean)->_$`dSplittingTree(V,C)``1242618 +osplitSquarefree`2`n`(UP,(UP)->UP)->Record(normal:Factored(UP),special:Factored(UP))`pMonomialExtensionTools(F,UP)``1242946 +osPol`1`n`(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))->Dpol`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1243282 +osqfree`1`n`(GR)->GR`pParametricLinearEquations(R,Var,Expon,GR)``1243315 +osqfrFactor`2`x`(R,Integer)->_$`dFactored(R)``1243394 osqrt`1`n`(Fraction(Integer))->S`xRealClosedField&(S)``0 osqrt`1`n`(Integer)->S`xRealClosedField&(S)``0 osqrt`1`n`(S)->S`xRadicalCategory&(S)``0 osqrt`1`n`(S)->S`xRealClosedField&(S)``0 -osqrt`1`x`(Fraction(Integer))->_$`cRealClosedField``1042784 -osqrt`1`x`(Integer)->_$`cRealClosedField``1042850 -osqrt`1`x`(_$)->_$`cRadicalCategory``1042916 -osqrt`1`x`(_$)->_$`cRealClosedField``1042975 -osqrt`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1043041 +osqrt`1`x`(_$)->_$`cRadicalCategory``1243641 +osqrt`1`x`(_$)->_$`cRealClosedField``1243700 +osqrt`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1243766 +osqrt`1`x`(Fraction(Integer))->_$`cRealClosedField``1243835 +osqrt`1`x`(Integer)->_$`cRealClosedField``1243901 osqrt`2`n`(S,NonNegativeInteger)->S`xRealClosedField&(S)``0 -osqrt`2`x`(_$,Integer)->_$`cPAdicIntegerCategory(p)``1043110 -osqrt`2`x`(_$,NonNegativeInteger)->_$`cRealClosedField``1043234 +osqrt`2`x`(_$,Integer)->_$`cPAdicIntegerCategory(p)``1243967 +osqrt`2`x`(_$,NonNegativeInteger)->_$`cRealClosedField``1244091 osquare?`1`n`(S)->Boolean`xMatrixCategory&(S,R,Row,Col)``0 osquare?`1`n`(S)->Boolean`xRectangularMatrixCategory&(S,m,n,R,Row,Col)``0 -osquare?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``1043311 -osquare?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``1043486 -osquareFreeFactors`1`n`(P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`1043661 -osquareFreeLexTriangular`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))`pLexTriangularPackage(R,ls)``1043778 -osquareFreePart`1`n`(P)->P`pUnivariatePolynomialSquareFree(RC,P)``1044199 -osquareFreePart`1`n`(S)->S`xPolynomialCategory&(S,R,E,VarSet)``0 -osquareFreePart`1`n`(S)->S`xUniqueFactorizationDomain&(S)``0 -osquareFreePart`1`n`(S)->S`xUnivariatePolynomialCategory&(S,R)``0 -osquareFreePart`1`x`(_$)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1044370 -osquareFreePart`1`x`(_$)->_$`cUniqueFactorizationDomain``1044506 -osquareFreePart`2`x`(P,_$)->List(Record(val:P,tower:_$))`cRegularTriangularSetCategory(R,E,V,P)``1044619 -osquareFreePolynomial`1`n`(SparseUnivariatePolynomial(S))->Factored(SparseUnivariatePolynomial(S))`xUnivariatePolynomialCategory&(S,R)``0 -osquareFreePolynomial`1`x`(SparseUnivariatePolynomial(_$))->Factored(SparseUnivariatePolynomial(_$))`cPolynomialFactorizationExplicit``1045141 -osquareFreePolynomial`1`x`(SparseUnivariatePolynomial(_$))->Factored(SparseUnivariatePolynomial(_$))`dExpression(R)`AND(has(R,GcdDomain),has(R,IntegralDomain))`1045256 -osquareFreePrim`1`n`(P)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1045310 -osquareFree`1`n`(I)->Factored(I)`pIntegerFactorizationPackage(I)``1045429 -osquareFree`1`n`(P)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1045515 -osquareFree`1`n`(P)->Factored(P)`pPolynomialSquareFree(VarSet,E,RC,P)``1045621 -osquareFree`1`n`(P)->Factored(P)`pUnivariatePolynomialSquareFree(RC,P)``1045799 +osquare?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``1244168 +osquare?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``1244438 +osquareFree`1`n`(I)->Factored(I)`pIntegerFactorizationPackage(I)``1244613 +osquareFree`1`n`(P)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1244699 +osquareFree`1`n`(P)->Factored(P)`pPolynomialSquareFree(VarSet,E,RC,P)``1244805 +osquareFree`1`n`(P)->Factored(P)`pUnivariatePolynomialSquareFree(RC,P)``1244983 osquareFree`1`n`(S)->Factored(S)`xField&(S)``0 osquareFree`1`n`(S)->Factored(S)`xIntegerNumberSystem&(S)``0 osquareFree`1`n`(S)->Factored(S)`xPolynomialCategory&(S,R,E,VarSet)``0 osquareFree`1`n`(S)->Factored(S)`xUnivariatePolynomialCategory&(S,R)``0 -osquareFree`1`n`(SparseUnivariatePolynomial(Fraction(P)))->Factored(SparseUnivariatePolynomial(Fraction(P)))`pSupFractionFactorizer(E,OV,R,P)``1045989 -osquareFree`1`n`(SparseUnivariatePolynomial(P))->Factored(SparseUnivariatePolynomial(P))`pMultivariateSquareFree(E,OV,R,P)``1046242 -osquareFree`1`x`(RegularChain(R,ls))->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1046416 -osquareFree`1`x`(_$)->Factored(_$)`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1046759 -osquareFree`1`x`(_$)->Factored(_$)`cUniqueFactorizationDomain``1046853 -osquareMatrix`1`n`(Matrix(R))->_$`dSquareMatrix(ndim,R)``1047038 +osquareFree`1`n`(SparseUnivariatePolynomial(Fraction(P)))->Factored(SparseUnivariatePolynomial(Fraction(P)))`pSupFractionFactorizer(E,OV,R,P)``1245173 +osquareFree`1`n`(SparseUnivariatePolynomial(P))->Factored(SparseUnivariatePolynomial(P))`pMultivariateSquareFree(E,OV,R,P)``1245426 +osquareFree`1`x`(_$)->Factored(_$)`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1245600 +osquareFree`1`x`(_$)->Factored(_$)`cUniqueFactorizationDomain``1245694 +osquareFree`1`x`(RegularChain(R,ls))->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls2)),OrderedVariableList(ls2),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls2))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1245879 +osquareFreeFactors`1`n`(P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)`has(R,GcdDomain)`1246222 +osquareFreeLexTriangular`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))`pLexTriangularPackage(R,ls)``1246339 +osquareFreePart`1`n`(P)->P`pUnivariatePolynomialSquareFree(RC,P)``1246760 +osquareFreePart`1`n`(S)->S`xPolynomialCategory&(S,R,E,VarSet)``0 +osquareFreePart`1`n`(S)->S`xUniqueFactorizationDomain&(S)``0 +osquareFreePart`1`n`(S)->S`xUnivariatePolynomialCategory&(S,R)``0 +osquareFreePart`1`x`(_$)->_$`cPolynomialCategory(R,E,VarSet)`has(R,GcdDomain)`1246931 +osquareFreePart`1`x`(_$)->_$`cUniqueFactorizationDomain``1247067 +osquareFreePart`2`x`(P,_$)->List(Record(val:P,tower:_$))`cRegularTriangularSetCategory(R,E,V,P)``1247180 +osquareFreePolynomial`1`n`(SparseUnivariatePolynomial(S))->Factored(SparseUnivariatePolynomial(S))`xUnivariatePolynomialCategory&(S,R)``0 +osquareFreePolynomial`1`x`(SparseUnivariatePolynomial(_$))->Factored(SparseUnivariatePolynomial(_$))`cPolynomialFactorizationExplicit``1247702 +osquareFreePolynomial`1`x`(SparseUnivariatePolynomial(_$))->Factored(SparseUnivariatePolynomial(_$))`dExpression(R)`AND(has(R,GcdDomain),has(R,IntegralDomain))`1247817 +osquareFreePrim`1`n`(P)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1247873 +osquareMatrix`1`n`(Matrix(R))->_$`dSquareMatrix(ndim,R)``1247992 osquareTop`1`n`(S)->S`xMatrixCategory&(S,R,Row,Col)``0 -osquareTop`1`x`(_$)->_$`cMatrixCategory(R,Row,Col)``1047157 -ostFunc1`1`n`((UTS)->UTS)->(Stream(Coef))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1047330 -ostFunc2`1`n`((UTS,UTS)->UTS)->(Stream(Coef),Stream(Coef))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1047464 -ostFuncN`1`n`((List(UTS))->UTS)->(List(Stream(Coef)))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1047598 -ostack`1`x`(List(S))->_$`dStack(S)``1047731 -ostandardBasisOfCyclicSubmodule`2`x`(List(Matrix(R)),Vector(R))->Matrix(R)`pRepresentationPackage2(R)`has(R,EuclideanDomain)`1047882 -ostartPolynomial`1`n`(UP)->Record(start:UP,factors:Factored(UP))`pComplexRootFindingPackage(R,UP)``1048565 -ostartStats!`1`n`(String)->Void`pTabulatedComputationPackage(Key,Entry)``1049019 -ostartTable!`3`x`(String,String,String)->Void`pQuasiComponentPackage(R,E,V,P,TS)``1049153 -ostartTable!`3`x`(String,String,String)->Void`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1049279 -ostartTableGcd!`3`x`(String,String,String)->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1049405 +osquareTop`1`x`(_$)->_$`cMatrixCategory(R,Row,Col)``1248111 +ostack`1`x`(List(S))->_$`dStack(S)``1248435 +ostandardBasisOfCyclicSubmodule`2`x`(List(Matrix(R)),Vector(R))->Matrix(R)`pRepresentationPackage2(R)`has(R,EuclideanDomain)`1248688 +ostartPolynomial`1`n`(UP)->Record(start:UP,factors:Factored(UP))`pComplexRootFindingPackage(R,UP)``1249371 +ostartStats!`1`n`(String)->Void`pTabulatedComputationPackage(Key,Entry)``1249819 +ostartTable!`3`x`(String,String,String)->Void`pQuasiComponentPackage(R,E,V,P,TS)``1249953 +ostartTable!`3`x`(String,String,String)->Void`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1250079 +ostartTableGcd!`3`x`(String,String,String)->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1250205 ostartTableGcd!`3`x`(String,String,String)->Void`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostartTableInvSet!`3`x`(String,String,String)->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1049531 +ostartTableInvSet!`3`x`(String,String,String)->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1250331 ostartTableInvSet!`3`x`(String,String,String)->Void`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostatus`1`n`(_$)->Boolean`dSplittingNode(V,C)``1049660 -ostatus`1`n`(_$)->Union(Boolean,"failed")`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``1049733 -ostiffnessAndStabilityFactor`1`x`(Matrix(Expression(DoubleFloat)))->Record(stiffnessFactor:Float,stabilityFactor:Float)`pd02AgentsPackage``1049875 -ostiffnessAndStabilityOfODEIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Record(stiffnessFactor:Float,stabilityFactor:Float)`pd02AgentsPackage``1050402 -ostirling1`2`x`(I,I)->I`pIntegerCombinatoricFunctions(I)``1050985 -ostirling2`2`x`(I,I)->I`pIntegerCombinatoricFunctions(I)``1051087 -ostopMusserTrials`0`n`()->PositiveInteger`pGaloisGroupFactorizer(UP)``1051191 -ostopMusserTrials`1`n`(PositiveInteger)->PositiveInteger`pGaloisGroupFactorizer(UP)``1051465 -ostopTable!`0`x`()->Void`pQuasiComponentPackage(R,E,V,P,TS)``1051760 -ostopTable!`0`x`()->Void`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1051852 -ostopTableGcd!`0`x`()->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1051944 +ostatus`1`n`(_$)->Boolean`dSplittingNode(V,C)``1250460 +ostatus`1`n`(_$)->Union(Boolean,"failed")`dQuasiAlgebraicSet(R,Var,Expon,Dpoly)``1250533 +ostepBlowUp`4`x`(DistributedMultivariatePolynomial(construct('X,'Y),K),AffinePlane(K),BLMET,K)->Record(mult:NonNegativeInteger,subMult:NonNegativeInteger,blUpRec:List(Record(recTransStr:DistributedMultivariatePolynomial(construct('X,'Y),K),recPoint:AffinePlane(K),recChart:BLMET,definingExtension:K)))`pBlowUpPackage(K,symb,PolyRing,E,BLMET)``1250675 +ostFunc1`1`n`((UTS)->UTS)->(Stream(Coef))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1250828 +ostFunc2`1`n`((UTS,UTS)->UTS)->(Stream(Coef),Stream(Coef))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1250962 +ostFuncN`1`n`((List(UTS))->UTS)->(List(Stream(Coef)))->Stream(Coef)`pUnivariateTaylorSeriesODESolver(Coef,UTS)``1251096 +ostiffnessAndStabilityFactor`1`x`(Matrix(Expression(DoubleFloat)))->Record(stiffnessFactor:Float,stabilityFactor:Float)`pd02AgentsPackage``1251229 +ostiffnessAndStabilityOfODEIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Record(stiffnessFactor:Float,stabilityFactor:Float)`pd02AgentsPackage``1251756 +ostirling1`2`x`(I,I)->I`pIntegerCombinatoricFunctions(I)``1252339 +ostirling2`2`x`(I,I)->I`pIntegerCombinatoricFunctions(I)``1252441 +ostop`0`x`()->_$`dFortranCode``1252545 +ostopMusserTrials`0`n`()->PositiveInteger`pGaloisGroupFactorizer(UP)``1252612 +ostopMusserTrials`1`n`(PositiveInteger)->PositiveInteger`pGaloisGroupFactorizer(UP)``1252886 +ostopTable!`0`x`()->Void`pQuasiComponentPackage(R,E,V,P,TS)``1253181 +ostopTable!`0`x`()->Void`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1253273 +ostopTableGcd!`0`x`()->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1253365 ostopTableGcd!`0`x`()->Void`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostopTableInvSet!`0`x`()->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1052036 +ostopTableInvSet!`0`x`()->Void`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1253457 ostopTableInvSet!`0`x`()->Void`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostop`0`x`()->_$`dFortranCode``1052131 ostoseIntegralLastSubResultant`3`x`(P,P,TS)->List(Record(val:P,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInternalLastSubResultant`3`x`(List(Record(val:List(P),tower:TS)),V,Boolean)->List(Record(val:P,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInternalLastSubResultant`5`x`(P,P,TS,Boolean,Boolean)->List(Record(val:P,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertible?`2`x`(P,TS)->Boolean`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertible?`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertible?reg`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostoseInvertible?sqfreg`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertibleSet`2`x`(P,TS)->List(TS)`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertibleSetreg`2`x`(P,TS)->List(TS)`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseInvertibleSetsqfreg`2`x`(P,TS)->List(TS)`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 +ostoseInvertible?sqfreg`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseLastSubResultant`3`x`(P,P,TS)->List(Record(val:P,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostosePrepareSubResAlgo`3`x`(P,P,TS)->List(Record(val:List(P),tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 ostoseSquareFreePart`2`x`(P,TS)->List(Record(val:P,tower:TS))`pSquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS)``0 -ostring?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1052198 -ostring`1`n`(_$)->_$`dOutputForm``1052287 -ostring`1`x`(Integer)->_$`cStringCategory``1052348 -ostring`1`x`(_$)->Str`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1052431 -ostring`1`x`(_$)->String`dSymbol``1052568 -ostripCommentsAndBlanks`1`x`(String)->String`pTemplateUtilities``1052671 -ostrongGenerators`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``1052813 +ostring`1`n`(_$)->_$`dOutputForm``1253552 +ostring?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1253613 +ostring`1`x`(Integer)->_$`cStringCategory``1253702 +ostring`1`x`(_$)->Str`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1253785 +ostring`1`x`(_$)->String`dSymbol``1253922 +ostripCommentsAndBlanks`1`x`(String)->String`pTemplateUtilities``1254025 +ostrongGenerators`1`x`(_$)->List(Permutation(S))`dPermutationGroup(S)``1254167 ostronglyReduce`2`n`(P,S)->P`xTriangularSetCategory&(S,R,E,V,P)``0 -ostronglyReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``1052898 +ostronglyReduce`2`x`(P,_$)->P`cTriangularSetCategory(R,E,V,P)``1254253 ostronglyReduced?`1`n`(S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -ostronglyReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``1053219 +ostronglyReduced?`1`x`(_$)->Boolean`cTriangularSetCategory(R,E,V,P)``1254574 ostronglyReduced?`2`n`(P,S)->Boolean`xTriangularSetCategory&(S,R,E,V,P)``0 -ostronglyReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``1053402 -ostructuralConstants`0`n`()->Vector(Matrix(R))`xFramedNonAssociativeAlgebra&(S,R)``1053555 -ostructuralConstants`0`x`()->Vector(Matrix(R))`cFramedNonAssociativeAlgebra(R)``1053810 +ostronglyReduced?`2`x`(P,_$)->Boolean`cTriangularSetCategory(R,E,V,P)``1254757 +ostructuralConstants`0`n`()->Vector(Matrix(R))`xFramedNonAssociativeAlgebra&(S,R)``1254910 +ostructuralConstants`0`x`()->Vector(Matrix(R))`cFramedNonAssociativeAlgebra(R)``1255165 ostructuralConstants`1`n`(Vector(S))->Vector(Matrix(R))`xFiniteRankNonAssociativeAlgebra&(S,R)``0 ostructuralConstants`1`n`(Vector(S))->Vector(Matrix(R))`xFramedNonAssociativeAlgebra&(S,R)``0 -ostructuralConstants`1`x`(List(Matrix(R)))->Vector(Matrix(R))`pStructuralConstantsPackage(R)``1054065 -ostructuralConstants`1`x`(Vector(_$))->Vector(Matrix(R))`cFiniteRankNonAssociativeAlgebra(R)``1054356 -ostructuralConstants`2`x`(List(Symbol),Matrix(Fraction(Polynomial(R))))->Vector(Matrix(Fraction(Polynomial(R))))`pStructuralConstantsPackage(R)``1054630 -ostructuralConstants`2`x`(List(Symbol),Matrix(Polynomial(R)))->Vector(Matrix(Polynomial(R)))`pStructuralConstantsPackage(R)``1055072 -osts2stst`2`n`(Symbol,Stream(Polynomial(R)))->Stream(Stream(Polynomial(R)))`pWeierstrassPreparation(R)``1055514 -osturmSequence`1`x`(ThePols)->List(ThePols)`pRealPolynomialUtilitiesPackage(TheField,ThePols)``1055564 -osturmVariationsOf`1`x`(List(TheField))->NonNegativeInteger`pRealPolynomialUtilitiesPackage(TheField,ThePols)`has(TheField,OrderedRing)`1055645 -ostyle`1`x`(String)->_$`dDrawOption``1055798 -ostyle`2`n`(List(DrawOption),String)->String`pDrawOptionFunctions0``1055974 -osubCase?`2`x`(Record(val:List(P),tower:TS),Record(val:List(P),tower:TS))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1056178 -osubCase?`2`x`(Record(val:List(P),tower:TS),Record(val:List(P),tower:TS))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1056292 -osubHeight`1`n`(_$)->Integer`dOutputForm``1056406 +ostructuralConstants`1`x`(List(Matrix(R)))->Vector(Matrix(R))`pStructuralConstantsPackage(R)``1255420 +ostructuralConstants`1`x`(Vector(_$))->Vector(Matrix(R))`cFiniteRankNonAssociativeAlgebra(R)``1255711 +ostructuralConstants`2`x`(List(Symbol),Matrix(Fraction(Polynomial(R))))->Vector(Matrix(Fraction(Polynomial(R))))`pStructuralConstantsPackage(R)``1255985 +ostructuralConstants`2`x`(List(Symbol),Matrix(Polynomial(R)))->Vector(Matrix(Polynomial(R)))`pStructuralConstantsPackage(R)``1256427 +osts2stst`2`n`(Symbol,Stream(Polynomial(R)))->Stream(Stream(Polynomial(R)))`pWeierstrassPreparation(R)``1256869 +oSturmHabicht`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)``1256919 +oSturmHabichtCoefficients`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->List(R)`pSturmHabichtPackage(R,x)``1257213 +oSturmHabichtMultiple`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->Integer`pSturmHabichtPackage(R,x)`has(R,GcdDomain)`1257338 +oSturmHabichtSequence`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->List(UnivariatePolynomial(x,R))`pSturmHabichtPackage(R,x)``1257640 +osturmSequence`1`x`(ThePols)->List(ThePols)`pRealPolynomialUtilitiesPackage(TheField,ThePols)``1257747 +osturmVariationsOf`1`x`(List(TheField))->NonNegativeInteger`pRealPolynomialUtilitiesPackage(TheField,ThePols)`has(TheField,OrderedRing)`1257828 +ostyle`1`x`(String)->_$`dDrawOption``1257981 +ostyle`2`n`(List(DrawOption),String)->String`pDrawOptionFunctions0``1258157 +osub`2`n`(_$,_$)->_$`dOutputForm``1258361 +osubCase?`2`x`(Record(val:List(P),tower:TS),Record(val:List(P),tower:TS))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1258439 +osubCase?`2`x`(Record(val:List(P),tower:TS),Record(val:List(P),tower:TS))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1258553 +osubHeight`1`n`(_$)->Integer`dOutputForm``1258667 osubMatrix`5`n`(S,Integer,Integer,Integer,Integer)->S`xMatrixCategory&(S,R,Row,Col)``0 -osubMatrix`5`x`(_$,Integer,Integer,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1056490 -osubNode?`3`n`(_$,_$,(C,C)->Boolean)->Boolean`dSplittingNode(V,C)``1056697 -osubNodeOf?`3`n`(SplittingNode(V,C),_$,(C,C)->Boolean)->Boolean`dSplittingTree(V,C)``1056891 -osubPolSet?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1057120 -osubPolSet?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1057250 -osubQuasiComponent?`2`x`(TS,List(TS))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1057380 -osubQuasiComponent?`2`x`(TS,List(TS))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1057537 -osubQuasiComponent?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1057694 -osubQuasiComponent?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1057852 -osubResultantChain`2`x`(_$,_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1058026 -osubResultantGcdEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``1058238 -osubResultantGcd`2`n`(polR,polR)->polR`pPseudoRemainderSequence(R,polR)``1058503 -osubResultantGcd`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1058647 -osubResultantGcd`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`1059027 -osubResultantsChain`2`n`(_$,_$)->List(_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`1059174 -osubSet`3`x`(Integer,Integer,Integer)->List(Integer)`pSymmetricGroupCombinatoricFunctions``1059333 -osubTriSet?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1059674 -osubTriSet?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1059786 -osub`2`n`(_$,_$)->_$`dOutputForm``1059898 -osubmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``1059976 -osubresultantSequence`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->List(UnivariatePolynomial(x,R))`pSturmHabichtPackage(R,x)``1060058 -osubresultantVector`2`n`(UP,UP)->PrimitiveArray(UP)`pSubResultantPackage(R,UP)``1060175 -osubscript`2`x`(_$,List(OutputForm))->_$`dSymbol``1060369 -osubscriptedVariables`1`x`(Expression(DoubleFloat))->Expression(DoubleFloat)`pd03AgentsPackage``1060471 +osubMatrix`5`x`(_$,Integer,Integer,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1258751 +osubmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``1259126 +osubMultV`1`x`(_$)->NonNegativeInteger`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osubNode?`3`n`(_$,_$,(C,C)->Boolean)->Boolean`dSplittingNode(V,C)``1259208 +osubNodeOf?`3`n`(SplittingNode(V,C),_$,(C,C)->Boolean)->Boolean`dSplittingTree(V,C)``1259402 +osubPolSet?`2`x`(List(P),List(P))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1259631 +osubPolSet?`2`x`(List(P),List(P))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1259761 +osubQuasiComponent?`2`x`(TS,List(TS))->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1259891 +osubQuasiComponent?`2`x`(TS,List(TS))->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1260048 +osubQuasiComponent?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1260205 +osubQuasiComponent?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1260326 +osubResultantChain`2`x`(_$,_$)->List(_$)`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1260491 +osubResultantGcd`2`n`(polR,polR)->polR`pPseudoRemainderSequence(R,polR)``1260703 +osubResultantGcd`2`x`(_$,_$)->_$`cRecursivePolynomialCategory(R,E,V)`has(R,IntegralDomain)`1260847 +osubResultantGcd`2`x`(_$,_$)->_$`cUnivariatePolynomialCategory(R)`has(R,IntegralDomain)`1261227 +osubResultantGcdEuclidean`2`n`(polR,polR)->Record(coef1:polR,coef2:polR,gcd:polR)`pPseudoRemainderSequence(R,polR)``1261374 +osubResultantsChain`2`n`(_$,_$)->List(_$)`dNewSparseUnivariatePolynomial(R)`has(R,IntegralDomain)`1261639 +osubresultantSequence`2`x`(UnivariatePolynomial(x,R),UnivariatePolynomial(x,R))->List(UnivariatePolynomial(x,R))`pSturmHabichtPackage(R,x)``1261798 +osubresultantVector`2`n`(UP,UP)->PrimitiveArray(UP)`pSubResultantPackage(R,UP)``1261915 +osubs1stVar`2`x`(PolyRing,PolyRing)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``0 +osubs2ndVar`2`x`(PolyRing,PolyRing)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``0 +osubscript`2`x`(_$,List(OutputForm))->_$`dSymbol``1262109 +osubscriptedVariables`1`x`(Expression(DoubleFloat))->Expression(DoubleFloat)`pd03AgentsPackage``1262211 osubset?`2`n`(A,A)->Boolean`xFiniteSetAggregate&(A,S)``0 -osubset?`2`x`(_$,_$)->Boolean`cSetAggregate(S)``1060525 -osubspace`0`n`()->_$`dSubSpace(n,R)``1060725 -osubspace`1`x`(_$)->SubSpace(3,R)`cThreeSpaceCategory(R)``1060764 -osubspace`1`x`(_$)->ThreeSpace(DoubleFloat)`dThreeDimensionalViewport``1060902 -osubspace`2`x`(_$,ThreeSpace(DoubleFloat))->_$`dThreeDimensionalViewport``1061086 +osubset?`2`x`(_$,_$)->Boolean`cSetAggregate(S)``1262265 +osubSet`3`x`(Integer,Integer,Integer)->List(Integer)`pSymmetricGroupCombinatoricFunctions``1262469 +osubsInVar`3`x`(PolyRing,PolyRing,Integer)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``0 +osubspace`0`n`()->_$`dSubSpace(n,R)``1262851 +osubspace`1`x`(_$)->SubSpace(3,R)`cThreeSpaceCategory(R)``1262894 +osubspace`1`x`(_$)->ThreeSpace(DoubleFloat)`dThreeDimensionalViewport``1263032 +osubspace`2`x`(_$,ThreeSpace(DoubleFloat))->_$`dThreeDimensionalViewport``1263216 osubst`2`n`(S,Equation(S))->S`xExpressionSpace&(S)``0 osubst`2`n`(S,Equation(S))->S`xFunctionSpace&(S,R)``0 osubst`2`n`(S,List(Equation(S)))->S`xExpressionSpace&(S)``0 osubst`2`n`(S,List(Equation(S)))->S`xFunctionSpace&(S,R)``0 -osubst`2`x`(_$,Equation(_$))->_$`cExpressionSpace``1061298 -osubst`2`x`(_$,List(Equation(_$)))->_$`cExpressionSpace``1061393 -osubst`2`x`(_$,_$)->_$`dEquation(S)`has(S,ExpressionSpace)`1061547 +osubst`2`x`(_$,_$)->_$`dEquation(S)`has(S,ExpressionSpace)`1263428 +osubst`2`x`(_$,Equation(_$))->_$`cExpressionSpace``1263560 +osubst`2`x`(_$,List(Equation(_$)))->_$`cExpressionSpace``1263655 osubst`3`n`(S,List(Kernel(S)),List(S))->S`xExpressionSpace&(S)``0 osubst`3`n`(S,List(Kernel(S)),List(S))->S`xFunctionSpace&(S,R)``0 -osubst`3`x`(_$,List(Kernel(_$)),List(_$))->_$`cExpressionSpace``1061679 -osubstitute`3`n`(S,S,_$)->_$`dListMultiDictionary(S)``1061839 -osubstring?`3`x`(_$,_$,Integer)->Boolean`cStringAggregate``1061948 +osubst`3`x`(_$,List(Kernel(_$)),List(_$))->_$`cExpressionSpace``1263809 +osubstitute`3`n`(S,S,_$)->_$`dListMultiDictionary(S)``1263969 +osubstring?`3`x`(_$,_$,Integer)->Boolean`cStringAggregate``1264078 osubtractIfCan`2`n`(S,S)->Union(S,"failed")`xAbelianGroup&(S)``0 -osubtractIfCan`2`x`(_$,_$)->Union(_$,"failed")`cCancellationAbelianMonoid``1062140 -osuchThat`2`n`(Pattern(R),(D)->Boolean)->Pattern(R)`pPatternFunctions1(R,D)``1062266 -osuchThat`2`n`(Pattern(R),List((D)->Boolean))->Pattern(R)`pPatternFunctions1(R,D)``1062388 -osuchThat`2`x`(F,(D)->Boolean)->F`pFunctionSpaceAttachPredicates(R,F,D)``1062547 -osuchThat`2`x`(F,List((D)->Boolean))->F`pFunctionSpaceAttachPredicates(R,F,D)``1062655 -osuchThat`2`x`(Symbol,(D)->Boolean)->Expression(Integer)`pAttachPredicates(D)``1062826 -osuchThat`2`x`(Symbol,List((D)->Boolean))->Expression(Integer)`pAttachPredicates(D)``1062899 -osuchThat`3`n`(Pattern(R),List(Symbol),(List(D))->Boolean)->Pattern(R)`pPatternFunctions1(R,D)``1063034 -osuchThat`3`x`(_$,List(Symbol),(List(F))->Boolean)->_$`dRewriteRule(Base,R,F)``1063172 -osuffix?`2`x`(_$,_$)->Boolean`cStringAggregate``1063315 -osumOfDivisors`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``1063664 -osumOfKthPowerDivisors`2`x`(Integer,NonNegativeInteger)->Integer`pIntegerNumberTheoryFunctions``1063858 -osumOfSquares`1`x`(Expression(DoubleFloat))->Union(Expression(DoubleFloat),"failed")`pe04AgentsPackage``1064116 -osumSquares`1`x`(Integer)->List(Integer)`pGaussianFactorizationPackage``1064234 -osum`1`n`(_$)->_$`dOutputForm``1064470 -osum`2`n`(P,V)->Record(num:P,den:Integer)`pInnerPolySum(E,V,R,P)``1064553 -osum`2`n`(_$,_$)->_$`dOutputForm``1064735 -osum`2`x`(F,SegmentBinding(F))->F`pFunctionSpaceSum(R,F)``1064856 -osum`2`x`(F,Symbol)->F`pFunctionSpaceSum(R,F)``1064963 -osum`2`x`(Fraction(Polynomial(R)),SegmentBinding(Fraction(Polynomial(R))))->Union(Fraction(Polynomial(R)),Expression(R))`pRationalFunctionSum(R)``1065065 -osum`2`x`(Fraction(Polynomial(R)),Symbol)->Union(Fraction(Polynomial(R)),Expression(R))`pRationalFunctionSum(R)``1065142 -osum`2`x`(Polynomial(R),SegmentBinding(Polynomial(R)))->Fraction(Polynomial(R))`pRationalFunctionSum(R)``1065324 -osum`2`x`(Polynomial(R),Symbol)->Fraction(Polynomial(R))`pRationalFunctionSum(R)``1065401 -osum`3`n`(P,V,Segment(P))->Record(num:P,den:Integer)`pInnerPolySum(E,V,R,P)``1065583 -osum`3`n`(_$,_$,_$)->_$`dOutputForm``1065662 -osummation`2`n`(F,SegmentBinding(F))->F`pCombinatorialFunction(R,F)``1065823 -osummation`2`n`(F,Symbol)->F`pCombinatorialFunction(R,F)``1065929 -osummation`2`x`(_$,SegmentBinding(_$))->_$`cCombinatorialOpsCategory``1066085 -osummation`2`x`(_$,Symbol)->_$`cCombinatorialOpsCategory``1066191 -osupDimElseRittWu?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1066347 -osupDimElseRittWu?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1066584 +osubtractIfCan`2`x`(_$,_$)->Union(_$,"failed")`cCancellationAbelianMonoid``1264274 +osubTriSet?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1264400 +osubTriSet?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1264512 +osuchThat`2`n`(Pattern(R),(D)->Boolean)->Pattern(R)`pPatternFunctions1(R,D)``1264624 +osuchThat`2`n`(Pattern(R),List((D)->Boolean))->Pattern(R)`pPatternFunctions1(R,D)``1264746 +osuchThat`2`x`(F,(D)->Boolean)->F`pFunctionSpaceAttachPredicates(R,F,D)``1264905 +osuchThat`2`x`(F,List((D)->Boolean))->F`pFunctionSpaceAttachPredicates(R,F,D)``1265013 +osuchThat`2`x`(Symbol,(D)->Boolean)->Expression(Integer)`pAttachPredicates(D)``1265184 +osuchThat`2`x`(Symbol,List((D)->Boolean))->Expression(Integer)`pAttachPredicates(D)``1265257 +osuchThat`3`n`(Pattern(R),List(Symbol),(List(D))->Boolean)->Pattern(R)`pPatternFunctions1(R,D)``1265392 +osuchThat`3`x`(_$,List(Symbol),(List(F))->Boolean)->_$`dRewriteRule(Base,R,F)``1265530 +osuffix?`2`x`(_$,_$)->Boolean`cStringAggregate``1265673 +osum`1`n`(_$)->_$`dOutputForm``1266040 +osum`2`n`(_$,_$)->_$`dOutputForm``1266123 +osum`2`n`(P,V)->Record(num:P,den:Integer)`pInnerPolySum(E,V,R,P)``1266244 +osum`2`x`(Fraction(Polynomial(R)),SegmentBinding(Fraction(Polynomial(R))))->Union(Fraction(Polynomial(R)),Expression(R))`pRationalFunctionSum(R)``1266426 +osum`2`x`(Fraction(Polynomial(R)),Symbol)->Union(Fraction(Polynomial(R)),Expression(R))`pRationalFunctionSum(R)``1266619 +osum`2`x`(F,SegmentBinding(F))->F`pFunctionSpaceSum(R,F)``1266920 +osum`2`x`(F,Symbol)->F`pFunctionSpaceSum(R,F)``1267027 +osum`2`x`(Polynomial(R),SegmentBinding(Polynomial(R)))->Fraction(Polynomial(R))`pRationalFunctionSum(R)``1267129 +osum`2`x`(Polynomial(R),Symbol)->Fraction(Polynomial(R))`pRationalFunctionSum(R)``1267298 +osum`3`n`(_$,_$,_$)->_$`dOutputForm``1267610 +osum`3`n`(P,V,Segment(P))->Record(num:P,den:Integer)`pInnerPolySum(E,V,R,P)``1267771 +osummary`0`x`()->Void`pApplicationProgramInterface``1267850 +osummation`2`n`(F,SegmentBinding(F))->F`pCombinatorialFunction(R,F)``1267958 +osummation`2`n`(F,Symbol)->F`pCombinatorialFunction(R,F)``1268064 +osummation`2`x`(_$,SegmentBinding(_$))->_$`cCombinatorialOpsCategory``1268220 +osummation`2`x`(_$,Symbol)->_$`cCombinatorialOpsCategory``1268326 +osumOfDivisors`1`x`(Integer)->Integer`pIntegerNumberTheoryFunctions``1268482 +osumOfKthPowerDivisors`2`x`(Integer,NonNegativeInteger)->Integer`pIntegerNumberTheoryFunctions``1268676 +osumOfSquares`1`x`(Expression(DoubleFloat))->Union(Expression(DoubleFloat),"failed")`pe04AgentsPackage``1268934 +osumSquares`1`x`(Integer)->List(Integer)`pGaussianFactorizationPackage``1269052 +osup`1`x`(_$)->R`cIntervalCategory(R)``1269288 +osup`2`x`(_$,_$)->_$`cOrderedAbelianMonoidSup``1269351 +osupDimElseRittWu?`2`x`(TS,TS)->Boolean`pQuasiComponentPackage(R,E,V,P,TS)``1269459 +osupDimElseRittWu?`2`x`(TS,TS)->Boolean`pSquareFreeQuasiComponentPackage(R,E,V,P,TS)``1269696 +osuper`2`n`(_$,_$)->_$`dOutputForm``1269933 +osuperHeight`1`n`(_$)->Integer`dOutputForm``1270015 +osuperscript`2`x`(_$,List(OutputForm))->_$`dSymbol``1270101 +osupersub`2`n`(_$,List(_$))->_$`dOutputForm``1270207 +osupp`1`x`(_$)->List(S)`cDivisorCategory(S)``1270340 +osuppOfPole`1`x`(_$)->List(S)`cDivisorCategory(S)``1270407 +osuppOfZero`1`x`(_$)->List(S)`cDivisorCategory(S)``1270517 osupRittWu?`2`n`(S,S)->Boolean`xRecursivePolynomialCategory&(S,R,E,V)``0 -osupRittWu?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``1066821 -osup`1`x`(_$)->R`cIntervalCategory(R)``1067021 -osup`2`x`(_$,_$)->_$`cOrderedAbelianMonoidSup``1067084 -osuperHeight`1`n`(_$)->Integer`dOutputForm``1067192 -osuper`2`n`(_$,_$)->_$`dOutputForm``1067278 -osuperscript`2`x`(_$,List(OutputForm))->_$`dSymbol``1067360 -osupersub`2`n`(_$,List(_$))->_$`dOutputForm``1067466 -osurface`3`x`(ComponentFunction,ComponentFunction,ComponentFunction)->_$`dParametricSurface(ComponentFunction)``1067599 +osupRittWu?`2`x`(_$,_$)->Boolean`cRecursivePolynomialCategory(R,E,V)``1270627 +osurface`3`x`(ComponentFunction,ComponentFunction,ComponentFunction)->_$`dParametricSurface(ComponentFunction)``1270827 +oswap`1`n`(UPUP)->UPUP`pCommuteUnivariatePolynomialCategory(R,UP,UPUP)``1270960 +oswap`1`x`(_$)->_$`dEquation(S)``1271028 oswap!`3`n`(S,Index,Index)->Void`xIndexedAggregate&(S,Index,Entry)``0 -oswap!`3`x`(_$,Index,Index)->Void`cIndexedAggregate(Index,Entry)`has(_$,ATTRIBUTE(shallowlyMutable))`1067732 +oswap!`3`x`(_$,Index,Index)->Void`cIndexedAggregate(Index,Entry)`has(_$,ATTRIBUTE(shallowlyMutable))`1271112 oswapColumns!`3`n`(S,Integer,Integer)->S`xMatrixCategory&(S,R,Row,Col)``0 -oswapColumns!`3`x`(_$,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1067863 +oswapColumns!`3`x`(_$,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1271243 oswapRows!`3`n`(S,Integer,Integer)->S`xMatrixCategory&(S,R,Row,Col)``0 -oswapRows!`3`x`(_$,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1068003 -oswap`1`n`(UPUP)->UPUP`pCommuteUnivariatePolynomialCategory(R,UP,UPUP)``1068137 -oswap`1`x`(_$)->_$`dEquation(S)``1068205 -osylvesterMatrix`2`n`(UP,UP)->M`pBezoutMatrix(R,UP,M,Row,Col)``1068289 -osylvesterSequence`2`x`(ThePols,ThePols)->List(ThePols)`pRealPolynomialUtilitiesPackage(TheField,ThePols)``1068402 -osymFunc`1`n`(List(R))->Vector(R)`pSymmetricFunctions(R)``1068549 -osymFunc`2`n`(R,PositiveInteger)->Vector(R)`pSymmetricFunctions(R)``1068746 -osymbol?`1`n`(_$)->Boolean`dPattern(R)``1068877 -osymbol?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1068933 -osymbolIfCan`1`n`(_$)->Union(Symbol,"failed")`dKernel(S)``1069022 -osymbolTableOf`2`x`(Symbol,_$)->SymbolTable`dTheSymbolTable``1069138 -osymbolTable`1`x`(List(Record(key:Symbol,entry:FortranType)))->_$`dSymbolTable``1069212 -osymbol`1`x`(_$)->Sym`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1069295 +oswapRows!`3`x`(_$,Integer,Integer)->_$`cMatrixCategory(R,Row,Col)``1271532 +osylvesterMatrix`2`n`(UP,UP)->M`pBezoutMatrix(R,UP,M,Row,Col)``1271812 +osylvesterSequence`2`x`(ThePols,ThePols)->List(ThePols)`pRealPolynomialUtilitiesPackage(TheField,ThePols)``1271925 +osymbNameV`1`x`(_$)->Symbol`cInfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET)``0 +osymbol?`1`n`(_$)->Boolean`dPattern(R)``1272072 +osymbol?`1`x`(_$)->Boolean`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1272128 +osymbol`1`x`(_$)->Sym`cSExpressionCategory(Str,Sym,Int,Flt,Expr)``1272217 +osymbolIfCan`1`n`(_$)->Union(Symbol,"failed")`dKernel(S)``1272354 +osymbolTable`1`x`(List(Record(key:Symbol,entry:FortranType)))->_$`dSymbolTable``1272470 +osymbolTableOf`2`x`(Symbol,_$)->SymbolTable`dTheSymbolTable``1272553 +osymFunc`1`n`(List(R))->Vector(R)`pSymmetricFunctions(R)``1272627 +osymFunc`2`n`(R,PositiveInteger)->Vector(R)`pSymmetricFunctions(R)``1272824 osymmetric?`1`n`(S)->Boolean`xMatrixCategory&(S,R,Row,Col)``0 osymmetric?`1`n`(S)->Boolean`xRectangularMatrixCategory&(S,m,n,R,Row,Col)``0 -osymmetric?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``1069432 -osymmetric?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``1069632 +osymmetric?`1`x`(_$)->Boolean`cMatrixCategory(R,Row,Col)``1272955 +osymmetric?`1`x`(_$)->Boolean`cRectangularMatrixCategory(m,n,R,Row,Col)``1273286 osymmetricDifference`2`n`(A,A)->A`xFiniteSetAggregate&(A,S)``0 osymmetricDifference`2`n`(A,A)->A`xSetAggregate&(A,S)``0 -osymmetricDifference`2`x`(_$,_$)->_$`cSetAggregate(S)``1069832 -osymmetricGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``1070266 -osymmetricGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``1070538 -osymmetricPower`2`x`(_$,NonNegativeInteger)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1070739 -osymmetricPower`3`n`(L,NonNegativeInteger,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``1070926 -osymmetricProduct`2`x`(_$,_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1071152 -osymmetricProduct`3`n`(L,L,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``1071359 +osymmetricDifference`2`x`(_$,_$)->_$`cSetAggregate(S)``1273486 +osymmetricGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``1273938 +osymmetricGroup`1`x`(PositiveInteger)->PermutationGroup(Integer)`pPermutationGroupExamples``1274196 +osymmetricPower`2`x`(_$,NonNegativeInteger)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1274394 +osymmetricPower`3`n`(L,NonNegativeInteger,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``1274581 +osymmetricProduct`2`x`(_$,_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1274807 +osymmetricProduct`3`n`(L,L,(A)->A)->L`pLinearOrdinaryDifferentialOperatorsOps(A,L)``1275014 osymmetricRemainder`2`n`(S,S)->S`xIntegerNumberSystem&(S)``0 -osymmetricRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``1071605 +osymmetricRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``1275260 osymmetricSquare`1`n`(S)->S`xLinearOrdinaryDifferentialOperatorCategory&(S,A)``0 -osymmetricSquare`1`x`(_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1071714 -osymmetricTensors`2`x`(List(Matrix(R)),PositiveInteger)->List(Matrix(R))`pRepresentationPackage1(R)``1071818 -osymmetricTensors`2`x`(Matrix(R),PositiveInteger)->Matrix(R)`pRepresentationPackage1(R)``1072390 -osystemCommand`1`x`(String)->Void`pMoreSystemCommands``1072929 -osystemSizeIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Float`pd02AgentsPackage``1073147 -otRange`1`n`(_$)->Segment(DoubleFloat)`dPlot3D``1073330 -otRange`1`n`(_$)->Segment(DoubleFloat)`dPlot``1073420 -otValues`1`n`(_$)->List(List(DoubleFloat))`dPlot3D``1073509 -ot`1`n`(NonNegativeInteger)->()->Float`pRandomFloatDistributions``1073668 -otab1`1`n`(List(List(S)))->List(List(List(S)))`pTableauxBumpers(S)``1073701 -otab`1`n`(List(S))->Tableau(List(S))`pTableauxBumpers(S)``1073773 -otableForDiscreteLogarithm`1`x`(Integer)->Table(PositiveInteger,NonNegativeInteger)`cFiniteFieldCategory``1073979 -otablePow`3`n`(NonNegativeInteger,R,List(BP))->Union(Vector(List(BP)),"failed")`pGenExEuclid(R,BP)``1074287 +osymmetricSquare`1`x`(_$)->_$`cLinearOrdinaryDifferentialOperatorCategory(A)`has(A,Field)`1275369 +osymmetricTensors`2`x`(List(Matrix(R)),PositiveInteger)->List(Matrix(R))`pRepresentationPackage1(R)``1275473 +osymmetricTensors`2`x`(Matrix(R),PositiveInteger)->Matrix(R)`pRepresentationPackage1(R)``1276054 +osystemCommand`1`x`(String)->Void`pMoreSystemCommands``1276588 +osystemSizeIF`1`x`(Record(xinit:DoubleFloat,xend:DoubleFloat,fn:Vector(Expression(DoubleFloat)),yinit:List(DoubleFloat),intvals:List(DoubleFloat),g:Expression(DoubleFloat),abserr:DoubleFloat,relerr:DoubleFloat))->Float`pd02AgentsPackage``1276806 +ot`1`n`(NonNegativeInteger)->()->Float`pRandomFloatDistributions``1276989 +otab1`1`n`(List(List(S)))->List(List(List(S)))`pTableauxBumpers(S)``1277022 +otab`1`n`(List(S))->Tableau(List(S))`pTableauxBumpers(S)``1277094 otable`0`n`()->S`xTableAggregate&(S,Key,Entry)``0 -otable`0`x`()->_$`cTableAggregate(Key,Entry)``1074598 +otable`0`x`()->_$`cTableAggregate(Key,Entry)``1277240 otable`1`n`(List(Record(key:Key,entry:Entry)))->S`xTableAggregate&(S,Key,Entry)``0 -otable`1`x`(List(Record(key:Key,entry:Entry)))->_$`cTableAggregate(Key,Entry)``1074671 -otableau`1`x`(List(List(S)))->_$`dTableau(S)``1074794 +otable`1`x`(List(Record(key:Key,entry:Entry)))->_$`cTableAggregate(Key,Entry)``1277480 +otableau`1`x`(List(List(S)))->_$`dTableau(S)``1277603 +otableForDiscreteLogarithm`1`x`(Integer)->Table(PositiveInteger,NonNegativeInteger)`cFiniteFieldCategory``1277678 +otablePow`3`n`(NonNegativeInteger,R,List(BP))->Union(Vector(List(BP)),"failed")`pGenExEuclid(R,BP)``1277986 otail`1`n`(A)->A`xLazyStreamAggregate&(A,S)``0 otail`1`n`(A)->A`xUnaryRecursiveAggregate&(A,S)``0 otail`1`n`(S)->S`xRecursivePolynomialCategory&(S,R,E,V)``0 -otail`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``1074869 -otail`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``1074997 -otail`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``1075133 -otan2cot`1`x`(F)->F`pTranscendentalManipulations(R,F)``1075313 -otan2trig`1`x`(F)->F`pTranscendentalManipulations(R,F)``1075411 -otanAn`2`n`(R,PositiveInteger)->SparseUnivariatePolynomial(R)`pTangentExpansions(R)``1075515 -otanIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1075623 -otanNa`2`n`(R,Integer)->R`pTangentExpansions(R)``1075710 -otanQ`2`x`(Fraction(Integer),F)->F`pElementaryFunctionStructurePackage(R,F)``1075820 -otanSum`1`n`(List(R))->R`pTangentExpansions(R)``1075901 -otan`1`n`(F)->F`pElementaryFunction(R,F)``1076069 +otail`1`x`(_$)->_$`cDoublyLinkedAggregate(S)``1278297 +otail`1`x`(_$)->_$`cRecursivePolynomialCategory(R,E,V)``1278425 +otail`1`x`(_$)->_$`cUnaryRecursiveAggregate(S)``1278561 +otan`1`n`(F)->F`pElementaryFunction(R,F)``1278745 otan`1`n`(S)->S`xComplexCategory&(S,R)``0 otan`1`n`(S)->S`xTrigonometricFunctionCategory&(S)``0 otan`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -otan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1076131 -otan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1076199 -otan`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1076267 -otan`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1076336 -otan`1`x`(_$)->_$`cTrigonometricFunctionCategory``1076407 -otan`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1076461 -otanh2coth`1`x`(F)->F`pTranscendentalManipulations(R,F)``1076528 -otanh2trigh`1`x`(F)->F`pTranscendentalManipulations(R,F)``1076630 -otanhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1076739 -otanh`1`n`(F)->F`pElementaryFunction(R,F)``1076828 +otan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1278807 +otan`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1278875 +otan`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1278943 +otan`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1279012 +otan`1`x`(_$)->_$`cTrigonometricFunctionCategory``1279083 +otan`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1279137 +otan2cot`1`x`(F)->F`pTranscendentalManipulations(R,F)``1279204 +otan2trig`1`x`(F)->F`pTranscendentalManipulations(R,F)``1279302 +otanAn`2`n`(R,PositiveInteger)->SparseUnivariatePolynomial(R)`pTangentExpansions(R)``1279406 +otanh`1`n`(F)->F`pElementaryFunction(R,F)``1279514 otanh`1`n`(S)->S`xComplexCategory&(S,R)``0 otanh`1`n`(S)->S`xHyperbolicFunctionCategory&(S)``0 otanh`1`n`(S)->S`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -otanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1076902 -otanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1076986 -otanh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1077070 -otanh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1077151 -otanh`1`x`(_$)->_$`cHyperbolicFunctionCategory``1077234 -otanh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1077300 -otanintegrate`3`n`(Fraction(UP),(UP)->UP,(Integer,F,F)->Union(List(F),"failed"))->Record(answer:IntegrationResult(Fraction(UP)),a0:F)`pTranscendentalIntegration(F,UP)``1077369 -otaylorIfCan`1`x`(_$)->Union(UTS,"failed")`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1077588 -otaylorQuoByVar`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)``1077744 -otaylorRep`1`x`(_$)->UTS`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1077841 -otaylor`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1077960 -otaylor`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1078141 -otaylor`1`x`(_$)->UTS`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1078209 -otaylor`2`x`((Integer)->FE,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1078350 -otaylor`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1078436 -otaylor`2`x`(FE,NonNegativeInteger)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1078548 -otaylor`3`x`((Integer)->FE,Equation(FE),UniversalSegment(NonNegativeInteger))->Any`pGenerateUnivariatePowerSeries(R,FE)``1078790 -otaylor`3`x`(FE,Equation(FE),NonNegativeInteger)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1078971 -otaylor`3`x`(FE,Symbol,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1079137 -otaylor`4`x`(FE,Symbol,Equation(FE),UniversalSegment(NonNegativeInteger))->Any`pGenerateUnivariatePowerSeries(R,FE)``1079221 -otensorProduct`1`x`(List(Matrix(R)))->List(Matrix(R))`pRepresentationPackage1(R)``1079400 -otensorProduct`1`x`(Matrix(R))->Matrix(R)`pRepresentationPackage1(R)``1079768 -otensorProduct`2`x`(List(Matrix(R)),List(Matrix(R)))->List(Matrix(R))`pRepresentationPackage1(R)``1079867 -otensorProduct`2`x`(Matrix(R),Matrix(R))->Matrix(R)`pRepresentationPackage1(R)``1080259 -oterms`1`n`(_$)->List(Record(coef:R,monom:M))`dMonoidRing(R,M)``1080543 -oterms`1`x`(_$)->List(Record(gen:S,exp:E))`cFreeAbelianMonoidCategory(S,E)``1080703 -oterms`1`x`(_$)->Stream(Record(k:Expon,c:Coef))`cUnivariatePowerSeriesCategory(Coef,Expon)``1080792 -otestDim`2`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->Union(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),"failed")`pGroebnerSolve(lv,F,R)``1080974 -otestModulus`2`n`(R,List(BP))->Boolean`pGenExEuclid(R,BP)``1081090 -otest`1`x`(_$)->Boolean`dBoolean``1081293 -otex`1`x`(_$)->List(String)`dTexFormat``1081389 -othetaCoord`1`n`(Point(R))->R`pPointPackage(R)``1081459 +otanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctions(Coef)``1279588 +otanh`1`n`(Stream(Coef))->Stream(Coef)`pStreamTranscendentalFunctionsNonCommutative(Coef)``1279672 +otanh`1`n`(ULS)->ULS`dElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS)``1279756 +otanh`1`n`(UPXS)->UPXS`dElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS)``1279837 +otanh`1`x`(_$)->_$`cHyperbolicFunctionCategory``1279920 +otanh`1`x`(_$)->_$`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1279986 +otanh2coth`1`x`(F)->F`pTranscendentalManipulations(R,F)``1280055 +otanh2trigh`1`x`(F)->F`pTranscendentalManipulations(R,F)``1280157 +otanhIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1280266 +otanIfCan`1`x`(K)->Union(K,"failed")`cPartialTranscendentalFunctions(K)``1280355 +otanintegrate`3`n`(Fraction(UP),(UP)->UP,(Integer,F,F)->Union(List(F),"failed"))->Record(answer:IntegrationResult(Fraction(UP)),a0:F)`pTranscendentalIntegration(F,UP)``1280442 +otanNa`2`n`(R,Integer)->R`pTangentExpansions(R)``1280661 +otanQ`2`x`(Fraction(Integer),F)->F`pElementaryFunctionStructurePackage(R,F)``1280771 +otanSum`1`n`(List(R))->R`pTangentExpansions(R)``1280852 +otaylor`1`x`(FE)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1281020 +otaylor`1`x`(Symbol)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1281205 +otaylor`1`x`(_$)->UTS`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1281273 +otaylor`2`x`(FE,Equation(FE))->Any`pExpressionToUnivariatePowerSeries(R,FE)``1281414 +otaylor`2`x`(FE,NonNegativeInteger)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1281526 +otaylor`2`x`((Integer)->FE,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1281772 +otaylor`3`x`(FE,Equation(FE),NonNegativeInteger)->Any`pExpressionToUnivariatePowerSeries(R,FE)``1281858 +otaylor`3`x`(FE,Symbol,Equation(FE))->Any`pGenerateUnivariatePowerSeries(R,FE)``1282024 +otaylor`3`x`((Integer)->FE,Equation(FE),UniversalSegment(NonNegativeInteger))->Any`pGenerateUnivariatePowerSeries(R,FE)``1282108 +otaylor`4`x`(FE,Symbol,Equation(FE),UniversalSegment(NonNegativeInteger))->Any`pGenerateUnivariatePowerSeries(R,FE)``1282289 +otaylorIfCan`1`x`(_$)->Union(UTS,"failed")`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1282468 +otaylorQuoByVar`1`n`(_$)->_$`dInnerSparseUnivariatePowerSeries(Coef)``1282624 +otaylorRep`1`x`(_$)->UTS`cUnivariateLaurentSeriesConstructorCategory(Coef,UTS)``1282721 +otensorProduct`1`x`(List(Matrix(R)))->List(Matrix(R))`pRepresentationPackage1(R)``1282840 +otensorProduct`1`x`(Matrix(R))->Matrix(R)`pRepresentationPackage1(R)``1283206 +otensorProduct`2`x`(List(Matrix(R)),List(Matrix(R)))->List(Matrix(R))`pRepresentationPackage1(R)``1283299 +otensorProduct`2`x`(Matrix(R),Matrix(R))->Matrix(R)`pRepresentationPackage1(R)``1283683 +oterms`1`n`(_$)->List(Record(coef:R,monom:M))`dMonoidRing(R,M)``1283965 +oterms`1`x`(_$)->List(Record(gen:S,exp:E))`cFreeAbelianMonoidCategory(S,E)``1284125 +oterms`1`x`(_$)->Stream(Record(k:Expon,c:Coef))`cUnivariatePowerSeriesCategory(Coef,Expon)``1284214 +otest`1`x`(_$)->Boolean`dBoolean``1284396 +otestDim`2`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),List(OrderedVariableList(lv)))->Union(List(HomogeneousDistributedMultivariatePolynomial(lv,F)),"failed")`pGroebnerSolve(lv,F,R)``1284492 +otestModulus`2`n`(R,List(BP))->Boolean`pGenExEuclid(R,BP)``1284608 +otex`1`x`(_$)->List(String)`dTexFormat``1284811 +otheCurve`0`x`()->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionField(K,symb,BLMET)``1284881 +otheCurve`0`x`()->DistributedMultivariatePolynomial(symb,K)`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``1284954 +otheCurve`0`x`()->PolyRing`pGeneralPackageForAlgebraicFunctionField(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,DesTree,BLMET)``1285027 +othetaCoord`1`n`(Point(R))->R`pPointPackage(R)``1285100 othird`1`n`(A)->S`xUnaryRecursiveAggregate&(A,S)``0 -othird`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``1081735 -otimes!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``1081858 -otimes`4`n`(C,C,Automorphism(R),(R)->R)->C`pUnivariateSkewPolynomialCategoryOps(R,C)``1082059 -otitle`1`x`(String)->_$`dDrawOption``1082180 -otitle`2`n`(List(DrawOption),String)->String`pDrawOptionFunctions0``1082322 -otitle`2`n`(_$,String)->Void`dTwoDimensionalViewport``1082526 -otitle`2`x`(_$,String)->Void`dThreeDimensionalViewport``1082682 -otoScale`1`x`(Boolean)->_$`dDrawOption``1082842 -otoScale`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``1083072 -otop!`1`x`(_$)->S`cDequeueAggregate(S)``1083280 -otopFortranOutputStack`0`x`()->String`pFortranOutputStackPackage``1083357 -otopPredicate`1`n`(_$)->Record(var:List(Symbol),pred:Any)`dPattern(R)``1083447 -otop`1`x`(_$)->S`cStackAggregate(S)``1083645 -otoroidal`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``1083823 -otorsion?`1`n`(FiniteDivisor(F,UP,UPUP,R))->Boolean`pPointsOfFiniteOrder(R0,F,UP,UPUP,R)``1084132 -otorsion?`1`n`(FiniteDivisor(Fraction(Integer),UP,UPUP,R))->Boolean`pPointsOfFiniteOrderRational(UP,UPUP,R)``1084172 -otorsionIfCan`1`n`(FiniteDivisor(F,UP,UPUP,R))->Union(Record(order:NonNegativeInteger,function:R),"failed")`pPointsOfFiniteOrder(R0,F,UP,UPUP,R)``1084212 -otorsionIfCan`1`n`(FiniteDivisor(Fraction(Integer),UP,UPUP,R))->Union(Record(order:NonNegativeInteger,function:R),"failed")`pPointsOfFiniteOrderRational(UP,UPUP,R)``1084257 -otoseInvertible?`2`x`(P,TS)->Boolean`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1084301 -otoseInvertible?`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1084455 -otoseInvertibleSet`2`x`(P,TS)->List(TS)`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1084609 -otoseLastSubResultant`3`x`(P,P,TS)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1084767 -otoseSquareFreePart`2`x`(P,TS)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1084931 +othird`1`x`(_$)->S`cUnaryRecursiveAggregate(S)``1285376 +otimes!`3`n`(Matrix(R),Matrix(R),Matrix(R))->Matrix(R)`pStorageEfficientMatrixOperations(R)``1285503 +otimes`4`n`(C,C,Automorphism(R),(R)->R)->C`pUnivariateSkewPolynomialCategoryOps(R,C)``1285704 +otitle`1`x`(String)->_$`dDrawOption``1285825 +otitle`2`n`(List(DrawOption),String)->String`pDrawOptionFunctions0``1285967 +otitle`2`n`(_$,String)->Void`dTwoDimensionalViewport``1286171 +otitle`2`x`(_$,String)->Void`dThreeDimensionalViewport``1286327 +otop!`1`x`(_$)->S`cDequeueAggregate(S)``1286487 +otop`1`x`(_$)->S`cStackAggregate(S)``1286564 +otop`1`x`(_$)->S`dArrayStack(S)``1286849 +otop`1`x`(_$)->S`dDequeue(S)``1286941 +otop!`1`x`(_$)->S`dDequeue(S)``1287027 +otop`1`x`(_$)->S`dStack(S)``1287125 +otopFortranOutputStack`0`x`()->String`pFortranOutputStackPackage``1287207 +otopPredicate`1`n`(_$)->Record(var:List(Symbol),pred:Any)`dPattern(R)``1287297 +otoroidal`1`x`(R)->(Point(R))->Point(R)`pCoordinateSystems(R)``1287495 +otorsion?`1`n`(FiniteDivisor(Fraction(Integer),UP,UPUP,R))->Boolean`pPointsOfFiniteOrderRational(UP,UPUP,R)``1287804 +otorsion?`1`n`(FiniteDivisor(F,UP,UPUP,R))->Boolean`pPointsOfFiniteOrder(R0,F,UP,UPUP,R)``1287844 +otorsionIfCan`1`n`(FiniteDivisor(Fraction(Integer),UP,UPUP,R))->Union(Record(order:NonNegativeInteger,function:R),"failed")`pPointsOfFiniteOrderRational(UP,UPUP,R)``1287884 +otorsionIfCan`1`n`(FiniteDivisor(F,UP,UPUP,R))->Union(Record(order:NonNegativeInteger,function:R),"failed")`pPointsOfFiniteOrder(R0,F,UP,UPUP,R)``1287928 +otoScale`1`x`(Boolean)->_$`dDrawOption``1287973 +otoScale`2`n`(List(DrawOption),Boolean)->Boolean`pDrawOptionFunctions0``1288203 +otoseInvertible?`2`x`(P,TS)->Boolean`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1288411 +otoseInvertible?`2`x`(P,TS)->List(Record(val:Boolean,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1288555 +otoseInvertibleSet`2`x`(P,TS)->List(TS)`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1288699 +otoseLastSubResultant`3`x`(P,P,TS)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1288847 +otoseSquareFreePart`2`x`(P,TS)->List(Record(val:P,tower:TS))`pRegularTriangularSetGcdPackage(R,E,V,P,TS)``1289001 ototalDegree`1`n`(S)->NonNegativeInteger`xPolynomialCategory&(S,R,E,VarSet)``0 ototalDegree`1`n`(S)->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 -ototalDegree`1`x`(_$)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``1085078 +ototalDegree`1`x`(_$)->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``1289138 +ototalDegree`1`x`(PolyRing)->NonNegativeInteger`pPackageForPoly(R,PolyRing,E,dim)``0 ototalDegree`2`n`(S,List(SingletonAsOrderedSet))->NonNegativeInteger`xUnivariatePolynomialCategory&(S,R)``0 ototalDegree`2`n`(S,List(VarSet))->NonNegativeInteger`xPolynomialCategory&(S,R,E,VarSet)``0 -ototalDegree`2`x`(_$,List(VarSet))->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``1085182 -ototalDifferential`1`n`(Expression(CoefRing))->_$`dDeRhamComplex(CoefRing,listIndVar)``1085325 -ototalGroebner`2`x`(List(Polynomial(F)),List(Symbol))->List(Polynomial(F))`pPolyGroebner(F)``1085429 -ototalLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``1085692 -ototalfract`1`x`(PRF)->Record(sup:Polynomial(R),inf:Polynomial(R))`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1085874 -ototolex`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(DistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``1086105 +ototalDegree`2`x`(_$,List(VarSet))->NonNegativeInteger`cPolynomialCategory(R,E,VarSet)``1289242 +ototalDifferential`1`n`(Expression(CoefRing))->_$`dDeRhamComplex(CoefRing,listIndVar)``1289385 +ototalfract`1`x`(PRF)->Record(sup:Polynomial(R),inf:Polynomial(R))`pMPolyCatRationalFunctionFactorizer(E,OV,R,PRF)``1289489 +ototalGroebner`2`x`(List(Polynomial(F)),List(Symbol))->List(Polynomial(F))`pPolyGroebner(F)``1289720 +ototalLex`2`n`(Vector(S),Vector(S))->Boolean`pOrderingFunctions(dim,S)``1289983 +ototolex`1`n`(List(HomogeneousDistributedMultivariatePolynomial(lv,F)))->List(DistributedMultivariatePolynomial(lv,F))`pLinGroebnerPackage(lv,F)``1290165 otower`1`n`(S)->List(Kernel(S))`xExpressionSpace&(S)``0 -otower`1`x`(_$)->List(Kernel(_$))`cExpressionSpace``1086141 -otrace2PowMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``1086246 -otraceMatrix`0`n`()->Matrix(R)`xFramedAlgebra&(S,R,UP)``1086406 -otraceMatrix`0`x`()->Matrix(R)`cFramedAlgebra(R,UP)``1086575 -otraceMatrix`1`n`(Vector(S))->Matrix(R)`xFiniteRankAlgebra&(S,R,UP)``0 -otraceMatrix`1`n`(Vector(S))->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 -otraceMatrix`1`x`(Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``1086744 -otracePowMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``1086858 +otower`1`x`(_$)->List(Kernel(_$))`cExpressionSpace``1290201 otrace`1`n`(S)->F`xFiniteAlgebraicExtensionField&(S,F)``0 otrace`1`n`(S)->R`xComplexCategory&(S,R)``0 otrace`1`n`(S)->R`xSquareMatrixCategory&(S,ndim,R,Row,Col)``0 -otrace`1`x`(_$)->F`cFiniteAlgebraicExtensionField(F)``1086981 -otrace`1`x`(_$)->R`cFiniteRankAlgebra(R,UP)``1087125 -otrace`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)``1087235 +otrace`1`x`(_$)->F`cFiniteAlgebraicExtensionField(F)``1290306 +otrace`1`x`(_$)->R`cFiniteRankAlgebra(R,UP)``1290450 +otrace`1`x`(_$)->R`cSquareMatrixCategory(ndim,R,Row,Col)``1290560 otrace`2`n`(S,PositiveInteger)->S`xFiniteAlgebraicExtensionField&(S,F)``0 -otrace`2`n`(Vector(GF),PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``1087372 -otrace`2`x`(_$,PositiveInteger)->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`1087471 -otrailingCoefficient`1`n`(_$)->R`dLaurentPolynomial(R,UP)``1087766 +otrace`2`n`(Vector(GF),PositiveInteger)->Vector(GF)`pInnerNormalBasisFieldFunctions(GF)``1290697 +otrace2PowMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``1290796 +otrace`2`x`(_$,PositiveInteger)->_$`cFiniteAlgebraicExtensionField(F)`has(F,Finite)`1290949 +otraceMatrix`0`n`()->Matrix(R)`xFramedAlgebra&(S,R,UP)``1291246 +otraceMatrix`0`x`()->Matrix(R)`cFramedAlgebra(R,UP)``1291415 +otraceMatrix`1`n`(Vector(S))->Matrix(R)`xFiniteRankAlgebra&(S,R,UP)``0 +otraceMatrix`1`n`(Vector(S))->Matrix(R)`xFramedAlgebra&(S,R,UP)``0 +otraceMatrix`1`x`(Vector(_$))->Matrix(R)`cFiniteRankAlgebra(R,UP)``1291584 +otracePowMod`3`x`(FP,NonNegativeInteger,FP)->FP`pDistinctDegreeFactorize(F,FP)``1291698 +otrailingCoefficient`1`n`(_$)->R`dLaurentPolynomial(R,UP)``1291821 +otRange`1`n`(_$)->Segment(DoubleFloat)`dPlot3D``1291866 +otRange`1`n`(_$)->Segment(DoubleFloat)`dPlot``1291956 otranscendenceDegree`0`n`()->NonNegativeInteger`xFiniteAlgebraicExtensionField&(S,F)``0 -otranscendenceDegree`0`x`()->NonNegativeInteger`cExtensionField(F)``1087814 +otranscendenceDegree`0`x`()->NonNegativeInteger`cExtensionField(F)``1292045 otranscendent?`1`n`(S)->Boolean`xExtensionField&(S,F)``0 otranscendent?`1`n`(S)->Boolean`xFiniteAlgebraicExtensionField&(S,F)``0 -otranscendent?`1`x`(_$)->Boolean`cExtensionField(F)``1087942 +otranscendent?`1`x`(_$)->Boolean`cExtensionField(F)``1292173 otranscendentalDecompose`2`x`(P,TS)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 otranscendentalDecompose`2`x`(P,TS)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 otranscendentalDecompose`3`x`(P,TS,NonNegativeInteger)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 otranscendentalDecompose`3`x`(P,TS,NonNegativeInteger)->Record(done:List(TS),todo:List(Record(val:List(P),tower:TS)))`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -otransform`1`n`(DistributedMultivariatePolynomial(lv,F))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``1088066 -otranslate`3`x`(_$,Float,Float)->Void`dThreeDimensionalViewport``1088104 -otranslate`4`n`(_$,PositiveInteger,Float,Float)->Void`dTwoDimensionalViewport``1088328 +otransCoord`1`x`(_$)->Integer`cBlowUpMethodCategory``0 +otransform`1`n`(DistributedMultivariatePolynomial(lv,F))->HomogeneousDistributedMultivariatePolynomial(lv,F)`pLinGroebnerPackage(lv,F)``1292297 +otranslate`2`x`(PolyRing,List(R))->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``1292335 +otranslate`3`x`(_$,Float,Float)->Void`dThreeDimensionalViewport``1292482 +otranslate`3`x`(PolyRing,List(R),Integer)->PolyRing`pPackageForPoly(R,PolyRing,E,dim)``1292706 +otranslate`3`x`(R,R,R)->_$`dDenavitHartenbergMatrix(R)``1292863 +otranslate`4`n`(_$,PositiveInteger,Float,Float)->Void`dTwoDimensionalViewport``1292973 +otranslateToOrigin`2`x`(DistributedMultivariatePolynomial(symb,K),ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField(K))->DistributedMultivariatePolynomial(symb,PseudoAlgebraicClosureOfFiniteField(K))`pPackageForAlgebraicFunctionFieldOverFiniteField(K,symb,BLMET)``0 +otranslateToOrigin`2`x`(PolyRing,ProjPt)->PolyRing`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``1293443 +otranslateToOrigin`3`x`(PolyRing,ProjPt,Integer)->PolyRing`pPolynomialPackageForCurve(K,PolyRing,E,dim,ProjPt)``1293535 +otranspose`1`n`(_$)->_$`dSquareMatrix(ndim,R)``1293627 otranspose`1`n`(Row)->S`xMatrixCategory&(S,R,Row,Col)``0 otranspose`1`n`(S)->S`xMatrixCategory&(S,R,Row,Col)``0 -otranspose`1`n`(_$)->_$`dSquareMatrix(ndim,R)``1088798 -otranspose`1`x`(Row)->_$`cMatrixCategory(R,Row,Col)``1088871 -otranspose`1`x`(_$)->_$`cMatrixCategory(R,Row,Col)``1088941 -otranspose`1`x`(_$)->_$`dCartesianTensor(minix,dim,R)``1089014 -otranspose`3`x`(_$,Integer,Integer)->_$`dCartesianTensor(minix,dim,R)``1089267 -otrapezoidal`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1089563 -otrapezoidalo`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1090271 -otraverse`2`n`(_$,List(NonNegativeInteger))->_$`dSubSpace(n,R)``1090973 -otree`1`x`(List(S))->_$`dTree(S)``1091319 -otree`1`x`(S)->_$`dTree(S)``1091394 -otree`2`x`(S,List(_$))->_$`dTree(S)``1091472 -otriangSolve`1`x`(List(Polynomial(R)))->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1091563 -otriangSolve`2`x`(List(Polynomial(R)),Boolean)->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1091652 -otriangSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1091741 +otranspose`1`x`(_$)->_$`cMatrixCategory(R,Row,Col)``1293700 +otranspose`1`x`(_$)->_$`dCartesianTensor(minix,dim,R)``1293896 +otranspose`1`x`(Row)->_$`cMatrixCategory(R,Row,Col)``1294362 +otranspose`3`x`(_$,Integer,Integer)->_$`dCartesianTensor(minix,dim,R)``1294501 +otrapezoidal`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1295123 +otrapezoidalo`7`x`((Float)->Float,Float,Float,Float,Float,Integer,Integer)->Record(value:Float,error:Float,totalpts:Integer,success:Boolean)`pNumericalQuadrature``1295831 +otraverse`2`n`(_$,List(NonNegativeInteger))->_$`dSubSpace(n,R)``1296533 +otree`1`x`(List(S))->_$`cDesingTreeCategory(S)``1296879 +otree`1`x`(List(S))->_$`dTree(S)``1296945 +otree`1`x`(S)->_$`cDesingTreeCategory(S)``1297075 +otree`1`x`(S)->_$`dTree(S)``1297153 +otree`2`x`(S,List(_$))->_$`cDesingTreeCategory(S)``1297272 +otree`2`x`(S,List(_$))->_$`dTree(S)``1297363 +otriangSolve`1`x`(List(Polynomial(R)))->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1297551 +otriangSolve`2`x`(List(Polynomial(R)),Boolean)->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1297640 +otriangSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(RegularChain(R,ls))`pZeroDimensionalSolvePackage(R,ls,ls2)``1297729 otriangular?`1`n`(S)->Boolean`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -otriangular?`1`x`(_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`1092818 -otriangularSystems`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Polynomial(R)))`pSystemSolvePackage(R)``1093036 -otriangulate`2`n`(Matrix(F),Vector(F))->Record(A:Matrix(F),eqs:List(Record(C:Matrix(F),g:Vector(F),eq:LO,rh:F)))`pSystemODESolver(F,LO)``1093391 -otriangulate`2`n`(Matrix(LO),Vector(F))->Record(mat:Matrix(LO),vec:Vector(F))`pSystemODESolver(F,LO)``1093755 -otrigs2explogs`3`n`(FG,List(Kernel(FG)),List(Symbol))->FG`pInnerTrigonometricManipulations(R,F,FG)``1093925 -otrigs`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``1094302 -otrigs`1`x`(F)->F`pTrigonometricManipulations(R,F)``1094431 -otrim`2`n`(S,Character)->S`xStringAggregate&(S)``0 +otriangular?`1`x`(_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)`has(R,IntegralDomain)`1298746 +otriangularSystems`2`x`(List(Fraction(Polynomial(R))),List(Symbol))->List(List(Polynomial(R)))`pSystemSolvePackage(R)``1298964 +otriangulate`2`n`(Matrix(F),Vector(F))->Record(A:Matrix(F),eqs:List(Record(C:Matrix(F),g:Vector(F),eq:LO,rh:F)))`pSystemODESolver(F,LO)``1299319 +otriangulate`2`n`(Matrix(LO),Vector(F))->Record(mat:Matrix(LO),vec:Vector(F))`pSystemODESolver(F,LO)``1299683 +otrigs`1`x`(F)->F`pComplexTrigonometricManipulations(R,F)``1299853 +otrigs`1`x`(F)->F`pTrigonometricManipulations(R,F)``1299982 +otrigs2explogs`3`n`(FG,List(Kernel(FG)),List(Symbol))->FG`pInnerTrigonometricManipulations(R,F,FG)``1300111 otrim`2`n`(S,CharacterClass)->S`xStringAggregate&(S)``0 -otrim`2`x`(_$,Character)->_$`cStringAggregate``1094560 -otrim`2`x`(_$,CharacterClass)->_$`cStringAggregate``1094738 +otrim`2`n`(S,Character)->S`xStringAggregate&(S)``0 +otrim`2`x`(_$,CharacterClass)->_$`cStringAggregate``1300488 +otrim`2`x`(_$,Character)->_$`cStringAggregate``1300677 otrivialIdeal?`1`n`(S)->Boolean`xPolynomialSetCategory&(S,R,E,VarSet,P)``0 -otrivialIdeal?`1`x`(_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)``1094927 -otrueEqual`2`n`(_$,_$)->Boolean`dInnerAlgebraicNumber``1095045 -otrue`0`x`()->_$`dBoolean``1095124 -otrunc`2`x`(_$,NonNegativeInteger)->_$`cFreeLieAlgebra(VarSet,R)``1095166 -otrunc`2`x`(_$,NonNegativeInteger)->_$`cXPolynomialsCat(vl,R)``1095285 +otrivialIdeal?`1`x`(_$)->Boolean`cPolynomialSetCategory(R,E,VarSet,P)``1300855 +otrue`0`x`()->_$`dBoolean``1300973 +otrueEqual`2`n`(_$,_$)->Boolean`dInnerAlgebraicNumber``1301015 +otrunc`2`x`(_$,NonNegativeInteger)->_$`cFreeLieAlgebra(VarSet,R)``1301094 +otrunc`2`x`(_$,NonNegativeInteger)->_$`cXPolynomialsCat(vl,R)``1301213 otruncate`1`n`(S)->S`xRealNumberSystem&(S)``0 -otruncate`1`x`(_$)->_$`cRealNumberSystem``1095373 -otruncate`2`x`(_$,Expon)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``1095462 -otruncate`3`x`(_$,Expon,Expon)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``1095594 -otryFunctionalDecomposition?`0`n`()->Boolean`pGaloisGroupFactorizer(UP)``1095755 -otryFunctionalDecomposition`1`n`(Boolean)->Boolean`pGaloisGroupFactorizer(UP)``1095901 -otubePlot`7`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),(DoubleFloat)->DoubleFloat,Integer)->TubePlot(Plot3D)`pExpressionTubePlot``1096095 -otubePlot`7`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),DoubleFloat,Integer)->TubePlot(Plot3D)`pExpressionTubePlot``1096369 -otubePlot`8`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),(DoubleFloat)->DoubleFloat,Integer,String)->TubePlot(Plot3D)`pExpressionTubePlot``1096633 -otubePlot`8`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),DoubleFloat,Integer,String)->TubePlot(Plot3D)`pExpressionTubePlot``1097001 -otubePointsDefault`0`x`()->PositiveInteger`pViewDefaultsPackage``1097366 -otubePointsDefault`1`x`(PositiveInteger)->PositiveInteger`pViewDefaultsPackage``1097504 -otubePoints`1`x`(PositiveInteger)->_$`dDrawOption``1097648 -otubePoints`2`n`(List(DrawOption),PositiveInteger)->PositiveInteger`pDrawOptionFunctions0``1097865 -otubeRadiusDefault`0`x`()->DoubleFloat`pViewDefaultsPackage``1098079 -otubeRadiusDefault`1`x`(Float)->DoubleFloat`pViewDefaultsPackage``1098157 -otubeRadius`1`x`(Float)->_$`dDrawOption``1098248 -otubeRadius`2`n`(List(DrawOption),Float)->Float`pDrawOptionFunctions0``1098394 -otube`3`n`(Curve,DoubleFloat,Integer)->TubePlot(Curve)`pNumericTubePlot(Curve)``1098608 -otube`3`n`(Curve,List(List(Point(DoubleFloat))),Boolean)->_$`dTubePlot(Curve)``1098699 -otwist`1`x`((A,B)->C)->(B,A)->C`pMappingPackage3(A,B,C)``1099013 -otwoFactor`2`n`(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),Integer)->Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))`pTwoFactorize(F)``1099113 -otypeList`2`x`(FortranScalarType,_$)->List(Union(name:Symbol,bounds:List(Union(S:Symbol,P:Polynomial(Integer)))))`dSymbolTable``1099432 -otypeLists`1`x`(_$)->List(List(Union(name:Symbol,bounds:List(Union(S:Symbol,P:Polynomial(Integer))))))`dSymbolTable``1099529 -ounary?`1`x`(_$)->Boolean`dBasicOperator``1099616 -ounaryFunction`1`n`(Symbol)->(D)->I`pMakeUnaryCompiledFunction(S,D,I)``1099670 -ouncouplingMatrices`1`n`(Matrix(R))->Vector(Matrix(R))`pAssociatedEquations(R,L)``1099721 +otruncate`1`x`(_$)->_$`cRealNumberSystem``1301301 +otruncate`2`x`(_$,Expon)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``1301390 +otruncate`3`x`(_$,Expon,Expon)->_$`cUnivariatePowerSeriesCategory(Coef,Expon)``1301522 +otryFunctionalDecomposition?`0`n`()->Boolean`pGaloisGroupFactorizer(UP)``1301683 +otryFunctionalDecomposition`1`n`(Boolean)->Boolean`pGaloisGroupFactorizer(UP)``1301829 +otube`3`n`(Curve,DoubleFloat,Integer)->TubePlot(Curve)`pNumericTubePlot(Curve)``1302023 +otube`3`n`(Curve,List(List(Point(DoubleFloat))),Boolean)->_$`dTubePlot(Curve)``1302114 +otubePlot`7`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),(DoubleFloat)->DoubleFloat,Integer)->TubePlot(Plot3D)`pExpressionTubePlot``1302428 +otubePlot`7`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),DoubleFloat,Integer)->TubePlot(Plot3D)`pExpressionTubePlot``1302702 +otubePlot`8`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),(DoubleFloat)->DoubleFloat,Integer,String)->TubePlot(Plot3D)`pExpressionTubePlot``1302966 +otubePlot`8`n`(Expression(Integer),Expression(Integer),Expression(Integer),(DoubleFloat)->DoubleFloat,Segment(DoubleFloat),DoubleFloat,Integer,String)->TubePlot(Plot3D)`pExpressionTubePlot``1303334 +otubePoints`1`x`(PositiveInteger)->_$`dDrawOption``1303699 +otubePoints`2`n`(List(DrawOption),PositiveInteger)->PositiveInteger`pDrawOptionFunctions0``1303916 +otubePointsDefault`0`x`()->PositiveInteger`pViewDefaultsPackage``1304130 +otubePointsDefault`1`x`(PositiveInteger)->PositiveInteger`pViewDefaultsPackage``1304268 +otubeRadius`1`x`(Float)->_$`dDrawOption``1304412 +otubeRadius`2`n`(List(DrawOption),Float)->Float`pDrawOptionFunctions0``1304558 +otubeRadiusDefault`0`x`()->DoubleFloat`pViewDefaultsPackage``1304772 +otubeRadiusDefault`1`x`(Float)->DoubleFloat`pViewDefaultsPackage``1304850 +otValues`1`n`(_$)->List(List(DoubleFloat))`dPlot3D``1304941 +otwist`1`x`((A,B)->C)->(B,A)->C`pMappingPackage3(A,B,C)``1305100 +otwoFactor`2`n`(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)),Integer)->Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(F)))`pTwoFactorize(F)``1305200 +otype`1`x`(_$)->Union("left","center","right","vertical","horizontal")`cBlowUpMethodCategory``0 +otypeList`2`x`(FortranScalarType,_$)->List(Union(name:Symbol,bounds:List(Union(S:Symbol,P:Polynomial(Integer)))))`dSymbolTable``1305519 +otypeLists`1`x`(_$)->List(List(Union(name:Symbol,bounds:List(Union(S:Symbol,P:Polynomial(Integer))))))`dSymbolTable``1305616 +ounary?`1`x`(_$)->Boolean`dBasicOperator``1305703 +ounaryFunction`1`n`(Symbol)->(D)->I`pMakeUnaryCompiledFunction(S,D,I)``1305757 +ouncouplingMatrices`1`n`(Matrix(R))->Vector(Matrix(R))`pAssociatedEquations(R,L)``1305808 ounexpand`1`n`(XDistributedPolynomial(Symbol,R))->_$`dXPolynomial(R)``0 -ounexpand`1`n`(XDistributedPolynomial(VarSet,R))->_$`dXRecursivePolynomial(VarSet,R)``1099956 -ouniform01`0`n`()->Float`pRandomFloatDistributions``1100018 -ouniform`1`n`(Segment(Integer))->()->Integer`pRandomIntegerDistributions``1100058 -ouniform`1`n`(Set(S))->()->S`pRandomDistributions(S)``1100097 -ouniform`2`n`(Float,Float)->()->Float`pRandomFloatDistributions``1100136 +ounexpand`1`n`(XDistributedPolynomial(VarSet,R))->_$`dXRecursivePolynomial(VarSet,R)``1306043 +ouniform01`0`n`()->Float`pRandomFloatDistributions``1306105 +ouniform`1`n`(Segment(Integer))->()->Integer`pRandomIntegerDistributions``1306145 +ouniform`1`n`(Set(S))->()->S`pRandomDistributions(S)``1306653 +ouniform`2`n`(Float,Float)->()->Float`pRandomFloatDistributions``1306692 ounion`2`n`(A,A)->A`xFiniteSetAggregate&(A,S)``0 ounion`2`n`(A,A)->A`xSetAggregate&(A,S)``0 ounion`2`n`(A,S)->A`xFiniteSetAggregate&(A,S)``0 ounion`2`n`(A,S)->A`xSetAggregate&(A,S)``0 -ounion`2`n`(List(Kernel(F)),List(Kernel(F)))->List(Kernel(F))`pIntegrationTools(R,F)``1100179 +ounion`2`n`(_$,_$)->_$`dPatternMatchResult(R,S)``1306735 +ounion`2`n`(List(Kernel(F)),List(Kernel(F)))->List(Kernel(F))`pIntegrationTools(R,F)``1306805 ounion`2`n`(S,A)->A`xFiniteSetAggregate&(A,S)``0 ounion`2`n`(S,A)->A`xSetAggregate&(A,S)``0 -ounion`2`n`(_$,_$)->_$`dPatternMatchResult(R,S)``1100265 -ounion`2`x`(S,_$)->_$`cSetAggregate(S)``1100335 -ounion`2`x`(_$,S)->_$`cSetAggregate(S)``1100534 -ounion`2`x`(_$,_$)->_$`cSetAggregate(S)``1100733 +ounion`2`x`(_$,_$)->_$`cSetAggregate(S)``1306891 +ounion`2`x`(_$,S)->_$`cSetAggregate(S)``1307020 +ounion`2`x`(S,_$)->_$`cSetAggregate(S)``1307219 +ounit`0`n`()->Union(S,"failed")`xFramedNonAssociativeAlgebra&(S,R)``0 +ounit`0`x`()->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1307418 ounit?`1`n`(S)->Boolean`xIntegralDomain&(S)``0 -ounit?`1`x`(_$)->Boolean`cIntegralDomain``1100862 +ounit?`1`x`(_$)->Boolean`cIntegralDomain``1307530 +ounit`1`x`(List(Float))->_$`dDrawOption``1307622 +ounit`1`x`(_$)->R`dFactored(R)``1307775 ounitCanonical`1`n`(S)->S`xField&(S)``0 ounitCanonical`1`n`(S)->S`xIntegralDomain&(S)``0 -ounitCanonical`1`x`(_$)->_$`cIntegralDomain``1100954 +ounitCanonical`1`x`(_$)->_$`cIntegralDomain``1308018 ounitNormal`1`n`(S)->Record(unit:S,canonical:S,associate:S)`xComplexCategory&(S,R)``0 ounitNormal`1`n`(S)->Record(unit:S,canonical:S,associate:S)`xField&(S)``0 ounitNormal`1`n`(S)->Record(unit:S,canonical:S,associate:S)`xIntegralDomain&(S)``0 -ounitNormal`1`x`(_$)->Record(unit:_$,canonical:_$,associate:_$)`cIntegralDomain``1101025 -ounitNormalize`1`x`(_$)->_$`dFactored(R)``1101337 -ounitVector`1`n`(IS)->_$`dGeneralModulePolynomial(vl,R,IS,E,ff,P)``1101538 -ounitVector`1`n`(Point(DoubleFloat))->Point(DoubleFloat)`pTubePlotTools``1101580 -ounitVector`1`x`(PositiveInteger)->_$`cDirectProductCategory(dim,R)`has(R,Ring)`1101725 -ounit`0`n`()->Union(S,"failed")`xFramedNonAssociativeAlgebra&(S,R)``0 -ounit`0`x`()->Union(_$,"failed")`cFiniteRankNonAssociativeAlgebra(R)`has(R,IntegralDomain)`1101819 -ounit`1`x`(List(Float))->_$`dDrawOption``1101931 -ounit`1`x`(_$)->R`dFactored(R)``1102084 -ounitsColorDefault`0`x`()->Palette`pViewDefaultsPackage``1102151 -ounitsColorDefault`1`x`(Palette)->Palette`pViewDefaultsPackage``1102247 -ounits`1`n`(_$)->List(Float)`dGraphImage``1102365 -ounits`2`n`(List(DrawOption),List(Float))->List(Float)`pDrawOptionFunctions0``1102550 -ounits`2`n`(_$,List(Float))->List(Float)`dGraphImage``1102753 -ounits`3`n`(_$,PositiveInteger,Palette)->Void`dTwoDimensionalViewport``1103053 -ounits`3`n`(_$,PositiveInteger,String)->Void`dTwoDimensionalViewport``1103305 -ounivariate?`1`n`(P)->Boolean`pPolynomialSetUtilitiesPackage(R,E,V,P)``1103570 -ounivariatePolynomial`2`n`(_$,NonNegativeInteger)->UnivariatePolynomial(var,Coef)`dSparseUnivariateTaylorSeries(Coef,var,cen)``1103684 -ounivariatePolynomial`2`n`(_$,NonNegativeInteger)->UnivariatePolynomial(var,Coef)`dUnivariateTaylorSeries(Coef,var,cen)``1103842 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ounivariate`2`n`(S,Kernel(S))->Fraction(SparseUnivariatePolynomial(S))`xFunctionSpace&(S,R)``0 -ounivariate`2`x`(Fraction(Polynomial(R)),Symbol)->Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(R))))`pRationalFunction(R)``1106348 -ounivariate`2`x`(Polynomial(R),Variable(x))->UnivariatePolynomial(x,Polynomial(R))`pPolynomialToUnivariatePolynomial(x,R)``1106452 -ounivariate`2`x`(_$,Kernel(_$))->Fraction(SparseUnivariatePolynomial(_$))`cFunctionSpace(R)`has(R,IntegralDomain)`1106622 -ounivariate`2`x`(_$,VarSet)->SparseUnivariatePolynomial(_$)`cPolynomialCategory(R,E,VarSet)``1106717 -ounivariate`3`n`(F,V,SparseUnivariatePolynomial(F))->SparseUnivariatePolynomial(F)`pPolynomialCategoryQuotientFunctions(E,V,R,P,F)``1106923 -ounivariate`4`n`(F,Kernel(F),Kernel(F),SparseUnivariatePolynomial(F))->SparseUnivariatePolynomial(Fraction(SparseUnivariatePolynomial(F)))`pGenusZeroIntegration(R,F,L)``1107069 -ounivcase`2`n`(P,OV)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1107123 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+ounivariateSolve`1`x`(RegularChain(R,ls))->List(Record(complexRoots:SparseUnivariatePolynomial(R),coordinates:List(Polynomial(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1312808 +ounivariateSolve`2`x`(List(Polynomial(R)),Boolean)->List(Record(complexRoots:SparseUnivariatePolynomial(R),coordinates:List(Polynomial(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1312971 +ounivariateSolve`3`x`(List(Polynomial(R)),Boolean,Boolean)->List(Record(complexRoots:SparseUnivariatePolynomial(R),coordinates:List(Polynomial(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1313085 +ounivariateSolve`4`x`(List(Polynomial(R)),Boolean,Boolean,Boolean)->List(Record(complexRoots:SparseUnivariatePolynomial(R),coordinates:List(Polynomial(R))))`pZeroDimensionalSolvePackage(R,ls,ls2)``1313209 +ounivcase`2`n`(P,OV)->Factored(P)`pMultivariateSquareFree(E,OV,R,P)``1313951 ouniverse`0`n`()->A`xFiniteSetAggregate&(A,S)``0 -ouniverse`0`x`()->_$`cFiniteSetAggregate(S)`has(S,Finite)`1107162 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-ounvectorise`3`n`(Vector(Expression(R)),Fraction(SparseUnivariatePolynomial(Expression(R))),Integer)->Fraction(SparseUnivariatePolynomial(Expression(R)))`pTransSolvePackageService(R)``1109515 +ounmakeSUP`1`x`(SparseUnivariatePolynomial(R))->_$`cUnivariatePolynomialCategory(R)``1314086 +ounparse`1`n`(_$)->String`dInputForm``1314249 +ounprotectedRemoveRedundantFactors`2`n`(P,P)->List(P)`pPolynomialSetUtilitiesPackage(R,E,V,P)``1314414 +ounrankImproperPartitions0`3`x`(Integer,Integer,Integer)->List(Integer)`pSymmetricGroupCombinatoricFunctions``1314865 +ounrankImproperPartitions1`3`x`(Integer,Integer,Integer)->List(Integer)`pSymmetricGroupCombinatoricFunctions``1315318 +ounravel`1`x`(List(R))->_$`dCartesianTensor(minix,dim,R)``1315886 +ountab`2`n`(List(List(S)),List(List(List(S))))->List(List(S))`pTableauxBumpers(S)``1316009 +oUnVectorise`1`n`(Vector(R))->_$`dModMonic(R,Rep)``1316138 +ounvectorise`1`n`(Vector(R))->UP`pGaloisGroupPolynomialUtilities(R,UP)``1316185 +ounvectorise`3`n`(Vector(Expression(R)),Fraction(SparseUnivariatePolynomial(Expression(R))),Integer)->Fraction(SparseUnivariatePolynomial(Expression(R)))`pTransSolvePackageService(R)``1316313 +oUP2ifCan`1`n`(UP)->Union(overq:SparseUnivariatePolynomial(Fraction(Integer)),overan:SparseUnivariatePolynomial(AlgebraicNumber),failed:Boolean)`pFunctionSpaceUnivariatePolynomialFactor(R,F,UP)``1316548 +oUP2UTS`1`n`(UP)->UTS`pUTSodetools(F,UP,L,UTS)``1316607 +oupdatD`2`n`(List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)),List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1316669 +oupdate`3`n`(_$,GraphImage,PositiveInteger)->Void`dTwoDimensionalViewport``1316704 oupDateBranches`5`x`(List(P),List(TS),List(Record(val:List(P),tower:TS)),Record(done:List(TS),todo:List(Record(val:List(P),tower:TS))),NonNegativeInteger)->List(Record(val:List(P),tower:TS))`pRegularSetDecompositionPackage(R,E,V,P,TS)``0 oupDateBranches`5`x`(List(P),List(TS),List(Record(val:List(P),tower:TS)),Record(done:List(TS),todo:List(Record(val:List(P),tower:TS))),NonNegativeInteger)->List(Record(val:List(P),tower:TS))`pSquareFreeRegularSetDecompositionPackage(R,E,V,P,TS)``0 -oupdatD`2`n`(List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)),List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol)))->List(Record(lcmfij:Expon,totdeg:NonNegativeInteger,poli:Dpol,polj:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1109750 -oupdatF`3`n`(Dpol,NonNegativeInteger,List(Record(totdeg:NonNegativeInteger,pol:Dpol)))->List(Record(totdeg:NonNegativeInteger,pol:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1109785 -oupdateStatus!`1`n`(_$)->_$`dSplittingTree(V,C)``1109820 -oupdate`3`n`(_$,GraphImage,PositiveInteger)->Void`dTwoDimensionalViewport``1109947 -oupperCase!`1`x`(_$)->_$`cStringAggregate``1110129 -oupperCase?`1`x`(_$)->Boolean`dCharacter``1110244 -oupperCase`0`x`()->_$`dCharacterClass``1110355 +oupdateStatus!`1`n`(_$)->_$`dSplittingTree(V,C)``1316886 +oupdatF`3`n`(Dpol,NonNegativeInteger,List(Record(totdeg:NonNegativeInteger,pol:Dpol)))->List(Record(totdeg:NonNegativeInteger,pol:Dpol))`pGroebnerInternalPackage(Dom,Expon,VarSet,Dpol)``1317013 +oupperCase`0`x`()->_$`dCharacterClass``1317048 oupperCase`1`n`(S)->S`xStringAggregate&(S)``0 -oupperCase`1`x`(_$)->_$`cStringAggregate``1110479 -oupperCase`1`x`(_$)->_$`dCharacter``1110560 -ouseEisensteinCriterion?`0`n`()->Boolean`pGaloisGroupFactorizer(UP)``1110729 -ouseEisensteinCriterion`1`n`(Boolean)->Boolean`pGaloisGroupFactorizer(UP)``1110858 -ouseNagFunctions`0`x`()->Boolean`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1111055 -ouseNagFunctions`1`x`(Boolean)->Boolean`dFortranExpression(basicSymbols,subscriptedSymbols,R)``1111188 -ouseSingleFactorBound?`0`n`()->Boolean`pGaloisGroupFactorizer(UP)``1111395 -ouseSingleFactorBound`1`n`(Boolean)->Boolean`pGaloisGroupFactorizer(UP)``1111567 -ouserOrdered?`0`n`()->Boolean`pUserDefinedPartialOrdering(S)``1111787 -ousingTable?`0`n`()->Boolean`pTabulatedComputationPackage(Key,Entry)``1111922 -ovalidExponential`3`x`(List(Kernel(F)),F,Symbol)->Union(F,"failed")`pElementaryFunctionStructurePackage(R,F)``1111998 +oupperCase?`1`x`(_$)->Boolean`dCharacter``1317147 +oupperCase!`1`x`(_$)->_$`cStringAggregate``1317455 +oupperCase`1`x`(_$)->_$`cStringAggregate``1317570 +oupperCase`1`x`(_$)->_$`dCharacter``1317651 +oUpTriBddDenomInv`2`n`(M,R)->M`pTriangularMatrixOperations(R,Row,Col,M)``1318038 +ouseEisensteinCriterion?`0`n`()->Boolean`pGaloisGroupFactorizer(UP)``1318249 +ouseEisensteinCriterion`1`n`(Boolean)->Boolean`pGaloisGroupFactorizer(UP)``1318378 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+owriteLine!`2`x`(_$,String)->String`dTextFile``1337701 +owronskianMatrix`1`n`(List(F))->Matrix(F)`pODETools(F,LODO)``1337863 +owronskianMatrix`2`n`(List(F),NonNegativeInteger)->Matrix(F)`pODETools(F,LODO)``1338005 +owrregime`2`n`(List(Record(eqzro:List(GR),neqzro:List(GR),wcond:List(Polynomial(R)),bsoln:Record(partsol:Vector(Fraction(Polynomial(R))),basis:List(Vector(Fraction(Polynomial(R))))))),String)->Integer`pParametricLinearEquations(R,Var,Expon,GR)``1338157 +oxCoord`1`n`(Point(R))->R`pPointPackage(R)``1338279 +oxn`1`n`(NonNegativeInteger)->SparseUnivariatePolynomial(GF)`pInnerNormalBasisFieldFunctions(GF)``1338533 +oxor`2`x`(_$,_$)->_$`cBitAggregate``1338591 +oxor`2`x`(_$,_$)->_$`dBoolean``1338699 +oxor`2`x`(_$,_$)->_$`dSingleInteger``1338791 +oxRange`1`x`(_$)->Segment(DoubleFloat)`cPlottablePlaneCurveCategory``1338897 +oxRange`1`x`(_$)->Segment(DoubleFloat)`cPlottableSpaceCurveCategory``1339004 +oY`1`n`((Stream(A))->Stream(A))->Stream(A)`pParadoxicalCombinatorsForStreams(A)``1339111 +oY`2`n`((List(Stream(A)))->List(Stream(A)),Integer)->List(Stream(A))`pParadoxicalCombinatorsForStreams(A)``1339179 +oyCoord`1`n`(Point(R))->R`pPointPackage(R)``1339341 oyCoordinates`1`n`(S)->Record(num:Vector(UP),den:UP)`xFunctionFieldCategory&(S,F,UP,UPUP)``0 -oyCoordinates`1`x`(_$)->Record(num:Vector(UP),den:UP)`cFunctionFieldCategory(F,UP,UPUP)``1131109 -oyRange`1`x`(_$)->Segment(DoubleFloat)`cPlottablePlaneCurveCategory``1131233 -oyRange`1`x`(_$)->Segment(DoubleFloat)`cPlottableSpaceCurveCategory``1131340 -oyellow`0`x`()->_$`dColor``1131447 -oyoungGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``1131526 -oyoungGroup`1`x`(Partition)->PermutationGroup(Integer)`pPermutationGroupExamples``1131651 -ozCoord`1`n`(Point(R))->R`pPointPackage(R)``1131788 -ozRange`1`x`(_$)->Segment(DoubleFloat)`cPlottableSpaceCurveCategory``1132059 -ozag`2`n`(_$,_$)->_$`dOutputForm``1132166 +oyCoordinates`1`x`(_$)->Record(num:Vector(UP),den:UP)`cFunctionFieldCategory(F,UP,UPUP)``1339596 +oyellow`0`x`()->_$`dColor``1339720 +oyoungGroup`1`x`(List(Integer))->PermutationGroup(Integer)`pPermutationGroupExamples``1339799 +oyoungGroup`1`x`(Partition)->PermutationGroup(Integer)`pPermutationGroupExamples``1339926 +oyRange`1`x`(_$)->Segment(DoubleFloat)`cPlottablePlaneCurveCategory``1340064 +oyRange`1`x`(_$)->Segment(DoubleFloat)`cPlottableSpaceCurveCategory``1340171 +oYun`1`x`(PolK)->Factored(PolK)`pFiniteFieldSquareFreeDecomposition(K,PolK)``0 +ozag`2`n`(_$,_$)->_$`dOutputForm``1340278 +ozCoord`1`n`(Point(R))->R`pPointPackage(R)``1340378 +ozero`1`n`(NonNegativeInteger)->S`xVectorCategory&(S,R)``0 ozero?`1`n`(S)->Boolean`xAbelianMonoid&(S)``0 ozero?`1`n`(S)->Boolean`xOctonionCategory&(S,R)``0 ozero?`1`n`(S)->Boolean`xQuaternionCategory&(S,R)``0 ozero?`1`n`(S)->Boolean`xUnivariateLaurentSeriesConstructorCategory&(S,Coef,UTS)``0 ozero?`1`n`(S)->Boolean`xUnivariatePuiseuxSeriesConstructorCategory&(S,Coef,ULS)``0 ozero?`1`n`(S)->Boolean`xUnivariateTaylorSeriesCategory&(S,Coef)``0 -ozero?`1`x`(_$)->Boolean`cAbelianMonoid``1132266 -ozero?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1132322 +ozero?`1`x`(_$)->Boolean`cAbelianMonoid``1340649 +ozero?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1340705 +ozero`1`x`(NonNegativeInteger)->_$`cVectorCategory(R)`has(R,AbelianMonoid)`1340779 +ozero`2`n`(NonNegativeInteger,NonNegativeInteger)->S`xMatrixCategory&(S,R,Row,Col)``0 ozero?`2`n`(ThePols,S)->Boolean`xRealRootCharacterizationCategory&(S,TheField,ThePols)``0 -ozero?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``1132396 -ozeroDim?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1132495 -ozeroDim?`2`x`(_$,List(VarSet))->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1132712 -ozeroDimPrimary?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``1132882 -ozeroDimPrime?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``1132969 -ozeroDimensional?`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->Boolean`pLexTriangularPackage(R,ls)``1133054 -ozeroDimensional?`1`n`(List(Polynomial(R)))->Boolean`pFGLMIfCanPackage(R,ls)``1133247 -ozeroMatrix`3`x`(NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)->_$`dThreeDimensionalMatrix(R)`has(R,Ring)`1133433 -ozeroMatrix`3`x`(Symbol,Polynomial(Integer),Polynomial(Integer))->FortranCode`pFortranCodePackage1``1133505 -ozeroMatrix`3`x`(Symbol,SegmentBinding(Polynomial(Integer)),SegmentBinding(Polynomial(Integer)))->FortranCode`pFortranCodePackage1``1133603 +ozero`2`x`(NonNegativeInteger,NonNegativeInteger)->_$`cMatrixCategory(R,Row,Col)``1340843 +ozero?`2`x`(ThePols,_$)->Boolean`cRealRootCharacterizationCategory(TheField,ThePols)``1340975 +ozeroDim?`1`x`(_$)->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1341074 +ozeroDim?`2`x`(_$,List(VarSet))->Boolean`dPolynomialIdeals(F,Expon,VarSet,DPoly)``1341291 +ozeroDimensional?`1`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))->Boolean`pLexTriangularPackage(R,ls)``1341461 +ozeroDimensional?`1`n`(List(Polynomial(R)))->Boolean`pFGLMIfCanPackage(R,ls)``1341654 +ozeroDimPrimary?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``1341840 +ozeroDimPrime?`1`x`(PolynomialIdeals(Fraction(Integer),DirectProduct(nv,NonNegativeInteger),OrderedVariableList(vl),DistributedMultivariatePolynomial(vl,Fraction(Integer))))->Boolean`pIdealDecompositionPackage(vl,nv)``1341927 +ozeroMatrix`3`x`(NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)->_$`dThreeDimensionalMatrix(R)`has(R,Ring)`1342012 +ozeroMatrix`3`x`(Symbol,Polynomial(Integer),Polynomial(Integer))->FortranCode`pFortranCodePackage1``1342084 +ozeroMatrix`3`x`(Symbol,SegmentBinding(Polynomial(Integer)),SegmentBinding(Polynomial(Integer)))->FortranCode`pFortranCodePackage1``1342182 ozeroOf`1`n`(Polynomial(S))->S`xAlgebraicallyClosedField&(S)``0 ozeroOf`1`n`(Polynomial(S))->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 -ozeroOf`1`n`(S)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 ozeroOf`1`n`(SparseUnivariatePolynomial(S))->S`xAlgebraicallyClosedField&(S)``0 ozeroOf`1`n`(SparseUnivariatePolynomial(S))->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 -ozeroOf`1`x`(Polynomial(_$))->_$`cAlgebraicallyClosedField``1133725 -ozeroOf`1`x`(SparseUnivariatePolynomial(_$))->_$`cAlgebraicallyClosedField``1133956 -ozeroOf`1`x`(_$)->_$`cAlgebraicallyClosedFunctionSpace(R)``1134131 -ozeroOf`2`n`(S,Symbol)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 +ozeroOf`1`n`(S)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 +ozeroOf`1`x`(_$)->_$`cAlgebraicallyClosedFunctionSpace(R)``1342304 +ozeroOf`1`x`(Polynomial(_$))->_$`cAlgebraicallyClosedField``1342535 +ozeroOf`1`x`(SparseUnivariatePolynomial(_$))->_$`cAlgebraicallyClosedField``1342905 ozeroOf`2`n`(SparseUnivariatePolynomial(S),Symbol)->S`xAlgebraicallyClosedField&(S)``0 ozeroOf`2`n`(SparseUnivariatePolynomial(S),Symbol)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 -ozeroOf`2`x`(SparseUnivariatePolynomial(_$),Symbol)->_$`cAlgebraicallyClosedField``1134362 -ozeroOf`2`x`(_$,Symbol)->_$`cAlgebraicallyClosedFunctionSpace(R)``1134570 -ozeroSetSplitIntoTriangularSystems`1`x`(List(P))->List(Record(close:_$,open:List(P)))`cTriangularSetCategory(R,E,V,P)``1134787 -ozeroSetSplit`1`x`(List(P))->List(_$)`cTriangularSetCategory(R,E,V,P)``1135158 -ozeroSetSplit`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(RegularChain(R,ls))`pLexTriangularPackage(R,ls)``1135386 -ozeroSetSplit`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))`pLexTriangularPackage(R,ls)``1135769 -ozeroSetSplit`2`n`(List(P),Boolean)->List(ST)`pLazardSetSolvingPackage(R,E,V,P,TS,ST)``1136164 -ozeroSetSplit`2`x`(List(P),Boolean)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``1136319 -ozeroSetSplit`3`x`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean,Boolean)->List(_$)`dRegularChain(R,ls)``1136835 -ozeroSetSplit`3`x`(List(P),Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``1137348 -ozeroSetSplit`3`x`(List(P),Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``1137681 -ozeroSetSplit`5`x`(List(P),Boolean,Boolean,Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``1138058 -ozeroSetSplit`5`x`(List(P),Boolean,Boolean,Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``1138204 -ozeroSquareMatrix`2`x`(Symbol,Polynomial(Integer))->FortranCode`pFortranCodePackage1``1138350 -ozeroVector`2`x`(Symbol,Polynomial(Integer))->FortranCode`pFortranCodePackage1``1138404 -ozero`1`n`(NonNegativeInteger)->S`xVectorCategory&(S,R)``0 -ozero`1`x`(NonNegativeInteger)->_$`cVectorCategory(R)`has(R,AbelianMonoid)`1138452 -ozero`2`n`(NonNegativeInteger,NonNegativeInteger)->S`xMatrixCategory&(S,R,Row,Col)``0 -ozero`2`x`(NonNegativeInteger,NonNegativeInteger)->_$`cMatrixCategory(R,Row,Col)``1138516 +ozeroOf`2`n`(S,Symbol)->S`xAlgebraicallyClosedFunctionSpace&(S,R)``0 +ozeroOf`2`x`(SparseUnivariatePolynomial(_$),Symbol)->_$`cAlgebraicallyClosedField``1343221 +ozeroOf`2`x`(_$,Symbol)->_$`cAlgebraicallyClosedFunctionSpace(R)``1343602 +ozeroSetSplit`1`x`(List(P))->List(_$)`cTriangularSetCategory(R,E,V,P)``1343819 +ozeroSetSplit`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(RegularChain(R,ls))`pLexTriangularPackage(R,ls)``1344047 +ozeroSetSplit`2`n`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean)->List(SquareFreeRegularTriangularSet(R,IndexedExponents(OrderedVariableList(ls)),OrderedVariableList(ls),NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))))`pLexTriangularPackage(R,ls)``1344430 +ozeroSetSplit`2`n`(List(P),Boolean)->List(ST)`pLazardSetSolvingPackage(R,E,V,P,TS,ST)``1344825 +ozeroSetSplit`2`x`(List(P),Boolean)->List(_$)`cRegularTriangularSetCategory(R,E,V,P)``1344970 +ozeroSetSplit`3`x`(List(NewSparseMultivariatePolynomial(R,OrderedVariableList(ls))),Boolean,Boolean)->List(_$)`dRegularChain(R,ls)``1345486 +ozeroSetSplit`3`x`(List(P),Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``1345989 +ozeroSetSplit`3`x`(List(P),Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``1346312 +ozeroSetSplit`5`x`(List(P),Boolean,Boolean,Boolean,Boolean)->List(_$)`dRegularTriangularSet(R,E,V,P)``1346671 +ozeroSetSplit`5`x`(List(P),Boolean,Boolean,Boolean,Boolean)->List(_$)`dSquareFreeRegularTriangularSet(R,E,V,P)``1346817 +ozeroSetSplitIntoTriangularSystems`1`x`(List(P))->List(Record(close:_$,open:List(P)))`cTriangularSetCategory(R,E,V,P)``1346963 ozerosOf`1`n`(Polynomial(S))->List(S)`xAlgebraicallyClosedField&(S)``0 ozerosOf`1`n`(Polynomial(S))->List(S)`xAlgebraicallyClosedFunctionSpace&(S,R)``0 ozerosOf`1`n`(S)->List(S)`xAlgebraicallyClosedFunctionSpace&(S,R)``0 ozerosOf`1`n`(SparseUnivariatePolynomial(S))->List(S)`xAlgebraicallyClosedField&(S)``0 ozerosOf`1`n`(SparseUnivariatePolynomial(S))->List(S)`xAlgebraicallyClosedFunctionSpace&(S,R)``0 -ozerosOf`1`x`(Polynomial(_$))->List(_$)`cAlgebraicallyClosedField``1138587 -ozerosOf`1`x`(SparseUnivariatePolynomial(_$))->List(_$)`cAlgebraicallyClosedField``1138951 -ozerosOf`1`x`(_$)->List(_$)`cAlgebraicallyClosedFunctionSpace(R)``1139259 -ozerosOf`2`n`(S,Symbol)->List(S)`xAlgebraicallyClosedFunctionSpace&(S,R)``0 +ozerosOf`1`x`(_$)->List(_$)`cAlgebraicallyClosedFunctionSpace(R)``1347334 +ozerosOf`1`x`(Polynomial(_$))->List(_$)`cAlgebraicallyClosedField``1347639 +ozerosOf`1`x`(SparseUnivariatePolynomial(_$))->List(_$)`cAlgebraicallyClosedField``1348181 ozerosOf`2`n`(SparseUnivariatePolynomial(S),Symbol)->List(S)`xAlgebraicallyClosedField&(S)``0 ozerosOf`2`n`(SparseUnivariatePolynomial(S),Symbol)->List(S)`xAlgebraicallyClosedFunctionSpace&(S,R)``0 -ozerosOf`2`x`(SparseUnivariatePolynomial(_$),Symbol)->List(_$)`cAlgebraicallyClosedField``1139564 -ozerosOf`2`x`(_$,Symbol)->List(_$)`cAlgebraicallyClosedFunctionSpace(R)``1139905 -ozerosOf`3`x`(Expression(DoubleFloat),List(Symbol),Segment(OrderedCompletion(DoubleFloat)))->Stream(DoubleFloat)`pExpertSystemContinuityPackage``1140246 -ozoom`2`n`(_$,Segment(DoubleFloat))->_$`dPlot``1140415 -ozoom`2`x`(_$,Float)->Void`dThreeDimensionalViewport``1140455 -ozoom`3`n`(_$,Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot``1140615 -ozoom`4`n`(_$,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``1140659 -ozoom`4`x`(_$,Float,Float,Float)->Void`dThreeDimensionalViewport``1140707 -o~=`2`n`(S,S)->Boolean`xBasicType&(S)``0 -o~=`2`x`(_$,_$)->Boolean`cBasicType``1141001 -o~`1`n`(S)->S`xBitAggregate&(S)``0 -o~`1`x`(_$)->_$`cLogic``1141066 -o~`1`x`(_$)->_$`dSingleInteger``1141129 -pAlgFactor`1`x`(UnivariatePolynomialCategory(AlgebraicNumber))->etc`(UP)`ALGFACT`0 -pAlgebraPackage`2`x`(R:IntegralDomain,A:FramedNonAssociativeAlgebra(R))->etc`(R,A)`ALGPKG`1141221 -pAlgebraicFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`AF`1141305 -pAlgebraicHermiteIntegration`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`INTHERAL`1141379 -pAlgebraicIntegrate`5`n`(R0:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(R0,F,UP,UPUP,R)`INTALG`1141414 -pAlgebraicIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTAF`1141503 -pAlgebraicManipulations`2`x`(R:IntegralDomain,F:Join(Field,etc))->etc`(R,F)`ALGMANIP`1141617 -pAlgebraicMultFact`3`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,P:PolynomialCategory(AlgebraicNumber,E,OV))->etc`(OV,E,P)`ALGMFACT`0 -pAnnaNumericalIntegrationPackage`0`x`()->etc``INTPACK`0 -pAnnaNumericalOptimizationPackage`0`x`()->etc``OPTPACK`0 -pAnnaOrdinaryDifferentialEquationPackage`0`x`()->etc``ODEPACK`0 -pAnnaPartialDifferentialEquationPackage`0`x`()->etc``PDEPACK`0 -pAnyFunctions1`1`x`(Type)->etc`(S)`ANY1`1141732 -pApplyRules`3`n`(Base:SetCategory,R:Join(Ring,etc),F:Join(FunctionSpace(R),etc))->etc`(Base,R,F)`APPRULE`1141942 -pApplyUnivariateSkewPolynomial`3`n`(R:Ring,M:LeftModule(R),P:UnivariateSkewPolynomialCategory(R))->etc`(R,M,P)`APPLYORE`1142029 -pAssociatedEquations`2`n`(R:IntegralDomain,L:LinearOrdinaryDifferentialOperatorCategory(R))->etc`(R,L)`ASSOCEQ`1142157 -pAttachPredicates`1`x`(Type)->etc`(D)`PMPRED`1142281 -pBalancedFactorisation`2`n`(R:Join(GcdDomain,etc),UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`BALFACT`1142399 -pBasicOperatorFunctions1`1`x`(SetCategory)->etc`(A)`BOP1`1142468 -pBezoutMatrix`5`n`(R:Ring,UP:UnivariatePolynomialCategory(R),M:MatrixCategory(R,Row,Col),FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->etc`(R,UP,M,Row,Col)`BEZOUT`1142605 -pBoundIntegerRoots`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`BOUNDZRO`1142721 -pBrillhartTests`1`n`(UnivariatePolynomialCategory(Integer))->etc`(UP)`BRILL`1142835 -pCRApackage`1`x`(EuclideanDomain)->etc`(R)`CRAPACK`1143447 -pCartesianTensorFunctions2`4`x`(Integer,dim:NonNegativeInteger,S:CommutativeRing,T:CommutativeRing)->etc`(minix,dim,S,T)`CARTEN2`1143483 -pChangeOfVariable`3`n`(F:UniqueFactorizationDomain,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)))->etc`(F,UP,UPUP)`CHVAR`1143590 -pCharacteristicPolynomialInMonogenicalAlgebra`3`n`(R:CommutativeRing,PolR:UnivariatePolynomialCategory(R),E:MonogenicAlgebra(R,PolR))->etc`(R,PolR,E)`CPIMA`1143654 -pCharacteristicPolynomialPackage`1`x`(CommutativeRing)->etc`(R)`CHARPOL`1143751 -pChineseRemainderToolsForIntegralBases`3`n`(K:FiniteFieldCategory,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R))->etc`(K,R,UP)`IBACHIN`1143856 -pCoerceVectorMatrixPackage`1`n`(CommutativeRing)->etc`(R)`CVMP`1144302 -pCombinatorialFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`COMBF`1144391 -pCommonDenominator`3`x`(R:IntegralDomain,Q:QuotientFieldCategory(R),A:FiniteLinearAggregate(Q))->etc`(R,Q,A)`CDEN`1144456 -pCommonOperators`0`n`()->etc``COMMONOP`1144620 -pCommuteUnivariatePolynomialCategory`3`n`(R:Ring,UP:UnivariatePolynomialCategory(R),UPUP:UnivariatePolynomialCategory(UP))->etc`(R,UP,UPUP)`COMMUPC`1144826 -pComplexFactorization`2`x`(RR:EuclideanDomain,PR:UnivariatePolynomialCategory(Complex(RR)))->etc`(RR,PR)`COMPFACT`0 -pComplexFunctions2`2`x`(CommutativeRing,S:CommutativeRing)->etc`(R,S)`COMPLEX2`0 -pComplexIntegerSolveLinearPolynomialEquation`2`n`(R:IntegerNumberSystem,CR:ComplexCategory(R))->etc`(R,CR)`CINTSLPE`0 -pComplexPatternMatch`3`n`(R:SetCategory,S:Join(PatternMatchable(R),etc),CS:ComplexCategory(S))->etc`(R,S,CS)`CPMATCH`0 -pComplexPattern`3`n`(R:SetCategory,S:Join(ConvertibleTo(Pattern(R)),etc),CS:ComplexCategory(S))->etc`(R,S,CS)`COMPLPAT`0 -pComplexRootFindingPackage`2`n`(R:Join(Field,etc),UP:UnivariatePolynomialCategory(Complex(R)))->etc`(R,UP)`CRFP`1144942 -pComplexRootPackage`2`x`(UnivariatePolynomialCategory(Complex(Integer)),Par:Join(Field,etc))->etc`(UP,Par)`CMPLXRT`0 -pComplexTrigonometricManipulations`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`CTRIGMNP`1145726 -pConstantLODE`3`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc),L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(R,F,L)`ODECONST`1145860 -pCoordinateSystems`1`x`(Join(Field,etc))->etc`(R)`COORDSYS`1145948 -pCycleIndicators`0`x`()->etc``CYCLES`1146206 -pCyclicStreamTools`2`n`(S:Type,ST:LazyStreamAggregate(S))->etc`(S,ST)`CSTTOOLS`1146243 -pCyclotomicPolynomialPackage`0`n`()->etc``CYCLOTOM`1146311 -pDefiniteIntegrationTools`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`DFINTTLS`1146347 -pDegreeReductionPackage`2`n`(Ring,R2:Join(IntegralDomain,etc))->etc`(R1,R2)`DEGRED`1146488 -pDiophantineSolutionPackage`0`x`()->etc``DIOSP`1146524 -pDirectProductFunctions2`3`x`(NonNegativeInteger,A:Type,B:Type)->etc`(dim,A,B)`DIRPROD2`0 -pDiscreteLogarithmPackage`1`n`(M:Join(Monoid,etc))->etc`(M)`DLP`0 -pDisplayPackage`0`x`()->etc``DISPLAY`1147257 -pDistinctDegreeFactorize`2`x`(F:FiniteFieldCategory,FP:UnivariatePolynomialCategory(F))->etc`(F,FP)`DDFACT`1147362 -pDoubleFloatSpecialFunctions`0`x`()->etc``DFSFUN`1147655 -pDoubleResultantPackage`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`DBLRESP`1147756 -pDrawComplex`0`x`()->etc``DRAWCX`0 -pDrawNumericHack`1`x`(Join(OrderedSet,etc))->etc`(R)`DRAWHACK`1147859 -pDrawOptionFunctions0`0`n`()->etc``DROPT0`0 -pDrawOptionFunctions1`1`n`(Type)->etc`(S)`DROPT1`0 -pEigenPackage`1`x`(GcdDomain)->etc`(R)`EP`1148277 -pElementaryFunctionDefiniteIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`DEFINTEF`1148631 -pElementaryFunctionLODESolver`3`x`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc),L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(R,F,L)`LODEEF`1148761 -pElementaryFunctionODESolver`2`x`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`ODEEF`1148941 -pElementaryFunctionSign`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`SIGNEF`1149113 -pElementaryFunctionStructurePackage`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`EFSTRUC`1149228 -pElementaryFunction`2`n`(R:Join(OrderedSet,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`EF`1149521 -pElementaryIntegration`2`n`(R:Join(GcdDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTEF`1149583 -pElementaryRischDESystem`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`RDEEFS`1149746 -pElementaryRischDE`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`RDEEF`1149952 -pEllipticFunctionsUnivariateTaylorSeries`2`n`(Coef:Field,UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`ELFUTS`1150160 -pEquationFunctions2`2`x`(Type,R:Type)->etc`(S,R)`EQ2`1150258 -pErrorFunctions`0`x`()->etc``ERROR`1150334 -pEuclideanGroebnerBasisPackage`4`x`(Dom:EuclideanDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBEUCLID`1152317 -pEvaluateCycleIndicators`1`n`(Algebra(Fraction(Integer)))->etc`(F)`EVALCYC`1153192 -pExpertSystemContinuityPackage1`2`x`(DoubleFloat,DoubleFloat)->etc`(A,B)`ESCONT1`0 -pExpertSystemContinuityPackage`0`x`()->etc``ESCONT`0 -pExpertSystemToolsPackage1`1`x`(OrderedRing)->etc`(R1)`ESTOOLS1`0 -pExpertSystemToolsPackage2`2`x`(Ring,R2:Ring)->etc`(R1,R2)`ESTOOLS2`0 -pExpertSystemToolsPackage`0`x`()->etc``ESTOOLS`0 -pExpressionFunctions2`2`x`(OrderedSet,S:OrderedSet)->etc`(R,S)`EXPR2`1153365 -pExpressionSpaceFunctions1`2`n`(ExpressionSpace,S:Type)->etc`(F,S)`ES1`1153461 -pExpressionSpaceFunctions2`2`x`(ExpressionSpace,F:ExpressionSpace)->etc`(E,F)`ES2`1153642 -pExpressionSpaceODESolver`2`x`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`EXPRODE`1153936 -pExpressionToOpenMath`1`x`(Join(OpenMath,etc))->etc`(R)`OMEXPR`1153993 -pExpressionToUnivariatePowerSeries`2`x`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`EXPR2UPS`1154117 -pExpressionTubePlot`0`n`()->etc``EXPRTUBE`1154207 -pFGLMIfCanPackage`2`n`(GcdDomain,List(Symbol))->etc`(R,ls)`FGLMICPK`1154419 -pFactoredFunctionUtilities`1`n`(IntegralDomain)->etc`(R)`FRUTIL`1154724 -pFactoredFunctions2`2`x`(IntegralDomain,S:IntegralDomain)->etc`(R,S)`FR2`1154837 -pFactoredFunctions`1`n`(IntegralDomain)->etc`(M)`FACTFUNC`1155111 -pFactoringUtilities`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:Ring,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`FACUTIL`1155168 -pFindOrderFinite`4`n`(F:Join(Finite,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`FORDER`1155330 -pFiniteDivisorFunctions2`8`x`(R1:Field,UP1:UnivariatePolynomialCategory(R1),UPUP1:UnivariatePolynomialCategory(Fraction(UP1)),F1:FunctionFieldCategory(R1,UP1,UPUP1),R2:Field,UP2:UnivariatePolynomialCategory(R2),UPUP2:UnivariatePolynomialCategory(Fraction(UP2)),F2:FunctionFieldCategory(R2,UP2,UPUP2))->etc`(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)`FDIV2`1155475 -pFiniteFieldFunctions`1`n`(FiniteFieldCategory)->etc`(GF)`FFF`1155602 -pFiniteFieldHomomorphisms`3`x`(FiniteAlgebraicExtensionField(GF),GF:FiniteFieldCategory,F2:FiniteAlgebraicExtensionField(GF))->etc`(F1,GF,F2)`FFHOM`1155778 -pFiniteFieldPolynomialPackage2`2`x`(F:Join(FieldOfPrimeCharacteristic,etc),GF:FiniteFieldCategory)->etc`(F,GF)`FFPOLY2`1156019 -pFiniteFieldPolynomialPackage`1`n`(FiniteFieldCategory)->etc`(GF)`FFPOLY`1156295 -pFiniteFieldSolveLinearPolynomialEquation`3`n`(F:FiniteFieldCategory,FP:UnivariatePolynomialCategory(F),FPP:UnivariatePolynomialCategory(FP))->etc`(F,FP,FPP)`FFSLPE`0 -pFiniteLinearAggregateFunctions2`4`x`(S:Type,A:FiniteLinearAggregate(S),R:Type,B:FiniteLinearAggregate(R))->etc`(S,A,R,B)`FLAGG2`1156462 -pFiniteLinearAggregateSort`2`x`(S:Type,V:Join(FiniteLinearAggregate(S),etc))->etc`(S,V)`FLASORT`1156774 -pFiniteSetAggregateFunctions2`4`x`(S:SetCategory,A:FiniteSetAggregate(S),R:SetCategory,B:FiniteSetAggregate(R))->etc`(S,A,R,B)`FSAGG2`1156863 -pFloatingComplexPackage`1`x`(Join(Field,etc))->etc`(Par)`FLOATCP`0 -pFloatingRealPackage`1`x`(Join(OrderedRing,etc))->etc`(Par)`FLOATRP`0 -pFortranCodePackage1`0`x`()->etc``FCPAK1`1157167 -pFortranOutputStackPackage`0`x`()->etc``FOP`1157791 -pFortranPackage`0`x`()->etc``FORT`1157838 -pFractionFunctions2`2`x`(IntegralDomain,B:IntegralDomain)->etc`(A,B)`FRAC2`1157904 -pFractionalIdealFunctions2`8`x`(R1:EuclideanDomain,F1:QuotientFieldCategory(R1),U1:UnivariatePolynomialCategory(F1),A1:Join(FramedAlgebra(F1,U1),etc),R2:EuclideanDomain,F2:QuotientFieldCategory(R2),U2:UnivariatePolynomialCategory(F2),A2:Join(FramedAlgebra(F2,U2),etc))->etc`(R1,F1,U1,A1,R2,F2,U2,A2)`FRIDEAL2`1158065 -pFramedNonAssociativeAlgebraFunctions2`4`x`(FramedNonAssociativeAlgebra(R),R:CommutativeRing,AS:FramedNonAssociativeAlgebra(S),S:CommutativeRing)->etc`(AR,R,AS,S)`FRNAAF2`1158248 -pFunctionFieldCategoryFunctions2`8`x`(R1:UniqueFactorizationDomain,UP1:UnivariatePolynomialCategory(R1),UPUP1:UnivariatePolynomialCategory(Fraction(UP1)),F1:FunctionFieldCategory(R1,UP1,UPUP1),R2:UniqueFactorizationDomain,UP2:UnivariatePolynomialCategory(R2),UPUP2:UnivariatePolynomialCategory(Fraction(UP2)),F2:FunctionFieldCategory(R2,UP2,UPUP2))->etc`(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)`FFCAT2`1158515 -pFunctionFieldIntegralBasis`3`n`(R:Join(EuclideanDomain,etc),UP:UnivariatePolynomialCategory(R),FramedAlgebra(R,UP))->etc`(R,UP,F)`FFINTBAS`1158575 -pFunctionSpaceAssertions`2`x`(R:OrderedSet,F:FunctionSpace(R))->etc`(R,F)`PMASSFS`1158978 -pFunctionSpaceAttachPredicates`3`x`(R:OrderedSet,F:FunctionSpace(R),D:Type)->etc`(R,F,D)`PMPREDFS`1159096 -pFunctionSpaceComplexIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`FSCINT`1159214 -pFunctionSpaceFunctions2`4`x`(R:Join(Ring,etc),A:FunctionSpace(R),S:Join(Ring,etc),B:FunctionSpace(S))->etc`(R,A,S,B)`FS2`1159343 -pFunctionSpaceIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`FSINT`1159505 -pFunctionSpacePrimitiveElement`2`x`(R:Join(IntegralDomain,etc),F:FunctionSpace(R))->etc`(R,F)`FSPRMELT`1159624 -pFunctionSpaceReduce`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`FSRED`1159732 -pFunctionSpaceSum`2`x`(R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`SUMFS`1159937 -pFunctionSpaceToExponentialExpansion`4`n`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc),x:Symbol,cen:FE)->etc`(R,FE,x,cen)`FS2EXPXP`1159984 -pFunctionSpaceToUnivariatePowerSeries`6`n`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc),Expon:OrderedRing,UPS:Join(UnivariatePowerSeriesCategory(FE,Expon),etc),PartialTranscendentalFunctions(UPS),Symbol)->etc`(R,FE,Expon,UPS,TRAN,x)`FS2UPS`1160075 -pFunctionSpaceUnivariatePolynomialFactor`3`n`(R:Join(IntegralDomain,etc),F:FunctionSpace(R),UP:UnivariatePolynomialCategory(F))->etc`(R,F,UP)`FSUPFACT`1160500 -pFunctionalSpecialFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`FSPECF`1160688 -pGaloisGroupFactorizationUtilities`3`n`(R:Ring,UP:UnivariatePolynomialCategory(R),F:Join(FloatingPointSystem,etc))->etc`(R,UP,F)`GALFACTU`1160752 -pGaloisGroupFactorizer`1`n`(UnivariatePolynomialCategory(Integer))->etc`(UP)`GALFACT`1160860 -pGaloisGroupPolynomialUtilities`2`n`(R:Ring,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`GALPOLYU`1160941 -pGaloisGroupUtilities`1`n`(Ring)->etc`(R)`GALUTIL`1161147 -pGaussianFactorizationPackage`0`x`()->etc``GAUSSFAC`1161221 -pGenExEuclid`2`n`(R:EuclideanDomain,BP:UnivariatePolynomialCategory(R))->etc`(R,BP)`GENEEZ`1161291 -pGenUFactorize`1`n`(EuclideanDomain)->etc`(R)`GENUFACT`1161872 -pGeneralHenselPackage`2`n`(RP:EuclideanDomain,TP:UnivariatePolynomialCategory(RP))->etc`(RP,TP)`GHENSEL`1162091 -pGeneralPolynomialGcdPackage`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:PolynomialFactorizationExplicit,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`GENPGCD`1162229 -pGeneralizedMultivariateFactorize`5`n`(OV:Join(OrderedSet,etc),E:OrderedAbelianMonoidSup,IntegralDomain,R:IntegralDomain,P:PolynomialCategory(R,E,OV))->etc`(OV,E,S,R,P)`GENMFACT`1162312 -pGenerateUnivariatePowerSeries`2`x`(R:Join(IntegralDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`GENUPS`1162475 -pGenusZeroIntegration`3`n`(R:Join(GcdDomain,etc),F:Join(FunctionSpace(R),etc),L:SetCategory)->etc`(R,F,L)`INTG0`1162624 -pGosperSummationMethod`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V),Q:Join(RetractableTo(Fraction(Integer)),etc))->etc`(E,V,R,P,Q)`GOSPER`1162998 -pGraphicsDefaults`0`x`()->etc``GRDEF`1163042 -pGrayCode`0`n`()->etc``GRAY`1163136 -pGroebnerFactorizationPackage`4`x`(Dom:Join(EuclideanDomain,etc),Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBF`1163277 -pGroebnerInternalPackage`4`n`(Dom:GcdDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBINTERN`1164332 -pGroebnerPackage`4`x`(Dom:GcdDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GB`1164486 -pGroebnerSolve`3`n`(List(Symbol),F:GcdDomain,GcdDomain)->etc`(lv,F,R)`GROEBSOL`1165541 -pHallBasis`0`x`()->etc``HB`1165819 -pHeuGcd`1`n`(UnivariatePolynomialCategory(Integer))->etc`(BP)`HEUGCD`1166393 -pIdealDecompositionPackage`2`x`(List(Symbol),nv:NonNegativeInteger)->etc`(vl,nv)`IDECOMP`1166555 -pIncrementingMaps`1`n`(Join(Monoid,etc))->etc`(R)`INCRMAPS`1166865 -pInfiniteProductCharacteristicZero`2`x`(Coef:Join(IntegralDomain,etc),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`INFPROD0`1166939 -pInfiniteProductFiniteField`4`x`(K:Join(Field,etc),UP:UnivariatePolynomialCategory(K),Coef:MonogenicAlgebra(K,UP),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(K,UP,Coef,UTS)`INPRODFF`1167059 -pInfiniteProductPrimeField`2`x`(Coef:Join(Field,etc),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`INPRODPF`1167166 -pInfiniteTupleFunctions2`2`x`(Type,B:Type)->etc`(A,B)`ITFUN2`1167270 -pInfiniteTupleFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`ITFUN3`1167332 -pInfinity`0`x`()->etc``INFINITY`1167394 -pInnerAlgFactor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),AlExt:Join(Field,etc),AlPol:UnivariatePolynomialCategory(AlExt))->etc`(F,UP,AlExt,AlPol)`IALGFACT`0 -pInnerCommonDenominator`4`n`(R:IntegralDomain,Q:QuotientFieldCategory(R),A:FiniteLinearAggregate(R),B:FiniteLinearAggregate(Q))->etc`(R,Q,A,B)`ICDEN`1167505 -pInnerMatrixLinearAlgebraFunctions`4`n`(R:Field,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`IMATLIN`1167674 -pInnerMatrixQuotientFieldFunctions`8`n`(R:IntegralDomain,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col),QF:QuotientFieldCategory(R),Row2:FiniteLinearAggregate(QF),Col2:FiniteLinearAggregate(QF),M2:MatrixCategory(QF,Row2,Col2))->etc`(R,Row,Col,M,QF,Row2,Col2,M2)`IMATQF`1167834 -pInnerModularGcd`4`n`(R:EuclideanDomain,BP:UnivariatePolynomialCategory(R),R,(R,NonNegativeInteger)->R)->etc`(R,BP,pMod,nextMod)`INMODGCD`0 -pInnerMultFact`4`n`(OV:OrderedSet,E:OrderedAbelianMonoidSup,R:Join(EuclideanDomain,etc),P:PolynomialCategory(R,E,OV))->etc`(OV,E,R,P)`INNMFACT`0 -pInnerNormalBasisFieldFunctions`1`n`(FiniteFieldCategory)->etc`(GF)`INBFF`1168098 -pInnerNumericEigenPackage`3`n`(Field,F:Field,Par:Join(Field,etc))->etc`(K,F,Par)`INEP`0 -pInnerNumericFloatSolvePackage`3`n`(GcdDomain,F:Field,Par:Join(Field,etc))->etc`(K,F,Par)`INFSP`0 -pInnerPolySign`2`n`(R:Ring,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`INPSIGN`1168245 -pInnerPolySum`4`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V))->etc`(E,V,R,P)`ISUMP`1168310 -pInnerTrigonometricManipulations`3`n`(R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc),FG:Join(FunctionSpace(Complex(R)),etc))->etc`(R,F,FG)`ITRIGMNP`1168351 -pInputFormFunctions1`1`n`(Type)->etc`(R)`INFORM1`1168535 -pIntegerBits`0`n`()->etc``INTBIT`1168578 -pIntegerCombinatoricFunctions`1`x`(IntegerNumberSystem)->etc`(I)`COMBINAT`0 -pIntegerFactorizationPackage`1`n`(IntegerNumberSystem)->etc`(I)`INTFACT`1168644 -pIntegerLinearDependence`1`x`(LinearlyExplicitRingOver(Integer))->etc`(R)`ZLINDEP`1169023 -pIntegerNumberTheoryFunctions`0`x`()->etc``INTHEORY`0 -pIntegerPrimesPackage`1`x`(IntegerNumberSystem)->etc`(I)`PRIMES`1169076 -pIntegerRetractions`1`x`(RetractableTo(Integer))->etc`(S)`INTRET`1169283 -pIntegerRoots`1`x`(IntegerNumberSystem)->etc`(I)`IROOT`1169398 -pIntegerSolveLinearPolynomialEquation`0`n`()->etc``INTSLPE`1169523 -pIntegralBasisPolynomialTools`4`n`(K:Ring,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R),L:Ring)->etc`(K,R,UP,L)`IBPTOOLS`1169705 -pIntegralBasisTools`3`n`(R:Join(EuclideanDomain,etc),UP:UnivariatePolynomialCategory(R),FramedAlgebra(R,UP))->etc`(R,UP,F)`IBATOOL`1169871 -pIntegrationResultFunctions2`2`x`(Field,F:Field)->etc`(E,F)`IR2`1169988 -pIntegrationResultRFToFunction`1`x`(Join(GcdDomain,etc))->etc`(R)`IRRF2F`1170154 -pIntegrationResultToFunction`2`x`(R:Join(GcdDomain,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`IR2F`1170461 -pIntegrationTools`2`n`(R:OrderedSet,F:FunctionSpace(R))->etc`(R,F)`INTTOOLS`1170663 -pInternalPrintPackage`0`n`()->etc``IPRNTPK`1170842 -pInternalRationalUnivariateRepresentationPackage`5`n`(R:Join(EuclideanDomain,etc),E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:SquareFreeRegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`IRURPK`1170915 -pInverseLaplaceTransform`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`INVLAPLA`1171465 -pIrrRepSymNatPackage`0`x`()->etc``IRSN`1171525 -pIrredPolyOverFiniteField`1`n`(FiniteFieldCategory)->etc`(GF)`IRREDFFX`1172102 -pKernelFunctions2`2`x`(OrderedSet,S:OrderedSet)->etc`(R,S)`KERNEL2`1172246 -pKovacic`2`n`(F:Join(CharacteristicZero,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`KOVACIC`1172310 -pLaplaceTransform`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`LAPLACE`1172469 -pLazardSetSolvingPackage`6`n`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),RegularTriangularSetCategory(R,E,V,P),ST:SquareFreeRegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS,ST)`LAZM3PK`1172529 -pLeadingCoefDetermination`4`n`(OV:OrderedSet,E:OrderedAbelianMonoidSup,Z:EuclideanDomain,P:PolynomialCategory(Z,E,OV))->etc`(OV,E,Z,P)`LEADCDET`1173401 -pLexTriangularPackage`2`n`(GcdDomain,ls:List(Symbol))->etc`(R,ls)`LEXTRIPK`1173546 -pLinGroebnerPackage`2`n`(List(Symbol),F:GcdDomain)->etc`(lv,F)`LGROBP`1174412 -pLinearDependence`2`n`(S:IntegralDomain,R:LinearlyExplicitRingOver(S))->etc`(S,R)`LINDEP`1174643 -pLinearOrdinaryDifferentialOperatorFactorizer`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`LODOF`1174678 -pLinearOrdinaryDifferentialOperatorsOps`2`n`(A:Field,L:LinearOrdinaryDifferentialOperatorCategory(A))->etc`(A,L)`LODOOPS`1174849 -pLinearPolynomialEquationByFractions`1`n`(PolynomialFactorizationExplicit)->etc`(R)`LPEFRAC`1174983 -pLinearSystemMatrixPackage1`1`x`(Field)->etc`(F)`LSMP1`1175239 -pLinearSystemMatrixPackage`4`x`(F:Field,Row:Join(FiniteLinearAggregate(F),etc),Col:Join(FiniteLinearAggregate(F),etc),M:MatrixCategory(F,Row,Col))->etc`(F,Row,Col,M)`LSMP`1175531 -pLinearSystemPolynomialPackage`4`x`(R:IntegralDomain,E:OrderedAbelianMonoidSup,OV:OrderedSet,P:PolynomialCategory(R,E,OV))->etc`(R,E,OV,P)`LSPP`1175606 -pLiouvillianFunction`2`n`(R:Join(OrderedSet,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`LF`1175700 -pListFunctions2`2`x`(Type,B:Type)->etc`(A,B)`LIST2`0 -pListFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`LIST3`0 -pListToMap`2`x`(SetCategory,B:Type)->etc`(A,B)`LIST2MAP`0 -pMPolyCatFunctions2`7`x`(VarSet:OrderedSet,E1:OrderedAbelianMonoidSup,E2:OrderedAbelianMonoidSup,R:Ring,S:Ring,PR:PolynomialCategory(R,E1,VarSet),PS:PolynomialCategory(S,E2,VarSet))->etc`(VarSet,E1,E2,R,S,PR,PS)`MPC2`1175776 -pMPolyCatFunctions3`7`n`(Vars1:OrderedSet,Vars2:OrderedSet,E1:OrderedAbelianMonoidSup,E2:OrderedAbelianMonoidSup,R:Ring,PR1:PolynomialCategory(R,E1,Vars1),PR2:PolynomialCategory(R,E2,Vars2))->etc`(Vars1,Vars2,E1,E2,R,PR1,PR2)`MPC3`1175909 -pMPolyCatPolyFactorizer`4`n`(E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),R:EuclideanDomain,PPR:PolynomialCategory(Polynomial(R),E,OV))->etc`(E,OV,R,PPR)`MPCPF`1175943 -pMPolyCatRationalFunctionFactorizer`4`x`(E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),R:IntegralDomain,PRF:PolynomialCategory(Fraction(Polynomial(R)),E,OV))->etc`(E,OV,R,PRF)`MPRFF`1176328 -pMRationalFactorize`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:Join(EuclideanDomain,etc),P:PolynomialCategory(Fraction(R),E,OV))->etc`(E,OV,R,P)`MRATFAC`1176719 -pMakeBinaryCompiledFunction`4`n`(ConvertibleTo(InputForm),D1:Type,D2:Type,I:Type)->etc`(S,D1,D2,I)`MKBCFUNC`1176955 -pMakeFloatCompiledFunction`1`x`(ConvertibleTo(InputForm))->etc`(S)`MKFLCFN`1177016 -pMakeFunction`1`x`(ConvertibleTo(InputForm))->etc`(S)`MKFUNC`1177244 -pMakeRecord`2`x`(Type,T:Type)->etc`(S,T)`MKRECORD`1177308 -pMakeUnaryCompiledFunction`3`n`(ConvertibleTo(InputForm),D:Type,I:Type)->etc`(S,D,I)`MKUCFUNC`1177444 -pMappingPackage1`1`x`(SetCategory)->etc`(A)`MAPPKG1`1177505 -pMappingPackage2`2`x`(SetCategory,C:SetCategory)->etc`(A,C)`MAPPKG2`1177541 -pMappingPackage3`3`x`(SetCategory,B:SetCategory,C:SetCategory)->etc`(A,B,C)`MAPPKG3`1177577 -pMappingPackageInternalHacks1`1`n`(SetCategory)->etc`(A)`MAPHACK1`1177613 -pMappingPackageInternalHacks2`2`n`(SetCategory,C:SetCategory)->etc`(A,C)`MAPHACK2`1177649 -pMappingPackageInternalHacks3`3`n`(SetCategory,B:SetCategory,C:SetCategory)->etc`(A,B,C)`MAPHACK3`1177685 -pMatrixCategoryFunctions2`8`x`(R1:Ring,Row1:FiniteLinearAggregate(R1),Col1:FiniteLinearAggregate(R1),M1:MatrixCategory(R1,Row1,Col1),R2:Ring,Row2:FiniteLinearAggregate(R2),Col2:FiniteLinearAggregate(R2),M2:MatrixCategory(R2,Row2,Col2))->etc`(R1,Row1,Col1,M1,R2,Row2,Col2,M2)`MATCAT2`1177721 -pMatrixCommonDenominator`2`x`(R:IntegralDomain,Q:QuotientFieldCategory(R))->etc`(R,Q)`MCDEN`1177874 -pMatrixLinearAlgebraFunctions`4`x`(R:CommutativeRing,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`MATLIN`1178027 -pMergeThing`1`x`(OrderedSet)->etc`(S)`MTHING`1178134 -pMeshCreationRoutinesForThreeDimensions`0`n`()->etc``MESH`1178186 -pModularDistinctDegreeFactorizer`1`x`(UnivariatePolynomialCategory(Integer))->etc`(U)`MDDFACT`1178353 -pModularHermitianRowReduction`1`n`(EuclideanDomain)->etc`(R)`MHROWRED`1178583 -pMonoidRingFunctions2`3`x`(Ring,S:Ring,M:Monoid)->etc`(R,S,M)`MRF2`1178760 -pMonomialExtensionTools`2`n`(F:Field,UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`MONOTOOL`1178892 -pMoreSystemCommands`0`x`()->etc``MSYSCMD`1178939 -pMultFiniteFactorize`4`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,F:FiniteFieldCategory,PG:PolynomialCategory(F,E,OV))->etc`(OV,E,F,PG)`MFINFACT`1179206 -pMultiVariableCalculusFunctions`4`x`(S:SetCategory,F:PartialDifferentialRing(S),FLAF:FiniteLinearAggregate(F),FLAS:Join(FiniteLinearAggregate(S),etc))->etc`(S,F,FLAF,FLAS)`MCALCFN`1179287 -pMultipleMap`6`n`(R1:IntegralDomain,UP1:UnivariatePolynomialCategory(R1),UPUP1:UnivariatePolynomialCategory(Fraction(UP1)),R2:IntegralDomain,UP2:UnivariatePolynomialCategory(R2),UPUP2:UnivariatePolynomialCategory(Fraction(UP2)))->etc`(R1,UP1,UPUP1,R2,UP2,UPUP2)`MMAP`1179573 -pMultivariateFactorize`4`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,R:Join(EuclideanDomain,etc),P:PolynomialCategory(R,E,OV))->etc`(OV,E,R,P)`MULTFACT`0 -pMultivariateLifting`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`MLIFT`1179630 -pMultivariateSquareFree`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`MULTSQFR`1179896 -pNAGLinkSupportPackage`0`x`()->etc``NAGSP`1180289 -pNPCoef`5`n`(UnivariatePolynomialCategory(R),E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(BP,E,OV,R,P)`NPCOEF`1180349 -pNagEigenPackage`0`x`()->etc``NAGF02`1180626 -pNagFittingPackage`0`x`()->etc``NAGE02`1180933 -pNagIntegrationPackage`0`x`()->etc``NAGD01`1182391 -pNagInterpolationPackage`0`x`()->etc``NAGE01`1182622 -pNagLapack`0`x`()->etc``NAGF07`1183156 -pNagLinearEquationSolvingPackage`0`x`()->etc``NAGF04`1183360 -pNagMatrixOperationsPackage`0`x`()->etc``NAGF01`1183768 -pNagOptimisationPackage`0`x`()->etc``NAGE04`1183938 -pNagOrdinaryDifferentialEquationsPackage`0`x`()->etc``NAGD02`1184517 -pNagPartialDifferentialEquationsPackage`0`x`()->etc``NAGD03`1185088 -pNagPolynomialRootsPackage`0`x`()->etc``NAGC02`1185219 -pNagRootFindingPackage`0`x`()->etc``NAGC05`1185381 -pNagSeriesSummationPackage`0`x`()->etc``NAGC06`1185648 -pNagSpecialFunctionsPackage`0`x`()->etc``NAGS`1185889 -pNewSparseUnivariatePolynomialFunctions2`2`n`(Ring,S:Ring)->etc`(R,S)`NSUP2`1186042 -pNonCommutativeOperatorDivision`2`n`(MonogenicLinearOperator(F),Field)->etc`(P,F)`NCODIV`1186367 -pNonLinearFirstOrderODESolver`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`NODE1`1186678 -pNonLinearSolvePackage`1`n`(IntegralDomain)->etc`(R)`NLINSOL`1186831 -pNoneFunctions1`1`x`(Type)->etc`(S)`NONE1`1187064 -pNormInMonogenicAlgebra`4`x`(R:GcdDomain,PolR:UnivariatePolynomialCategory(R),E:MonogenicAlgebra(R,PolR),PolE:UnivariatePolynomialCategory(E))->etc`(R,PolR,E,PolE)`NORMMA`0 -pNormRetractPackage`5`n`(F:FiniteFieldCategory,ExtF:FiniteAlgebraicExtensionField(F),SUEx:UnivariatePolynomialCategory(ExtF),ExtP:UnivariatePolynomialCategory(SUEx),PositiveInteger)->etc`(F,ExtF,SUEx,ExtP,n)`NORMRETR`1187237 -pNormalizationPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`NORMPK`1187271 -pNumberFieldIntegralBasis`2`n`(UP:UnivariatePolynomialCategory(Integer),FramedAlgebra(Integer,UP))->etc`(UP,F)`NFINTBAS`1188039 -pNumberFormats`0`n`()->etc``NUMFMT`1188286 -pNumberTheoreticPolynomialFunctions`1`x`(CommutativeRing)->etc`(R)`NTPOLFN`1188438 -pNumericComplexEigenPackage`1`x`(Join(Field,etc))->etc`(Par)`NCEP`0 -pNumericContinuedFraction`1`x`(FloatingPointSystem)->etc`(F)`NCNTFRAC`1188503 -pNumericRealEigenPackage`1`x`(Join(Field,etc))->etc`(Par)`NREP`0 -pNumericTubePlot`1`n`(PlottableSpaceCurveCategory)->etc`(Curve)`NUMTUBE`1188641 -pNumeric`1`x`(ConvertibleTo(Float))->etc`(S)`NUMERIC`1188853 -pNumericalOrdinaryDifferentialEquations`0`x`()->etc``NUMODE`1188953 -pNumericalQuadrature`0`x`()->etc``NUMQUAD`1193696 -pODEIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`ODEINT`1197111 -pODETools`2`n`(F:Field,LODO:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(F,LODO)`ODETOOLS`1197277 -pOctonionCategoryFunctions2`4`x`(OctonionCategory(R),R:CommutativeRing,OS:OctonionCategory(S),S:CommutativeRing)->etc`(OR,R,OS,S)`OCTCT2`1197342 -pOneDimensionalArrayFunctions2`2`x`(Type,B:Type)->etc`(A,B)`ARRAY12`1197522 -pOnePointCompletionFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`ONECOMP2`1197680 -pOpenMathPackage`0`x`()->etc``OMPKG`1197784 -pOpenMathServerPackage`0`x`()->etc``OMSERVER`1197890 -pOperationsQuery`0`x`()->etc``OPQUERY`1198258 -pOrderedCompletionFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`ORDCOMP2`1198339 -pOrderingFunctions`2`n`(NonNegativeInteger,S:OrderedAbelianMonoid)->etc`(dim,S)`ORDFUNS`1198441 -pOrthogonalPolynomialFunctions`1`x`(CommutativeRing)->etc`(R)`ORTHPOL`1198570 -pOutputPackage`0`x`()->etc``OUT`1198646 -pPAdicWildFunctionFieldIntegralBasis`4`n`(K:FiniteFieldCategory,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R),MonogenicAlgebra(R,UP))->etc`(K,R,UP,F)`PWFFINTB`1198702 -pPadeApproximantPackage`3`x`(R:Field,x:Symbol,pt:R)->etc`(R,x,pt)`PADEPAC`1199251 -pPadeApproximants`3`n`(R:Field,PS:UnivariateTaylorSeriesCategory(R),UP:UnivariatePolynomialCategory(R))->etc`(R,PS,UP)`PADE`1199617 -pParadoxicalCombinatorsForStreams`1`n`(Type)->etc`(A)`YSTREAM`1199974 -pParametricLinearEquations`4`n`(R:Join(EuclideanDomain,etc),Var:Join(OrderedSet,etc),Expon:OrderedAbelianMonoidSup,GR:PolynomialCategory(R,Expon,Var))->etc`(R,Var,Expon,GR)`PLEQN`1200042 -pParametricPlaneCurveFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARPC2`1200082 -pParametricSpaceCurveFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARSC2`1200116 -pParametricSurfaceFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARSU2`1200150 -pPartialFractionPackage`1`n`(Join(EuclideanDomain,etc))->etc`(R)`PFRPAC`1200184 -pPartitionsAndPermutations`0`x`()->etc``PARTPERM`1200462 -pPatternFunctions1`2`n`(SetCategory,D:Type)->etc`(R,D)`PATTERN1`1200626 -pPatternFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`PATTERN2`1200653 -pPatternMatchAssertions`0`x`()->etc``PMASS`1200684 -pPatternMatchFunctionSpace`3`n`(S:SetCategory,R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc))->etc`(S,R,F)`PMFS`1200802 -pPatternMatchIntegerNumberSystem`1`n`(IntegerNumberSystem)->etc`(I)`PMINS`1200878 -pPatternMatchIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTPM`1200947 -pPatternMatchKernel`2`n`(S:SetCategory,E:Join(OrderedSet,etc))->etc`(S,E)`PMKERNEL`1201142 -pPatternMatchListAggregate`3`n`(S:SetCategory,R:PatternMatchable(S),L:ListAggregate(R))->etc`(S,R,L)`PMLSAGG`1201210 -pPatternMatchPolynomialCategory`5`n`(S:SetCategory,E:OrderedAbelianMonoidSup,V:OrderedSet,R:Join(Ring,etc),P:Join(PolynomialCategory(R,E,V),etc))->etc`(S,E,V,R,P)`PMPLCAT`1201276 -pPatternMatchPushDown`3`n`(S:SetCategory,A:PatternMatchable(S),B:Join(SetCategory,etc))->etc`(S,A,B)`PMDOWN`1201348 -pPatternMatchQuotientFieldCategory`3`n`(S:SetCategory,R:Join(IntegralDomain,etc),Q:QuotientFieldCategory(R))->etc`(S,R,Q)`PMQFCAT`1201425 -pPatternMatchResultFunctions2`3`x`(SetCategory,A:SetCategory,B:SetCategory)->etc`(R,A,B)`PATRES2`1201495 -pPatternMatchSymbol`1`n`(SetCategory)->etc`(S)`PMSYM`1201542 -pPatternMatchTools`3`n`(S:SetCategory,R:Join(Ring,etc),P:Join(Ring,etc))->etc`(S,R,P)`PMTOOLS`1201610 -pPatternMatch`3`x`(Base:SetCategory,Subject:PatternMatchable(Base),Pat:ConvertibleTo(Pattern(Base)))->etc`(Base,Subject,Pat)`PATMATCH`1201670 -pPermanent`2`x`(PositiveInteger,R:Join(Ring,etc))->etc`(n,R)`PERMAN`1201741 -pPermutationGroupExamples`0`x`()->etc``PGE`1201837 -pPiCoercions`1`x`(Join(OrderedSet,etc))->etc`(R)`PICOERCE`1202242 -pPlotFunctions1`1`n`(ConvertibleTo(InputForm))->etc`(S)`PLOT1`1202433 -pPlotTools`0`n`()->etc``PLOTTOOL`1202586 -pPointFunctions2`2`x`(Ring,R2:Ring)->etc`(R1,R2)`PTFUNC2`0 -pPointPackage`1`n`(Ring)->etc`(R)`PTPACK`0 -pPointsOfFiniteOrderRational`3`n`(UP:UnivariatePolynomialCategory(Fraction(Integer)),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(Fraction(Integer),UP,UPUP))->etc`(UP,UPUP,R)`PFOQ`1202629 -pPointsOfFiniteOrderTools`2`n`(UP:UnivariatePolynomialCategory(Fraction(Integer)),UPUP:UnivariatePolynomialCategory(Fraction(UP)))->etc`(UP,UPUP)`PFOTOOLS`1202730 -pPointsOfFiniteOrder`5`n`(R0:Join(OrderedSet,etc),F:FunctionSpace(R0),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(R0,F,UP,UPUP,R)`PFO`1202860 -pPolToPol`2`n`(List(Symbol),R:Ring)->etc`(lv,R)`POLTOPOL`1202961 -pPolyGroebner`1`x`(GcdDomain)->etc`(F)`PGROEB`1203042 -pPolynomialAN2Expression`0`x`()->etc``PAN2EXPR`1203762 -pPolynomialCategoryLifting`5`n`(E:OrderedAbelianMonoidSup,Vars:OrderedSet,R:Ring,P:PolynomialCategory(R,E,Vars),S:Join(SetCategory,etc))->etc`(E,Vars,R,P,S)`POLYLIFT`1203882 -pPolynomialCategoryQuotientFunctions`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:Ring,P:PolynomialCategory(R,E,V),F:Join(Field,etc))->etc`(E,V,R,P,F)`POLYCATQ`1204179 -pPolynomialComposition`2`x`(UnivariatePolynomialCategory(R),Ring)->etc`(UP,R)`PCOMP`1204302 -pPolynomialDecomposition`2`x`(UnivariatePolynomialCategory(F),Field)->etc`(UP,F)`PDECOMP`1204336 -pPolynomialFactorizationByRecursionUnivariate`2`n`(R:PolynomialFactorizationExplicit,S:UnivariatePolynomialCategory(R))->etc`(R,S)`PFBRU`1204370 -pPolynomialFactorizationByRecursion`4`n`(R:PolynomialFactorizationExplicit,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,S:PolynomialCategory(R,E,VarSet))->etc`(R,E,VarSet,S)`PFBR`1204663 -pPolynomialFunctions2`2`x`(Ring,S:Ring)->etc`(R,S)`POLY2`1204878 -pPolynomialGcdPackage`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`PGCD`0 -pPolynomialInterpolationAlgorithms`2`n`(F:Field,P:UnivariatePolynomialCategory(F))->etc`(F,P)`PINTERPA`1205021 -pPolynomialInterpolation`2`n`(Symbol,F:Field)->etc`(xx,F)`PINTERP`1205074 -pPolynomialNumberTheoryFunctions`0`n`()->etc``PNTHEORY`0 -pPolynomialRoots`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V),F:Join(Field,etc))->etc`(E,V,R,P,F)`POLYROOT`1205127 -pPolynomialSetUtilitiesPackage`4`n`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(R,E,V,P)`PSETPK`1205202 -pPolynomialSolveByFormulas`2`n`(UnivariatePolynomialCategory(F),F:Join(Field,etc))->etc`(UP,F)`SOLVEFOR`1205491 -pPolynomialSquareFree`4`n`(VarSet:OrderedSet,E:OrderedAbelianMonoidSup,RC:GcdDomain,P:PolynomialCategory(RC,E,VarSet))->etc`(VarSet,E,RC,P)`PSQFR`1205730 -pPolynomialToUnivariatePolynomial`2`x`(Symbol,R:Ring)->etc`(x,R)`POLY2UP`1206160 -pPowerSeriesLimitPackage`2`x`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`LIMITPS`1206392 -pPrecomputedAssociatedEquations`2`n`(R:IntegralDomain,L:LinearOrdinaryDifferentialOperatorCategory(R))->etc`(R,L)`PREASSOC`1206637 -pPrimitiveArrayFunctions2`2`x`(Type,B:Type)->etc`(A,B)`PRIMARR2`1206814 -pPrimitiveElement`1`n`(Join(Field,etc))->etc`(F)`PRIMELT`1206966 -pPrimitiveRatDE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),L:LinearOrdinaryDifferentialOperatorCategory(UP),LQ:LinearOrdinaryDifferentialOperatorCategory(Fraction(UP)))->etc`(F,UP,L,LQ)`ODEPRIM`1207064 -pPrimitiveRatRicDE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),L:LinearOrdinaryDifferentialOperatorCategory(UP),LinearOrdinaryDifferentialOperatorCategory(Fraction(UP)))->etc`(F,UP,L,LQ)`ODEPRRIC`1207294 -pPrintPackage`0`x`()->etc``PRINT`1207359 -pPseudoLinearNormalForm`1`n`(Field)->etc`(K)`PSEUDLIN`1207423 -pPseudoRemainderSequence`2`n`(R:IntegralDomain,polR:UnivariatePolynomialCategory(R))->etc`(R,polR)`PRS`1207539 -pPureAlgebraicIntegration`3`n`(R:Join(GcdDomain,etc),F:Join(FunctionSpace(R),etc),L:SetCategory)->etc`(R,F,L)`INTPAF`1208588 -pPureAlgebraicLODE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`ODEPAL`1208757 -pPushVariables`4`n`(R:Ring,E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),PPR:PolynomialCategory(Polynomial(R),E,OV))->etc`(R,E,OV,PPR)`PUSHVAR`1208850 -pQuasiAlgebraicSet2`2`n`(List(Symbol),nv:NonNegativeInteger)->etc`(vl,nv)`QALGSET2`1208886 -pQuasiComponentPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`QCMPACK`1210140 -pQuaternionCategoryFunctions2`4`x`(QuaternionCategory(R),R:CommutativeRing,QS:QuaternionCategory(S),S:CommutativeRing)->etc`(QR,R,QS,S)`QUATCT2`1210879 -pQuotientFieldCategoryFunctions2`4`x`(A:IntegralDomain,B:IntegralDomain,R:QuotientFieldCategory(A),S:QuotientFieldCategory(B))->etc`(A,B,R,S)`QFCAT2`1211076 -pRadicalEigenPackage`0`x`()->etc``REP`1211184 -pRadicalSolvePackage`1`x`(Join(EuclideanDomain,etc))->etc`(R)`SOLVERAD`1211465 -pRadixUtilities`0`x`()->etc``RADUTIL`1211637 -pRandomDistributions`1`n`(SetCategory)->etc`(S)`RDIST`1211703 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+ozoom`4`n`(_$,Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))->_$`dPlot3D``1350716 +ozoom`4`x`(_$,Float,Float,Float)->Void`dThreeDimensionalViewport``1350768 +ozRange`1`x`(_$)->Segment(DoubleFloat)`cPlottableSpaceCurveCategory``1351062 +pAffineAlgebraicSetComputeWithGroebnerBasis`5`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K))->etc`(K,symb,PolyRing,E,ProjPt)`AFALGGRO`1351169 +pAffineAlgebraicSetComputeWithResultant`5`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K))->etc`(K,symb,PolyRing,E,ProjPt)`AFALGRES`1351218 +pAlgebraicFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`AF`1351267 +pAlgebraicHermiteIntegration`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`INTHERAL`1351341 +pAlgebraicIntegrate`5`n`(R0:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(R0,F,UP,UPUP,R)`INTALG`1351377 +pAlgebraicIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTAF`1351466 +pAlgebraicManipulations`2`x`(R:IntegralDomain,F:Join(Field,etc))->etc`(R,F)`ALGMANIP`1351580 +pAlgebraicMultFact`3`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,P:PolynomialCategory(AlgebraicNumber,E,OV))->etc`(OV,E,P)`ALGMFACT`1351695 +pAlgebraPackage`2`x`(R:IntegralDomain,A:FramedNonAssociativeAlgebra(R))->etc`(R,A)`ALGPKG`1351906 +pAlgFactor`1`x`(UnivariatePolynomialCategory(AlgebraicNumber))->etc`(UP)`ALGFACT`1351990 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+pBasicOperatorFunctions1`1`x`(SetCategory)->etc`(A)`BOP1`1353735 +pBezier`1`x`(Ring)->etc`(R)`BEZIER`1353872 +pBezoutMatrix`5`n`(R:Ring,UP:UnivariatePolynomialCategory(R),M:MatrixCategory(R,Row,Col),FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->etc`(R,UP,M,Row,Col)`BEZOUT`1353941 +pBlasLevelOne`0`x`()->etc``BLAS1`1354057 +pBlowUpPackage`5`x`(K:Field,symb:List(Symbol),PolyRing:FiniteAbelianMonoidRing(K,E),DirectProductCategory(#(symb),NonNegativeInteger),BLMET:BlowUpMethodCategory)->etc`(K,symb,PolyRing,E,BLMET)`BLUPPACK`1354129 +pBoundIntegerRoots`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`BOUNDZRO`1354178 +pBrillhartTests`1`n`(UnivariatePolynomialCategory(Integer))->etc`(UP)`BRILL`1354292 +pCartesianTensorFunctions2`4`x`(Integer,dim:NonNegativeInteger,S:CommutativeRing,T:CommutativeRing)->etc`(minix,dim,S,T)`CARTEN2`1354331 +pChangeOfVariable`3`n`(F:UniqueFactorizationDomain,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)))->etc`(F,UP,UPUP)`CHVAR`1354438 +pCharacteristicPolynomialInMonogenicalAlgebra`3`n`(R:CommutativeRing,PolR:UnivariatePolynomialCategory(R),E:MonogenicAlgebra(R,PolR))->etc`(R,PolR,E)`CPIMA`1354502 +pCharacteristicPolynomialPackage`1`x`(CommutativeRing)->etc`(R)`CHARPOL`1354599 +pChineseRemainderToolsForIntegralBases`3`n`(K:FiniteFieldCategory,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R))->etc`(K,R,UP)`IBACHIN`1354704 +pCoerceVectorMatrixPackage`1`n`(CommutativeRing)->etc`(R)`CVMP`1354743 +pCombinatorialFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`COMBF`1354834 +pCommonDenominator`3`x`(R:IntegralDomain,Q:QuotientFieldCategory(R),A:FiniteLinearAggregate(Q))->etc`(R,Q,A)`CDEN`1354899 +pCommonOperators`0`n`()->etc``COMMONOP`1355063 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+pComplexTrigonometricManipulations`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`CTRIGMNP`1356919 +pConstantLODE`3`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc),L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(R,F,L)`ODECONST`1357053 +pCoordinateSystems`1`x`(Join(Field,etc))->etc`(R)`COORDSYS`1357141 +pCRApackage`1`x`(EuclideanDomain)->etc`(R)`CRAPACK`1357399 +pCycleIndicators`0`x`()->etc``CYCLES`1357440 +pCyclicStreamTools`2`n`(S:Type,ST:LazyStreamAggregate(S))->etc`(S,ST)`CSTTOOLS`1357492 +pCyclotomicPolynomialPackage`0`n`()->etc``CYCLOTOM`1357560 +pd01AgentsPackage`0`x`()->etc``D01AGNT`1357599 +pd01WeightsPackage`0`x`()->etc``D01WGTS`1357988 +pd02AgentsPackage`0`x`()->etc``D02AGNT`1358297 +pd03AgentsPackage`0`x`()->etc``D03AGNT`1358421 +pDefiniteIntegrationTools`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`DFINTTLS`1358544 +pDegreeReductionPackage`2`n`(Ring,R2:Join(IntegralDomain,etc))->etc`(R1,R2)`DEGRED`1358685 +pDesingTreePackage`11`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),E:DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DIVISOR:DivisorCategory(Plc),InfClsPoint:InfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET),DesTree:DesingTreeCategory(InfClsPoint),BLMET:BlowUpMethodCategory)->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfClsPoint,De--sTree,BLMET)`DTP`1358724 +pDiophantineSolutionPackage`0`x`()->etc``DIOSP`1358884 +pDirectProductFunctions2`3`x`(NonNegativeInteger,A:Type,B:Type)->etc`(dim,A,B)`DIRPROD2`1359633 +pDiscreteLogarithmPackage`1`n`(M:Join(Monoid,etc))->etc`(M)`DLP`1359937 +pDisplayPackage`0`x`()->etc``DISPLAY`1360057 +pDistinctDegreeFactorize`2`x`(F:FiniteFieldCategory,FP:UnivariatePolynomialCategory(F))->etc`(F,FP)`DDFACT`1360162 +pDoubleFloatSpecialFunctions`0`x`()->etc``DFSFUN`1360455 +pDoubleResultantPackage`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`DBLRESP`1360556 +pDrawComplex`0`x`()->etc``DRAWCX`1360659 +pDrawNumericHack`1`x`(Join(OrderedSet,etc))->etc`(R)`DRAWHACK`1360746 +pDrawOptionFunctions0`0`n`()->etc``DROPT0`1361229 +pDrawOptionFunctions1`1`n`(Type)->etc`(S)`DROPT1`1361268 +pe04AgentsPackage`0`x`()->etc``E04AGNT`1361307 +pEigenPackage`1`x`(GcdDomain)->etc`(R)`EP`1361523 +pElementaryFunction`2`n`(R:Join(OrderedSet,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`EF`1361877 +pElementaryFunctionDefiniteIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`DEFINTEF`1361939 +pElementaryFunctionLODESolver`3`x`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc),L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(R,F,L)`LODEEF`1362069 +pElementaryFunctionODESolver`2`x`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`ODEEF`1362249 +pElementaryFunctionSign`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`SIGNEF`1362421 +pElementaryFunctionStructurePackage`2`x`(R:Join(IntegralDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`EFSTRUC`1362536 +pElementaryIntegration`2`n`(R:Join(GcdDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTEF`1362829 +pElementaryRischDE`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`RDEEF`1362993 +pElementaryRischDESystem`2`n`(R:Join(GcdDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`RDEEFS`1363048 +pEllipticFunctionsUnivariateTaylorSeries`2`n`(Coef:Field,UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`ELFUTS`1363103 +pEquationFunctions2`2`x`(Type,R:Type)->etc`(S,R)`EQ2`1363201 +pErrorFunctions`0`x`()->etc``ERROR`1363277 +pEuclideanGroebnerBasisPackage`4`x`(Dom:EuclideanDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBEUCLID`1365193 +pEvaluateCycleIndicators`1`n`(Algebra(Fraction(Integer)))->etc`(F)`EVALCYC`1366054 +pExpertSystemContinuityPackage`0`x`()->etc``ESCONT`1366197 +pExpertSystemContinuityPackage1`2`x`(DoubleFloat,DoubleFloat)->etc`(A,B)`ESCONT1`1366343 +pExpertSystemToolsPackage`0`x`()->etc``ESTOOLS`1366432 +pExpertSystemToolsPackage1`1`x`(OrderedRing)->etc`(R1)`ESTOOLS1`1366561 +pExpertSystemToolsPackage2`2`x`(Ring,R2:Ring)->etc`(R1,R2)`ESTOOLS2`1366719 +pExpressionFunctions2`2`x`(OrderedSet,S:OrderedSet)->etc`(R,S)`EXPR2`1366877 +pExpressionSolve`4`x`(R:Join(OrderedSet,etc),F:FunctionSpace(R),UTSF:UnivariateTaylorSeriesCategory(F),UnivariateTaylorSeriesCategory(SparseUnivariatePolynomialExpressions(F)))->etc`(R,F,UTSF,UTSSUPF)`EXPRSOL`1366916 +pExpressionSpaceFunctions1`2`n`(ExpressionSpace,S:Type)->etc`(F,S)`ES1`1366955 +pExpressionSpaceFunctions2`2`x`(ExpressionSpace,F:ExpressionSpace)->etc`(E,F)`ES2`1367136 +pExpressionSpaceODESolver`2`x`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`EXPRODE`1367430 +pExpressionToOpenMath`1`x`(Join(OpenMath,etc))->etc`(R)`OMEXPR`1367487 +pExpressionToUnivariatePowerSeries`2`x`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`EXPR2UPS`1367611 +pExpressionTubePlot`0`n`()->etc``EXPRTUBE`1367701 +pFactoredFunctions`1`n`(IntegralDomain)->etc`(M)`FACTFUNC`1367779 +pFactoredFunctions2`2`x`(IntegralDomain,S:IntegralDomain)->etc`(R,S)`FR2`1367836 +pFactoredFunctionUtilities`1`n`(IntegralDomain)->etc`(R)`FRUTIL`1368110 +pFactoringUtilities`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:Ring,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`FACUTIL`1368223 +pFactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber`1`x`(PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory)->etc`(K)`FACTEXT`1368385 +pFactorisationOverPseudoAlgebraicClosureOfRationalNumber`1`x`(PseudoAlgebraicClosureOfRationalNumberCategory)->etc`(K)`FACTRN`1368463 +pFGLMIfCanPackage`2`n`(GcdDomain,List(Symbol))->etc`(R,ls)`FGLMICPK`1368541 +pFindOrderFinite`4`n`(F:Join(Finite,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`FORDER`1368840 +pFiniteAbelianMonoidRingFunctions2`5`x`(E:OrderedAbelianMonoid,R1:Ring,A1:FiniteAbelianMonoidRing(R1,E),R2:Ring,A2:FiniteAbelianMonoidRing(R2,E))->etc`(E,R1,A1,R2,A2)`FAMR2`1368896 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+pFiniteFieldSolveLinearPolynomialEquation`3`n`(F:FiniteFieldCategory,FP:UnivariatePolynomialCategory(F),FPP:UnivariatePolynomialCategory(FP))->etc`(F,FP,FPP)`FFSLPE`1370573 +pFiniteFieldSquareFreeDecomposition`2`x`(K:FiniteFieldCategory,PolK:UnivariatePolynomialCategory(K))->etc`(K,PolK)`FFSQFR`1370674 +pFiniteLinearAggregateFunctions2`4`x`(S:Type,A:FiniteLinearAggregate(S),R:Type,B:FiniteLinearAggregate(R))->etc`(S,A,R,B)`FLAGG2`1370761 +pFiniteLinearAggregateSort`2`x`(S:Type,V:Join(FiniteLinearAggregate(S),etc))->etc`(S,V)`FLASORT`1371073 +pFiniteSetAggregateFunctions2`4`x`(S:SetCategory,A:FiniteSetAggregate(S),R:SetCategory,B:FiniteSetAggregate(R))->etc`(S,A,R,B)`FSAGG2`1371232 +pFloatingComplexPackage`1`x`(Join(Field,etc))->etc`(Par)`FLOATCP`1371536 +pFloatingRealPackage`1`x`(Join(OrderedRing,etc))->etc`(Par)`FLOATRP`1371881 +pFortranCodePackage1`0`x`()->etc``FCPAK1`1372187 +pFortranOutputStackPackage`0`x`()->etc``FOP`1372811 +pFortranPackage`0`x`()->etc``FORT`1372858 +pFractionalIdealFunctions2`8`x`(R1:EuclideanDomain,F1:QuotientFieldCategory(R1),U1:UnivariatePolynomialCategory(F1),A1:Join(FramedAlgebra(F1,U1),etc),R2:EuclideanDomain,F2:QuotientFieldCategory(R2),U2:UnivariatePolynomialCategory(F2),A2:Join(FramedAlgebra(F2,U2),etc))->etc`(R1,F1,U1,A1,R2,F2,U2,A2)`FRIDEAL2`1372924 +pFractionFreeFastGaussian`2`x`(D:Join(IntegralDomain,etc),V:AbelianMonoidRing(D,NonNegativeInteger))->etc`(D,V)`FFFG`1372974 +pFractionFreeFastGaussianFractions`3`x`(D:Join(IntegralDomain,etc),V:FiniteAbelianMonoidRing(D,NonNegativeInteger),VF:FiniteAbelianMonoidRing(Fraction(D),NonNegativeInteger))->etc`(D,V,VF)`FFFGF`1373364 +pFractionFunctions2`2`x`(IntegralDomain,B:IntegralDomain)->etc`(A,B)`FRAC2`1373615 +pFramedNonAssociativeAlgebraFunctions2`4`x`(FramedNonAssociativeAlgebra(R),R:CommutativeRing,AS:FramedNonAssociativeAlgebra(S),S:CommutativeRing)->etc`(AR,R,AS,S)`FRNAAF2`1373776 +pFunctionalSpecialFunction`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`FSPECF`1374043 +pFunctionFieldCategoryFunctions2`8`x`(R1:UniqueFactorizationDomain,UP1:UnivariatePolynomialCategory(R1),UPUP1:UnivariatePolynomialCategory(Fraction(UP1)),F1:FunctionFieldCategory(R1,UP1,UPUP1),R2:UniqueFactorizationDomain,UP2:UnivariatePolynomialCategory(R2),UPUP2:UnivariatePolynomialCategory(Fraction(UP2)),F2:FunctionFieldCategory(R2,UP2,UPUP2))->etc`(R1,UP1,UPUP1,F1,R2,UP2,UPUP2,F2)`FFCAT2`1374107 +pFunctionFieldIntegralBasis`3`n`(R:Join(EuclideanDomain,etc),UP:UnivariatePolynomialCategory(R),FramedAlgebra(R,UP))->etc`(R,UP,F)`FFINTBAS`1374167 +pFunctionSpaceAssertions`2`x`(R:OrderedSet,F:FunctionSpace(R))->etc`(R,F)`PMASSFS`1374622 +pFunctionSpaceAttachPredicates`3`x`(R:OrderedSet,F:FunctionSpace(R),D:Type)->etc`(R,F,D)`PMPREDFS`1374683 +pFunctionSpaceComplexIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`FSCINT`1374744 +pFunctionSpaceFunctions2`4`x`(R:Join(Ring,etc),A:FunctionSpace(R),S:Join(Ring,etc),B:FunctionSpace(S))->etc`(R,A,S,B)`FS2`1374912 +pFunctionSpaceIntegration`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`FSINT`1375109 +pFunctionSpacePrimitiveElement`2`x`(R:Join(IntegralDomain,etc),F:FunctionSpace(R))->etc`(R,F)`FSPRMELT`1375264 +pFunctionSpaceReduce`2`n`(R:Join(OrderedSet,etc),F:FunctionSpace(R))->etc`(R,F)`FSRED`1375372 +pFunctionSpaceSum`2`x`(R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`SUMFS`1375633 +pFunctionSpaceToExponentialExpansion`4`n`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc),x:Symbol,cen:FE)->etc`(R,FE,x,cen)`FS2EXPXP`1375679 +pFunctionSpaceToUnivariatePowerSeries`6`n`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc),Expon:OrderedRing,UPS:Join(UnivariatePowerSeriesCategory(FE,Expon),etc),PartialTranscendentalFunctions(UPS),Symbol)->etc`(R,FE,Expon,UPS,TRAN,x)`FS2UPS`1375770 +pFunctionSpaceUnivariatePolynomialFactor`3`n`(R:Join(IntegralDomain,etc),F:FunctionSpace(R),UP:UnivariatePolynomialCategory(F))->etc`(R,F,UP)`FSUPFACT`1376195 +pGaloisGroupFactorizationUtilities`3`n`(R:Ring,UP:UnivariatePolynomialCategory(R),F:Join(FloatingPointSystem,etc))->etc`(R,UP,F)`GALFACTU`1376242 +pGaloisGroupFactorizer`1`n`(UnivariatePolynomialCategory(Integer))->etc`(UP)`GALFACT`1376350 +pGaloisGroupPolynomialUtilities`2`n`(R:Ring,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`GALPOLYU`1376431 +pGaloisGroupUtilities`1`n`(Ring)->etc`(R)`GALUTIL`1376624 +pGaussianFactorizationPackage`0`x`()->etc``GAUSSFAC`1376698 +pGeneralHenselPackage`2`n`(RP:EuclideanDomain,TP:UnivariatePolynomialCategory(RP))->etc`(RP,TP)`GHENSEL`1376768 +pGeneralizedMultivariateFactorize`5`n`(OV:Join(OrderedSet,etc),E:OrderedAbelianMonoidSup,IntegralDomain,R:IntegralDomain,P:PolynomialCategory(R,E,OV))->etc`(OV,E,S,R,P)`GENMFACT`1376867 +pGeneralPackageForAlgebraicFunctionField`11`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),E:DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DIVISOR:DivisorCategory(Plc),InfClsPoint:InfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET),DesTree:DesingTreeCategory(InfClsPoint),BLMET:BlowUpMethodCategory)->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc,--DIVISOR,InfClsPoint,DesTree,BLMET)`GPAFF`1377016 +pGeneralPolynomialGcdPackage`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:PolynomialFactorizationExplicit,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`GENPGCD`1377104 +pGenerateUnivariatePowerSeries`2`x`(R:Join(IntegralDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`GENUPS`1377187 +pGenExEuclid`2`n`(R:EuclideanDomain,BP:UnivariatePolynomialCategory(R))->etc`(R,BP)`GENEEZ`1377336 +pGenUFactorize`1`n`(EuclideanDomain)->etc`(R)`GENUFACT`1377864 +pGenusZeroIntegration`3`n`(R:Join(GcdDomain,etc),F:Join(FunctionSpace(R),etc),L:SetCategory)->etc`(R,F,L)`INTG0`1378057 +pGosperSummationMethod`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V),Q:Join(RetractableTo(Fraction(Integer)),etc))->etc`(E,V,R,P,Q)`GOSPER`1378516 +pGraphicsDefaults`0`x`()->etc``GRDEF`1378560 +pGrayCode`0`n`()->etc``GRAY`1378654 +pGroebnerFactorizationPackage`4`x`(Dom:Join(EuclideanDomain,etc),Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBF`1378795 +pGroebnerInternalPackage`4`n`(Dom:GcdDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GBINTERN`1379850 +pGroebnerPackage`4`x`(Dom:GcdDomain,Expon:OrderedAbelianMonoidSup,VarSet:OrderedSet,Dpol:PolynomialCategory(Dom,Expon,VarSet))->etc`(Dom,Expon,VarSet,Dpol)`GB`1379927 +pGroebnerSolve`3`n`(List(Symbol),F:GcdDomain,GcdDomain)->etc`(lv,F,R)`GROEBSOL`1380982 +pGuess`6`x`(F:Field,S:GcdDomain,EXPRR:Join(FunctionSpace(Integer),etc),R:Join(OrderedSet,etc),(R)->F,(F)->EXPRR)->etc`(F,S,EXPRR,R,retract,coerce)`GUESS`1381169 +pGuessAlgebraicNumber`0`x`()->etc``GUESSAN`1381336 +pGuessFinite`1`x`(Join(FiniteFieldCategory,etc))->etc`(F)`GUESSF`1381408 +pGuessFiniteFunctions`1`x`(Join(FiniteFieldCategory,etc))->etc`(F)`GUESSF1`1381487 +pGuessInteger`0`x`()->etc``GUESSINT`1381566 +pGuessPolynomial`0`x`()->etc``GUESSP`1381636 +pGuessUnivariatePolynomial`1`x`(Symbol)->etc`(q)`GUESSUP`1381708 +pHallBasis`0`x`()->etc``HB`1381791 +pHeuGcd`1`n`(UnivariatePolynomialCategory(Integer))->etc`(BP)`HEUGCD`1382053 +pIdealDecompositionPackage`2`x`(List(Symbol),nv:NonNegativeInteger)->etc`(vl,nv)`IDECOMP`1382215 +pIncrementingMaps`1`n`(Join(Monoid,etc))->etc`(R)`INCRMAPS`1382511 +pInfiniteProductCharacteristicZero`2`x`(Coef:Join(IntegralDomain,etc),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`INFPROD0`1382585 +pInfiniteProductFiniteField`4`x`(K:Join(Field,etc),UP:UnivariatePolynomialCategory(K),Coef:MonogenicAlgebra(K,UP),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(K,UP,Coef,UTS)`INPRODFF`1382705 +pInfiniteProductPrimeField`2`x`(Coef:Join(Field,etc),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`INPRODPF`1382812 +pInfiniteTupleFunctions2`2`x`(Type,B:Type)->etc`(A,B)`ITFUN2`1382916 +pInfiniteTupleFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`ITFUN3`1382978 +pInfinity`0`x`()->etc``INFINITY`1383040 +pInnerAlgFactor`4`n`(F:Field,UP:UnivariatePolynomialCategory(F),AlExt:Join(Field,etc),AlPol:UnivariatePolynomialCategory(AlExt))->etc`(F,UP,AlExt,AlPol)`IALGFACT`1383115 +pInnerCommonDenominator`4`n`(R:IntegralDomain,Q:QuotientFieldCategory(R),A:FiniteLinearAggregate(R),B:FiniteLinearAggregate(Q))->etc`(R,Q,A,B)`ICDEN`1383301 +pInnerMatrixLinearAlgebraFunctions`4`n`(R:Field,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`IMATLIN`1383470 +pInnerMatrixQuotientFieldFunctions`8`n`(R:IntegralDomain,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col),QF:QuotientFieldCategory(R),Row2:FiniteLinearAggregate(QF),Col2:FiniteLinearAggregate(QF),M2:MatrixCategory(QF,Row2,Col2))->etc`(R,Row,Col,M,QF,Row2,Col2,M2)`IMATQF`1383630 +pInnerModularGcd`4`n`(R:EuclideanDomain,BP:UnivariatePolynomialCategory(R),R,(R,NonNegativeInteger)->R)->etc`(R,BP,pMod,nextMod)`INMODGCD`1383894 +pInnerMultFact`4`n`(OV:OrderedSet,E:OrderedAbelianMonoidSup,R:Join(EuclideanDomain,etc),P:PolynomialCategory(R,E,OV))->etc`(OV,E,R,P)`INNMFACT`1384212 +pInnerNormalBasisFieldFunctions`1`n`(FiniteFieldCategory)->etc`(GF)`INBFF`1384468 +pInnerNumericEigenPackage`3`n`(Field,F:Field,Par:Join(Field,etc))->etc`(K,F,Par)`INEP`1384615 +pInnerNumericFloatSolvePackage`3`n`(GcdDomain,F:Field,Par:Join(Field,etc))->etc`(K,F,Par)`INFSP`1384786 +pInnerPolySign`2`n`(R:Ring,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`INPSIGN`1385386 +pInnerPolySum`4`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V))->etc`(E,V,R,P)`ISUMP`1385451 +pInnerTrigonometricManipulations`3`n`(R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc),FG:Join(FunctionSpace(Complex(R)),etc))->etc`(R,F,FG)`ITRIGMNP`1385506 +pInputFormFunctions1`1`n`(Type)->etc`(R)`INFORM1`1385690 +pIntegerBits`0`n`()->etc``INTBIT`1385733 +pIntegerCombinatoricFunctions`1`x`(IntegerNumberSystem)->etc`(I)`COMBINAT`1385799 +pIntegerFactorizationPackage`1`n`(IntegerNumberSystem)->etc`(I)`INTFACT`1385909 +pIntegerLinearDependence`1`x`(LinearlyExplicitRingOver(Integer))->etc`(R)`ZLINDEP`1386274 +pIntegerNumberTheoryFunctions`0`x`()->etc``INTHEORY`1386327 +pIntegerPrimesPackage`1`x`(IntegerNumberSystem)->etc`(I)`PRIMES`1386408 +pIntegerRetractions`1`x`(RetractableTo(Integer))->etc`(S)`INTRET`1386615 +pIntegerRoots`1`x`(IntegerNumberSystem)->etc`(I)`IROOT`1386673 +pIntegerSolveLinearPolynomialEquation`0`n`()->etc``INTSLPE`1386784 +pIntegralBasisPolynomialTools`4`n`(K:Ring,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R),L:Ring)->etc`(K,R,UP,L)`IBPTOOLS`1386966 +pIntegralBasisTools`3`n`(R:Join(EuclideanDomain,etc),UP:UnivariatePolynomialCategory(R),FramedAlgebra(R,UP))->etc`(R,UP,F)`IBATOOL`1387104 +pIntegrationResultFunctions2`2`x`(Field,F:Field)->etc`(E,F)`IR2`1387221 +pIntegrationResultRFToFunction`1`x`(Join(GcdDomain,etc))->etc`(R)`IRRF2F`1387272 +pIntegrationResultToFunction`2`x`(R:Join(GcdDomain,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`IR2F`1387534 +pIntegrationTools`2`n`(R:OrderedSet,F:FunctionSpace(R))->etc`(R,F)`INTTOOLS`1387795 +pInterfaceGroebnerPackage`5`x`(K:Field,List(Symbol),E:OrderedAbelianMonoidSup,OV:OrderedSet,R:PolynomialCategory(K,E,OV))->etc`(K,symb,E,OV,R)`INTERGB`1387827 +pInternalPrintPackage`0`n`()->etc``IPRNTPK`1387905 +pInternalRationalUnivariateRepresentationPackage`5`n`(R:Join(EuclideanDomain,etc),E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:SquareFreeRegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`IRURPK`1387978 +pInterpolateFormsPackage`8`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DIVISOR:DivisorCategory(Plc))->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR)`INTFRSP`1388163 +pIntersectionDivisorPackage`11`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),E:DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS),DIVISOR:DivisorCategory(Plc),InfClsPoint:InfinitlyClosePointCategory(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,BLMET),DesTree:DesingTreeCategory(InfClsPoint),BLMET:BlowUpMethodCategory)->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc,DIVISOR,InfCl--sPoint,DesTree,BLMET)`INTDIVP`1388212 +pInverseLaplaceTransform`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`INVLAPLA`1388261 +pIrredPolyOverFiniteField`1`n`(FiniteFieldCategory)->etc`(GF)`IRREDFFX`1388321 +pIrrRepSymNatPackage`0`x`()->etc``IRSN`1388465 +pKernelFunctions2`2`x`(OrderedSet,S:OrderedSet)->etc`(R,S)`KERNEL2`1389041 +pKovacic`2`n`(F:Join(CharacteristicZero,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`KOVACIC`1389105 +pLaplaceTransform`2`x`(R:Join(EuclideanDomain,etc),F:Join(TranscendentalFunctionCategory,etc))->etc`(R,F)`LAPLACE`1389264 +pLazardSetSolvingPackage`6`n`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),RegularTriangularSetCategory(R,E,V,P),ST:SquareFreeRegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS,ST)`LAZM3PK`1389324 +pLeadingCoefDetermination`4`n`(OV:OrderedSet,E:OrderedAbelianMonoidSup,Z:EuclideanDomain,P:PolynomialCategory(Z,E,OV))->etc`(OV,E,Z,P)`LEADCDET`1389854 +pLexTriangularPackage`2`n`(GcdDomain,ls:List(Symbol))->etc`(R,ls)`LEXTRIPK`1389999 +pLinearDependence`2`n`(S:IntegralDomain,R:LinearlyExplicitRingOver(S))->etc`(S,R)`LINDEP`1390742 +pLinearOrdinaryDifferentialOperatorFactorizer`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`LODOF`1390777 +pLinearOrdinaryDifferentialOperatorsOps`2`n`(A:Field,L:LinearOrdinaryDifferentialOperatorCategory(A))->etc`(A,L)`LODOOPS`1390948 +pLinearPolynomialEquationByFractions`1`n`(PolynomialFactorizationExplicit)->etc`(R)`LPEFRAC`1391082 +pLinearSystemFromPowerSeriesPackage`2`x`(K:Field,PCS:LocalPowerSeriesCategory(K))->etc`(K,PCS)`LISYSER`1391338 +pLinearSystemMatrixPackage1`1`x`(Field)->etc`(F)`LSMP1`1391370 +pLinearSystemMatrixPackage`4`x`(F:Field,Row:Join(FiniteLinearAggregate(F),etc),Col:Join(FiniteLinearAggregate(F),etc),M:MatrixCategory(F,Row,Col))->etc`(F,Row,Col,M)`LSMP`1391662 +pLinearSystemPolynomialPackage`4`x`(R:IntegralDomain,E:OrderedAbelianMonoidSup,OV:OrderedSet,P:PolynomialCategory(R,E,OV))->etc`(R,E,OV,P)`LSPP`1391737 +pLinesOpPack`1`x`(Field)->etc`(K)`LOP`1391831 +pLinGroebnerPackage`2`n`(List(Symbol),F:GcdDomain)->etc`(lv,F)`LGROBP`1391945 +pLiouvillianFunction`2`n`(R:Join(OrderedSet,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`LF`1392162 +pListFunctions2`2`x`(Type,B:Type)->etc`(A,B)`LIST2`1392238 +pListFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`LIST3`1392386 +pListToMap`2`x`(SetCategory,B:Type)->etc`(A,B)`LIST2MAP`1392536 +pLocalParametrizationOfSimplePointPackage`7`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS))->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc)`LPARSPT`1392953 +pMakeBinaryCompiledFunction`4`n`(ConvertibleTo(InputForm),D1:Type,D2:Type,I:Type)->etc`(S,D1,D2,I)`MKBCFUNC`1393002 +pMakeFloatCompiledFunction`1`x`(ConvertibleTo(InputForm))->etc`(S)`MKFLCFN`1393087 +pMakeFunction`1`x`(ConvertibleTo(InputForm))->etc`(S)`MKFUNC`1393378 +pMakeRecord`2`x`(Type,T:Type)->etc`(S,T)`MKRECORD`1393508 +pMakeUnaryCompiledFunction`3`n`(ConvertibleTo(InputForm),D:Type,I:Type)->etc`(S,D,I)`MKUCFUNC`1393644 +pMappingPackage1`1`x`(SetCategory)->etc`(A)`MAPPKG1`1393768 +pMappingPackage2`2`x`(SetCategory,C:SetCategory)->etc`(A,C)`MAPPKG2`1393804 +pMappingPackage3`3`x`(SetCategory,B:SetCategory,C:SetCategory)->etc`(A,B,C)`MAPPKG3`1393840 +pMappingPackage4`2`x`(SetCategory,B:Ring)->etc`(A,B)`MAPPKG4`1393876 +pMappingPackageInternalHacks1`1`n`(SetCategory)->etc`(A)`MAPHACK1`1393979 +pMappingPackageInternalHacks2`2`n`(SetCategory,C:SetCategory)->etc`(A,C)`MAPHACK2`1394015 +pMappingPackageInternalHacks3`3`n`(SetCategory,B:SetCategory,C:SetCategory)->etc`(A,B,C)`MAPHACK3`1394051 +pMatrixCategoryFunctions2`8`x`(R1:Ring,Row1:FiniteLinearAggregate(R1),Col1:FiniteLinearAggregate(R1),M1:MatrixCategory(R1,Row1,Col1),R2:Ring,Row2:FiniteLinearAggregate(R2),Col2:FiniteLinearAggregate(R2),M2:MatrixCategory(R2,Row2,Col2))->etc`(R1,Row1,Col1,M1,R2,Row2,Col2,M2)`MATCAT2`1394087 +pMatrixCommonDenominator`2`x`(R:IntegralDomain,Q:QuotientFieldCategory(R))->etc`(R,Q)`MCDEN`1394240 +pMatrixLinearAlgebraFunctions`4`x`(R:CommutativeRing,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`MATLIN`1394393 +pMergeThing`1`x`(OrderedSet)->etc`(S)`MTHING`1394500 +pMeshCreationRoutinesForThreeDimensions`0`n`()->etc``MESH`1394552 +pModularDistinctDegreeFactorizer`1`x`(UnivariatePolynomialCategory(Integer))->etc`(U)`MDDFACT`1394591 +pModularHermitianRowReduction`1`n`(EuclideanDomain)->etc`(R)`MHROWRED`1394821 +pMonoidRingFunctions2`3`x`(Ring,S:Ring,M:Monoid)->etc`(R,S,M)`MRF2`1394861 +pMonomialExtensionTools`2`n`(F:Field,UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`MONOTOOL`1394993 +pMoreSystemCommands`0`x`()->etc``MSYSCMD`1395040 +pMPolyCatFunctions2`7`x`(VarSet:OrderedSet,E1:OrderedAbelianMonoidSup,E2:OrderedAbelianMonoidSup,R:Ring,S:Ring,PR:PolynomialCategory(R,E1,VarSet),PS:PolynomialCategory(S,E2,VarSet))->etc`(VarSet,E1,E2,R,S,PR,PS)`MPC2`1395300 +pMPolyCatFunctions3`7`n`(Vars1:OrderedSet,Vars2:OrderedSet,E1:OrderedAbelianMonoidSup,E2:OrderedAbelianMonoidSup,R:Ring,PR1:PolynomialCategory(R,E1,Vars1),PR2:PolynomialCategory(R,E2,Vars2))->etc`(Vars1,Vars2,E1,E2,R,PR1,PR2)`MPC3`1395330 +pMPolyCatPolyFactorizer`4`n`(E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),R:EuclideanDomain,PPR:PolynomialCategory(Polynomial(R),E,OV))->etc`(E,OV,R,PPR)`MPCPF`1395369 +pMPolyCatRationalFunctionFactorizer`4`x`(E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),R:IntegralDomain,PRF:PolynomialCategory(Fraction(Polynomial(R)),E,OV))->etc`(E,OV,R,PRF)`MPRFF`1395740 +pMRationalFactorize`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:Join(EuclideanDomain,etc),P:PolynomialCategory(Fraction(R),E,OV))->etc`(E,OV,R,P)`MRATFAC`1396117 +pMultFiniteFactorize`4`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,F:FiniteFieldCategory,PG:PolynomialCategory(F,E,OV))->etc`(OV,E,F,PG)`MFINFACT`1396339 +pMultipleMap`6`n`(R1:IntegralDomain,UP1:UnivariatePolynomialCategory(R1),UPUP1:UnivariatePolynomialCategory(Fraction(UP1)),R2:IntegralDomain,UP2:UnivariatePolynomialCategory(R2),UPUP2:UnivariatePolynomialCategory(Fraction(UP2)))->etc`(R1,UP1,UPUP1,R2,UP2,UPUP2)`MMAP`1396420 +pMultiVariableCalculusFunctions`4`x`(S:SetCategory,F:PartialDifferentialRing(S),FLAF:FiniteLinearAggregate(F),FLAS:Join(FiniteLinearAggregate(S),etc))->etc`(S,F,FLAF,FLAS)`MCALCFN`1396477 +pMultivariateFactorize`4`x`(OV:OrderedSet,E:OrderedAbelianMonoidSup,R:Join(EuclideanDomain,etc),P:PolynomialCategory(R,E,OV))->etc`(OV,E,R,P)`MULTFACT`1396735 +pMultivariateLifting`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`MLIFT`1396884 +pMultivariateSquareFree`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`MULTSQFR`1397150 +pNagEigenPackage`0`x`()->etc``NAGF02`1397508 +pNagFittingPackage`0`x`()->etc``NAGE02`1397774 +pNagIntegrationPackage`0`x`()->etc``NAGD01`1399183 +pNagInterpolationPackage`0`x`()->etc``NAGE01`1399365 +pNagLapack`0`x`()->etc``NAGF07`1399850 +pNagLinearEquationSolvingPackage`0`x`()->etc``NAGF04`1400005 +pNAGLinkSupportPackage`0`x`()->etc``NAGSP`1400392 +pNagMatrixOperationsPackage`0`x`()->etc``NAGF01`1400452 +pNagOptimisationPackage`0`x`()->etc``NAGE04`1400573 +pNagOrdinaryDifferentialEquationsPackage`0`x`()->etc``NAGD02`1401103 +pNagPartialDifferentialEquationsPackage`0`x`()->etc``NAGD03`1401625 +pNagPolynomialRootsPackage`0`x`()->etc``NAGC02`1401707 +pNagRootFindingPackage`0`x`()->etc``NAGC05`1401820 +pNagSeriesSummationPackage`0`x`()->etc``NAGC06`1402038 +pNagSpecialFunctionsPackage`0`x`()->etc``NAGS`1402230 +pNewSparseUnivariatePolynomialFunctions2`2`n`(Ring,S:Ring)->etc`(R,S)`NSUP2`1402343 +pNewtonInterpolation`1`n`(IntegralDomain)->etc`(F)`NEWTON`1402668 +pNewtonPolygon`4`x`(K:Ring,PolyRing:FiniteAbelianMonoidRing(K,E),DirectProductCategory(dim,NonNegativeInteger),NonNegativeInteger)->etc`(K,PolyRing,E,dim)`NPOLYGON`1402944 +pNonCommutativeOperatorDivision`2`n`(MonogenicLinearOperator(F),Field)->etc`(P,F)`NCODIV`1402993 +pNoneFunctions1`1`x`(Type)->etc`(S)`NONE1`1403384 +pNonLinearFirstOrderODESolver`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`NODE1`1403557 +pNonLinearSolvePackage`1`n`(IntegralDomain)->etc`(R)`NLINSOL`1403710 +pNormalizationPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`NORMPK`1403943 +pNormInMonogenicAlgebra`4`x`(R:GcdDomain,PolR:UnivariatePolynomialCategory(R),E:MonogenicAlgebra(R,PolR),PolE:UnivariatePolynomialCategory(E))->etc`(R,PolR,E,PolE)`NORMMA`1404083 +pNormRetractPackage`5`n`(F:FiniteFieldCategory,ExtF:FiniteAlgebraicExtensionField(F),SUEx:UnivariatePolynomialCategory(ExtF),ExtP:UnivariatePolynomialCategory(SUEx),PositiveInteger)->etc`(F,ExtF,SUEx,ExtP,n)`NORMRETR`1404199 +pNPCoef`5`n`(UnivariatePolynomialCategory(R),E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(BP,E,OV,R,P)`NPCOEF`1404238 +pNumberFieldIntegralBasis`2`n`(UP:UnivariatePolynomialCategory(Integer),FramedAlgebra(Integer,UP))->etc`(UP,F)`NFINTBAS`1404515 +pNumberFormats`0`n`()->etc``NUMFMT`1404762 +pNumberTheoreticPolynomialFunctions`1`x`(CommutativeRing)->etc`(R)`NTPOLFN`1404914 +pNumeric`1`x`(ConvertibleTo(Float))->etc`(S)`NUMERIC`1404979 +pNumericalOrdinaryDifferentialEquations`0`x`()->etc``NUMODE`1405079 +pNumericalQuadrature`0`x`()->etc``NUMQUAD`1410055 +pNumericComplexEigenPackage`1`x`(Join(Field,etc))->etc`(Par)`NCEP`1413040 +pNumericContinuedFraction`1`x`(FloatingPointSystem)->etc`(F)`NCNTFRAC`1413311 +pNumericRealEigenPackage`1`x`(Join(Field,etc))->etc`(Par)`NREP`1413435 +pNumericTubePlot`1`n`(PlottableSpaceCurveCategory)->etc`(Curve)`NUMTUBE`1413669 +pOctonionCategoryFunctions2`4`x`(OctonionCategory(R),R:CommutativeRing,OS:OctonionCategory(S),S:CommutativeRing)->etc`(OR,R,OS,S)`OCTCT2`1413747 +pODEIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedFunctionSpace(R),etc))->etc`(R,F)`ODEINT`1413927 +pODETools`2`n`(F:Field,LODO:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(F,LODO)`ODETOOLS`1414093 +pOneDimensionalArrayFunctions2`2`x`(Type,B:Type)->etc`(A,B)`ARRAY12`1414158 +pOnePointCompletionFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`ONECOMP2`1414302 +pOpenMathPackage`0`x`()->etc``OMPKG`1414351 +pOpenMathServerPackage`0`x`()->etc``OMSERVER`1414457 +pOperationsQuery`0`x`()->etc``OPQUERY`1414825 +pOrderedCompletionFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`ORDCOMP2`1414906 +pOrderingFunctions`2`n`(NonNegativeInteger,S:OrderedAbelianMonoid)->etc`(dim,S)`ORDFUNS`1414953 +pOrthogonalPolynomialFunctions`1`x`(CommutativeRing)->etc`(R)`ORTHPOL`1415068 +pOutputPackage`0`x`()->etc``OUT`1415144 +pPackageForAlgebraicFunctionField`3`x`(Field,symb:List(Symbol),BLMET:BlowUpMethodCategory)->etc`(K,symb,BLMET)`PAFF`1415200 +pPackageForAlgebraicFunctionFieldOverFiniteField`3`x`(FiniteFieldCategory,symb:List(Symbol),BLMET:BlowUpMethodCategory)->etc`(K,symb,BLMET)`PAFFFF`1415287 +pPackageForPoly`4`x`(R:Ring,PolyRing:FiniteAbelianMonoidRing(R,E),E:DirectProductCategory(dim,NonNegativeInteger),NonNegativeInteger)->etc`(R,PolyRing,E,dim)`PFORP`1415374 +pPadeApproximantPackage`3`x`(R:Field,x:Symbol,pt:R)->etc`(R,x,pt)`PADEPAC`1415423 +pPadeApproximants`3`n`(R:Field,PS:UnivariateTaylorSeriesCategory(R),UP:UnivariatePolynomialCategory(R))->etc`(R,PS,UP)`PADE`1415543 +pPAdicWildFunctionFieldIntegralBasis`4`n`(K:FiniteFieldCategory,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R),MonogenicAlgebra(R,UP))->etc`(K,R,UP,F)`PWFFINTB`1415663 +pParadoxicalCombinatorsForStreams`1`n`(Type)->etc`(A)`YSTREAM`1416212 +pParametricLinearEquations`4`n`(R:Join(EuclideanDomain,etc),Var:Join(OrderedSet,etc),Expon:OrderedAbelianMonoidSup,GR:PolynomialCategory(R,Expon,Var))->etc`(R,Var,Expon,GR)`PLEQN`1416280 +pParametricPlaneCurveFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARPC2`1417596 +pParametricSpaceCurveFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARSC2`1417635 +pParametricSurfaceFunctions2`2`x`(Type,CF2:Type)->etc`(CF1,CF2)`PARSU2`1417674 +pParametrizationPackage`7`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjectiveSpaceCategory(K),PCS:LocalPowerSeriesCategory(K),Plc:PlacesCategory(K,PCS))->etc`(K,symb,PolyRing,E,ProjPt,PCS,Plc)`PARAMP`1417713 +pPartialFractionPackage`1`n`(Join(EuclideanDomain,etc))->etc`(R)`PFRPAC`1417762 +pPartitionsAndPermutations`0`x`()->etc``PARTPERM`1418040 +pPatternFunctions1`2`n`(SetCategory,D:Type)->etc`(R,D)`PATTERN1`1418204 +pPatternFunctions2`2`x`(SetCategory,S:SetCategory)->etc`(R,S)`PATTERN2`1418243 +pPatternMatch`3`x`(Base:SetCategory,Subject:PatternMatchable(Base),Pat:ConvertibleTo(Pattern(Base)))->etc`(Base,Subject,Pat)`PATMATCH`1418273 +pPatternMatchAssertions`0`x`()->etc``PMASS`1418344 +pPatternMatchFunctionSpace`3`n`(S:SetCategory,R:Join(IntegralDomain,etc),F:Join(FunctionSpace(R),etc))->etc`(S,R,F)`PMFS`1418405 +pPatternMatchIntegerNumberSystem`1`n`(IntegerNumberSystem)->etc`(I)`PMINS`1418481 +pPatternMatchIntegration`2`n`(R:Join(OrderedSet,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`INTPM`1418550 +pPatternMatchKernel`2`n`(S:SetCategory,E:Join(OrderedSet,etc))->etc`(S,E)`PMKERNEL`1418745 +pPatternMatchListAggregate`3`n`(S:SetCategory,R:PatternMatchable(S),L:ListAggregate(R))->etc`(S,R,L)`PMLSAGG`1418813 +pPatternMatchPolynomialCategory`5`n`(S:SetCategory,E:OrderedAbelianMonoidSup,V:OrderedSet,R:Join(Ring,etc),P:Join(PolynomialCategory(R,E,V),etc))->etc`(S,E,V,R,P)`PMPLCAT`1418879 +pPatternMatchPushDown`3`n`(S:SetCategory,A:PatternMatchable(S),B:Join(SetCategory,etc))->etc`(S,A,B)`PMDOWN`1418951 +pPatternMatchQuotientFieldCategory`3`n`(S:SetCategory,R:Join(IntegralDomain,etc),Q:QuotientFieldCategory(R))->etc`(S,R,Q)`PMQFCAT`1419028 +pPatternMatchResultFunctions2`3`x`(SetCategory,A:SetCategory,B:SetCategory)->etc`(R,A,B)`PATRES2`1419098 +pPatternMatchSymbol`1`n`(SetCategory)->etc`(S)`PMSYM`1419145 +pPatternMatchTools`3`n`(S:SetCategory,R:Join(Ring,etc),P:Join(Ring,etc))->etc`(S,R,P)`PMTOOLS`1419213 +pPermanent`2`x`(PositiveInteger,R:Join(Ring,etc))->etc`(n,R)`PERMAN`1419273 +pPermutationGroupExamples`0`x`()->etc``PGE`1419363 +pPiCoercions`1`x`(Join(OrderedSet,etc))->etc`(R)`PICOERCE`1419768 +pPlotFunctions1`1`n`(ConvertibleTo(InputForm))->etc`(S)`PLOT1`1419888 +pPlotTools`0`n`()->etc``PLOTTOOL`1420041 +pPointFunctions2`2`x`(Ring,R2:Ring)->etc`(R1,R2)`PTFUNC2`1420084 +pPointPackage`1`n`(Ring)->etc`(R)`PTPACK`1420123 +pPointsOfFiniteOrder`5`n`(R0:Join(OrderedSet,etc),F:FunctionSpace(R0),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(R0,F,UP,UPUP,R)`PFO`1420162 +pPointsOfFiniteOrderRational`3`n`(UP:UnivariatePolynomialCategory(Fraction(Integer)),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(Fraction(Integer),UP,UPUP))->etc`(UP,UPUP,R)`PFOQ`1420263 +pPointsOfFiniteOrderTools`2`n`(UP:UnivariatePolynomialCategory(Fraction(Integer)),UPUP:UnivariatePolynomialCategory(Fraction(UP)))->etc`(UP,UPUP)`PFOTOOLS`1420364 +pPolToPol`2`n`(List(Symbol),R:Ring)->etc`(lv,R)`POLTOPOL`1420398 +pPolyGroebner`1`x`(GcdDomain)->etc`(F)`PGROEB`1420479 +pPolynomialAN2Expression`0`x`()->etc``PAN2EXPR`1421185 +pPolynomialCategoryLifting`5`n`(E:OrderedAbelianMonoidSup,Vars:OrderedSet,R:Ring,P:PolynomialCategory(R,E,Vars),S:Join(SetCategory,etc))->etc`(E,Vars,R,P,S)`POLYLIFT`1421305 +pPolynomialCategoryQuotientFunctions`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:Ring,P:PolynomialCategory(R,E,V),F:Join(Field,etc))->etc`(E,V,R,P,F)`POLYCATQ`1421602 +pPolynomialComposition`2`x`(UnivariatePolynomialCategory(R),Ring)->etc`(UP,R)`PCOMP`1421763 +pPolynomialDecomposition`2`x`(UnivariatePolynomialCategory(F),Field)->etc`(UP,F)`PDECOMP`1421950 +pPolynomialFactorizationByRecursion`4`n`(R:PolynomialFactorizationExplicit,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,S:PolynomialCategory(R,E,VarSet))->etc`(R,E,VarSet,S)`PFBR`1422137 +pPolynomialFactorizationByRecursionUnivariate`2`n`(R:PolynomialFactorizationExplicit,S:UnivariatePolynomialCategory(R))->etc`(R,S)`PFBRU`1422352 +pPolynomialFunctions2`2`x`(Ring,S:Ring)->etc`(R,S)`POLY2`1422631 +pPolynomialGcdPackage`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:EuclideanDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`PGCD`1422760 +pPolynomialInterpolation`2`n`(Symbol,F:Field)->etc`(xx,F)`PINTERP`1423072 +pPolynomialInterpolationAlgorithms`2`n`(F:Field,P:UnivariatePolynomialCategory(F))->etc`(F,P)`PINTERPA`1423125 +pPolynomialNumberTheoryFunctions`0`n`()->etc``PNTHEORY`1423178 +pPolynomialPackageForCurve`5`x`(K:Field,PolyRing:FiniteAbelianMonoidRing(K,E),DirectProductCategory(dim,NonNegativeInteger),NonNegativeInteger,ProjPt:ProjectiveSpaceCategory(K))->etc`(K,PolyRing,E,dim,ProjPt)`PLPKCRV`1423272 +pPolynomialRoots`5`n`(E:OrderedAbelianMonoidSup,V:OrderedSet,R:IntegralDomain,P:PolynomialCategory(R,E,V),F:Join(Field,etc))->etc`(E,V,R,P,F)`POLYROOT`1423321 +pPolynomialSetUtilitiesPackage`4`n`(R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(R,E,V,P)`PSETPK`1423396 +pPolynomialSolveByFormulas`2`n`(UnivariatePolynomialCategory(F),F:Join(Field,etc))->etc`(UP,F)`SOLVEFOR`1423685 +pPolynomialSquareFree`4`n`(VarSet:OrderedSet,E:OrderedAbelianMonoidSup,RC:GcdDomain,P:PolynomialCategory(RC,E,VarSet))->etc`(VarSet,E,RC,P)`PSQFR`1423924 +pPolynomialToUnivariatePolynomial`2`x`(Symbol,R:Ring)->etc`(x,R)`POLY2UP`1424354 +pPowerSeriesLimitPackage`2`x`(R:Join(GcdDomain,etc),FE:Join(AlgebraicallyClosedField,etc))->etc`(R,FE)`LIMITPS`1424586 +pPrecomputedAssociatedEquations`2`n`(R:IntegralDomain,L:LinearOrdinaryDifferentialOperatorCategory(R))->etc`(R,L)`PREASSOC`1424831 +pPrimitiveArrayFunctions2`2`x`(Type,B:Type)->etc`(A,B)`PRIMARR2`1425008 +pPrimitiveElement`1`n`(Join(Field,etc))->etc`(F)`PRIMELT`1425146 +pPrimitiveRatDE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),L:LinearOrdinaryDifferentialOperatorCategory(UP),LQ:LinearOrdinaryDifferentialOperatorCategory(Fraction(UP)))->etc`(F,UP,L,LQ)`ODEPRIM`1425244 +pPrimitiveRatRicDE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),L:LinearOrdinaryDifferentialOperatorCategory(UP),LinearOrdinaryDifferentialOperatorCategory(Fraction(UP)))->etc`(F,UP,L,LQ)`ODEPRRIC`1425446 +pPrintPackage`0`x`()->etc``PRINT`1425511 +pProjectiveAlgebraicSetPackage`5`x`(K:Field,symb:List(Symbol),PolyRing:PolynomialCategory(K,E,OrderedVariableList(symb)),DirectProductCategory(#(symb),NonNegativeInteger),ProjPt:ProjectiveSpaceCategory(K))->etc`(K,symb,PolyRing,E,ProjPt)`PRJALGPK`1425575 +pPseudoLinearNormalForm`1`n`(Field)->etc`(K)`PSEUDLIN`1425624 +pPseudoRemainderSequence`2`n`(R:IntegralDomain,polR:UnivariatePolynomialCategory(R))->etc`(R,polR)`PRS`1425740 +pPureAlgebraicIntegration`3`n`(R:Join(GcdDomain,etc),F:Join(FunctionSpace(R),etc),L:SetCategory)->etc`(R,F,L)`INTPAF`1426106 +pPureAlgebraicLODE`4`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F,UP,UPUP))->etc`(F,UP,UPUP,R)`ODEPAL`1426316 +pPushVariables`4`n`(R:Ring,E:OrderedAbelianMonoidSup,OV:Join(OrderedSet,etc),PPR:PolynomialCategory(Polynomial(R),E,OV))->etc`(R,E,OV,PPR)`PUSHVAR`1426409 +pQuasiAlgebraicSet2`2`n`(List(Symbol),nv:NonNegativeInteger)->etc`(vl,nv)`QALGSET2`1426448 +pQuasiComponentPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`QCMPACK`1427702 +pQuaternionCategoryFunctions2`4`x`(QuaternionCategory(R),R:CommutativeRing,QS:QuaternionCategory(S),S:CommutativeRing)->etc`(QR,R,QS,S)`QUATCT2`1427866 +pQuotientFieldCategoryFunctions2`4`x`(A:IntegralDomain,B:IntegralDomain,R:QuotientFieldCategory(A),S:QuotientFieldCategory(B))->etc`(A,B,R,S)`QFCAT2`1428063 +pRadicalEigenPackage`0`x`()->etc``REP`1428171 +pRadicalSolvePackage`1`x`(Join(EuclideanDomain,etc))->etc`(R)`SOLVERAD`1428452 +pRadixUtilities`0`x`()->etc``RADUTIL`1428624 +pRandomDistributions`1`n`(SetCategory)->etc`(S)`RDIST`1428690 pRandomFloatDistributions`0`n`()->etc``RFDIST`0 -pRandomIntegerDistributions`0`n`()->etc``RIDIST`1211752 -pRandomNumberSource`0`x`()->etc``RANDSRC`1211802 -pRationalFactorize`1`n`(UnivariatePolynomialCategory(Fraction(Integer)))->etc`(RP)`RATFACT`0 -pRationalFunctionDefiniteIntegration`1`x`(Join(EuclideanDomain,etc))->etc`(R)`DEFINTRF`1211993 -pRationalFunctionFactor`1`x`(UnivariatePolynomialCategory(Fraction(Polynomial(Integer))))->etc`(UP)`RFFACT`0 -pRationalFunctionFactorizer`1`x`(EuclideanDomain)->etc`(R)`RFFACTOR`1212119 -pRationalFunctionIntegration`1`x`(Join(IntegralDomain,etc))->etc`(F)`INTRF`1212405 -pRationalFunctionLimitPackage`1`x`(GcdDomain)->etc`(R)`LIMITRF`1212487 -pRationalFunctionSign`1`x`(GcdDomain)->etc`(R)`SIGNRF`1212540 -pRationalFunctionSum`1`x`(Join(IntegralDomain,etc))->etc`(R)`SUMRF`1212612 -pRationalFunction`1`x`(IntegralDomain)->etc`(R)`RF`1212656 -pRationalIntegration`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`INTRAT`1212753 -pRationalLODE`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`ODERAT`1212834 -pRationalRetractions`1`x`(RetractableTo(Fraction(Integer)))->etc`(S)`RATRET`1212984 -pRationalRicDE`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`ODERTRIC`1213098 -pRationalUnivariateRepresentationPackage`2`n`(Join(EuclideanDomain,etc),List(Symbol))->etc`(R,ls)`RURPK`1213162 -pRealPolynomialUtilitiesPackage`2`x`(TheField:Field,ThePols:UnivariatePolynomialCategory(TheField))->etc`(TheField,ThePols)`POLUTIL`1213598 -pRealSolvePackage`0`n`()->etc``REALSOLV`1213699 -pRealZeroPackageQ`1`x`(UnivariatePolynomialCategory(Fraction(Integer)))->etc`(Pol)`REAL0Q`1213816 -pRealZeroPackage`1`x`(UnivariatePolynomialCategory(Integer))->etc`(Pol)`REAL0`1214121 -pRectangularMatrixCategoryFunctions2`10`x`(m:NonNegativeInteger,n:NonNegativeInteger,R1:Ring,Row1:DirectProductCategory(n,R1),Col1:DirectProductCategory(m,R1),M1:RectangularMatrixCategory(m,n,R1,Row1,Col1),R2:Ring,Row2:DirectProductCategory(n,R2),Col2:DirectProductCategory(m,R2),M2:RectangularMatrixCategory(m,n,R2,Row2,Col2))->etc`(m,n,R1,Row1,Col1,M1,R2,Row2,Col2,M2)`RMCAT2`1214425 -pReduceLODE`5`n`(F:Field,L:LinearOrdinaryDifferentialOperatorCategory(F),UP:UnivariatePolynomialCategory(F),A:MonogenicAlgebra(F,UP),LO:LinearOrdinaryDifferentialOperatorCategory(A))->etc`(F,L,UP,A,LO)`ODERED`1214599 -pReducedDivisor`5`n`(F1:Field,UP:UnivariatePolynomialCategory(F1),UPUP:UnivariatePolynomialCategory(Fraction(UP)),R:FunctionFieldCategory(F1,UP,UPUP),F2:Join(Finite,etc))->etc`(F1,UP,UPUP,R,F2)`RDIV`1214700 -pReductionOfOrder`2`n`(F:Field,L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(F,L)`REDORDER`1214849 -pRegularSetDecompositionPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`RSDCMPK`1214999 -pRegularTriangularSetGcdPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`RSETGCD`1216503 -pRepeatedDoubling`1`n`(Join(SetCategory,etc))->etc`(S)`REPDB`1217283 -pRepeatedSquaring`1`n`(Join(SetCategory,etc))->etc`(S)`REPSQ`1217337 -pRepresentationPackage1`1`x`(Ring)->etc`(R)`REP1`1217391 -pRepresentationPackage2`1`x`(Ring)->etc`(R)`REP2`1217906 -pResolveLatticeCompletion`1`x`(Type)->etc`(S)`RESLATC`1218475 -pRetractSolvePackage`2`n`(Q:IntegralDomain,R:Join(IntegralDomain,etc))->etc`(Q,R)`RETSOL`1218573 -pSAERationalFunctionAlgFactor`3`x`(UP:UnivariatePolynomialCategory(Fraction(Polynomial(Integer))),SAE:Join(Field,etc),UPA:UnivariatePolynomialCategory(SAE))->etc`(UP,SAE,UPA)`SAERFFC`0 -pScriptFormulaFormat1`1`x`(SetCategory)->etc`(S)`FORMULA1`1218724 -pSegmentBindingFunctions2`2`x`(Type,S:Type)->etc`(R,S)`SEGBIND2`1218889 -pSegmentFunctions2`2`x`(Type,S:Type)->etc`(R,S)`SEG2`1218991 -pSimpleAlgebraicExtensionAlgFactor`3`x`(UP:UnivariatePolynomialCategory(Fraction(Integer)),SAE:Join(Field,etc),UPA:UnivariatePolynomialCategory(SAE))->etc`(UP,SAE,UPA)`SAEFACT`0 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-pSquareFreeRegularTriangularSetGcdPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`SFRGCD`1222597 -pStorageEfficientMatrixOperations`1`n`(Ring)->etc`(R)`MATSTOR`1223489 -pStreamFunctions1`1`x`(Type)->etc`(S)`STREAM1`1223788 -pStreamFunctions2`2`x`(Type,B:Type)->etc`(A,B)`STREAM2`1223849 -pStreamFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`STREAM3`1223911 -pStreamInfiniteProduct`1`n`(Join(IntegralDomain,etc))->etc`(Coef)`STINPROD`1223975 -pStreamTaylorSeriesOperations`1`n`(Ring)->etc`(A)`STTAYLOR`1224154 -pStreamTranscendentalFunctionsNonCommutative`1`n`(Algebra(Fraction(Integer)))->etc`(Coef)`STTFNC`1224299 -pStreamTranscendentalFunctions`1`n`(Algebra(Fraction(Integer)))->etc`(Coef)`STTF`1224504 -pStructuralConstantsPackage`1`x`(Field)->etc`(R)`SCPKG`1224667 -pSturmHabichtPackage`2`x`(OrderedIntegralDomain,x:Symbol)->etc`(R,x)`SHP`1224854 -pSubResultantPackage`2`n`(R:IntegralDomain,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`SUBRESP`1225016 -pSupFractionFactorizer`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:GcdDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`SUPFRACF`1225286 -pSymmetricFunctions`1`n`(Ring)->etc`(R)`SYMFUNC`1225490 -pSymmetricGroupCombinatoricFunctions`0`x`()->etc``SGCF`1225557 -pSystemODESolver`2`n`(F:Field,LO:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(F,LO)`ODESYS`1225763 -pSystemSolvePackage`1`x`(IntegralDomain)->etc`(R)`SYSSOLP`0 -pTableauxBumpers`1`n`(OrderedSet)->etc`(S)`TABLBUMP`1225887 -pTabulatedComputationPackage`2`n`(SetCategory,Entry:SetCategory)->etc`(Key,Entry)`TBCMPPK`1226086 -pTangentExpansions`1`n`(Field)->etc`(R)`TANEXP`1226524 -pTemplateUtilities`0`x`()->etc``TEMUTL`1226577 -pTexFormat1`1`x`(SetCategory)->etc`(S)`TEX1`1226642 -pToolsForSign`1`n`(Ring)->etc`(R)`TOOLSIGN`1226786 -pTopLevelDrawFunctionsForAlgebraicCurves`2`x`(R:Join(IntegralDomain,etc),Ex:FunctionSpace(R))->etc`(R,Ex)`DRAWCURV`1226831 -pTopLevelDrawFunctionsForCompiledFunctions`0`x`()->etc``DRAWCFUN`1226950 -pTopLevelDrawFunctionsForPoints`0`x`()->etc``DRAWPT`1227065 -pTopLevelDrawFunctions`1`x`(Join(ConvertibleTo(InputForm),etc))->etc`(Ex)`DRAW`1227193 -pTopLevelThreeSpace`0`x`()->etc``TOPSP`0 -pTransSolvePackageService`1`n`(Join(IntegralDomain,etc))->etc`(R)`SOLVESER`1227288 -pTransSolvePackage`1`x`(Join(OrderedSet,etc))->etc`(R)`SOLVETRA`1227846 -pTranscendentalHermiteIntegration`2`n`(F:Field,UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`INTHERTR`1228696 -pTranscendentalIntegration`2`n`(F:Field,UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`INTTR`1228747 -pTranscendentalManipulations`2`x`(R:Join(OrderedSet,etc),F:Join(FunctionSpace(R),etc))->etc`(R,F)`TRMANIP`1228838 -pTranscendentalRischDESystem`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`RDETRS`1228963 -pTranscendentalRischDE`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`RDETR`1229132 -pTriangularMatrixOperations`4`n`(R:IntegralDomain,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`TRIMAT`1229288 -pTrigonometricManipulations`2`x`(R:Join(GcdDomain,etc),F:Join(AlgebraicallyClosedField,etc))->etc`(R,F)`TRIGMNIP`1229763 -pTubePlotTools`0`n`()->etc``TUBETOOL`1229914 -pTwoDimensionalPlotClipping`0`n`()->etc``CLIP`1229990 -pTwoFactorize`1`n`(FiniteFieldCategory)->etc`(F)`TWOFACT`1230103 -pUTSodetools`4`n`(F:Ring,UP:UnivariatePolynomialCategory(F),L:LinearOrdinaryDifferentialOperatorCategory(UP),UTS:UnivariateTaylorSeriesCategory(F))->etc`(F,UP,L,UTS)`UTSODETL`1230270 -pUnivariateFactorize`1`n`(UnivariatePolynomialCategory(Integer))->etc`(ZP)`UNIFACT`1230399 -pUnivariateLaurentSeriesFunctions2`6`x`(Coef1:Ring,Coef2:Ring,var1:Symbol,var2:Symbol,cen1:Coef1,cen2:Coef2)->etc`(Coef1,Coef2,var1,var2,cen1,cen2)`ULS2`1230576 -pUnivariatePolynomialCategoryFunctions2`4`x`(R:Ring,PR:UnivariatePolynomialCategory(R),S:Ring,PS:UnivariatePolynomialCategory(S))->etc`(R,PR,S,PS)`UPOLYC2`1230753 -pUnivariatePolynomialCommonDenominator`3`x`(R:IntegralDomain,Q:QuotientFieldCategory(R),UP:UnivariatePolynomialCategory(Q))->etc`(R,Q,UP)`UPCDEN`1230896 -pUnivariatePolynomialDecompositionPackage`2`n`(R:Join(IntegralDomain,etc),UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`UPDECOMP`1231088 -pUnivariatePolynomialDivisionPackage`2`n`(R:IntegralDomain,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`UPDIVP`1231273 -pUnivariatePolynomialFunctions2`4`x`(Symbol,R:Ring,y:Symbol,S:Ring)->etc`(x,R,y,S)`UP2`1231419 -pUnivariatePolynomialMultiplicationPackage`2`x`(R:Ring,U:UnivariatePolynomialCategory(R))->etc`(R,U)`UPMP`1231762 -pUnivariatePolynomialSquareFree`2`n`(RC:IntegralDomain,P:Join(UnivariatePolynomialCategory(RC),etc))->etc`(RC,P)`UPSQFREE`1232052 -pUnivariatePuiseuxSeriesFunctions2`6`x`(Coef1:Ring,Coef2:Ring,var1:Symbol,var2:Symbol,cen1:Coef1,cen2:Coef2)->etc`(Coef1,Coef2,var1,var2,cen1,cen2)`UPXS2`1232727 -pUnivariateSkewPolynomialCategoryOps`2`n`(R:Ring,C:UnivariateSkewPolynomialCategory(R))->etc`(R,C)`OREPCTO`1232877 -pUnivariateTaylorSeriesFunctions2`4`x`(Coef1:Ring,Coef2:Ring,UTS1:UnivariateTaylorSeriesCategory(Coef1),UTS2:UnivariateTaylorSeriesCategory(Coef2))->etc`(Coef1,Coef2,UTS1,UTS2)`UTS2`1233005 -pUnivariateTaylorSeriesODESolver`2`n`(Coef:Algebra(Fraction(Integer)),UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(Coef,UTS)`UTSODE`1233181 -pUniversalSegmentFunctions2`2`x`(Type,S:Type)->etc`(R,S)`UNISEG2`1233332 -pUserDefinedPartialOrdering`1`n`(SetCategory)->etc`(S)`UDPO`1233409 -pUserDefinedVariableOrdering`0`x`()->etc``UDVO`1233475 -pVectorFunctions2`2`x`(Type,B:Type)->etc`(A,B)`VECTOR2`0 -pViewDefaultsPackage`0`x`()->etc``VIEWDEF`1233708 -pViewportPackage`0`n`()->etc``VIEW`1233796 -pWeierstrassPreparation`1`n`(Field)->etc`(R)`WEIER`1233922 -pWildFunctionFieldIntegralBasis`4`n`(K:FiniteFieldCategory,R:UnivariatePolynomialCategory(K),UP:UnivariatePolynomialCategory(R),FramedAlgebra(R,UP))->etc`(K,R,UP,F)`WFFINTBS`1234493 -pXExponentialPackage`3`n`(R:Join(Ring,etc),VarSet:OrderedSet,XPOLY:XPolynomialsCat(VarSet,R))->etc`(R,VarSet,XPOLY)`XEXPPKG`1234855 -pZeroDimensionalSolvePackage`3`x`(Join(OrderedRing,etc),ls:List(Symbol),ls2:List(Symbol))->etc`(R,ls,ls2)`ZDSOLVE`1235032 -pd01AgentsPackage`0`x`()->etc``D01AGNT`0 -pd01WeightsPackage`0`x`()->etc``D01WGTS`0 -pd02AgentsPackage`0`x`()->etc``D02AGNT`0 -pd03AgentsPackage`0`x`()->etc``D03AGNT`0 -pe04AgentsPackage`0`x`()->etc``E04AGNT`0 -xAbelianGroup&`1`n`(AbelianGroup)->etc`(S)`ABELGRP-`1236356 -xAbelianMonoid&`1`n`(AbelianMonoid)->etc`(S)`ABELMON-`1236484 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-xOctonionCategory&`2`n`(OctonionCategory(R),R:CommutativeRing)->etc`(S,R)`OC-`1246749 -xOneDimensionalArrayAggregate&`2`n`(OneDimensionalArrayAggregate(S),S:Type)->etc`(A,S)`A1AGG-`0 -xOrderedRing&`1`n`(OrderedRing)->etc`(S)`ORDRING-`1246971 -xOrderedSet&`1`n`(OrderedSet)->etc`(S)`ORDSET-`1247105 -xPartialDifferentialRing&`2`n`(PartialDifferentialRing(S),S:SetCategory)->etc`(A,S)`PDRING-`1247365 -xPolynomialCategory&`4`n`(PolynomialCategory(R,E,VarSet),R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet)->etc`(S,R,E,VarSet)`POLYCAT-`1247471 -xPolynomialFactorizationExplicit&`1`n`(PolynomialFactorizationExplicit)->etc`(S)`PFECAT-`1247641 -xPolynomialSetCategory&`5`n`(PolynomialSetCategory(R,E,VarSet,P),R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,P:RecursivePolynomialCategory(R,E,VarSet))->etc`(S,R,E,VarSet,P)`PSETCAT-`1247944 -xPowerSeriesCategory&`4`n`(PowerSeriesCategory(Coef,Expon,Var),Coef:Ring,Expon:OrderedAbelianMonoid,Var:OrderedSet)->etc`(S,Coef,Expon,Var)`PSCAT-`1248558 -xQuaternionCategory&`2`n`(QuaternionCategory(R),R:CommutativeRing)->etc`(S,R)`QUATCAT-`1248683 -xQuotientFieldCategory&`2`n`(QuotientFieldCategory(S),S:IntegralDomain)->etc`(A,S)`QFCAT-`1248821 -xRadicalCategory&`1`n`(RadicalCategory)->etc`(S)`RADCAT-`0 -xRealClosedField&`1`n`(RealClosedField)->etc`(S)`RCFIELD-`1248913 -xRealNumberSystem&`1`n`(RealNumberSystem)->etc`(S)`RNS-`0 -xRealRootCharacterizationCategory&`3`n`(RealRootCharacterizationCategory(TheField,ThePols),TheField:Join(OrderedRing,etc),ThePols:UnivariatePolynomialCategory(TheField))->etc`(S,TheField,ThePols)`RRCC-`1249008 -xRectangularMatrixCategory&`6`n`(RectangularMatrixCategory(m,n,R,Row,Col),m:NonNegativeInteger,n:NonNegativeInteger,R:Ring,Row:DirectProductCategory(n,R),Col:DirectProductCategory(m,R))->etc`(S,m,n,R,Row,Col)`RMATCAT-`1249120 -xRecursiveAggregate&`2`n`(RecursiveAggregate(S),S:Type)->etc`(A,S)`RCAGG-`0 -xRecursivePolynomialCategory&`4`n`(RecursivePolynomialCategory(R,E,V),R:Ring,E:OrderedAbelianMonoidSup,V:OrderedSet)->etc`(S,R,E,V)`RPOLCAT-`1249349 -xRegularTriangularSetCategory&`5`n`(RegularTriangularSetCategory(R,E,V,P),R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(S,R,E,V,P)`RSETCAT-`1249828 -xRetractableTo&`2`n`(RetractableTo(S),S:Type)->etc`(A,S)`RETRACT-`1252732 -xRing&`1`n`(Ring)->etc`(S)`RING-`1252907 -xSemiGroup&`1`n`(SemiGroup)->etc`(S)`SGROUP-`1253005 -xSetAggregate&`2`n`(SetAggregate(S),S:SetCategory)->etc`(A,S)`SETAGG-`0 -xSetCategory&`1`n`(SetCategory)->etc`(S)`SETCAT-`1253135 -xSquareMatrixCategory&`5`n`(SquareMatrixCategory(ndim,R,Row,Col),ndim:NonNegativeInteger,R:Ring,Row:DirectProductCategory(ndim,R),Col:DirectProductCategory(ndim,R))->etc`(S,ndim,R,Row,Col)`SMATCAT-`1253407 -xStreamAggregate&`2`n`(StreamAggregate(S),S:Type)->etc`(A,S)`STAGG-`0 -xStringAggregate&`1`n`(StringAggregate)->etc`(S)`SRAGG-`0 -xTableAggregate&`3`n`(TableAggregate(Key,Entry),Key:SetCategory,Entry:SetCategory)->etc`(S,Key,Entry)`TBAGG-`0 -xTranscendentalFunctionCategory&`1`n`(TranscendentalFunctionCategory)->etc`(S)`TRANFUN-`1253663 -xTriangularSetCategory&`5`n`(TriangularSetCategory(R,E,V,P),R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(S,R,E,V,P)`TSETCAT-`1253724 -xTrigonometricFunctionCategory&`1`n`(TrigonometricFunctionCategory)->etc`(S)`TRIGCAT-`1255162 -xTwoDimensionalArrayCategory&`4`n`(TwoDimensionalArrayCategory(R,Row,Col),R:Type,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->etc`(S,R,Row,Col)`ARR2CAT-`1255211 -xUnaryRecursiveAggregate&`2`n`(UnaryRecursiveAggregate(S),S:Type)->etc`(A,S)`URAGG-`0 -xUniqueFactorizationDomain&`1`n`(UniqueFactorizationDomain)->etc`(S)`UFD-`1255766 -xUnivariateLaurentSeriesConstructorCategory&`3`n`(UnivariateLaurentSeriesConstructorCategory(Coef,UTS),Coef:Ring,UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(S,Coef,UTS)`ULSCCAT-`1255939 -xUnivariatePolynomialCategory&`2`n`(UnivariatePolynomialCategory(R),R:Ring)->etc`(S,R)`UPOLYC-`1256235 -xUnivariatePowerSeriesCategory&`3`n`(UnivariatePowerSeriesCategory(Coef,Expon),Coef:Ring,Expon:OrderedAbelianMonoid)->etc`(S,Coef,Expon)`UPSCAT-`1256383 -xUnivariatePuiseuxSeriesConstructorCategory&`3`n`(UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),Coef:Ring,ULS:UnivariateLaurentSeriesCategory(Coef))->etc`(S,Coef,ULS)`UPXSCCA-`1256730 -xUnivariateSkewPolynomialCategory&`2`n`(UnivariateSkewPolynomialCategory(R),R:Ring)->etc`(S,R)`OREPCAT-`1257029 -xUnivariateTaylorSeriesCategory&`2`n`(UnivariateTaylorSeriesCategory(Coef),Coef:Ring)->etc`(S,Coef)`UTSCAT-`1257412 -xVectorCategory&`2`n`(VectorCategory(R),R:Type)->etc`(S,R)`VECTCAT-`0 -xVectorSpace&`2`n`(VectorSpace(S),S:Field)->etc`(A,S)`VSPACE-`1257511 +pRandomIntegerDistributions`0`n`()->etc``RIDIST`1428739 +pRandomNumberSource`0`x`()->etc``RANDSRC`1428789 +pRationalFactorize`1`n`(UnivariatePolynomialCategory(Fraction(Integer)))->etc`(RP)`RATFACT`1428945 +pRationalFunction`1`x`(IntegralDomain)->etc`(R)`RF`1429443 +pRationalFunctionDefiniteIntegration`1`x`(Join(EuclideanDomain,etc))->etc`(R)`DEFINTRF`1429540 +pRationalFunctionFactor`1`x`(UnivariatePolynomialCategory(Fraction(Polynomial(Integer))))->etc`(UP)`RFFACT`1429710 +pRationalFunctionFactorizer`1`x`(EuclideanDomain)->etc`(R)`RFFACTOR`1429831 +pRationalFunctionIntegration`1`x`(Join(IntegralDomain,etc))->etc`(F)`INTRF`1430117 +pRationalFunctionLimitPackage`1`x`(GcdDomain)->etc`(R)`LIMITRF`1430199 +pRationalFunctionSign`1`x`(GcdDomain)->etc`(R)`SIGNRF`1430252 +pRationalFunctionSum`1`x`(Join(IntegralDomain,etc))->etc`(R)`SUMRF`1430324 +pRationalIntegration`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`INTRAT`1430368 +pRationalInterpolation`2`n`(Symbol,F:Field)->etc`(xx,F)`RINTERP`1430479 +pRationalLODE`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`ODERAT`1430541 +pRationalRetractions`1`x`(RetractableTo(Fraction(Integer)))->etc`(S)`RATRET`1430677 +pRationalRicDE`2`n`(F:Join(Field,etc),UP:UnivariatePolynomialCategory(F))->etc`(F,UP)`ODERTRIC`1430734 +pRationalUnivariateRepresentationPackage`2`n`(Join(EuclideanDomain,etc),List(Symbol))->etc`(R,ls)`RURPK`1430798 +pRealPolynomialUtilitiesPackage`2`x`(TheField:Field,ThePols:UnivariatePolynomialCategory(TheField))->etc`(TheField,ThePols)`POLUTIL`1431182 +pRealSolvePackage`0`n`()->etc``REALSOLV`1431283 +pRealZeroPackage`1`x`(UnivariatePolynomialCategory(Integer))->etc`(Pol)`REAL0`1431385 +pRealZeroPackageQ`1`x`(UnivariatePolynomialCategory(Fraction(Integer)))->etc`(Pol)`REAL0Q`1431675 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+pReductionOfOrder`2`n`(F:Field,L:LinearOrdinaryDifferentialOperatorCategory(F))->etc`(F,L)`REDORDER`1432479 +pRegularSetDecompositionPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`RSDCMPK`1432629 +pRegularTriangularSetGcdPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`RSETGCD`1433947 +pRepeatedDoubling`1`n`(Join(SetCategory,etc))->etc`(S)`REPDB`1434096 +pRepeatedSquaring`1`n`(Join(SetCategory,etc))->etc`(S)`REPSQ`1434150 +pRepresentationPackage1`1`x`(Ring)->etc`(R)`REP1`1434204 +pRepresentationPackage2`1`x`(Ring)->etc`(R)`REP2`1434723 +pResolveLatticeCompletion`1`x`(Type)->etc`(S)`RESLATC`1435296 +pRetractSolvePackage`2`n`(Q:IntegralDomain,R:Join(IntegralDomain,etc))->etc`(Q,R)`RETSOL`1435394 +pRootsFindingPackage`1`x`(Field)->etc`(K)`RFP`1435545 +pSAERationalFunctionAlgFactor`3`x`(UP:UnivariatePolynomialCategory(Fraction(Polynomial(Integer))),SAE:Join(Field,etc),UPA:UnivariatePolynomialCategory(SAE))->etc`(UP,SAE,UPA)`SAERFFC`1436174 +pScriptFormulaFormat1`1`x`(SetCategory)->etc`(S)`FORMULA1`1436308 +pSegmentBindingFunctions2`2`x`(Type,S:Type)->etc`(R,S)`SEGBIND2`1436473 +pSegmentFunctions2`2`x`(Type,S:Type)->etc`(R,S)`SEG2`1436575 +pSimpleAlgebraicExtensionAlgFactor`3`x`(UP:UnivariatePolynomialCategory(Fraction(Integer)),SAE:Join(Field,etc),UPA:UnivariatePolynomialCategory(SAE))->etc`(UP,SAE,UPA)`SAEFACT`1436652 +pSimplifyAlgebraicNumberConvertPackage`0`x`()->etc``SIMPAN`1436798 +pSmithNormalForm`4`x`(R:EuclideanDomain,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R),M:MatrixCategory(R,Row,Col))->etc`(R,Row,Col,M)`SMITH`1436891 +pSortedCache`1`n`(CachableSet)->etc`(S)`SCACHE`1436997 +pSortPackage`2`n`(S:Type,A:Join(IndexedAggregate(Integer,S),etc))->etc`(S,A)`SORTPAK`1437356 +pSparseUnivariatePolynomialFunctions2`2`x`(Ring,S:Ring)->etc`(R,S)`SUP2`1437404 +pSpecialOutputPackage`0`x`()->etc``SPECOUT`1437729 +pSquareFreeQuasiComponentPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`SFQCMPK`1437830 +pSquareFreeRegularSetDecompositionPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:SquareFreeRegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`SRDCMPK`1438003 +pSquareFreeRegularTriangularSetGcdPackage`5`x`(R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V),TS:RegularTriangularSetCategory(R,E,V,P))->etc`(R,E,V,P,TS)`SFRGCD`1439240 +pStorageEfficientMatrixOperations`1`n`(Ring)->etc`(R)`MATSTOR`1439490 +pStreamFunctions1`1`x`(Type)->etc`(S)`STREAM1`1439789 +pStreamFunctions2`2`x`(Type,B:Type)->etc`(A,B)`STREAM2`1439850 +pStreamFunctions3`3`x`(Type,B:Type,C:Type)->etc`(A,B,C)`STREAM3`1439912 +pStreamInfiniteProduct`1`n`(Join(IntegralDomain,etc))->etc`(Coef)`STINPROD`1439976 +pStreamTaylorSeriesOperations`1`n`(Ring)->etc`(A)`STTAYLOR`1440155 +pStreamTranscendentalFunctions`1`n`(Algebra(Fraction(Integer)))->etc`(Coef)`STTF`1440300 +pStreamTranscendentalFunctionsNonCommutative`1`n`(Algebra(Fraction(Integer)))->etc`(Coef)`STTFNC`1440463 +pStructuralConstantsPackage`1`x`(Field)->etc`(R)`SCPKG`1440668 +pSturmHabichtPackage`2`x`(OrderedIntegralDomain,x:Symbol)->etc`(R,x)`SHP`1440855 +pSubResultantPackage`2`n`(R:IntegralDomain,UP:UnivariatePolynomialCategory(R))->etc`(R,UP)`SUBRESP`1441017 +pSupFractionFactorizer`4`n`(E:OrderedAbelianMonoidSup,OV:OrderedSet,R:GcdDomain,P:PolynomialCategory(R,E,OV))->etc`(E,OV,R,P)`SUPFRACF`1441276 +pSymmetricFunctions`1`n`(Ring)->etc`(R)`SYMFUNC`1441466 +pSymmetricGroupCombinatoricFunctions`0`x`()->etc``SGCF`1441533 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+xPartialDifferentialRing&`2`n`(PartialDifferentialRing(S),S:SetCategory)->etc`(A,S)`PDRING-`1477475 +xPolynomialCategory&`4`n`(PolynomialCategory(R,E,VarSet),R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet)->etc`(S,R,E,VarSet)`POLYCAT-`1477770 +xPolynomialFactorizationExplicit&`1`n`(PolynomialFactorizationExplicit)->etc`(S)`PFECAT-`1477940 +xPolynomialSetCategory&`5`n`(PolynomialSetCategory(R,E,VarSet,P),R:Ring,E:OrderedAbelianMonoidSup,VarSet:OrderedSet,P:RecursivePolynomialCategory(R,E,VarSet))->etc`(S,R,E,VarSet,P)`PSETCAT-`1478243 +xPowerSeriesCategory&`4`n`(PowerSeriesCategory(Coef,Expon,Var),Coef:Ring,Expon:OrderedAbelianMonoid,Var:OrderedSet)->etc`(S,Coef,Expon,Var)`PSCAT-`1478857 +xQuaternionCategory&`2`n`(QuaternionCategory(R),R:CommutativeRing)->etc`(S,R)`QUATCAT-`1478982 +xQuotientFieldCategory&`2`n`(QuotientFieldCategory(S),S:IntegralDomain)->etc`(A,S)`QFCAT-`1479120 +xRadicalCategory&`1`n`(RadicalCategory)->etc`(S)`RADCAT-`1479212 +xRealClosedField&`1`n`(RealClosedField)->etc`(S)`RCFIELD-`1479283 +xRealNumberSystem&`1`n`(RealNumberSystem)->etc`(S)`RNS-`1479378 +xRealRootCharacterizationCategory&`3`n`(RealRootCharacterizationCategory(TheField,ThePols),TheField:Join(OrderedRing,etc),ThePols:UnivariatePolynomialCategory(TheField))->etc`(S,TheField,ThePols)`RRCC-`1479673 +xRectangularMatrixCategory&`6`n`(RectangularMatrixCategory(m,n,R,Row,Col),m:NonNegativeInteger,n:NonNegativeInteger,R:Ring,Row:DirectProductCategory(n,R),Col:DirectProductCategory(m,R))->etc`(S,m,n,R,Row,Col)`RMATCAT-`1479784 +xRecursiveAggregate&`2`n`(RecursiveAggregate(S),S:Type)->etc`(A,S)`RCAGG-`1480013 +xRecursivePolynomialCategory&`4`n`(RecursivePolynomialCategory(R,E,V),R:Ring,E:OrderedAbelianMonoidSup,V:OrderedSet)->etc`(S,R,E,V)`RPOLCAT-`1480459 +xRegularTriangularSetCategory&`5`n`(RegularTriangularSetCategory(R,E,V,P),R:GcdDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(S,R,E,V,P)`RSETCAT-`1480938 +xRetractableTo&`2`n`(RetractableTo(S),S:Type)->etc`(A,S)`RETRACT-`1483181 +xRing&`1`n`(Ring)->etc`(S)`RING-`1483356 +xSemiGroup&`1`n`(SemiGroup)->etc`(S)`SGROUP-`1483454 +xSetAggregate&`2`n`(SetAggregate(S),S:SetCategory)->etc`(A,S)`SETAGG-`1483792 +xSetCategory&`1`n`(SetCategory)->etc`(S)`SETCAT-`1484118 +xSquareMatrixCategory&`5`n`(SquareMatrixCategory(ndim,R,Row,Col),ndim:NonNegativeInteger,R:Ring,Row:DirectProductCategory(ndim,R),Col:DirectProductCategory(ndim,R))->etc`(S,ndim,R,Row,Col)`SMATCAT-`1484391 +xStreamAggregate&`2`n`(StreamAggregate(S),S:Type)->etc`(A,S)`STAGG-`1484647 +xStringAggregate&`1`n`(StringAggregate)->etc`(S)`SRAGG-`1485018 +xTableAggregate&`3`n`(TableAggregate(Key,Entry),Key:SetCategory,Entry:SetCategory)->etc`(S,Key,Entry)`TBAGG-`1485122 +xTranscendentalFunctionCategory&`1`n`(TranscendentalFunctionCategory)->etc`(S)`TRANFUN-`1485243 +xTriangularSetCategory&`5`n`(TriangularSetCategory(R,E,V,P),R:IntegralDomain,E:OrderedAbelianMonoidSup,V:OrderedSet,P:RecursivePolynomialCategory(R,E,V))->etc`(S,R,E,V,P)`TSETCAT-`1485304 +xTrigonometricFunctionCategory&`1`n`(TrigonometricFunctionCategory)->etc`(S)`TRIGCAT-`1486542 +xTwoDimensionalArrayCategory&`4`n`(TwoDimensionalArrayCategory(R,Row,Col),R:Type,Row:FiniteLinearAggregate(R),Col:FiniteLinearAggregate(R))->etc`(S,R,Row,Col)`ARR2CAT-`1486591 +xUnaryRecursiveAggregate&`2`n`(UnaryRecursiveAggregate(S),S:Type)->etc`(A,S)`URAGG-`1486643 +xUniqueFactorizationDomain&`1`n`(UniqueFactorizationDomain)->etc`(S)`UFD-`1487181 +xUnivariateLaurentSeriesConstructorCategory&`3`n`(UnivariateLaurentSeriesConstructorCategory(Coef,UTS),Coef:Ring,UTS:UnivariateTaylorSeriesCategory(Coef))->etc`(S,Coef,UTS)`ULSCCAT-`1487354 +xUnivariatePolynomialCategory&`2`n`(UnivariatePolynomialCategory(R),R:Ring)->etc`(S,R)`UPOLYC-`1487650 +xUnivariatePowerSeriesCategory&`3`n`(UnivariatePowerSeriesCategory(Coef,Expon),Coef:Ring,Expon:OrderedAbelianMonoid)->etc`(S,Coef,Expon)`UPSCAT-`1487798 +xUnivariatePuiseuxSeriesConstructorCategory&`3`n`(UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),Coef:Ring,ULS:UnivariateLaurentSeriesCategory(Coef))->etc`(S,Coef,ULS)`UPXSCCA-`1488158 +xUnivariateSkewPolynomialCategory&`2`n`(UnivariateSkewPolynomialCategory(R),R:Ring)->etc`(S,R)`OREPCAT-`1488457 +xUnivariateTaylorSeriesCategory&`2`n`(UnivariateTaylorSeriesCategory(Coef),Coef:Ring)->etc`(S,Coef)`UTSCAT-`1488754 +xVectorCategory&`2`n`(VectorCategory(R),R:Type)->etc`(S,R)`VECTCAT-`1488853 +xVectorSpace&`2`n`(VectorSpace(S),S:Field)->etc`(A,S)`VSPACE-`1489273 diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase old mode 100755 new mode 100644 index 9750692..e0fe1db --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,2970 +1,3221 @@ -(680518 . 3269429137) -(((*1 *1 *1 *2) (-12 (-5 *2 (-578 (-786))) (-5 *1 (-786)))) ((*1 *2 *1) (-12 (-5 *2 (-2 (|:| -3606 (-578 (-786))) (|:| -3405 (-578 (-786))) (|:| |presup| (-578 (-786))) (|:| -3411 (-578 (-786))) (|:| |args| (-578 (-786))))) (-5 *1 (-1070))))) -(((*1 *2 *3) (-12 (-5 *3 (-1148 *1)) (-4 *1 (-335 *4)) (-4 *4 (-156)) (-5 *2 (-621 *4)))) ((*1 *2) (-12 (-4 *4 (-156)) (-5 *2 (-621 *4)) (-5 *1 (-385 *3 *4)) (-4 *3 (-386 *4)))) ((*1 *2) (-12 (-4 *1 (-386 *3)) (-4 *3 (-156)) (-5 *2 (-621 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *2 (-578 (-1053))) (-5 *1 (-970)) (-5 *3 (-1053))))) -(((*1 *2 *2 *2 *2 *2 *2) (-12 (-4 *2 (-13 (-331) (-10 -8 (-15 ** ($ $ (-375 (-501))))))) (-5 *1 (-1026 *3 *2)) (-4 *3 (-1125 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-997 (-997 *3))) (-5 *1 (-825 *3)) (-4 *3 (-1001))))) -(((*1 *1) (-12 (-4 *3 (-1001)) (-5 *1 (-805 *2 *3 *4)) (-4 *2 (-1001)) (-4 *4 (-601 *3)))) ((*1 *1) (-12 (-5 *1 (-808 *2 *3)) (-4 *2 (-1001)) (-4 *3 (-1001))))) -(((*1 *2 *3) (-12 (-4 *4 (-777)) (-5 *2 (-2 (|:| |f1| (-578 *4)) (|:| |f2| (-578 (-578 (-578 *4)))) (|:| |f3| (-578 (-578 *4))) (|:| |f4| (-578 (-578 (-578 *4)))))) (-5 *1 (-1076 *4)) (-5 *3 (-578 (-578 (-578 *4))))))) -(((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-756))))) -(((*1 *2 *3) (-12 (-4 *4 (-959)) (-4 *2 (-13 (-372) (-950 *4) (-331) (-1090) (-254))) (-5 *1 (-410 *4 *3 *2)) (-4 *3 (-1125 *4)))) ((*1 *1 *1) (-4 *1 (-500))) ((*1 *2 *1) (-12 (-5 *2 (-839)) (-5 *1 (-606 *3)) (-4 *3 (-777)))) ((*1 *2 *1) (-12 (-5 *2 (-839)) (-5 *1 (-610 *3)) (-4 *3 (-777)))) ((*1 *2 *1) (-12 (-5 *2 (-701)) (-5 *1 (-749 *3)) (-4 *3 (-777)))) ((*1 *2 *1) (-12 (-5 *2 (-701)) (-5 *1 (-813 *3)) (-4 *3 (-777)))) ((*1 *2 *1) (-12 (-4 *1 (-909 *3)) (-4 *3 (-1104)) (-5 *2 (-701)))) ((*1 *2 *1) (-12 (-5 *2 (-701)) (-5 *1 (-1102 *3)) (-4 *3 (-1104)))) ((*1 *2 *1) (-12 (-4 *1 (-1147 *2)) (-4 *2 (-1104)) (-4 *2 (-916)) (-4 *2 (-959))))) -(((*1 *1 *1 *2 *3 *1) (-12 (-5 *2 (-701)) (-5 *1 (-711 *3)) (-4 *3 (-959)))) ((*1 *1 *1 *2 *3 *1) (-12 (-5 *1 (-875 *3 *2)) (-4 *2 (-123)) (-4 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(-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-511)))) ((*1 *2 *1) (-12 (-4 *1 (-548 *3 *4)) (-4 *3 (-1001)) (-4 *4 (-1104)) (-5 *2 (-578 *4))))) -(((*1 *2 *3) (-12 (-4 *4 (-959)) (-4 *3 (-1125 *4)) (-4 *2 (-1142 *4)) (-5 *1 (-1144 *4 *3 *5 *2)) (-4 *5 (-593 *3))))) -(((*1 *1 *2 *2) (-12 (-5 *2 (-3 (|:| I (-282 (-501))) (|:| -2958 (-282 (-346))) (|:| CF (-282 (-152 (-346)))) (|:| |switch| (-1069)))) (-5 *1 (-1069))))) -(((*1 *1 *1 *1) (-5 *1 (-786)))) -(((*1 *2 *3) (-12 (-4 *4 (-13 (-508) (-777) (-950 (-501)))) (-5 *2 (-107)) (-5 *1 (-164 *4 *3)) (-4 *3 (-13 (-27) (-1090) (-389 (-152 *4)))))) ((*1 *2 *1) (-12 (-5 *2 (-107)) (-5 *1 (-402)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-419) (-777) (-950 (-501)) (-577 (-501)))) (-5 *2 (-107)) (-5 *1 (-1094 *4 *3)) (-4 *3 (-13 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+(|FreeAbelianGroup| |FreeAbelianMonoid|) +(|IndexedMatrix| |IndexedTwoDimensionalArray| |Matrix| |TwoDimensionalArray|) +(|InnerMatrixQuotientFieldFunctions| |MatrixLinearAlgebraFunctions|) +(|MatrixLinearAlgebraFunctions|) +(|AlgebraicMultFact| |MultivariateFactorize|) +(|FiniteFieldNormalBasisExtensionByPolynomial|) +(|NumericComplexEigenPackage| |NumericRealEigenPackage|) +(|ComplexRootPackage| |FloatingComplexPackage| |FloatingRealPackage| |InnerNumericEigenPackage|) +(|BalancedPAdicInteger| |PAdicInteger|) +(|DefiniteIntegrationTools| |RationalFunctionLimitPackage| |RationalFunctionSign|) +(|RationalFunctionSum|) +(|InnerFiniteField| |PrimeField|) +(|SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries|) +(|Table|) +(|SparseMultivariateTaylorSeries| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) +(|ComplexTrigonometricManipulations| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |TrigonometricManipulations|) +(|AssociationList| |BalancedPAdicRational| |BasicOperatorFunctions1| |BinaryExpansion| |Bits| |Boolean| |CharacterClass| |CommonOperators| |Complex| |ComplexCategory&| |DataList| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |EqTable| |ExponentialExpansion| |Expression| |Factored| |FlexibleArray| |Float| |FortranPackage| |FortranProgram| |Fraction| |FunctionSpace&| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |HashTable| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedOneDimensionalArray| |IndexedString| |IndexedVector| |InnerTable| |InputFormFunctions1| |Integer| |IntegerNumberSystem&| |Kernel| |KeyedAccessFile| |Library| |LiouvillianFunction| |List| |ListMultiDictionary| |MachineComplex| |MachineInteger| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |Matrix| |ModMonic| |Multiset| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OpenMathPackage| |OrderedVariableList| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |Pi| |Point| |Polynomial| |PolynomialCategory&| |PrimitiveArray| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadixExpansion| |RectangularMatrix| |RecursivePolynomialCategory&| |RegularChain| |RegularTriangularSet| |Result| |RomanNumeral| |RoutinesTable| |SequentialDifferentialPolynomial| |Set| |SingleInteger| |SparseMultivariatePolynomial| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SquareFreeRegularTriangularSet| |SquareMatrix| |Stream| |String| |StringTable| |Symbol| |SymbolTable| |Table| |TemplateUtilities| |TopLevelDrawFunctions| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |WuWenTsunTriangularSet|) +(|FunctionSpace&|) +(|AbelianGroup&| |AbelianMonoidRing&| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgFactor| |Algebra&| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |ArrayStack| |Asp10| |Asp19| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp55| |Asp73| |Asp74| |Asp77| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |AxiomServer| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |Bezier| |BezoutMatrix| |BinaryExpansion| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Color| |CombinatorialFunction| |Commutator| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexRootFindingPackage| |ComplexRootPackage| |ContinuedFraction| |CoordinateSystems| |CycleIndicators| |CyclotomicPolynomialPackage| |DataList| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DesingTreePackage| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |DivisionRing&| |Divisor| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |EigenPackage| |ElementaryFunction| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EllipticFunctionsUnivariateTaylorSeries| |Equation| |EuclideanDomain&| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtensibleLinearAggregate&| |Factored| |FactoredFunctions| |FactoredFunctions2| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSquareFreeDecomposition| |FiniteLinearAggregate&| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FloatingPointSystem&| |FortranCode| |FortranExpression| |FortranProgram| |FortranTemplate| |FourierSeries| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FullyRetractableTo&| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |GraphImage| |GraphicsDefaults| |GrayCode| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Group&| |Guess| |GuessFinite| |GuessFiniteFunctions| |GuessOption| |GuessOptionFunctions0| |HallBasis| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperbolicFunctionCategory&| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfinitlyClosePoint| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySign| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |Integer| |IntegerBits| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRetractions| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegralBasisTools| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |Interval| |InverseLaplaceTransform| |IrrRepSymNatPackage| |KeyedAccessFile| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LazyStreamAggregate&| |LeadingCoefDetermination| |LeftAlgebra&| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| |LinesOpPack| |LiouvillianFunction| |List| |ListAggregate&| |ListMonoidOps| |ListToMap| |LocalAlgebra| |LocalParametrizationOfSimplePointPackage| |Localize| |LyndonWord| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |MakeFloatCompiledFunction| |MappingPackage1| |MathMLFormat| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |MonogenicAlgebra&| |MonoidRing| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NPCoef| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewtonInterpolation| |NewtonPolygon| |NonAssociativeRing&| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NottinghamGroup| |NumberFieldIntegralBasis| |NumberFormats| |NumberTheoreticPolynomialFunctions| |NumericContinuedFraction| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODEIntegration| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |OpenMathDevice| |OpenMathEncoding| |OpenMathError| |OpenMathServerPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedRing&| |OrderedVariableList| |OrderingFunctions| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |Palette| |ParadoxicalCombinatorsForStreams| |ParametricLinearEquations| |ParametrizationPackage| |PartialFraction| |Partition| |PartitionsAndPermutations| |Pattern| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchPolynomialCategory| |PendantTree| |Permanent| |Permutation| |PermutationGroup| |PermutationGroupExamples| |Pi| |PiCoercions| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |PointFunctions2| |PointPackage| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialCategory&| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialNumberTheoryFunctions| |PolynomialPackageForCurve| |PolynomialRing| |PolynomialRoots| |PolynomialSolveByFormulas| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |QuadraticForm| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadicalCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RadixUtilities| |RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions| |RandomNumberSource| |RationalFactorize| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalInterpolation| |RationalLODE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RectangularMatrix| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecurrenceOperator| |RecursivePolynomialCategory&| |ReduceLODE| |ReductionOfOrder| |RegularTriangularSet| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RightOpenIntervalRootCharacterization| |Ring&| |RomanNumeral| |RootsFindingPackage| |RoutinesTable| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentFunctions2| |SequentialDifferentialPolynomial| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SortPackage| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SplittingTree| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stream| |StreamAggregate&| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |String| |StringAggregate&| |StructuralConstantsPackage| |SturmHabichtPackage| |SubSpace| |Symbol| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Tableau| |TableauxBumpers| |TangentExpansions| |TaylorSeries| |TaylorSolve| |TemplateUtilities| |TexFormat| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ToolsForSign| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TransSolvePackage| |TransSolvePackageService| |TranscendentalFunctionCategory&| |TranscendentalIntegration| |TranscendentalManipulations| |TranscendentalRischDE| |TranscendentalRischDESystem| |Tree| |TriangularMatrixOperations| |TriangularSetCategory&| |TrigonometricManipulations| |TubePlotTools| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UTSodetools| |UnaryRecursiveAggregate&| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |Vector| |VectorCategory&| |ViewDefaultsPackage| |ViewportPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|RandomIntegerDistributions|) +(|ComplexRootFindingPackage| |GaloisGroupUtilities| |Guess| |IntegerNumberSystem&| |IrrRepSymNatPackage| |MultivariateLifting| |RepresentationPackage1| |SetOfMIntegersInOneToN| |SymmetricGroupCombinatoricFunctions|) +(|CyclotomicPolynomialPackage| |Factored| |GaussianFactorizationPackage| |IntegerNumberSystem&| |NumberFieldIntegralBasis|) +(|ElementaryFunctionStructurePackage|) +(|InnerPrimeField|) +(|CycleIndicators| |FiniteFieldPolynomialPackage| |PolynomialNumberTheoryFunctions|) +(|ComplexIntegerSolveLinearPolynomialEquation| |GaloisGroupFactorizer| |GaussianFactorizationPackage| |HeuGcd| |InnerMultFact| |IntegerFactorizationPackage| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |MultivariateSquareFree| |PointsOfFiniteOrder| |PointsOfFiniteOrderTools| |PolynomialGcdPackage| |PolynomialNumberTheoryFunctions| |PrimeField| |UnivariateFactorize|) +(|DoubleFloatSpecialFunctions|) +(|ComplexRootFindingPackage| |Float| |GaloisGroupFactorizer| |GenExEuclid| |IntegerFactorizationPackage| |IntegerPrimesPackage| |PatternMatchIntegerNumberSystem| |UnivariateFactorize|) +(|Integer|) +(|PAdicWildFunctionFieldIntegralBasis|) +(|FunctionFieldIntegralBasis| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |WildFunctionFieldIntegralBasis|) +(|AnnaNumericalIntegrationPackage| |d01AgentsPackage|) +(|AlgebraicIntegrate| |AlgebraicIntegration| |ElementaryIntegration| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenusZeroIntegration| |IntegrationResultFunctions2| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |PureAlgebraicIntegration| |RationalFunctionIntegration| |RationalIntegration| |TranscendentalIntegration|) +(|ElementaryIntegration| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenusZeroIntegration| |IntegrationResultRFToFunction| |PureAlgebraicIntegration| |RationalFunctionIntegration|) +(|RationalFunctionDefiniteIntegration|) +(|FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultRFToFunction|) +(|ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultRFToFunction| |LaplaceTransform| |PureAlgebraicIntegration|) +(|AffineAlgebraicSetComputeWithGroebnerBasis|) +(|RegularSetDecompositionPackage| |SquareFreeRegularSetDecompositionPackage| |TabulatedComputationPackage|) +(|RationalUnivariateRepresentationPackage| |ZeroDimensionalSolvePackage|) +(|GeneralPackageForAlgebraicFunctionField|) +(|GeneralPackageForAlgebraicFunctionField|) +(|ElementaryFunctionSign| |TransSolvePackage|) +(|PAdicWildFunctionFieldIntegralBasis|) +(|AlgFactor| |AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedFunctionSpace&| |ApplyRules| |CombinatorialFunction| |ComplexTrigonometricManipulations| |DefiniteIntegrationTools| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |ExpressionFunctions2| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |FortranExpression| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceFunctions2| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenusZeroIntegration| |Guess| |InnerAlgebraicNumber| 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|LinearOrdinaryDifferentialOperator2| |LiouvillianFunction| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |MathMLFormat| |Matrix| |MatrixCategory&| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |Multiset| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonAssociativeRing&| |NonNegativeInteger| |None| |NormalizationPackage| |NottinghamGroup| |NumberFormats| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalOrdinaryDifferentialEquations| |NumericalPDEProblem| |NumericalQuadrature| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |OpenMathEncoding| |OpenMathError| 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|SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeRegularTriangularSet| |SquareMatrix| |SquareMatrixCategory&| |Stack| |Stream| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |String| |StringAggregate&| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Switch| |Symbol| |SymbolTable| |SymmetricPolynomial| |Table| |TableAggregate&| |Tableau| |TabulatedComputationPackage| |TaylorSeries| |TaylorSolve| |TexFormat| |TexFormat1| |TextFile| |TheSymbolTable| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctionsForCompiledFunctions| |Tree| |TriangularSetCategory&| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalViewport| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UniversalSegment| |Variable| |Vector| |Void| |WeightedPolynomials| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |d03fafAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|GenUFactorize| |Guess| |IndexCard| |InternalRationalUnivariateRepresentationPackage| |NormalizationPackage| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |RationalInterpolation| |RationalUnivariateRepresentationPackage| |SparseUnivariatePolynomialExpressions| |TabulatedComputationPackage| |TaylorSolve| |ZeroDimensionalSolvePackage|) +(|PAdicRational|) +(|BalancedPAdicRational| |PAdicRational|) +(|BlowUpPackage| |DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |NewtonPolygon| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PolynomialPackageForCurve|) +(|DrawOption| |DrawOptionFunctions0| |GraphImage| |TopLevelDrawFunctionsForAlgebraicCurves| 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|PatternMatchResult| |PatternMatchSymbol| |PatternMatchTools| |Polynomial| |PolynomialCategory&| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RecursivePolynomialCategory&| |RewriteRule| |RomanNumeral| |SequentialDifferentialPolynomial| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |Symbol| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial|) +(|ApplyRules| |PatternMatchResult| |PatternMatchTools| |RewriteRule|) +(|Expression|) +(|IntegerNumberSystem&|) +(|ElementaryFunctionDefiniteIntegration| |ElementaryIntegration| |FunctionSpaceComplexIntegration| |LaplaceTransform|) +(|Expression| |PatternMatchFunctionSpace|) +(|PatternMatch|) +(|PatternMatch| |PatternMatchListAggregate|) +(|Expression| |PolynomialCategory&|) +(|ComplexPatternMatch| |PatternMatchFunctionSpace| |PatternMatchPolynomialCategory| |PatternMatchQuotientFieldCategory|) 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|PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |Polynomial| |PolynomialCategory&| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RomanNumeral| |SequentialDifferentialPolynomial| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |Symbol| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial|) +(|ComplexPatternMatch| |PatternMatchPushDown|) +(|Symbol|) +(|PatternMatchFunctionSpace| |PatternMatchPolynomialCategory|) +(|IrrRepSymNatPackage| |PermutationGroup| |PermutationGroupExamples| |RepresentationPackage1|) +(|PermutationGroupExamples|) +(|FortranExpression| |PiCoercions|) +(|FortranExpression|) +(|PackageForAlgebraicFunctionField|) +(|PackageForAlgebraicFunctionFieldOverFiniteField|) +(|TopLevelDrawFunctionsForAlgebraicCurves|) +(|Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField|) +(|GraphicsDefaults| 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|MyExpression| |MyUnivariatePolynomial| |NewSparseMultivariatePolynomial| |NonLinearSolvePackage| |Numeric| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrdinaryWeightedPolynomials| |ParametricLinearEquations| |PartialFractionPackage| |PatternMatch| |Pi| |PlaneAlgebraicCurvePlot| |PolToPol| |PolynomialAN2Expression| |PolynomialFunctions2| |PolynomialIdeals| |PolynomialToUnivariatePolynomial| |PrimitiveElement| |PushVariables| |RadicalEigenPackage| |RadicalSolvePackage| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalInterpolation| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealSolvePackage| |RecursivePolynomialCategory&| |RepresentationPackage1| |RetractSolvePackage| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariateTaylorSeries| |StructuralConstantsPackage| |SymbolTable| |SystemSolvePackage| |TaylorSeries| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |UnivariateFormalPowerSeries| |UnivariateLaurentSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |WeierstrassPreparation| |ZeroDimensionalSolvePackage| |e04AgentsPackage| |e04mbfAnnaType| |e04nafAnnaType|) +(|CombinatorialFunction| |DifferentialSparseMultivariatePolynomial| |ElementaryFunctionStructurePackage| |Expression| |ExpressionSpaceODESolver| |FunctionSpace&| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GosperSummationMethod| |Guess| |InnerTrigonometricManipulations| |MRationalFactorize| |ParametricLinearEquations| |PolynomialAN2Expression| |PolynomialCategory&| |PolynomialFunctions2| |QuasiAlgebraicSet2| |RationalFunction| |RealSolvePackage| |TransSolvePackage| 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|MultFiniteFactorize| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NagEigenPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonAssociativeAlgebra&| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NottinghamGroup| |NumberFieldIntegralBasis| |NumberFormats| |Numeric| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |Octonion| |OctonionCategory&| |OnePointCompletion| |Operator| |OppositeMonogenicLinearOperator| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |ParametricLinearEquations| |PartialFraction| |Partition| |PatternMatchIntegration| |Permanent| |Permutation| |PermutationGroupExamples| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialSolveByFormulas| |PositiveInteger| |PowerSeriesCategory&| |PrecomputedAssociatedEquations| |PrimeField| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoRemainderSequence| |PureAlgebraicIntegration| |QuadraticForm| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomFloatDistributions| |RandomIntegerDistributions| |RandomNumberSource| |RealClosedField&| |RealClosure| |RealRootCharacterizationCategory&| |RealZeroPackage| |RectangularMatrix| |RecursivePolynomialCategory&| |ReduceLODE| |RegularTriangularSetCategory&| |RepeatedDoubling| |RepeatedSquaring| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |Ruleset| |SemiGroup&| |SequentialDifferentialPolynomial| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StreamTranscendentalFunctions| |SturmHabichtPackage| |SubSpace| |SymmetricFunctions| |SymmetricPolynomial| |TangentExpansions| |TaylorSeries| |TaylorSolve| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TranscendentalFunctionCategory&| |TranscendentalIntegration| |TranscendentalManipulations| |TubePlotTools| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialMultiplicationPackage| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |ViewDefaultsPackage| |ViewportPackage| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|DefiniteIntegrationTools| |ElementaryFunctionSign| |LaplaceTransform| |d01AgentsPackage|) +(|AssociatedEquations|) +(|FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldNormalBasis| |InterfaceGroebnerPackage|) +(|BlasLevelOne| |Character| |DistinctDegreeFactorize| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |IndexedFlexibleArray| |InnerIndexedTwoDimensionalArray| |InnerNumericFloatSolvePackage| |LinearSystemMatrixPackage| |MatrixLinearAlgebraFunctions| |ModMonic| |NumberFormats| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |RadicalFunctionField| |ReductionOfOrder| |StorageEfficientMatrixOperations| |SubResultantPackage| |Symbol| |ThreeDimensionalMatrix| |TranscendentalIntegration| |Tuple|) +(|FunctionSpacePrimitiveElement|) +(|PrimitiveRatRicDE| |RationalLODE| |RationalRicDE|) +(|RationalRicDE|) +(|NAGLinkSupportPackage|) +(|PolynomialIdeals| |QuasiAlgebraicSet|) +(|DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |IntersectionDivisorPackage|) +(|InfClsPt| |PackageForAlgebraicFunctionField| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField|) +(|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| 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|PAdicRationalConstructor| |PseudoAlgebraicClosureOfFiniteField| |SemiGroup&| |SparseUnivariatePolynomial|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |ExpertSystemToolsPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |RoutinesTable| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |d03fafAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|NonLinearSolvePackage|) +(|ApplyRules| |TranscendentalManipulations|) +(|RealClosure|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |BlowUpPackage| |ProjectiveAlgebraicSetPackage|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AttributeButtons| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |d03fafAnnaType| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|Any| |AnyFunctions1| |ApplicationProgramInterface| |AxiomServer| |FortranCode| |FortranPackage| |FortranProgram| |FortranScalarType| |InputForm| |NAGLinkSupportPackage| |NumberFormats| |OpenMathPackage| |Result| |SymbolTable|) +(|SExpression|) +(|ScriptFormulaFormat1|) +(|AnnaNumericalIntegrationPackage| |Asp19| |Asp8| |CombinatorialFunction| |DrawComplex| |ElementaryFunctionDefiniteIntegration| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExpressionTubePlot| |FortranCode| |FortranCodePackage1| |FunctionSpaceSum| |GraphImage| |Guess| |InnerPolySum| |LiouvillianFunction| |MeshCreationRoutinesForThreeDimensions| |ParametricLinearEquations| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotFunctions1| |PlotTools| |RandomIntegerDistributions| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SegmentBinding| |SegmentBindingFunctions2| |SegmentFunctions2| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TwoDimensionalPlotClipping| |UniversalSegment| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d03AgentsPackage| |e04AgentsPackage| |e04gcfAnnaType|) +(|AnnaNumericalIntegrationPackage| |Asp19| |Asp8| |CombinatorialFunction| |DrawNumericHack| |ElementaryFunctionDefiniteIntegration| |Expression| |FortranCode| |FortranCodePackage1| |FunctionSpaceSum| |Guess| |LiouvillianFunction| |MyExpression| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SegmentBindingFunctions2| |TopLevelDrawFunctions|) +(|DrawNumericHack| |RationalFunctionSum|) +(|SegmentBindingFunctions2| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) +(|SequentialDifferentialPolynomial|) +(|ApplicationProgramInterface| |BasicOperator| |ExpressionSpace&| |Factored| |GaloisGroupFactorizer| |GeneralPolynomialSet| |IntegerPrimesPackage| |ModularHermitianRowReduction| |MonoidRing| |ParametricLinearEquations| |Pattern| |Permutation| |PermutationGroup| |PolynomialSetCategory&| |QuasiAlgebraicSet| |RandomDistributions| |SymmetricGroupCombinatoricFunctions| |ThreeDimensionalViewport| |ThreeSpace|) +(|AlgebraicFunctionField| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtensionByPolynomial| |RadicalFunctionField|) +(|AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgebraGivenByStructuralConstants| |AlgebraicFunctionField| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BinaryExpansion| |BinaryFile| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlasLevelOne| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |Commutator| |Complex| |ComplexRootFindingPackage| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DrawOption| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionSign| |EqTable| |Equation| |EuclideanModularRing| |Exit| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExtAlgBasis| |Factored| |File| |FileName| |FiniteDivisor| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FlexibleArray| |Float| |FortranCode| |FortranExpression| |FortranProgram| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionalIdeal| |FramedModule| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionCalled| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GraphImage| |GuessOption| |GuessOptionFunctions0| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerNormalBasisFieldFunctions| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InputForm| |Integer| |IntegerMod| |IntegrationResult| |Interval| |Kernel| |KeyedAccessFile| |LaurentPolynomial| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |MathMLFormat| |Matrix| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |Multiset| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonNegativeInteger| |None| |NottinghamGroup| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalPDEProblem| |NumericalQuadrature| |Octonion| |OneDimensionalArray| |OnePointCompletion| |OpenMathConnection| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OpenMathServerPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedCompletionFunctions2| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |PartialFraction| |Partition| |Pattern| |PatternMatchIntegration| |PatternMatchListResult| |PatternMatchResult| |PendantTree| |Permutation| |PermutationGroup| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |Plcs| |PoincareBirkhoffWittLyndonBasis| |Point| |Polynomial| |PolynomialIdeals| |PolynomialRing| |PositiveInteger| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveArray| |Product| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |QuadraticForm| |QuasiAlgebraicSet| |Quaternion| |Queue| |RadicalFunctionField| |RadixExpansion| |RandomDistributions| |RationalFunctionLimitPackage| |RationalFunctionSign| |RealClosure| |RectangularMatrix| |Reference| |RegularChain| |RegularTriangularSet| |ResidueRing| |Result| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentBinding| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetCategory&| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeRegularTriangularSet| |SquareMatrix| |Stack| |Stream| |String| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Symbol| |SymmetricPolynomial| |Table| |TaylorSeries| |TexFormat| |TextFile| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |Tree| |Tuple| |TwoDimensionalArray| |TwoDimensionalViewport| |UTSodetools| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UniversalSegment| |Variable| |Vector| |WeightedPolynomials| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |d03fafAnnaType| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) 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|ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |Expression| |ExpressionSpaceODESolver| |FunctionSpace&| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GosperSummationMethod| |Guess| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |LaplaceTransform| |MRationalFactorize| |MultFiniteFactorize| |MultivariatePolynomial| |MyExpression| |NewSparseMultivariatePolynomial| |NonLinearFirstOrderODESolver| |ODEIntegration| |OrderlyDifferentialPolynomial| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PointsOfFiniteOrder| |Polynomial| |PureAlgebraicIntegration| |RecurrenceOperator| |SequentialDifferentialPolynomial| |TransSolvePackage| |TranscendentalManipulations|) +(|TaylorSeries|) +(|SparseUnivariatePuiseuxSeries|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryExpansion| |BlowUpPackage| |BoundIntegerRoots| |CharacteristicPolynomialInMonogenicalAlgebra| |ChineseRemainderToolsForIntegralBases| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPatternMatch| |ComplexRootPackage| |ConstantLODE| |ContinuedFraction| |CyclotomicPolynomialPackage| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |DoubleResultantPackage| |EigenPackage| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |EuclideanModularRing| |ExpertSystemContinuityPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpaceODESolver| |FGLMIfCanPackage| |Factored| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteRankNonAssociativeAlgebra&| |Float| |FloatingComplexPackage| |FortranExpression| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedNonAssociativeAlgebra&| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GcdDomain&| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GroebnerSolve| |Guess| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| 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|ModularField| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NPCoef| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewtonInterpolation| |NonLinearFirstOrderODESolver| |NonLinearSolvePackage| |NormInMonogenicAlgebra| |NormRetractPackage| |NumberTheoreticPolynomialFunctions| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |PartialFraction| |PartialFractionPackage| |PatternMatchIntegration| |Pi| |PiCoercions| |PlaneAlgebraicCurvePlot| |PointsOfFiniteOrder| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| 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|DesingTree| |DictionaryOperations&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DrawComplex| |DrawOption| |DrawOptionFunctions0| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |EqTable| |Equation| |ErrorFunctions| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |Exit| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionTubePlot| |ExtAlgBasis| |Factored| |File| |FileName| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteRankNonAssociativeAlgebra&| |FlexibleArray| |Float| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranOutputStackPackage| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionCalled| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |Guess| |GuessOption| |GuessOptionFunctions0| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |Integer| |IntegerMod| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalPrintPackage| |InternalRationalUnivariateRepresentationPackage| |Interval| |Kernel| |KeyedAccessFile| |LaplaceTransform| |LaurentPolynomial| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LiouvillianFunction| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |MakeFloatCompiledFunction| |MathMLFormat| |Matrix| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |MoreSystemCommands| |Multiset| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonNegativeInteger| |None| |NormalizationPackage| |NottinghamGroup| |NumberFormats| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| 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|PlaneAlgebraicCurvePlot| |Plcs| |PoincareBirkhoffWittLyndonBasis| |Point| |PointsOfFiniteOrder| |Polynomial| |PolynomialIdeals| |PolynomialRing| |PositiveInteger| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveArray| |Product| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PureAlgebraicIntegration| |QuadraticForm| |QuasiAlgebraicSet| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |QueryEquation| |Queue| |RadicalFunctionField| |RadixExpansion| |RationalFunctionDefiniteIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalUnivariateRepresentationPackage| |RealClosure| |RectangularMatrix| |RecurrenceOperator| |RecursivePolynomialCategory&| |Reference| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetGcdPackage| |RepresentationPackage2| |ResidueRing| |Result| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentBinding| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetCategory&| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |Stack| |Stream| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |String| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Switch| |Symbol| |SymbolTable| |SymmetricPolynomial| |Table| |Tableau| |TabulatedComputationPackage| |TaylorSeries| |TemplateUtilities| |TexFormat| |TextFile| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |ToolsForSign| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TranscendentalManipulations| |Tree| |TrigonometricManipulations| |Tuple| |TwoDimensionalArray| |TwoDimensionalViewport| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UniversalSegment| |Variable| |Vector| |ViewDefaultsPackage| |ViewportPackage| |WeightedPolynomials| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |d03fafAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|InnerNumericFloatSolvePackage| |TranscendentalIntegration|) +(|ThreeSpace|) +(|MeshCreationRoutinesForThreeDimensions| |SubSpace| |ThreeDimensionalViewport| |ThreeSpace|) +(|EigenPackage| |PolynomialIdeals| |RadicalEigenPackage| |RadicalSolvePackage|) +(|Expression|) +(|Asp12| |Asp30| |Asp35| |Asp55| |Asp74| |Asp8| |FortranCode|) 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|ConstantLODE| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DesingTreePackage| |DifferentialExtension&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DrawOption| |DrawOptionFunctions0| |DrawOptionFunctions1| |EigenPackage| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |Equation| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |FGLMIfCanPackage| |Factored| |FiniteFieldCyclicGroupExtensionByPolynomial| 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