diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index efb09f8..7a26d5b 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -7769,7 +7769,8 @@ digraph pic { --R cot : % -> % coth : % -> % --R csc : % -> % csch : % -> % --R dilog : % -> % erf : % -> % ---R exp : % -> % integral : (%,Symbol) -> % +--R exp : % -> % fresnelC : % -> % +--R fresnelS : % -> % integral : (%,Symbol) -> % --R li : % -> % log : % -> % --R pi : () -> % sec : % -> % --R sech : % -> % sin : % -> % @@ -7823,17 +7824,19 @@ o )show LiouvillianFunctionCategory \cross{LFCAT}{dilog} & \cross{LFCAT}{erf} & \cross{LFCAT}{exp} & -\cross{LFCAT}{integral} \\ +\cross{LFCAT}{frsenelC} \\ +\cross{LFCAT}{frsenelS} & +\cross{LFCAT}{integral} & \cross{LFCAT}{li} & \cross{LFCAT}{log} & -\cross{LFCAT}{pi} & +\cross{LFCAT}{pi} \\ \cross{LFCAT}{sec} & -\cross{LFCAT}{sech} \\ +\cross{LFCAT}{sech} & \cross{LFCAT}{sin} & \cross{LFCAT}{sinh} & -\cross{LFCAT}{tan} & +\cross{LFCAT}{tan} \\ \cross{LFCAT}{tanh} & -\cross{LFCAT}{?**?} \\ +\cross{LFCAT}{?**?} &&& \end{tabular} These are directly exported but not implemented: @@ -7844,6 +7847,8 @@ These are directly exported but not implemented: erf : % -> % li : % -> % Si : % -> % + fresnelC : % -> % + fresnelS : % -> % \end{verbatim} These exports come from \refto{PrimitiveFunctionCategory}() @@ -7913,6 +7918,12 @@ LiouvillianFunctionCategory(): Category == erf : $ -> $ ++ erf(x) returns the error function of x, i.e. ++ \spad{2 / sqrt(%pi)} times the integral of \spad{exp(-x**2) dx}. + fresnelS : $ -> $ + ++ fresnelS is the Fresnel integral S, defined by + ++ S(x) = integrate(sin(t^2),t=0..x) + fresnelC : $ -> $ + ++ fresnelC is the Fresnel integral C, defined by + ++ C(x) = integrate(cos(t^2),t=0..x) @ <>= diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index d31717e..11803bb 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -33787,6 +33787,8 @@ Expression(R:OrderedSet): Exports == Implementation where Ci x == Ci(x)$LF li x == li(x)$LF dilog x == dilog(x)$LF + fresnelS x == fresnelS(x)$LF + fresnelC x == fresnelC(x)$LF integral(x:%, n:Symbol) == integral(x, n)$LF integral(x:%, s:SegmentBinding %) == integral(x, s)$LF diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index d40a654..850d053 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -7983,6 +7983,8 @@ CommonOperators(): Exports == Implementation where opli := operator("li"::Symbol, 1) operf := operator("erf"::Symbol, 1) opli2 := operator("dilog"::Symbol, 1) + opfis := operator("fresnelS"::Symbol, 1) + opfic := operator("fresnelC"::Symbol, 1) opGamma := operator("Gamma"::Symbol, 1) opGamma2 := operator("Gamma2"::Symbol, 2) opBeta := operator("Beta"::Symbol, 2) @@ -8012,7 +8014,8 @@ CommonOperators(): Exports == Implementation where opasinh, opacosh, opatanh, opacoth, opasech, opacsch] trigop := concat(rtrigop, htrigop) elemop := concat(trigop, [oppi, oplog, opexp]) - primop := [opei, opli, opsi, opci, operf, opli2, opint, opdint] + primop := [opei, opli, opsi, opci, operf, opli2, opint, opdint, + opfis, opfic] combop := [opfact, opperm, opbinom, oppow, opsum, opdsum, opprod, opdprod] specop := [opGamma, opGamma2, opBeta, opdigamma, oppolygamma, opabs, @@ -58711,6 +58714,10 @@ LiouvillianFunction(R, F): Exports == Implementation where ++ erf(f) denotes the error function dilog : F -> F ++ dilog(f) denotes the dilogarithm + fresnelS : F -> F + ++ fresnelS(f) denotes the Fresnel integral S + fresnelC : F -> F + ++ fresnelC(f) denotes the Fresnel integral C integral: (F, SE) -> F ++ integral(f,x) indefinite integral of f with respect to x. integral: (F, SegmentBinding F) -> F @@ -58741,6 +58748,8 @@ LiouvillianFunction(R, F): Exports == Implementation where opci := operator("Ci"::Symbol)$CommonOperators opli2 := operator("dilog"::Symbol)$CommonOperators operf := operator("erf"::Symbol)$CommonOperators + opfis := operator("fresnelS"::Symbol)$CommonOperators + opfic := operator("fresnelC"::Symbol)$CommonOperators Si x == opsi x Ci x == opci x @@ -58748,6 +58757,8 @@ LiouvillianFunction(R, F): Exports == Implementation where erf x == operf x li x == opli x dilog x == opli2 x + fresnelS x == opfis x + fresnelC x == opfic x belong? op == has?(op, "prim") isi x == kernel(opsi, x) @@ -58755,6 +58766,8 @@ LiouvillianFunction(R, F): Exports == Implementation where ierf x == (zero? x => 0; kernel(operf, x)) -- ili2 x == (one? x => INV; kernel(opli2, x)) ili2 x == ((x = 1) => INV; kernel(opli2, x)) + ifis(x:F):F == (zero? x => 0; kernel(opfis,x)) + ific(x:F):F == (zero? x => 0; kernel(opfic,x)) integrand l == eval(first l, retract(second l)@K, third l) integral(f:F, x:SE) == opint [eval(f, k:=kernel(x)$K, dummy), dummy, k::F] @@ -58811,6 +58824,8 @@ LiouvillianFunction(R, F): Exports == Implementation where is?(op, "li"::Symbol) => opli is?(op, "erf"::Symbol) => operf is?(op, "dilog"::Symbol) => opli2 + is?(op, "fresnelC"::Symbol) => opfis + is?(op, "fresnelS"::Symbol) => opfic error "Not a Liouvillian operator" evaluate(opei, iei)$BasicOperatorFunctions1(F) @@ -58819,6 +58834,8 @@ LiouvillianFunction(R, F): Exports == Implementation where evaluate(opci, ici) evaluate(operf, ierf) evaluate(opli2, ili2) + evaluate(opfis, ifis) + evaluate(opfic, ific) evaluate(opint, iint) derivative(opsi, (z1:F):F +-> sin(z1) / z1) derivative(opci, (z1:F):F +-> cos(z1) / z1) @@ -58826,6 +58843,8 @@ LiouvillianFunction(R, F): Exports == Implementation where derivative(opli, (z1:F):F +-> inv log(z1)) derivative(operf, (z1:F):F +-> 2 * exp(-(z1**2)) / sqrt(pi())) derivative(opli2, (z1:F):F +-> log(z1) / (1 - z1)) + derivative(opfis, (z1:F):F +-> sin(z1**2)) + derivative(opfic, (z1:F):F +-> cos(z1**2)) setProperty(opint,SPECIALEQUAL,eqint@((K,K) -> Boolean) pretend None) setProperty(opint,SPECIALDIFF,dvint@((List F,SE) -> F) pretend None) setProperty(opdint,SPECIALDIFF,dvdint@((List F,SE)->F) pretend None) @@ -132084,7 +132103,9 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where is?(ker,"acsc" :: Symbol) => true is?(ker,"acsch" :: Symbol) => true is?(ker,"acoth" :: Symbol) => true - false + is?(ker,"fresnelS" :: Symbol) => true + is?(ker,"fresnelC" :: Symbol) => true + error "finiteValueAtInfinity? true, but unknown value at infinity" knownValueAtInfinity?: Kernel FE -> Boolean knownValueAtInfinity? ker == @@ -132214,6 +132235,9 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where is?(ker,"asec" :: Symbol) => pi()/(2 :: FE) is?(ker,"acsc" :: Symbol) => 0 is?(ker,"acsch" :: Symbol) => 0 + is?(ker,"fresnelS" :: Symbol) => -sqrt(pi()/(8::FE)) + is?(ker,"fresnelC" :: Symbol) => -sqrt(pi()/(8::FE)) + error "finiteValueAtInfinity? true, but unknown value at infinity" -- ker must be acoth 0 val :: OFE diff --git a/changelog b/changelog index bae62de..4c30807 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,15 @@ +20100713 wxh src/axiom-website/patches.html 20100713.01.wxh.patch +20100713 wxh src/share/algebra/users.daase/index.kaf update for fresnel +20100713 wxh src/share/algebra/operation.daase update for fresnel +20100713 wxh src/share/algebra/interp.daase update for fresnel +20100713 wxh src/share/algebra/dependents.daase/index.kaf update for fresnel +20100713 wxh src/share/algebra/compress.daase update for fresel +20100713 wxh src/share/algebra/category.daase update for fresnel +20100713 wxh src/share/algebra/browse.daase update for fresnel +20100713 wxh src/algebra/Makefile add ignore for EXPR compile +20100713 wxh books/bookvol10.4 add fresnelS, fresnelC to LF, COMMONOP, LIMITPS +20100713 wxh books/bookvol10.3 add fresnelS, fresnelC to EXPR +20100713 wxh books/bookvol10.2 add fresnelS, fresnelC to LFCAT 20100712 tpd src/axiom-website/patches.html 20100712.02.tpd.patch 20100712 tpd src/input/Makefile add derivefail.input 20100712 tpd src/input/derivefail.input failing integrals from derive 6.10 diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 0f325cf..04407cf 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -15290,7 +15290,7 @@ LAYER18=\ /*"EXPR" -> {"PI"; "VECTOR"; "IVECTOR"; "IARRAY1"; "VECTCAT-"; "QFCAT"}*/ /*"EXPR" -> {"FEVALAB"; "DIFEXT"; "DIFRING"; "STEP"; "OINTDOM"; "ORDRING"}*/ /*"EXPR" -> {"OAGROUP"; "OCAMON"; "OAMON"; "OASGP"; "REAL"; "UPOLYC"}*/ -/*"EXPR" -> {"INS"; "FPS"; "RNS"}*/ +/*"EXPR" -> {"INS"; "FPS"; "RNS"; "LF"}*/ "EXPRSOL" [color="#FF4488",href="bookvol10.4.pdf#nameddest=EXPRSOL"] "EXPRSOL" -> "UTSSOL" /* by loadlib */ @@ -16571,6 +16571,16 @@ ${MID}/clique2.spad: ${CLIQUE2FILES} @ cp ${MID}/PAFFFF.nrlib/code.o ${OUT}/PAFFFF.o @ +<>= +EXPRDEPS = LF + +${MID}/EXPR.nrlib/code.o: ${MID}/EXPR.spad + @echo 1 newcode EXPR.o depends on LF.o + @ ( cd ${MID} ; \ + echo -e ")lib ${EXPRDEPS} \n )co EXPR.spad" | ${INTERPSYS} ) + @ cp ${MID}/EXPR.nrlib/code.o ${OUT}/EXPR.o + +@ \section{Broken Files} These files are Aldor files \begin{verbatim} diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 1a47357..def7cc5 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2992,5 +2992,7 @@ books/bookvol4 document the Makefile build process
src/axiom-website/index.html fix CATS href in sidebar
20100712.02.tpd.patch src/input/derivefail.input failing integrals from derive 6.10
+20100713.01.wxh.patch +books/bookvol10.* add fresnelS, fresnelC to LF, COMMONOP, LIMITPS, EXPR
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 77e2634..3983e54 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2465038 . 3487447480) +(2465526 . 3488060042) (-18 A S) ((|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) ((|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."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-20 S) ((|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}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|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)"))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . 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 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}."))) @@ -46,7 +46,7 @@ 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 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4516 . T) (-4514 . T) (-4513 . T) ((-4521 "*") . T) (-4512 . T) (-4517 . T) (-4511 . T) (-3973 . T)) +((-4518 . T) (-4516 . T) (-4515 . T) ((-4523 "*") . T) (-4514 . T) (-4519 . T) (-4513 . T) (-3973 . T)) NIL (-30) ((|constructor| (NIL "Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.")) (|refine| (($ $ (|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"))) @@ -68,7 +68,7 @@ NIL ((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) NIL NIL -(-35 -2570 K) +(-35 -1965 K) ((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) NIL NIL @@ -83,7 +83,7 @@ NIL (-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 -((|HasAttribute| |#1| (QUOTE -4519))) +((|HasAttribute| |#1| (QUOTE -4521))) (-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."))) ((-3973 . T)) @@ -94,7 +94,7 @@ NIL NIL (-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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-42 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{(b+c)::\\% = (b::\\%) + (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(b*c)::\\% = (b::\\%) * (c::\\%)}\\spad{\\br} \\tab{5}\\spad{(1::R)::\\% = 1::\\%}\\spad{\\br} \\tab{5}\\spad{b*x = (b::\\%)*x}\\spad{\\br} \\tab{5}\\spad{r*(a*b) = (r*a)*b = a*(r*b)}")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -102,16 +102,16 @@ NIL NIL (-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."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-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 -(-45 -1478 UP UPUP -3094) +(-45 -1478 UP UPUP -2477) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} is not documented"))) -((-4512 |has| (-409 |#2|) (-365)) (-4517 |has| (-409 |#2|) (-365)) (-4511 |has| (-409 |#2|) (-365)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-148))) (|HasCategory| (-409 |#2|) (QUOTE (-150))) (|HasCategory| (-409 |#2|) (QUOTE (-350))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (-2198 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-350)))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2198 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2198 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2198 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) +((-4514 |has| (-409 |#2|) (-365)) (-4519 |has| (-409 |#2|) (-365)) (-4513 |has| (-409 |#2|) (-365)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-409 |#2|) (QUOTE (-148))) (|HasCategory| (-409 |#2|) (QUOTE (-150))) (|HasCategory| (-409 |#2|) (QUOTE (-350))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (-2199 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-350)))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2199 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2199 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2199 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-46 R -1478) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL @@ -126,23 +126,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-301)))) (-49 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4516 |has| |#1| (-558)) (-4514 . T) (-4513 . T)) +((-4518 |has| |#1| (-558)) (-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-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."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-842)))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-842)))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))))) (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (-52 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-53) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1037) (QUOTE (-568))))) (-54) ((|constructor| (NIL "This domain implements anonymous functions"))) @@ -150,7 +150,7 @@ NIL NIL (-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| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4516 . T)) +((-4518 . T)) NIL (-56 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -178,7 +178,7 @@ NIL NIL (-62 R |Row| |Col|) ((|constructor| (NIL "Two dimensional array categories and domains")) (|map!| (($ (|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"))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-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}"))) @@ -186,65 +186,65 @@ NIL NIL (-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]"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-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}."))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) -(-66 -3391) +(-66 -3393) ((|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 -(-67 -3391) +(-67 -3393) ((|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 -(-68 -3391) +(-68 -3393) ((|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 -(-69 -3391) +(-69 -3393) ((|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 -(-70 -3391) +(-70 -3393) ((|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 -(-71 -3391) +(-71 -3393) ((|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 -(-72 -3391) +(-72 -3393) ((|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 -(-73 -3391) +(-73 -3393) ((|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 -(-74 -3391) +(-74 -3393) ((|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 -(-75 -3391) +(-75 -3393) ((|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 -(-76 -3391) +(-76 -3393) ((|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 -(-77 -3391) +(-77 -3393) ((|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 -(-78 -3391) +(-78 -3393) ((|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 -(-79 -3391) +(-79 -3393) ((|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 @@ -256,55 +256,55 @@ NIL ((|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 -(-82 -3391) +(-82 -3393) ((|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 -(-83 -3391) +(-83 -3393) ((|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 -(-84 -3391) +(-84 -3393) ((|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 -(-85 -3391) +(-85 -3393) ((|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 -(-86 -3391) +(-86 -3393) ((|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 -(-87 -3391) +(-87 -3393) ((|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 -(-88 -3391) +(-88 -3393) ((|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 -(-89 -3391) +(-89 -3393) ((|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 -(-90 -3391) +(-90 -3393) ((|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 -(-91 -3391) +(-91 -3393) ((|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 -(-92 -3391) +(-92 -3393) ((|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 -(-93 -3391) +(-93 -3393) ((|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 -(-94 -3391) +(-94 -3393) ((|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 @@ -314,7 +314,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-365)))) (-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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-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}."))) @@ -326,15 +326,15 @@ NIL NIL (-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\"."))) -((-4519 . T)) +((-4521 . T)) NIL (-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."))) -((-4519 . T) ((-4521 "*") . T) (-4520 . T) (-4516 . T) (-4514 . T) (-4513 . T) (-4512 . T) (-4517 . T) (-4511 . T) (-4510 . T) (-4509 . T) (-4508 . T) (-4507 . T) (-4515 . T) (-4518 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4506 . T) (-3996 . T)) +((-4521 . T) ((-4523 "*") . T) (-4522 . T) (-4518 . T) (-4516 . T) (-4515 . T) (-4514 . T) (-4519 . T) (-4513 . T) (-4512 . T) (-4511 . T) (-4510 . T) (-4509 . T) (-4517 . T) (-4520 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4508 . T) (-3999 . T)) NIL (-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}."))) -((-4516 . T)) +((-4518 . T)) NIL (-102) ((|constructor| (NIL "This package provides a functions to support a web server for the new Axiom Browser functions."))) @@ -354,7 +354,7 @@ NIL NIL (-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)"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-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]"))) @@ -363,10 +363,10 @@ 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 (-4521 "*")))) +((|HasAttribute| |#1| (QUOTE (-4523 "*")))) (-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"))) -((-4519 . T)) +((-4521 . T)) NIL (-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."))) @@ -374,19 +374,19 @@ NIL NIL (-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."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2198 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2199 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) (-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") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL (-114) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| (-121) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-121) (QUOTE (-842))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-121) (QUOTE (-1090))) (-12 (|HasCategory| (-121) (LIST (QUOTE -303) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1090))))) (-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})"))) @@ -410,7 +410,7 @@ 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}"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . 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."))) @@ -430,16 +430,16 @@ NIL NIL (-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}."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-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}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-125 |#1|) (QUOTE (-904))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-125 |#1|) (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-150))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-125 |#1|) (QUOTE (-1021))) (|HasCategory| (-125 |#1|) (QUOTE (-815))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (QUOTE (-1136))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (QUOTE (-225))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -125) (|devaluate| |#1|)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (QUOTE (-301))) (|HasCategory| (-125 |#1|) (QUOTE (-550))) (|HasCategory| (-125 |#1|) (QUOTE (-842))) (-2198 (|HasCategory| (-125 |#1|) (QUOTE (-815))) (|HasCategory| (-125 |#1|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-904)))) (|HasCategory| (-125 |#1|) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-125 |#1|) (QUOTE (-904))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-125 |#1|) (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-150))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-125 |#1|) (QUOTE (-1021))) (|HasCategory| (-125 |#1|) (QUOTE (-815))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (QUOTE (-1136))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-125 |#1|) (QUOTE (-225))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -125) (|devaluate| |#1|)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (QUOTE (-301))) (|HasCategory| (-125 |#1|) (QUOTE (-550))) (|HasCategory| (-125 |#1|) (QUOTE (-842))) (-2199 (|HasCategory| (-125 |#1|) (QUOTE (-815))) (|HasCategory| (-125 |#1|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-125 |#1|) (QUOTE (-904)))) (|HasCategory| (-125 |#1|) (QUOTE (-148))))) (-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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4520))) +((|HasAttribute| |#1| (QUOTE -4522))) (-128 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) ((-3973 . T)) @@ -450,7 +450,7 @@ NIL NIL (-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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-131 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical and of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical not of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{\\spad{b}}."))) @@ -458,7 +458,7 @@ NIL NIL (-132) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical or of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical and of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical not of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{\\spad{b}}."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-133 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -466,15 +466,15 @@ NIL NIL (-134 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-135 S) ((|constructor| (NIL "BinaryTournament creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")) (|insert!| (($ |#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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-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])"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-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."))) @@ -486,32 +486,32 @@ NIL NIL (-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") $ $) "\\indented{1}{\\spad{x - y} returns an element \\spad{z} such that} \\indented{1}{\\spad{z+y=x} or \"failed\" if no such element exists.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} \\spad{c2}-\\spad{c2} \\spad{X} A1:=Aleph 1 \\spad{X} \\spad{A1}-\\spad{c2}")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4521 "*") . T)) +(((-4523 "*") . T)) NIL -(-140 |minix| -2570 S T$) +(-140 |minix| -1965 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-141 |minix| -2570 R) +(-141 |minix| -1965 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 (-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}."))) -((-4519 . T) (-4509 . T) (-4520 . T)) -((|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-370))) (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-370)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) +((-4521 . T) (-4511 . T) (-4522 . T)) +((|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-370))) (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-370)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) (-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 (-144) ((|constructor| (NIL "This is a low-level domain which implements matrices (two dimensional arrays) of complex double precision floating point numbers. Indexing is 0 based,{} there is no bound checking (unless provided by lower level).")) (|qnew| (($ (|Integer|) (|Integer|)) "\\indented{1}{qnew(\\spad{n},{} \\spad{m}) creates a new uninitialized \\spad{n} by \\spad{m} matrix.} \\blankline \\spad{X} t1:CDFMAT:=qnew(3,{}4)"))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-169 (-215)) (QUOTE (-1090))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (|HasCategory| (-169 (-215)) (QUOTE (-301))) (|HasCategory| (-169 (-215)) (QUOTE (-558))) (|HasAttribute| (-169 (-215)) (QUOTE (-4521 "*"))) (|HasCategory| (-169 (-215)) (QUOTE (-172))) (|HasCategory| (-169 (-215)) (QUOTE (-365)))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-169 (-215)) (QUOTE (-1090))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (|HasCategory| (-169 (-215)) (QUOTE (-301))) (|HasCategory| (-169 (-215)) (QUOTE (-558))) (|HasAttribute| (-169 (-215)) (QUOTE (-4523 "*"))) (|HasCategory| (-169 (-215)) (QUOTE (-172))) (|HasCategory| (-169 (-215)) (QUOTE (-365)))) (-145) ((|constructor| (NIL "This is a low-level domain which implements vectors (one dimensional arrays) of complex double precision floating point numbers. Indexing is 0 based,{} there is no bound checking (unless provided by lower level).")) (|vector| (($ (|List| (|Complex| (|DoubleFloat|)))) "\\indented{1}{vector(\\spad{l}) converts the list \\spad{l} to a vector.} \\blankline \\spad{X} t1:List(Complex(DoubleFloat))\\spad{:=}[1+2*\\%\\spad{i},{}3+4*\\%\\spad{i},{}\\spad{-5}-6*\\%\\spad{i}] \\spad{X} t2:CDFVEC:=vector(\\spad{t1})")) (|qnew| (($ (|Integer|)) "\\indented{1}{qnew(\\spad{n}) creates a new uninitialized vector of length \\spad{n}.} \\blankline \\spad{X} t1:CDFVEC:=qnew 7"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| (-169 (-215)) (QUOTE (-1090))) (|HasCategory| (-169 (-215)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-169 (-215)) (QUOTE (-842))) (-2198 (|HasCategory| (-169 (-215)) (QUOTE (-842))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-169 (-215)) (QUOTE (-25))) (|HasCategory| (-169 (-215)) (QUOTE (-23))) (|HasCategory| (-169 (-215)) (QUOTE (-21))) (|HasCategory| (-169 (-215)) (QUOTE (-716))) (|HasCategory| (-169 (-215)) (QUOTE (-1047))) (-12 (|HasCategory| (-169 (-215)) (QUOTE (-1002))) (|HasCategory| (-169 (-215)) (QUOTE (-1047)))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-842)))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| (-169 (-215)) (QUOTE (-1090))) (|HasCategory| (-169 (-215)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-169 (-215)) (QUOTE (-842))) (-2199 (|HasCategory| (-169 (-215)) (QUOTE (-842))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-169 (-215)) (QUOTE (-25))) (|HasCategory| (-169 (-215)) (QUOTE (-23))) (|HasCategory| (-169 (-215)) (QUOTE (-21))) (|HasCategory| (-169 (-215)) (QUOTE (-716))) (|HasCategory| (-169 (-215)) (QUOTE (-1047))) (-12 (|HasCategory| (-169 (-215)) (QUOTE (-1002))) (|HasCategory| (-169 (-215)) (QUOTE (-1047)))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-842)))) (-12 (|HasCategory| (-169 (-215)) (LIST (QUOTE -303) (LIST (QUOTE -169) (QUOTE (-215))))) (|HasCategory| (-169 (-215)) (QUOTE (-1090)))))) (-146) ((|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 @@ -522,7 +522,7 @@ NIL NIL (-148) ((|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."))) -((-4516 . T)) +((-4518 . T)) NIL (-149 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}."))) @@ -530,7 +530,7 @@ NIL NIL (-150) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4516 . T)) +((-4518 . T)) NIL (-151 -1478 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}."))) @@ -543,14 +543,14 @@ NIL (-153 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 -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasAttribute| |#1| (QUOTE -4519))) +((|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasAttribute| |#1| (QUOTE -4521))) (-154 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."))) ((-3973 . T)) NIL (-155 |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 1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]} (\\spad{1<=i1(\\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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-213 |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}."))) -((-4516 . T)) +((-4518 . T)) NIL (-214 R -1478) ((|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."))) @@ -790,31 +790,31 @@ NIL NIL (-215) ((|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}."))) -((-3996 . T) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3999 . T) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-216) ((|constructor| (NIL "This is a low-level domain which implements matrices (two dimensional arrays) of double precision floating point numbers. Indexing is 0 based,{} there is no bound checking (unless provided by lower level).")) (|qnew| (($ (|Integer|) (|Integer|)) "\\indented{1}{qnew(\\spad{n},{} \\spad{m}) creates a new uninitialized \\spad{n} by \\spad{m} matrix.} \\blankline \\spad{X} t1:DFMAT:=qnew(3,{}4)"))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-215) (QUOTE (-1090))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))) (|HasCategory| (-215) (QUOTE (-301))) (|HasCategory| (-215) (QUOTE (-558))) (|HasAttribute| (-215) (QUOTE (-4521 "*"))) (|HasCategory| (-215) (QUOTE (-172))) (|HasCategory| (-215) (QUOTE (-365)))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-215) (QUOTE (-1090))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))) (|HasCategory| (-215) (QUOTE (-301))) (|HasCategory| (-215) (QUOTE (-558))) (|HasAttribute| (-215) (QUOTE (-4523 "*"))) (|HasCategory| (-215) (QUOTE (-172))) (|HasCategory| (-215) (QUOTE (-365)))) (-217) ((|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 (-218) ((|constructor| (NIL "This is a low-level domain which implements vectors (one dimensional arrays) of double precision floating point numbers. Indexing is 0 based,{} there is no bound checking (unless provided by lower level).")) (|qnew| (($ (|Integer|)) "\\indented{1}{qnew(\\spad{n}) creates a new uninitialized vector of length \\spad{n}.} \\blankline \\spad{X} t1:DFVEC:=qnew(7)"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| (-215) (QUOTE (-1090))) (|HasCategory| (-215) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-215) (QUOTE (-842))) (-2198 (|HasCategory| (-215) (QUOTE (-842))) (|HasCategory| (-215) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-215) (QUOTE (-25))) (|HasCategory| (-215) (QUOTE (-23))) (|HasCategory| (-215) (QUOTE (-21))) (|HasCategory| (-215) (QUOTE (-716))) (|HasCategory| (-215) (QUOTE (-1047))) (-12 (|HasCategory| (-215) (QUOTE (-1002))) (|HasCategory| (-215) (QUOTE (-1047)))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-842)))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| (-215) (QUOTE (-1090))) (|HasCategory| (-215) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-215) (QUOTE (-842))) (-2199 (|HasCategory| (-215) (QUOTE (-842))) (|HasCategory| (-215) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-215) (QUOTE (-25))) (|HasCategory| (-215) (QUOTE (-23))) (|HasCategory| (-215) (QUOTE (-21))) (|HasCategory| (-215) (QUOTE (-716))) (|HasCategory| (-215) (QUOTE (-1047))) (-12 (|HasCategory| (-215) (QUOTE (-1002))) (|HasCategory| (-215) (QUOTE (-1047)))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-842)))) (-12 (|HasCategory| (-215) (LIST (QUOTE -303) (QUOTE (-215)))) (|HasCategory| (-215) (QUOTE (-1090)))))) (-219 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}"))) -((-4519 . T) (-4520 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4521 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) +((-4521 . T) (-4522 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4523 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-220 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 NIL (-221 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."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-222 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}."))) @@ -822,7 +822,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225)))) (-223 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}."))) -((-4516 . T)) +((-4518 . T)) NIL (-224 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -830,39 +830,39 @@ NIL NIL (-225) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\\spad{\\br} \\tab{5}\\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4516 . T)) +((-4518 . T)) NIL (-226 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -((|HasAttribute| |#1| (QUOTE -4519))) +((|HasAttribute| |#1| (QUOTE -4521))) (-227 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}."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-228) ((|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 NIL -(-229 S -2570 R) +(-229 S -1965 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 -((|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-840))) (|HasAttribute| |#3| (QUOTE -4516)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-716))) (|HasCategory| |#3| (QUOTE (-137))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-1090)))) -(-230 -2570 R) +((|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-840))) (|HasAttribute| |#3| (QUOTE -4518)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-716))) (|HasCategory| |#3| (QUOTE (-137))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1047))) (|HasCategory| |#3| (QUOTE (-1090)))) +(-230 -1965 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"))) -((-4513 |has| |#2| (-1047)) (-4514 |has| |#2| (-1047)) (-4516 |has| |#2| (-6 -4516)) ((-4521 "*") |has| |#2| (-172)) (-4519 . T) (-3973 . T)) +((-4515 |has| |#2| (-1047)) (-4516 |has| |#2| (-1047)) (-4518 |has| |#2| (-6 -4518)) ((-4523 "*") |has| |#2| (-172)) (-4521 . T) (-3973 . T)) NIL -(-231 -2570 A B) +(-231 -1965 A B) ((|constructor| (NIL "This package provides operations which all take as arguments direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\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| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\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 -(-232 -2570 R) +(-232 -1965 R) ((|constructor| (NIL "This type represents the finite direct or cartesian product of an underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4513 |has| |#2| (-1047)) (-4514 |has| |#2| (-1047)) (-4516 |has| |#2| (-6 -4516)) ((-4521 "*") |has| |#2| (-172)) (-4519 . 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(|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1047)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1090))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-172)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-365)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-370)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-840)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1047)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))))) (-233 |Coef|) ((|constructor| (NIL "DirichletRing is the ring of arithmetical functions with Dirichlet convolution as multiplication")) (|additive?| (((|Boolean|) $ (|PositiveInteger|)) "\\spad{additive?(a,{} n)} returns \\spad{true} if the first \\spad{n} coefficients of a are additive")) (|multiplicative?| (((|Boolean|) $ (|PositiveInteger|)) "\\spad{multiplicative?(a,{} n)} returns \\spad{true} if the first \\spad{n} coefficients of a are multiplicative")) (|zeta| (($) "\\spad{zeta()} returns the function which is constantly one"))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) ((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) ((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-172)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-234) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|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."))) @@ -870,11 +870,11 @@ NIL NIL (-235 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|) $) "\\spad{degree(d)} returns the degree of the divisor \\spad{d}"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-236 S) ((|constructor| (NIL "The following is part of the PAFF package"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| (-568) (QUOTE (-787)))) (-237 S) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (^ (($ $ (|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}."))) @@ -882,7 +882,7 @@ NIL NIL (-238) ((|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}."))) -((-4512 . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-239 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."))) @@ -890,35 +890,35 @@ NIL NIL (-240 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}"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-241 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 (-242 |vl| R) ((|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 lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|HasCategory| |#3| (QUOTE (-840)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))))) (-245 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 (-225)))) (-246 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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-247 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}."))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-248) ((|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."))) @@ -958,15 +958,15 @@ NIL NIL (-257 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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4517)) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#3| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-258 S) ((|constructor| (NIL "This category is part of the PAFF package")) (|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}."))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-259 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"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-260 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."))) @@ -1038,7 +1038,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090)))) (-277 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}."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-278 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}."))) @@ -1059,18 +1059,18 @@ NIL (-282 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 -4520))) +((|HasAttribute| |#1| (QUOTE -4522))) (-283 |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 -(-284 S R |Mod| -3627 -1347 |exactQuo|) +(-284 S R |Mod| -3121 -3645 |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"))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-285) ((|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."))) -((-4512 . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-286 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."))) @@ -1082,12 +1082,12 @@ NIL NIL (-288 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.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (-290) ((|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 @@ -1134,7 +1134,7 @@ NIL NIL (-301) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-302 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1158,8 +1158,8 @@ NIL NIL (-307 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))}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-150))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-1021))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-1136))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -281) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (-2198 (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-150))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-1021))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-1136))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -303) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (LIST (QUOTE -281) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1229) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-301))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (-2199 (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-815))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-904)))) (|HasCategory| (-1229 |#1| |#2| |#3| |#4|) (QUOTE (-148))))) (-308 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 @@ -1170,8 +1170,8 @@ NIL NIL (-310 R) ((|constructor| (NIL "Top-level mathematical expressions involving symbolic functions.")) 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(QUOTE (-1047)))) (|HasCategory| |#1| (QUOTE (-21)))) (|HasCategory| |#1| (QUOTE (-25))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1047)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (QUOTE (-25)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2199 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#1| (QUOTE (-1102)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (QUOTE (-1102)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-1047)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1102)))) 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(|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 @@ -1186,8 +1186,8 @@ NIL NIL (-314 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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-315 K) ((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) NIL @@ -1206,7 +1206,7 @@ NIL NIL (-319 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."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| (-568) (QUOTE (-787)))) (-320 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1226,19 +1226,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172)))) (-324 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-325 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."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-326 S -1478) ((|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 (-370)))) (-327 -1478) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-328) ((|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."))) @@ -1278,7 +1278,7 @@ NIL NIL (-337 |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."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#3| (LIST (QUOTE -1037) (QUOTE (-381)))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1037) (QUOTE (-568))))) (-338 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}."))) @@ -1290,29 +1290,29 @@ NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-365)))) (-340 -1478 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}"))) -((-4512 |has| (-409 |#2|) (-365)) (-4517 |has| (-409 |#2|) (-365)) (-4511 |has| (-409 |#2|) (-365)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 |has| (-409 |#2|) (-365)) (-4519 |has| (-409 |#2|) (-365)) (-4513 |has| (-409 |#2|) (-365)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-341 |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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2198 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2199 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) (-342 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-343 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-344 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 -(-345 -3190 V VF) +(-345 -3192 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 NIL -(-346 -3190 V) +(-346 -3192 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 NIL @@ -1330,7 +1330,7 @@ NIL NIL (-350) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-351 R UP -1478) ((|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}"))) @@ -1338,24 +1338,24 @@ NIL NIL (-352 |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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2198 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2199 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) (-353 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-354 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-355 |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}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2198 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-905 |#1|) (QUOTE (-150))) (|HasCategory| (-905 |#1|) (QUOTE (-370))) (|HasCategory| (-905 |#1|) (QUOTE (-148))) (-2199 (|HasCategory| (-905 |#1|) (QUOTE (-148))) (|HasCategory| (-905 |#1|) (QUOTE (-370))))) (-356 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-357 -1478 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 @@ -1374,15 +1374,15 @@ NIL NIL (-361 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}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2198 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-148))) (-2199 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370))))) (-362 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 (-363 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4516 . T)) +((-4518 . T)) NIL (-364 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{a*(b/a) = b}\\spad{\\br} \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1390,7 +1390,7 @@ NIL NIL (-365) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{a*(b/a) = b}\\spad{\\br} \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-366 |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."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-558)))) (-369 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4516 |has| |#1| (-558)) (-4514 . T) (-4513 . T)) +((-4518 |has| |#1| (-558)) (-4516 . T) (-4515 . T)) NIL (-370) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1418,7 +1418,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-365)))) (-372 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-373 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1427,14 +1427,14 @@ NIL (-374 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4520)) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4522)) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090)))) (-375 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4519 . T) (-3973 . T)) +((-4521 . T) (-3973 . T)) NIL (-376 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}.")) (|eval| (($ $ (|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) (-4514 . T) (-4513 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4516 . T) (-4515 . T)) NIL (-377 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."))) @@ -1446,7 +1446,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-379 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}"))) -((-4516 . T)) +((-4518 . T)) NIL (-380 |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}."))) @@ -1454,7 +1454,7 @@ NIL NIL (-381) ((|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}."))) -((-4502 . T) (-4510 . T) (-3996 . T) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4504 . T) (-4512 . T) (-3999 . T) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-382 |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}."))) @@ -1462,11 +1462,11 @@ NIL NIL (-383 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}"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-384 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}."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-385) ((|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}."))) @@ -1478,7 +1478,7 @@ NIL NIL (-387 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."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-388 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1486,7 +1486,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-842)))) (-389) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-390) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1498,7 +1498,7 @@ NIL NIL (-392 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-393) ((|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"))) @@ -1528,7 +1528,7 @@ NIL ((|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 NIL -(-400 -3391 |returnType| |arguments| |symbols|) +(-400 -3393 |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 @@ -1546,15 +1546,15 @@ NIL NIL (-404) ((|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-405 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline 1: base of the exponent where the actual implemenations are usually binary or decimal)\\spad{\\br} 2: precision of the mantissa (arbitrary or fixed)\\spad{\\br} 3: rounding error for operations \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4502)) (|HasAttribute| |#1| (QUOTE -4510))) +((|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4512))) (-406) ((|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\"."))) -((-3996 . T) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3999 . T) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-407 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."))) @@ -1566,15 +1566,15 @@ NIL NIL (-409 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."))) -((-4506 -12 (|has| |#1| (-6 -4517)) (|has| |#1| (-453)) (|has| |#1| (-6 -4506))) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-1136))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasAttribute| |#1| (QUOTE -4517)) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-453)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +((-4508 -12 (|has| |#1| (-6 -4519)) (|has| |#1| (-453)) (|has| |#1| (-6 -4508))) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-1136))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasAttribute| |#1| (QUOTE -4519)) (|HasAttribute| |#1| (QUOTE -4508)) (|HasCategory| |#1| (QUOTE (-453)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-823))))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-410 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 (-411 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-412 A S) ((|constructor| (NIL "A is fully retractable to \\spad{B} means that A is retractable to \\spad{B} and if \\spad{B} is retractable to the integers or rational numbers then so is A. In particular,{} what we are asserting is that there are no integers (rationals) in A which don\\spad{'t} retract into \\spad{B}."))) @@ -1590,7 +1590,7 @@ NIL NIL (-415 R -1478 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4516 . T)) +((-4518 . T)) NIL (-416 R -1478 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) @@ -1606,12 +1606,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-419 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4516 |has| |#1| (-558)) (-4514 . T) (-4513 . T)) +((-4518 |has| |#1| (-558)) (-4516 . T) (-4515 . T)) NIL (-420 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})"))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -281) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-1199))))) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -303) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -281) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-1199))))) (-421 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 @@ -1638,7 +1638,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-370)))) (-427 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note that \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4519 . T) (-4509 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4511 . T) (-4522 . T) (-3973 . T)) NIL (-428 R -1478) ((|constructor| (NIL "Top-level complex function integration \\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) @@ -1646,8 +1646,8 @@ NIL NIL (-429 R E) ((|constructor| (NIL "This domain converts terms into Fourier series")) (|makeCos| (($ |#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"))) -((-4506 -12 (|has| |#1| (-6 -4506)) (|has| |#2| (-6 -4506))) (-4513 . T) (-4514 . T) (-4516 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#2| (QUOTE -4506)))) +((-4508 -12 (|has| |#1| (-6 -4508)) (|has| |#2| (-6 -4508))) (-4515 . T) (-4516 . T) (-4518 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4508)) (|HasAttribute| |#2| (QUOTE -4508)))) (-430 R -1478) ((|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 @@ -1658,7 +1658,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (-432 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}."))) -((-4516 -2198 (|has| |#1| (-1047)) (|has| |#1| (-478))) (-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) ((-4521 "*") |has| |#1| (-558)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-558)) (-4511 |has| |#1| (-558)) (-3973 . T)) +((-4518 -2199 (|has| |#1| (-1047)) (|has| |#1| (-478))) (-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) ((-4523 "*") |has| |#1| (-558)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-558)) (-4513 |has| |#1| (-558)) (-3973 . T)) NIL (-433 R -1478) ((|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."))) @@ -1742,16 +1742,16 @@ NIL NIL (-453) ((|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}."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-454 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"))) -((-4516 |has| (-409 (-953 |#1|)) (-558)) (-4514 . T) (-4513 . T)) +((-4518 |has| (-409 (-953 |#1|)) (-558)) (-4516 . T) (-4515 . T)) ((|HasCategory| (-409 (-953 |#1|)) (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| (-409 (-953 |#1|)) (QUOTE (-558)))) (-455 |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"))) -(((-4521 "*") |has| |#2| (-172)) (-4512 |has| |#2| (-558)) (-4517 |has| |#2| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4517)) (|HasCategory| |#2| (QUOTE (-453))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) +(((-4523 "*") |has| |#2| (-172)) (-4514 |has| |#2| (-558)) (-4519 |has| |#2| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) (-456) ((|constructor| (NIL "This package provides support for gnuplot. These routines generate output files contain gnuplot scripts that may be processed directly by gnuplot. This is especially convenient in the axiom-wiki environment where gnuplot is called from LaTeX via gnuplottex.")) (|gnuDraw| (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)) "\\indented{1}{\\spad{gnuDraw} provides 3d surface plotting,{} default options} \\blankline \\spad{X} gnuDraw(sin(\\spad{x})*cos(\\spad{y}),{}\\spad{x=}-6..4,{}\\spad{y=}-4..6,{}\"out3d.dat\") \\spad{X} )\\spad{sys} gnuplot -persist out3d.dat") (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|))) "\\indented{1}{\\spad{gnuDraw} provides 3d surface plotting with options} \\blankline \\spad{X} gnuDraw(sin(\\spad{x})*cos(\\spad{y}),{}\\spad{x=}-6..4,{}\\spad{y=}-4..6,{}\"out3d.dat\",{}title==\"out3d\") \\spad{X} )\\spad{sys} gnuplot -persist out3d.dat") (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)) "\\indented{1}{\\spad{gnuDraw} provides 2d plotting,{} default options} \\blankline \\spad{X} gnuDraw(\\spad{D}(cos(exp(\\spad{z}))/exp(\\spad{z^2}),{}\\spad{z}),{}\\spad{z=}-5..5,{}\"out2d.dat\") \\spad{X} )\\spad{sys} gnuplot -persist out2d.dat") (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|) (|List| (|DrawOption|))) "\\indented{1}{\\spad{gnuDraw} provides 2d plotting with options} \\blankline \\spad{X} gnuDraw(\\spad{D}(cos(exp(\\spad{z}))/exp(\\spad{z^2}),{}\\spad{z}),{}\\spad{z=}-5..5,{}\"out2d.dat\",{}title==\"out2d\") \\spad{X} )\\spad{sys} gnuplot -persist out2d.dat"))) NIL @@ -1782,7 +1782,7 @@ NIL NIL (-463 |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"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-464) ((|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."))) @@ -1802,7 +1802,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-370)))) (-468 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}}."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1090))) (-12 (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558)))) (-469 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}."))) @@ -1842,19 +1842,19 @@ NIL NIL (-478) ((|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}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4516 . T)) +((-4518 . T)) NIL (-479 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-480 |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."))) -((-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090))))) +((-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090))))) (-481 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."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1090))) (-12 (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370)))) (-482) ((|constructor| (NIL "This package exports guessing of sequences of rational functions"))) @@ -1872,7 +1872,7 @@ NIL ((|constructor| (NIL "This package exports guessing of sequences of rational numbers"))) NIL ((-12 (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))))) -(-486 -1478 S EXPRR R -2854 -2745) +(-486 -1478 S EXPRR R -2857 -2747) ((|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 -1037) (QUOTE (-1161)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161)))))) @@ -1886,27 +1886,27 @@ NIL NIL (-489) ((|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}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-490 |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."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (-491) ((|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. 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 (-492 |vl| R) ((|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 total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4521 "*") |has| |#2| (-172)) (-4512 |has| |#2| (-558)) (-4517 |has| |#2| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4517)) (|HasCategory| |#2| (QUOTE (-453))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) -(-493 -2570 S) +(((-4523 "*") |has| |#2| (-172)) (-4514 |has| |#2| (-558)) (-4519 |has| |#2| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) +(-493 -1965 S) ((|constructor| (NIL "This type represents the finite direct or cartesian product of an underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4513 |has| |#2| (-1047)) (-4514 |has| |#2| (-1047)) (-4516 |has| |#2| (-6 -4516)) ((-4521 "*") |has| |#2| (-172)) (-4519 . T)) -((|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-840))) (-2198 (|HasCategory| |#2| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-172))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1047)))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1047)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-225))) 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\\spad{X} a:Heap INT:= heap [1,{}2,{}3,{}4,{}5] \\spad{X} extract! a \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Heap INT:= heap [1,{}2,{}3,{}4,{}5] \\spad{X} b:=copy a \\spad{X} eq?(a,{}\\spad{b})")) (|empty| (($) "\\blankline \\spad{X} b:=empty()\\$(Heap INT)")) (|empty?| (((|Boolean|) $) "\\blankline \\spad{X} a:Heap INT:= heap [1,{}2,{}3,{}4,{}5] \\spad{X} empty? a")) (|copy| (($ $) "\\blankline \\spad{X} a:Heap INT:= heap [1,{}2,{}3,{}4,{}5] \\spad{X} copy a")) (|bag| (($ (|List| |#1|)) "\\blankline \\spad{X} bag([1,{}2,{}3,{}4,{}5])\\$Heap(INT)")) (|heap| (($ (|List| |#1|)) "\\indented{1}{heap(\\spad{ls}) creates a heap of elements consisting of the} \\indented{1}{elements of \\spad{ls}.} \\blankline \\spad{E} i:Heap INT \\spad{:=} heap [1,{}6,{}3,{}7,{}5,{}2,{}4]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-495 -1478 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."))) @@ -1918,12 +1918,12 @@ NIL NIL (-497) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2198 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2199 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) (-498 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 -4519)) (|HasAttribute| |#1| (QUOTE -4520)) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4521)) (|HasAttribute| |#1| (QUOTE -4522)) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-499 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) ((-3973 . T)) @@ -1946,15 +1946,15 @@ NIL NIL (-504) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1037) (QUOTE (-568))))) (-505 S |mn|) ((|constructor| (NIL "This is the basic one dimensional array data type."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-506 R |mnRow| |mnCol|) ((|constructor| (NIL "This domain implements two dimensional arrays"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-507 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"))) @@ -1966,7 +1966,7 @@ NIL NIL (-509 |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}."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| (-121) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-121) (QUOTE (-842))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-121) (QUOTE (-1090))) (-12 (|HasCategory| (-121) (LIST (QUOTE -303) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1090))))) (-510 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)}."))) @@ -2030,32 +2030,32 @@ NIL ((|HasCategory| |#2| (QUOTE (-787)))) (-525 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}"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-526 |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}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-581 |#1|) (QUOTE (-150))) (|HasCategory| (-581 |#1|) (QUOTE (-370))) (|HasCategory| (-581 |#1|) (QUOTE (-148))) (-2198 (|HasCategory| (-581 |#1|) (QUOTE (-148))) (|HasCategory| (-581 |#1|) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-581 |#1|) (QUOTE (-150))) (|HasCategory| (-581 |#1|) (QUOTE (-370))) (|HasCategory| (-581 |#1|) (QUOTE (-148))) (-2199 (|HasCategory| (-581 |#1|) (QUOTE (-148))) (|HasCategory| (-581 |#1|) (QUOTE (-370))))) (-527 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "There is no description for this domain"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-528 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."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-529 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 -4520))) +((|HasAttribute| |#3| (QUOTE -4522))) (-530 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 -4520))) +((|HasAttribute| |#7| (QUOTE -4522))) (-531 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."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4521 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) +((-4521 . T) (-4522 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4523 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-532 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 @@ -2130,12 +2130,12 @@ NIL NIL (-550) ((|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."))) -((-4517 . T) (-4518 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4519 . T) (-4520 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-551 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (-552 R -1478) ((|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 @@ -2150,7 +2150,7 @@ NIL NIL (-555 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."))) -((-3996 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3999 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-556 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}.}"))) @@ -2162,7 +2162,7 @@ NIL NIL (-558) ((|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."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-559 R -1478) ((|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."))) @@ -2202,7 +2202,7 @@ NIL NIL (-568) ((|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}."))) -((-4501 . T) (-4507 . T) (-4511 . T) (-4506 . T) (-4517 . T) (-4518 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4503 . T) (-4509 . T) (-4513 . T) (-4508 . T) (-4519 . T) (-4520 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-569) ((|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}."))) @@ -2230,7 +2230,7 @@ NIL NIL (-575 R) ((|constructor| (NIL "This domain is an implementation of interval arithmetic and transcendental functions over intervals."))) -((-3996 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3999 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-576) ((|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."))) @@ -2250,11 +2250,11 @@ NIL NIL (-580 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-581 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| $ (QUOTE (-150))) (|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-370)))) (-582) ((|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."))) @@ -2270,7 +2270,7 @@ NIL NIL (-585 -1478) ((|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}."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-1161))))) (-586 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"))) @@ -2294,19 +2294,19 @@ NIL NIL (-591 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| (-147) (QUOTE (-1090))) (|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-842))) (-2198 (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-842)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| (-147) (QUOTE (-1090))) (|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-842))) (-2199 (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-842)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) (-592 E V R P) ((|constructor| (NIL "Tools for the summation packages of polynomials")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-593 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain used for creating sparse Taylor and Laurent series.")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|))))) (|HasCategory| (-568) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|))))) (|HasCategory| (-568) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161))))))) (-594 |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.}"))) -((-4514 |has| |#1| (-558)) (-4513 |has| |#1| (-558)) ((-4521 "*") |has| |#1| (-558)) (-4512 |has| |#1| (-558)) (-4516 . T)) +((-4516 |has| |#1| (-558)) (-4515 |has| |#1| (-558)) ((-4523 "*") |has| |#1| (-558)) (-4514 |has| |#1| (-558)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-558)))) (-595 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),{}..]}."))) @@ -2326,31 +2326,31 @@ NIL NIL (-599 R |mn|) ((|constructor| (NIL "This type represents vector like objects with varying lengths and a user-specified initial index."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-600 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 -((|HasAttribute| |#1| (QUOTE -4520)) (|HasCategory| |#2| (QUOTE (-842))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#3| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4522)) (|HasCategory| |#2| (QUOTE (-842))) (|HasAttribute| |#1| (QUOTE -4521)) (|HasCategory| |#3| (QUOTE (-1090)))) (-601 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) ((-3973 . T)) NIL (-602 R A) ((|constructor| (NIL "AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4516 -2198 (-2139 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4514 . T) (-4513 . T)) -((|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))))) +((-4518 -2199 (-2141 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4516 . T) (-4515 . T)) +((|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))))) (-603 |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."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (QUOTE (-1090))))) (-604 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 NIL (-605 |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| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-606 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2378,11 +2378,11 @@ NIL NIL (-612 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4516 . T)) +((-4518 . T)) NIL (-613 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}."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-840)))) (-614 R -1478) ((|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."))) @@ -2390,7 +2390,7 @@ NIL NIL (-615 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"))) -((-4514 . T) (-4513 . T) ((-4521 "*") . T) (-4512 . T) (-4516 . T)) +((-4516 . T) (-4515 . T) ((-4523 "*") . T) (-4514 . T) (-4518 . T)) ((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568))))) (-616 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."))) @@ -2402,18 +2402,18 @@ NIL NIL (-618 |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}}."))) -((-4516 . T)) +((-4518 . T)) NIL (-619 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 (-620) -((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) +((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|fresnelC| (($ $) "fresnelC is the Fresnel integral \\spad{C},{} defined by \\spad{C}(\\spad{x}) = integrate(cos(\\spad{t^2}),{}\\spad{t=0}..\\spad{x})")) (|fresnelS| (($ $) "fresnelS is the Fresnel integral \\spad{S},{} defined by \\spad{S}(\\spad{x}) = integrate(sin(\\spad{t^2}),{}\\spad{t=0}..\\spad{x})")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL (-621 R -1478) -((|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"))) +((|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}.")) (|fresnelC| ((|#2| |#2|) "\\spad{fresnelC(f)} denotes the Fresnel integral \\spad{C}")) (|fresnelS| ((|#2| |#2|) "\\spad{fresnelS(f)} denotes the Fresnel integral \\spad{S}")) (|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 (-622 |lv| -1478) @@ -2422,20 +2422,20 @@ NIL NIL (-623) ((|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."))) -((-4520 . T)) -((|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4083) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (QUOTE (-1090)))) (-2198 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (QUOTE (-1090))))) +((-4522 . T)) +((|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4085) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (QUOTE (-1090)))) (-2199 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (QUOTE (-1090))))) (-624 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-625 R) ((|constructor| (NIL "The category of Lie Algebras. It is used by the domains of non-commutative algebra,{} LiePolynomial and XPBWPolynomial.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4514 . T) (-4513 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4516 . T) (-4515 . T)) NIL (-626 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4516 -2198 (-2139 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4514 . T) (-4513 . T)) -((|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))))) +((-4518 -2199 (-2141 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4516 . T) (-4515 . T)) +((|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))))) (-627 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 @@ -2447,10 +2447,10 @@ NIL (-629 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 (-365))) (-3044 (|HasCategory| |#1| (QUOTE (-365))))) +((|HasCategory| |#1| (QUOTE (-365))) (-3046 (|HasCategory| |#1| (QUOTE (-365))))) (-630 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}."))) -((-4516 . T)) +((-4518 . T)) NIL (-631 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}."))) @@ -2466,15 +2466,15 @@ NIL NIL (-634 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."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-635 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 (-636 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (-637 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline Axioms\\spad{\\br} \\tab{5}\\spad{ (a*b)*x = a*(b*x) }\\spad{\\br} \\tab{5}\\spad{ (a+b)*x = (a*x)+(b*x) }\\spad{\\br} \\tab{5}\\spad{ a*(x+y) = (a*x)+(a*y) }")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) @@ -2487,14 +2487,14 @@ NIL (-639 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 -4520))) +((|HasAttribute| |#1| (QUOTE -4522))) (-640 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})}."))) ((-3973 . T)) NIL (-641 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}."))) -(((-4521 "*") . T) (-4512 . T) (-4511 . T) (-4517 . T) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") . T) (-4514 . T) (-4513 . T) (-4519 . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-642 R -1478 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."))) @@ -2502,11 +2502,11 @@ NIL NIL (-643 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}"))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-365)))) (-644 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-365)))) (-645 S A) ((|constructor| (NIL "LinearOrdinaryDifferentialOperatorCategory is the category of differential operators with coefficients in a ring A with a given derivation. \\blankline Multiplication of operators corresponds to functional composition:\\spad{\\br} (\\spad{L1} * \\spad{L2}).(\\spad{f}) = \\spad{L1} \\spad{L2} \\spad{f}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2514,15 +2514,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-646 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}."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-647 -1478 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)))) -(-648 A -2060) +(-648 A -1571) ((|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}"))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-365)))) (-649 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."))) @@ -2538,7 +2538,7 @@ NIL NIL (-652 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}."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) ((|HasCategory| |#1| (QUOTE (-786)))) (-653 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."))) @@ -2554,7 +2554,7 @@ NIL NIL (-656 |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) (-4514 . T) (-4513 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4516 . T) (-4515 . T)) ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-172)))) (-657 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}."))) @@ -2562,7 +2562,7 @@ NIL NIL (-658 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}."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-659 -1478) ((|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}."))) @@ -2578,8 +2578,8 @@ NIL NIL (-662 |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."))) -((-4516 . T) (-4519 . T) (-4513 . T) (-4514 . T)) -((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4521 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2198 (|HasAttribute| |#2| (QUOTE (-4521 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4518 . T) (-4521 . T) (-4515 . T) (-4516 . T)) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4523 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2199 (|HasAttribute| |#2| (QUOTE (-4523 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-172)))) (-663 |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 @@ -2595,7 +2595,7 @@ NIL (-666 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 (-1090))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-667 |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 @@ -2635,10 +2635,10 @@ NIL (-676 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 (-172))) (|HasAttribute| |#2| (QUOTE (-4521 "*"))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558)))) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE (-4523 "*"))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558)))) (-677 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"))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-678 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."))) @@ -2646,8 +2646,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558)))) (-679 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."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4521 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4523 "*"))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-680 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 @@ -2662,11 +2662,11 @@ NIL NIL (-683) ((|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"))) -((-4512 . T) (-4517 |has| (-688) (-365)) (-4511 |has| (-688) (-365)) (-4003 . T) (-4518 |has| (-688) (-6 -4518)) (-4515 |has| (-688) (-6 -4515)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-688) (QUOTE (-150))) (|HasCategory| (-688) (QUOTE (-148))) (|HasCategory| (-688) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-688) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-688) (QUOTE (-370))) (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-688) (QUOTE (-225))) (|HasCategory| (-688) (QUOTE (-350))) (-2198 (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-350)))) (|HasCategory| (-688) (LIST (QUOTE -281) (QUOTE (-688)) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -303) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-688) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-688) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-688) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-688) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-688) (QUOTE (-1021))) (|HasCategory| (-688) (QUOTE (-1181))) (-12 (|HasCategory| (-688) (QUOTE (-1002))) (|HasCategory| (-688) (QUOTE (-1181)))) (|HasCategory| (-688) (QUOTE (-550))) (|HasCategory| (-688) (QUOTE (-1056))) (-12 (|HasCategory| (-688) (QUOTE (-1056))) (|HasCategory| (-688) (QUOTE (-1181)))) (-2198 (|HasCategory| (-688) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-688) (QUOTE (-365)))) (|HasCategory| (-688) (QUOTE (-301))) (-2198 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-350)))) (|HasCategory| (-688) (QUOTE (-904))) (-12 (|HasCategory| (-688) (QUOTE (-225))) (|HasCategory| (-688) (QUOTE (-365)))) (-12 (|HasCategory| (-688) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-688) (QUOTE (-365)))) (|HasCategory| (-688) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-688) (QUOTE (-842))) (|HasCategory| (-688) (QUOTE (-558))) (|HasAttribute| (-688) (QUOTE -4518)) (|HasAttribute| (-688) (QUOTE -4515)) (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-365))) (-12 (|HasCategory| (-688) (QUOTE (-350))) (|HasCategory| (-688) (QUOTE (-904))))) (-2198 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (-12 (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-904)))) (-12 (|HasCategory| (-688) (QUOTE (-350))) (|HasCategory| (-688) (QUOTE (-904))))) (-2198 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-365)))) (-2198 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-558)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-148)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-350))))) +((-4514 . T) (-4519 |has| (-688) (-365)) (-4513 |has| (-688) (-365)) (-4005 . T) (-4520 |has| (-688) (-6 -4520)) (-4517 |has| (-688) (-6 -4517)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-688) (QUOTE (-150))) (|HasCategory| (-688) (QUOTE (-148))) (|HasCategory| (-688) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-688) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-688) (QUOTE (-370))) (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-688) (QUOTE (-225))) (|HasCategory| (-688) (QUOTE (-350))) (-2199 (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-350)))) (|HasCategory| (-688) (LIST (QUOTE -281) (QUOTE (-688)) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -303) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-688)))) (|HasCategory| (-688) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-688) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-688) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-688) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-688) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-688) (QUOTE (-1021))) (|HasCategory| (-688) (QUOTE (-1181))) (-12 (|HasCategory| (-688) (QUOTE (-1002))) (|HasCategory| (-688) (QUOTE (-1181)))) (|HasCategory| (-688) (QUOTE (-550))) (|HasCategory| (-688) (QUOTE (-1056))) (-12 (|HasCategory| (-688) (QUOTE (-1056))) (|HasCategory| (-688) (QUOTE (-1181)))) (-2199 (|HasCategory| (-688) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-688) (QUOTE (-365)))) (|HasCategory| (-688) (QUOTE (-301))) (-2199 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-350)))) (|HasCategory| (-688) (QUOTE (-904))) (-12 (|HasCategory| (-688) (QUOTE (-225))) (|HasCategory| (-688) (QUOTE (-365)))) (-12 (|HasCategory| (-688) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-688) (QUOTE (-365)))) (|HasCategory| (-688) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-688) (QUOTE (-842))) (|HasCategory| (-688) (QUOTE (-558))) (|HasAttribute| (-688) (QUOTE -4520)) (|HasAttribute| (-688) (QUOTE -4517)) (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-365))) (-12 (|HasCategory| (-688) (QUOTE (-350))) (|HasCategory| (-688) (QUOTE (-904))))) (-2199 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (-12 (|HasCategory| (-688) (QUOTE (-365))) (|HasCategory| (-688) (QUOTE (-904)))) (-12 (|HasCategory| (-688) (QUOTE (-350))) (|HasCategory| (-688) (QUOTE (-904))))) (-2199 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-365)))) (-2199 (-12 (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-558)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-148)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-688) (QUOTE (-301))) (|HasCategory| (-688) (QUOTE (-904)))) (|HasCategory| (-688) (QUOTE (-350))))) (-684 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}."))) -((-4520 . T) (-3973 . T)) +((-4522 . T) (-3973 . T)) NIL (-685 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}."))) @@ -2682,7 +2682,7 @@ NIL NIL (-688) ((|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}"))) -((-3996 . T) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3999 . T) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-689 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."))) @@ -2690,7 +2690,7 @@ NIL NIL (-690) ((|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}"))) -((-4518 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4520 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-691 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"))) @@ -2712,7 +2712,7 @@ NIL ((|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 -(-696 S -3190 I) +(-696 S -3192 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 @@ -2722,7 +2722,7 @@ NIL NIL (-698 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)}.")) (|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)}.}"))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-699 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2732,25 +2732,25 @@ NIL ((|constructor| (NIL "This package is based on the TeXFormat domain by Robert \\spad{S}. Sutor \\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|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 NIL -(-701 R |Mod| -3627 -1347 |exactQuo|) +(-701 R |Mod| -3121 -3645 |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{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| $) "\\spad{modulus(x)} is not documented"))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-702 R |Rep|) ((|constructor| (NIL "This package has not been documented")) (|frobenius| (($ $) "\\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"))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4515 |has| |#1| (-365)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1136))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-350))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4517)) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1136))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-350))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-703 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| $) "\\spad{exponent(x)} is not documented"))) NIL NIL (-704 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150)))) -(-705 R |Mod| -3627 -1347 |exactQuo|) +(-705 R |Mod| -3121 -3645 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4516 . T)) +((-4518 . T)) NIL (-706 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)}"))) @@ -2758,11 +2758,11 @@ NIL NIL (-707 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)}"))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-708 -1478) ((|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]]}."))) -((-4516 . T)) +((-4518 . T)) NIL (-709 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."))) @@ -2786,7 +2786,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-350))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-370)))) (-714 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."))) -((-4512 |has| |#1| (-365)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 |has| |#1| (-365)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-715 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."))) @@ -2800,11 +2800,11 @@ NIL ((|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 -(-718 |VarSet| -1993 E2 R S PR PS) +(-718 |VarSet| -4464 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 -(-719 |Vars1| |Vars2| -1993 E2 R PR1 PR2) +(-719 |Vars1| |Vars2| -4464 E2 R PR1 PR2) ((|constructor| (NIL "This package has no description")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL @@ -2814,8 +2814,8 @@ NIL NIL (-721 |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."))) -(((-4521 "*") |has| |#2| (-172)) (-4512 |has| |#2| (-558)) (-4517 |has| |#2| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4517)) (|HasCategory| |#2| (QUOTE (-453))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) +(((-4523 "*") |has| |#2| (-172)) (-4514 |has| |#2| (-558)) (-4519 |has| |#2| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-852 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) (-722 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2830,15 +2830,15 @@ NIL NIL (-725 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over \\spad{f}(a)\\spad{g}(\\spad{b}) such that ab = \\spad{c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) (-4518 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-842)))) (-726 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4509 . T) (-4520 . T) (-3973 . T)) +((-4511 . T) (-4522 . T) (-3973 . T)) NIL (-727 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}."))) -((-4519 . T) (-4509 . T) (-4520 . T)) +((-4521 . T) (-4511 . T) (-4522 . T)) ((|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-728) ((|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."))) @@ -2850,7 +2850,7 @@ NIL NIL (-730 |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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4514 . T) (-4513 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-731 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"))) @@ -2862,19 +2862,19 @@ NIL NIL (-733 |q| R) ((|constructor| (NIL "This domain has no description"))) -((-4517 |has| |#2| (-558)) (-4511 |has| |#2| (-558)) (-4516 -2198 (|has| |#2| (-478)) (|has| |#2| (-1047))) (-4514 |has| |#2| (-172)) (-4513 |has| |#2| (-172)) ((-4521 "*") |has| |#2| (-558)) (-4512 |has| |#2| (-558))) -((|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-2198 (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1047)))) (-2198 (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1047)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558)))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1037) (QUOTE (-568))))) +((-4519 |has| |#2| (-558)) (-4513 |has| |#2| (-558)) (-4518 -2199 (|has| |#2| (-478)) (|has| |#2| (-1047))) (-4516 |has| |#2| (-172)) (-4515 |has| |#2| (-172)) ((-4523 "*") |has| |#2| (-558)) (-4514 |has| |#2| (-558))) +((|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (-2199 (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1047)))) (-2199 (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1047)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558)))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1047))) (|HasCategory| $ (LIST (QUOTE -1037) (QUOTE (-568))))) (-734 |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."))) -(((-4521 "*") |has| |#2| (-172)) (-4512 |has| |#2| (-558)) (-4515 |has| |#2| (-365)) (-4517 |has| |#2| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . 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T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1136))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) (-735 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 (-736 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}."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-737) ((|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}."))) @@ -2982,7 +2982,7 @@ NIL NIL (-763) ((|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."))) -(((-4521 "*") . T)) +(((-4523 "*") . T)) NIL (-764 R -1478) ((|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."))) @@ -3010,13 +3010,13 @@ NIL NIL (-770 -1478) ((|constructor| (NIL "This is an implmenentation of the Nottingham Group"))) -((-4516 . T)) +((-4518 . T)) NIL (-771 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 -(-772 K |PolyRing| E -2570) +(-772 K |PolyRing| E -1965) ((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL @@ -3026,27 +3026,27 @@ NIL NIL (-774 K) ((|constructor| (NIL "This domain is part of the PAFF package"))) -(((-4521 "*") . T) (-4512 . T) (-4511 . T) (-4517 . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-568)) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-568)) (|:| |c| |#1|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-2 (|:| |k| (-568)) (|:| |c| |#1|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| |k| (-568)) (|:| |c| |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE |k|) (QUOTE (-568))) (LIST (QUOTE |:|) (QUOTE |c|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-568)) (|:| |c| |#1|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568)))))) +(((-4523 "*") . T) (-4514 . T) (-4513 . T) (-4519 . T) (-4515 . T) (-4516 . T) (-4518 . 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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 (-777 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.")) 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T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1136))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-778 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 -43) (LIST (QUOTE -409) (QUOTE (-568)))))) (-779 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."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-780 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}."))) @@ -3098,16 +3098,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1056))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-370)))) (-792 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL -(-793 -2198 R OS S) +(-793 -2199 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-794 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is octon which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation \\spad{O} = \\spad{Q} + QE."))) -((-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1056))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-2198 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-2198 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))))) +((-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1056))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (-2199 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-2199 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))))) (-795) ((|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 @@ -3168,17 +3168,17 @@ NIL ((|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 NIL -(-810 -2570 S |f|) +(-810 -1965 S |f|) ((|constructor| (NIL "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}."))) -((-4513 |has| |#2| (-1047)) (-4514 |has| |#2| (-1047)) (-4516 |has| |#2| (-6 -4516)) ((-4521 "*") |has| |#2| (-172)) (-4519 . 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T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-813 (-1161)) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-813 (-1161)) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-813 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-813 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-813 (-1161)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-812 |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."))) -(((-4521 "*") |has| |#2| (-365)) (-4512 |has| |#2| (-365)) (-4517 |has| |#2| (-365)) (-4511 |has| |#2| (-365)) (-4516 . T) (-4514 . T) (-4513 . T)) +(((-4523 "*") |has| |#2| (-365)) (-4514 |has| |#2| (-365)) (-4519 |has| |#2| (-365)) (-4513 |has| |#2| (-365)) (-4518 . T) (-4516 . T) (-4515 . T)) ((|HasCategory| |#2| (QUOTE (-365)))) (-813 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}))."))) @@ -3190,7 +3190,7 @@ NIL NIL (-815) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible"))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-816) ((|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}"))) @@ -3218,7 +3218,7 @@ NIL NIL (-822 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}."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-225)))) (-823) ((|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."))) @@ -3230,7 +3230,7 @@ NIL NIL (-825 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4519 . T) (-4509 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4511 . T) (-4522 . T) (-3973 . T)) NIL (-826) ((|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."))) @@ -3242,11 +3242,11 @@ NIL NIL (-828 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."))) -((-4516 |has| |#1| (-840))) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-550))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-21))) (-2198 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-840))))) +((-4518 |has| |#1| (-840))) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-550))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-21))) (-2199 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-840))))) (-829 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150)))) (-830) ((|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)."))) @@ -3270,13 +3270,13 @@ NIL NIL (-835 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."))) -((-4516 |has| |#1| (-840))) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-550))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-21))) (-2198 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-840))))) +((-4518 |has| |#1| (-840))) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-550))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-21))) (-2199 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-840))))) (-836) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-837 -2570 S) +(-837 -1965 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 @@ -3290,7 +3290,7 @@ NIL NIL (-840) ((|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."))) -((-4516 . T)) +((-4518 . T)) NIL (-841 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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3306,19 +3306,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172)))) (-844 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and NonCommutativeOperatorDivision")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-845 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 (-365))) (|HasCategory| |#1| (QUOTE (-558)))) -(-846 R |sigma| -1325) +(-846 R |sigma| -3488) ((|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."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-365)))) -(-847 |x| R |sigma| -1325) +(-847 |x| R |sigma| -3488) ((|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."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-365)))) (-848 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..)}."))) @@ -3342,36 +3342,36 @@ NIL NIL (-853 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"))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-854) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-855 |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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-860) (QUOTE (-150))) (|HasCategory| (-860) (QUOTE (-148))) (|HasCategory| (-860) (QUOTE (-370))) (|HasCategory| (-409 (-568)) (QUOTE (-150))) (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (-2198 (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (|HasCategory| (-860) (QUOTE (-148))) (|HasCategory| (-860) (QUOTE (-370)))) (-2198 (|HasCategory| (-409 (-568)) (QUOTE (-370))) (|HasCategory| (-860) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-860) (QUOTE (-150))) (|HasCategory| (-860) (QUOTE (-148))) (|HasCategory| (-860) (QUOTE (-370))) (|HasCategory| (-409 (-568)) (QUOTE (-150))) (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (-2199 (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (|HasCategory| (-860) (QUOTE (-148))) (|HasCategory| (-860) (QUOTE (-370)))) (-2199 (|HasCategory| (-409 (-568)) (QUOTE (-370))) (|HasCategory| (-860) (QUOTE (-370))))) (-856) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-857 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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-370)))) (-858) ((|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)."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-859) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-860) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-409 (-568)) (QUOTE (-150))) (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (-2198 (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-409 (-568)) (QUOTE (-150))) (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))) (-2199 (|HasCategory| (-409 (-568)) (QUOTE (-148))) (|HasCategory| (-409 (-568)) (QUOTE (-370))))) (-861 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 @@ -3382,20 +3382,20 @@ NIL NIL (-863 |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}."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-864 |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)."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-865 |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)."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-864 |#1|) (QUOTE (-904))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-864 |#1|) (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-150))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-864 |#1|) (QUOTE (-1021))) (|HasCategory| (-864 |#1|) (QUOTE (-815))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (QUOTE (-1136))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (QUOTE (-225))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -864) (|devaluate| |#1|)) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (QUOTE (-301))) (|HasCategory| (-864 |#1|) (QUOTE (-550))) (|HasCategory| (-864 |#1|) (QUOTE (-842))) (-2198 (|HasCategory| (-864 |#1|) (QUOTE (-815))) (|HasCategory| (-864 |#1|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-904)))) (|HasCategory| (-864 |#1|) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-864 |#1|) (QUOTE (-904))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-864 |#1|) (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-150))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-864 |#1|) (QUOTE (-1021))) (|HasCategory| (-864 |#1|) (QUOTE (-815))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (QUOTE (-1136))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-864 |#1|) (QUOTE (-225))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -523) (QUOTE (-1161)) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -303) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (LIST (QUOTE -281) (LIST (QUOTE -864) (|devaluate| |#1|)) (LIST (QUOTE -864) (|devaluate| |#1|)))) (|HasCategory| (-864 |#1|) (QUOTE (-301))) (|HasCategory| (-864 |#1|) (QUOTE (-550))) (|HasCategory| (-864 |#1|) (QUOTE (-842))) (-2199 (|HasCategory| (-864 |#1|) (QUOTE (-815))) (|HasCategory| (-864 |#1|) (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-864 |#1|) (QUOTE (-904)))) (|HasCategory| (-864 |#1|) (QUOTE (-148))))) (-866 |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)}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1136))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-842))) (-2198 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1136))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -281) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-842))) (-2199 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-842)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) (-867 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 @@ -3459,7 +3459,7 @@ NIL (-882 |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 -1037) (QUOTE (-1161)))) (-12 (-3044 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161))))) (-3044 (|HasCategory| |#2| (QUOTE (-1047))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (-3044 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161))))))) +((|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161)))) (-12 (-3046 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161))))) (-3046 (|HasCategory| |#2| (QUOTE (-1047))))) (-12 (|HasCategory| |#2| (QUOTE (-1047))) (-3046 (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161))))))) (-883 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 @@ -3468,7 +3468,7 @@ NIL ((|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 -(-885 R -3190) +(-885 R -3192) ((|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 @@ -3510,7 +3510,7 @@ NIL NIL (-895 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}."))) -((-4516 . T)) +((-4518 . T)) NIL (-896 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])"))) @@ -3522,7 +3522,7 @@ NIL NIL (-898 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."))) -((-4516 . T)) +((-4518 . T)) NIL (-899 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|)) $) "\\spad{coerce(gp)} returns the generators of the group \\spad{gp}."))) @@ -3530,8 +3530,8 @@ NIL NIL (-900 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections on a set \\spad{S},{} which move only a finite number of points. A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular multiplication is defined as composition of maps:\\spad{\\br} \\spad{pi1} * \\spad{pi2} = \\spad{pi1} \\spad{o} \\spad{pi2}.\\spad{\\br} The internal representation of permuatations are two lists of equal length representing preimages and images.")) (|coerceImages| (($ (|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."))) -((-4516 . T)) -((|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-842))))) +((-4518 . T)) +((|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-842))))) (-901 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 @@ -3546,11 +3546,11 @@ NIL ((|HasCategory| |#1| (QUOTE (-148)))) (-904) ((|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}."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-905 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) ((|HasCategory| $ (QUOTE (-150))) (|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-370)))) (-906 R0 -1478 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"))) @@ -3560,7 +3560,7 @@ NIL ((|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 -(-908 R |PolyRing| E -2570) +(-908 R |PolyRing| E -1965) ((|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 @@ -3570,7 +3570,7 @@ NIL NIL (-910 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|) $) "\\indented{1}{coerce(\\spad{p}) sums up the components of the partial fraction and} \\indented{1}{returns a single fraction.} \\blankline \\spad{X} a:=(13/74)::PFR(INT) \\spad{X} a::FRAC(INT)"))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-911 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{partialFraction(\\spad{rf},{} var) returns the partial fraction decomposition} \\indented{1}{of the rational function \\spad{rf} with respect to the variable var.} \\blankline \\spad{X} a:=x+1/(\\spad{y+1}) \\spad{X} partialFraction(a,{}\\spad{y})\\$PFRPAC(INT)"))) @@ -3594,11 +3594,11 @@ NIL NIL (-916) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-917) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for positive integers.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4521 "*") . T)) +(((-4523 "*") . T)) NIL (-918 -1478 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) @@ -3644,7 +3644,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-929 K |PolyRing| E -2570 |ProjPt|) +(-929 K |PolyRing| E -1965 |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 @@ -3680,11 +3680,11 @@ NIL ((|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 -881) (|devaluate| |#1|)))) -(-938 R -1478 -3190) +(-938 R -1478 -3192) ((|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 -(-939 -3190) +(-939 -3192) ((|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 @@ -3706,8 +3706,8 @@ NIL NIL (-944 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-945 |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 @@ -3727,10 +3727,10 @@ NIL (-949 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 (-904))) (|HasAttribute| |#2| (QUOTE -4517)) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-842)))) +((|HasCategory| |#2| (QUOTE (-904))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-842)))) (-950 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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-951 E V R P -1478) ((|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}."))) @@ -3742,8 +3742,8 @@ NIL NIL (-953 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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4517)) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1161) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-954 E V R P -1478) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL @@ -3762,8 +3762,8 @@ NIL NIL (-958 S) ((|constructor| (NIL "This provides a fast array type with no bound checking on elt\\spad{'s}. Minimum index is 0 in this type,{} cannot be changed"))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-959) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 @@ -3786,12 +3786,12 @@ NIL NIL (-964 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}"))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-137)))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4517))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-453))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-137)))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519))) (-965 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)"))) -((-4516 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) -((-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-2198 (-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 (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-2198 (-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 (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-842)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-842)))))) +((-4518 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) +((-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-137))) (|HasCategory| |#2| (QUOTE (-137)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-2199 (-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 (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-2199 (-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 (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-842)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-842)))))) (-966 K) ((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL @@ -3800,13 +3800,13 @@ NIL ((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL NIL -(-968 -2570 K) +(-968 -1965 K) ((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) NIL NIL (-969 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}."))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-970 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}}"))) @@ -3826,7 +3826,7 @@ NIL NIL (-974 |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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-975) ((|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}."))) @@ -3838,7 +3838,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-558)))) (-977 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."))) -((-4519 . T) (-3973 . T)) +((-4521 . T) (-3973 . T)) NIL (-978 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."))) @@ -3854,7 +3854,7 @@ NIL NIL (-981 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}."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-982 R1 R2) ((|constructor| (NIL "This package has no description")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3902,7 +3902,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-1136)))) (-993 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}."))) -((-3973 . T) (-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3973 . T) (-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-994 |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}."))) @@ -3910,7 +3910,7 @@ NIL NIL (-995 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."))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-996 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}."))) @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1056))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-285)))) (-997 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}."))) -((-4512 |has| |#1| (-285)) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 |has| |#1| (-285)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-998 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})"))) @@ -3926,11 +3926,11 @@ NIL NIL (-999 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."))) -((-4512 |has| |#1| (-285)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-285))) (-2198 (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-1056))) (|HasCategory| |#1| (QUOTE (-550))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))))) +((-4514 |has| |#1| (-285)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-285))) (-2199 (|HasCategory| |#1| (QUOTE (-285))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -523) (QUOTE (-1161)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -281) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-1056))) (|HasCategory| |#1| (QUOTE (-550))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))))) (-1000 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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-1001 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}."))) @@ -3942,12 +3942,12 @@ NIL NIL (-1003 -1478 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4512 |has| (-409 |#2|) (-365)) (-4517 |has| (-409 |#2|) (-365)) (-4511 |has| (-409 |#2|) (-365)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-148))) (|HasCategory| (-409 |#2|) (QUOTE (-150))) (|HasCategory| (-409 |#2|) (QUOTE (-350))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (-2198 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-350)))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2198 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2198 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2198 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) +((-4514 |has| (-409 |#2|) (-365)) (-4519 |has| (-409 |#2|) (-365)) (-4513 |has| (-409 |#2|) (-365)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-409 |#2|) (QUOTE (-148))) (|HasCategory| (-409 |#2|) (QUOTE (-150))) (|HasCategory| (-409 |#2|) (QUOTE (-350))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (-2199 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-350)))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2199 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2199 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-2199 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-225))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-350))))) (-1004 |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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2198 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-568) (QUOTE (-904))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-1161)))) (|HasCategory| (-568) (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-150))) (|HasCategory| (-568) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-1021))) (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-1136))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| (-568) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| (-568) (QUOTE (-225))) (|HasCategory| (-568) (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| (-568) (LIST (QUOTE -523) (QUOTE (-1161)) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -303) (QUOTE (-568)))) (|HasCategory| (-568) (LIST (QUOTE -281) (QUOTE (-568)) (QUOTE (-568)))) (|HasCategory| (-568) (QUOTE (-301))) (|HasCategory| (-568) (QUOTE (-550))) (|HasCategory| (-568) (QUOTE (-842))) (-2199 (|HasCategory| (-568) (QUOTE (-815))) (|HasCategory| (-568) (QUOTE (-842)))) (|HasCategory| (-568) (LIST (QUOTE -630) (QUOTE (-568)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| (-568) (QUOTE (-904)))) (|HasCategory| (-568) (QUOTE (-148))))) (-1005) ((|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 @@ -3967,7 +3967,7 @@ NIL (-1009 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 -4520)) (|HasCategory| |#2| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4522)) (|HasCategory| |#2| (QUOTE (-1090)))) (-1010 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}."))) ((-3973 . T)) @@ -3978,7 +3978,7 @@ NIL NIL (-1012) ((|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}}"))) -((-4512 . T) (-4517 . T) (-4511 . T) (-4514 . T) (-4513 . T) ((-4521 "*") . T) (-4516 . T)) +((-4514 . T) (-4519 . T) (-4513 . T) (-4516 . T) (-4515 . T) ((-4523 "*") . T) (-4518 . T)) NIL (-1013 R -1478) ((|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."))) @@ -4022,8 +4022,8 @@ NIL NIL (-1023 |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"))) -((-4512 . T) (-4517 . T) (-4511 . T) (-4514 . T) (-4513 . T) ((-4521 "*") . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (QUOTE (-568)))) (-2198 (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))))) +((-4514 . T) (-4519 . T) (-4513 . T) (-4516 . T) (-4515 . T) ((-4523 "*") . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (QUOTE (-568)))) (-2199 (|HasCategory| (-409 (-568)) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))))) (-1024 R -1478) ((|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 @@ -4038,12 +4038,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1090)))) (-1027 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."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1090))) (-12 (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370)))) (-1028 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 (-4521 "*")))) +((|HasAttribute| |#1| (QUOTE (-4523 "*")))) (-1029 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 @@ -4066,12 +4066,12 @@ NIL NIL (-1034 -1478 |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"))) -(((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1035) ((|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.}"))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4083) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090)))) (|HasCategory| (-1161) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-2198 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4085) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090)))) (|HasCategory| (-1161) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-2199 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090))))) (-1036 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 @@ -4106,7 +4106,7 @@ NIL NIL (-1044 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."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| (-775 |#1| (-852 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-775 |#1| (-852 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-775 |#1| (-852 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -775) (|devaluate| |#1|) (LIST (QUOTE -852) (|devaluate| |#2|))))) (|HasCategory| (-775 |#1| (-852 |#2|)) (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| (-852 |#2|) (QUOTE (-370)))) (-1045) ((|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}}"))) @@ -4118,7 +4118,7 @@ NIL NIL (-1047) ((|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."))) -((-4516 . T)) +((-4518 . T)) NIL (-1048 |xx| -1478) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) @@ -4130,12 +4130,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-301))) (|HasCategory| |#4| (QUOTE (-365))) (|HasCategory| |#4| (QUOTE (-558))) (|HasCategory| |#4| (QUOTE (-172)))) (-1050 |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"))) -((-4519 . T) (-3973 . T) (-4514 . T) (-4513 . T)) +((-4521 . T) (-3973 . T) (-4516 . T) (-4515 . T)) NIL (-1051 |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}."))) -((-4519 . T) (-4514 . T) (-4513 . T)) -((|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-172))) (-2198 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-172)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-365)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))))) +((-4521 . T) (-4516 . T) (-4515 . T)) +((|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (QUOTE (-301))) (|HasCategory| |#3| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-172))) (-2199 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-172)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-365)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))))) (-1052 |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 @@ -4154,7 +4154,7 @@ NIL NIL (-1056) ((|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."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1057 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4162,19 +4162,19 @@ NIL NIL (-1058) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting integers to roman numerals.")) (|roman| (($ (|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."))) -((-4507 . T) (-4511 . T) (-4506 . T) (-4517 . T) (-4518 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4509 . T) (-4513 . T) (-4508 . T) (-4519 . T) (-4520 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1059) ((|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}"))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4083) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090)))) (|HasCategory| (-1161) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-2198 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (QUOTE (-1090)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (QUOTE (-1161))) (LIST (QUOTE |:|) (QUOTE -4085) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090)))) (|HasCategory| (-1161) (QUOTE (-842))) (|HasCategory| (-57) (QUOTE (-1090))) (-2199 (|HasCategory| (-57) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (QUOTE (-1090)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -303) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1090))))) (-1060 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -43) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -993) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-1161))))) (-1061 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-1062 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}"))) @@ -4194,7 +4194,7 @@ NIL NIL (-1066 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}."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1067 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."))) @@ -4222,8 +4222,8 @@ NIL NIL (-1073 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."))) -((-4512 |has| |#1| (-365)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-350)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-350))))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-365)))) (-2198 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-350))))) +((-4514 |has| |#1| (-365)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-350))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-350)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-350))))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-365)))) (-2199 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-350))))) (-1074 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 @@ -4242,8 +4242,8 @@ NIL NIL (-1078 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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4517)) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1079 (-1161)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-1079 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 @@ -4278,7 +4278,7 @@ NIL NIL (-1087 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}."))) -((-4509 . T) (-3973 . T)) +((-4511 . T) (-3973 . T)) NIL (-1088) ((|constructor| (NIL "This is part of the PAFF package,{} related to projective space."))) @@ -4298,8 +4298,8 @@ NIL NIL (-1092 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)}"))) -((-4519 . T) (-4509 . T) (-4520 . T)) -((|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4521 . T) (-4511 . T) (-4522 . T)) +((|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-842))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-1093 |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 @@ -4326,7 +4326,7 @@ NIL NIL (-1099 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."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1100) ((|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."))) @@ -4342,8 +4342,8 @@ NIL NIL (-1103 |dimtot| |dim1| S) ((|constructor| (NIL "This type represents the finite direct or cartesian product of an underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4513 |has| |#3| (-1047)) (-4514 |has| |#3| (-1047)) (-4516 |has| |#3| (-6 -4516)) ((-4521 "*") |has| |#3| (-172)) (-4519 . 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-303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-365)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-370)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-716)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-788)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-840)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1047)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -303) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1090)))))) (-1104 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 @@ -4362,19 +4362,19 @@ NIL NIL (-1108) ((|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."))) -((-4507 . T) (-4511 . T) (-4506 . T) (-4517 . T) (-4518 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4509 . T) (-4513 . T) (-4508 . T) (-4519 . T) (-4520 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1109 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| $) "\\indented{1}{push!(\\spad{x},{}\\spad{s}) pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s}} \\indented{1}{so as to have a new first (top) element \\spad{x}.} \\indented{1}{Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.} \\blankline \\spad{X} a:Stack INT:= stack [1,{}2,{}3,{}4,{}5] \\spad{X} push! a \\spad{X} a"))) -((-4519 . T) (-4520 . T) (-3973 . T)) +((-4521 . T) (-4522 . T) (-3973 . T)) NIL (-1110 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-365))) (|HasAttribute| |#3| (QUOTE (-4521 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +((|HasCategory| |#3| (QUOTE (-365))) (|HasAttribute| |#3| (QUOTE (-4523 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) (-1111 |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."))) -((-3973 . T) (-4519 . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-3973 . T) (-4521 . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1112 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}."))) @@ -4382,15 +4382,15 @@ NIL NIL (-1113 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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4517)) (|HasCategory| |#1| (QUOTE (-453))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-904))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasAttribute| |#1| (QUOTE -4519)) (|HasCategory| |#1| (QUOTE (-453))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (|HasCategory| |#1| (QUOTE (-453))) (|HasCategory| |#1| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-148))))) (-1114 |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)"))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-558))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-365)))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-558))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-365)))) (-1115 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."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1116 UP -1478) ((|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"))) @@ -4434,19 +4434,19 @@ NIL NIL (-1126 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."))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| (-1125 |#1| |#2|) (QUOTE (-1090))) (-12 (|HasCategory| (-1125 |#1| |#2|) (LIST (QUOTE -303) (LIST (QUOTE -1125) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1125 |#1| |#2|) (QUOTE (-1090))))) (-1127 |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}."))) -((-4516 . T) (-4508 |has| |#2| (-6 (-4521 "*"))) (-4519 . T) (-4513 . T) (-4514 . T)) -((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4521 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-365))) (-2198 (|HasAttribute| |#2| (QUOTE (-4521 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4518 . T) (-4510 |has| |#2| (-6 (-4523 "*"))) (-4521 . T) (-4515 . T) (-4516 . T)) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4523 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-365))) (-2199 (|HasAttribute| |#2| (QUOTE (-4523 "*"))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-172)))) (-1128 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note that \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} \\indented{2}{reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.}")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1129) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1130 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."))) @@ -4454,11 +4454,11 @@ NIL NIL (-1131 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."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1090))) (-12 (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370)))) (-1132 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]"))) -((-4519 . T) (-4520 . T)) +((-4521 . T) (-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-1133 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})}."))) @@ -4470,8 +4470,8 @@ NIL NIL (-1135 |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."))) -((-4520 . T)) -((|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090)))) (-2198 (|HasCategory| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090))))) +((-4522 . T)) +((|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-1090))) (-12 (|HasCategory| |#2| (LIST (QUOTE -303) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090)))) (-2199 (|HasCategory| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090))))) (-1136) ((|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 @@ -4494,20 +4494,20 @@ NIL NIL (-1141 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."))) -((-4520 . T)) +((-4522 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-568) (QUOTE (-842)))) (-1142) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1143) ((|constructor| (NIL "This is the domain of character strings. Strings are 1 based."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-842)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| (-147) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-147) (QUOTE (-842))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| (-147) (QUOTE (-1090))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-842)))) (-12 (|HasCategory| (-147) (LIST (QUOTE -303) (QUOTE (-147)))) (|HasCategory| (-147) (QUOTE (-1090)))))) (-1144 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4519 . T) (-4520 . T)) -((|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3649) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4083) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (QUOTE (-1090)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090))) (-2198 (|HasCategory| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) +((-4521 . T) (-4522 . T)) +((|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (QUOTE (-1090))) (-12 (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (LIST (QUOTE -303) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3651) (QUOTE (-1143))) (LIST (QUOTE |:|) (QUOTE -4085) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (QUOTE (-1090)))) (|HasCategory| (-1143) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090))) (-2199 (|HasCategory| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-1145 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 @@ -4534,8 +4534,8 @@ NIL NIL (-1151 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent 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{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in \\spad{(x - 3)} with 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}.")) 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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 (-1157 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. Note that if the coefficient ring is a field,{} this domain forms a euclidean domain.")) 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T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1159 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\spadtype{SparseUnivariateTaylorSeries} 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{SparseUnivariateTaylorSeries}(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.")) (|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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1160) ((|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} 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."))) @@ -4658,7 +4658,7 @@ NIL NIL (-1182 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| $)) "\\indented{1}{tree(\\spad{nd},{}\\spad{ls}) creates a tree with value \\spad{nd},{} and children \\spad{ls}.} \\blankline \\spad{X} t1:=tree [1,{}2,{}3,{}4] \\spad{X} tree(5,{}[\\spad{t1}])"))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090))))) (-1183 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) @@ -4686,12 +4686,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-370)))) (-1189 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1190 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-558))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-365)))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-150))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-558))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-365)))) (-1191 |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 @@ -4726,7 +4726,7 @@ NIL NIL (-1199) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1200 |Coef|) ((|constructor| (NIL "This package has no description"))) @@ -4734,15 +4734,15 @@ NIL NIL (-1201 |Coef|) ((|constructor| (NIL "This domain has no description"))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1202 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series This package allows one to apply a function to the coefficients of a univariate Laurent series.")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent 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 1. We may integrate a series when we can divide coefficients by integers.")) (|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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1204 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)}."))) @@ -4750,16 +4750,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-1205 |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 that \\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)}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-3973 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-3973 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1206 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. 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The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spad{UnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent series in \\spad{(x - 3)} with 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}.")) 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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 @@ -4794,8 +4794,8 @@ NIL NIL (-1216 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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T)) -((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1136))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (-2198 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4517)) (|HasCategory| |#2| (QUOTE (-453))) (-2198 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2198 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) +(((-4523 "*") |has| |#2| (-172)) (-4514 |has| |#2| (-558)) (-4517 |has| |#2| (-365)) (-4519 |has| |#2| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-381))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -881) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-568))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-381)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -887) (QUOTE (-568)))))) (-12 (|HasCategory| (-1075) (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-541))))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -630) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-150))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1136))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (-2199 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4519)) (|HasCategory| |#2| (QUOTE (-453))) (-2199 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (-2199 (-12 (|HasCategory| $ (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-148))))) (-1217 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 @@ -4806,15 +4806,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-453))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1136)))) (-1219 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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4515 |has| |#1| (-365)) (-4517 |has| |#1| (-6 -4517)) (-4514 . T) (-4513 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4519 |has| |#1| (-6 -4519)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-1220 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 -895) (QUOTE (-1161)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2745) (LIST (|devaluate| |#2|) (QUOTE (-1161)))))) +((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2747) (LIST (|devaluate| |#2|) (QUOTE (-1161)))))) (-1221 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1222 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4826,7 +4826,7 @@ NIL NIL (-1224 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1225 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)}."))) @@ -4834,24 +4834,24 @@ NIL NIL (-1226 |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)}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1227 |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)}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1228 |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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4517 |has| |#1| (-365)) (-4511 |has| |#1| (-365)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2198 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4519 |has| |#1| (-365)) (-4513 |has| |#1| (-365)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568))) (|devaluate| |#1|))))) (|HasCategory| (-409 (-568)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2199 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1229 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))}."))) -(((-4521 "*") |has| (-1228 |#2| |#3| |#4|) (-172)) (-4512 |has| (-1228 |#2| |#3| |#4|) (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-150))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-172))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-453))) (-2198 (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-558)))) +(((-4523 "*") |has| (-1228 |#2| |#3| |#4|) (-172)) (-4514 |has| (-1228 |#2| |#3| |#4|) (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-150))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-172))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (QUOTE (-568)))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-453))) (-2199 (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (LIST (QUOTE -1037) (LIST (QUOTE -409) (QUOTE (-568)))))) (|HasCategory| (-1228 |#2| |#3| |#4|) (QUOTE (-558)))) (-1230 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note that if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4520))) +((|HasAttribute| |#1| (QUOTE -4522))) (-1231 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note that if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note that \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) ((-3973 . T)) @@ -4863,15 +4863,15 @@ NIL (-1233 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-568)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasSignature| |#2| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3837) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1161))))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1181))) (|HasSignature| |#2| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1845) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1161))))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#2| (QUOTE (-365)))) (-1234 |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."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1235 |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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1236 |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 @@ -4886,8 +4886,8 @@ NIL NIL (-1239 |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}."))) -(((-4521 "*") |has| |#1| (-172)) (-4512 |has| |#1| (-558)) (-4513 . T) (-4514 . T) (-4516 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2198 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2745) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -3837) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2055) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) +(((-4523 "*") |has| |#1| (-172)) (-4514 |has| |#1| (-558)) (-4515 . T) (-4516 . T) (-4518 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2199 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-150))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1161)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-763)) (|devaluate| |#1|))))) (|HasCategory| (-763) (QUOTE (-1102))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-763))))) (|HasSignature| |#1| (LIST (QUOTE -2747) (LIST (|devaluate| |#1|) (QUOTE (-1161)))))) (|HasCategory| |#1| (QUOTE (-365))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-568)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1181)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasSignature| |#1| (LIST (QUOTE -1845) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1161))))) (|HasSignature| |#1| (LIST (QUOTE -2057) (LIST (LIST (QUOTE -634) (QUOTE (-1161))) (|devaluate| |#1|))))))) (-1240 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL @@ -4898,7 +4898,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1002))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1242 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4520 . T) (-4519 . T) (-3973 . T)) +((-4522 . T) (-4521 . T) (-3973 . T)) NIL (-1243 A B) ((|constructor| (NIL "This package provides operations which all take as arguments vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4906,8 +4906,8 @@ NIL NIL (-1244 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4520 . T) (-4519 . T)) -((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2198 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2198 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) +((-4522 . T) (-4521 . T)) +((|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-842))) (-2199 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| (-568) (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#1| (QUOTE (-1047))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1047)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))) (-2199 (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-842)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -303) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1090)))))) (-1245) ((|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|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4934,7 +4934,7 @@ NIL NIL (-1251 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4514 . T) (-4513 . T)) +((-4516 . T) (-4515 . T)) NIL (-1252 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."))) @@ -4946,27 +4946,27 @@ NIL NIL (-1254 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"))) -((-4514 |has| |#1| (-172)) (-4513 |has| |#1| (-172)) (-4516 . T)) +((-4516 |has| |#1| (-172)) (-4515 |has| |#1| (-172)) (-4518 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-1255 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}}."))) -((-4520 . T) (-4519 . T)) +((-4522 . T) (-4521 . T)) ((|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1090))) (-12 (|HasCategory| |#4| (LIST (QUOTE -303) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370)))) (-1256 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}."))) -((-4513 . T) (-4514 . T) (-4516 . T)) +((-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1257 |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."))) -((-4516 . T) (-4512 |has| |#2| (-6 -4512)) (-4514 . T) (-4513 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4512))) +((-4518 . T) (-4514 |has| |#2| (-6 -4514)) (-4516 . T) (-4515 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4514))) (-1258 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 (-1259 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4512 |has| |#2| (-6 -4512)) (-4514 . T) (-4513 . T) (-4516 . T)) +((-4514 |has| |#2| (-6 -4514)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-1260 S -1478) ((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) @@ -4974,28 +4974,28 @@ NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-150)))) (-1261 -1478) ((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4511 . T) (-4517 . T) (-4512 . T) ((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +((-4513 . T) (-4519 . T) (-4514 . T) ((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL (-1262 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations.")) (|log| (($ $ (|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}}."))) -((-4512 |has| |#2| (-6 -4512)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -707) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasAttribute| |#2| (QUOTE -4512))) +((-4514 |has| |#2| (-6 -4514)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -707) (LIST (QUOTE -409) (QUOTE (-568))))) (|HasAttribute| |#2| (QUOTE -4514))) (-1263 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4512 |has| |#2| (-6 -4512)) (-4514 . T) (-4513 . T) (-4516 . T)) +((-4514 |has| |#2| (-6 -4514)) (-4516 . T) (-4515 . T) (-4518 . T)) NIL (-1264 R) ((|constructor| (NIL "This type supports multivariate polynomials whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4512 |has| |#1| (-6 -4512)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4512))) +((-4514 |has| |#1| (-6 -4514)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4514))) (-1265 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4516 . T) (-4517 |has| |#1| (-6 -4517)) (-4512 |has| |#1| (-6 -4512)) (-4514 . T) (-4513 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4516)) (|HasAttribute| |#1| (QUOTE -4517)) (|HasAttribute| |#1| (QUOTE -4512))) +((-4518 . T) (-4519 |has| |#1| (-6 -4519)) (-4514 |has| |#1| (-6 -4514)) (-4516 . T) (-4515 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4518)) (|HasAttribute| |#1| (QUOTE -4519)) (|HasAttribute| |#1| (QUOTE -4514))) (-1266 |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."))) -((-4512 |has| |#2| (-6 -4512)) (-4514 . T) (-4513 . T) (-4516 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4512))) +((-4514 |has| |#2| (-6 -4514)) (-4516 . T) (-4515 . T) (-4518 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4514))) (-1267 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 @@ -5010,7 +5010,7 @@ NIL NIL (-1270 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4521 "*") . T) (-4513 . T) (-4514 . T) (-4516 . T)) +(((-4523 "*") . T) (-4515 . T) (-4516 . T) (-4518 . T)) NIL NIL NIL @@ -5032,4 +5032,4 @@ NIL NIL NIL NIL -((-1275 NIL 2465018 2465023 2465028 2465033) (-3 NIL 2464998 2465003 2465008 2465013) (-2 NIL 2464978 2464983 2464988 2464993) (-1 NIL 2464958 2464963 2464968 2464973) (0 NIL 2464938 2464943 2464948 2464953) (-1270 "bookvol10.3.pamphlet" 2464747 2464760 2464876 2464933) (-1269 "bookvol10.4.pamphlet" 2463791 2463802 2464737 2464742) (-1268 "bookvol10.4.pamphlet" 2454031 2454053 2463781 2463786) (-1267 "bookvol10.4.pamphlet" 2453524 2453535 2454021 2454026) (-1266 "bookvol10.3.pamphlet" 2452759 2452779 2453380 2453449) (-1265 "bookvol10.3.pamphlet" 2450488 2450501 2452477 2452576) (-1264 "bookvol10.3.pamphlet" 2450058 2450069 2450344 2450413) (-1263 "bookvol10.2.pamphlet" 2449375 2449391 2449984 2450053) (-1262 "bookvol10.3.pamphlet" 2447872 2447892 2449155 2449224) (-1261 "bookvol10.2.pamphlet" 2446332 2446347 2447774 2447867) (-1260 NIL 2444772 2444789 2446216 2446221) (-1259 "bookvol10.2.pamphlet" 2441797 2441813 2444698 2444767) (-1258 "bookvol10.4.pamphlet" 2441108 2441134 2441787 2441792) (-1257 "bookvol10.3.pamphlet" 2440737 2440753 2440964 2441033) (-1256 "bookvol10.2.pamphlet" 2440436 2440447 2440693 2440732) (-1255 "bookvol10.3.pamphlet" 2436710 2436727 2440138 2440165) (-1254 "bookvol10.3.pamphlet" 2435724 2435768 2436568 2436635) (-1253 "bookvol10.4.pamphlet" 2433287 2433309 2435714 2435719) (-1252 "bookvol10.4.pamphlet" 2431493 2431504 2433277 2433282) (-1251 "bookvol10.2.pamphlet" 2431166 2431177 2431461 2431488) (-1250 NIL 2430859 2430872 2431156 2431161) (-1249 "bookvol10.3.pamphlet" 2430449 2430458 2430849 2430854) (-1248 "bookvol10.4.pamphlet" 2428071 2428080 2430439 2430444) (-1247 "bookvol10.4.pamphlet" 2423268 2423277 2428061 2428066) (-1246 "bookvol10.3.pamphlet" 2407022 2407031 2423258 2423263) (-1245 "bookvol10.3.pamphlet" 2394759 2394768 2407012 2407017) (-1244 "bookvol10.3.pamphlet" 2393656 2393667 2393907 2393934) (-1243 "bookvol10.4.pamphlet" 2392298 2392311 2393646 2393651) (-1242 "bookvol10.2.pamphlet" 2390186 2390197 2392254 2392293) (-1241 NIL 2387893 2387906 2389963 2389968) (-1240 "bookvol10.3.pamphlet" 2387673 2387688 2387883 2387888) (-1239 "bookvol10.3.pamphlet" 2382857 2382879 2386140 2386237) (-1238 "bookvol10.4.pamphlet" 2382760 2382788 2382847 2382852) (-1237 "bookvol10.4.pamphlet" 2382068 2382092 2382716 2382721) (-1236 "bookvol10.4.pamphlet" 2380220 2380240 2382058 2382063) (-1235 "bookvol10.3.pamphlet" 2375009 2375037 2378687 2378784) (-1234 "bookvol10.2.pamphlet" 2372460 2372476 2374907 2375004) (-1233 NIL 2369555 2369573 2372004 2372009) (-1232 "bookvol10.4.pamphlet" 2369178 2369213 2369545 2369550) (-1231 "bookvol10.2.pamphlet" 2363776 2363787 2369158 2369173) (-1230 NIL 2358348 2358361 2363732 2363737) (-1229 "bookvol10.3.pamphlet" 2355991 2356017 2357429 2357562) (-1228 "bookvol10.3.pamphlet" 2353126 2353154 2354123 2354272) (-1227 "bookvol10.3.pamphlet" 2350883 2350903 2351258 2351407) (-1226 "bookvol10.2.pamphlet" 2349341 2349361 2350729 2350878) (-1225 NIL 2347941 2347963 2349331 2349336) (-1224 "bookvol10.2.pamphlet" 2346522 2346538 2347787 2347936) (-1223 "bookvol10.4.pamphlet" 2346063 2346116 2346512 2346517) (-1222 "bookvol10.4.pamphlet" 2344475 2344489 2346053 2346058) (-1221 "bookvol10.2.pamphlet" 2342055 2342079 2344373 2344470) (-1220 NIL 2339341 2339367 2341661 2341666) (-1219 "bookvol10.2.pamphlet" 2334315 2334326 2339183 2339336) (-1218 NIL 2329181 2329194 2334051 2334056) (-1217 "bookvol10.4.pamphlet" 2328646 2328665 2329171 2329176) (-1216 "bookvol10.3.pamphlet" 2325597 2325612 2326196 2326349) (-1215 "bookvol10.4.pamphlet" 2324487 2324500 2325587 2325592) (-1214 "bookvol10.4.pamphlet" 2324050 2324064 2324477 2324482) (-1213 "bookvol10.4.pamphlet" 2322287 2322301 2324040 2324045) (-1212 "bookvol10.4.pamphlet" 2321494 2321510 2322277 2322282) (-1211 "bookvol10.4.pamphlet" 2320856 2320877 2321484 2321489) (-1210 "bookvol10.3.pamphlet" 2320209 2320220 2320775 2320780) (-1209 "bookvol10.4.pamphlet" 2319702 2319715 2320165 2320170) (-1208 "bookvol10.4.pamphlet" 2318803 2318815 2319692 2319697) (-1207 "bookvol10.3.pamphlet" 2309463 2309491 2310448 2310877) (-1206 "bookvol10.3.pamphlet" 2303500 2303520 2303872 2304021) (-1205 "bookvol10.2.pamphlet" 2301093 2301113 2303320 2303495) (-1204 NIL 2298820 2298842 2301049 2301054) (-1203 "bookvol10.2.pamphlet" 2297036 2297052 2298666 2298815) (-1202 "bookvol10.4.pamphlet" 2296578 2296631 2297026 2297031) (-1201 "bookvol10.3.pamphlet" 2294971 2294987 2295045 2295142) (-1200 "bookvol10.4.pamphlet" 2294886 2294902 2294961 2294966) (-1199 "bookvol10.2.pamphlet" 2293951 2293960 2294812 2294881) (-1198 NIL 2293078 2293089 2293941 2293946) (-1197 "bookvol10.4.pamphlet" 2291925 2291934 2293068 2293073) (-1196 "bookvol10.4.pamphlet" 2289411 2289422 2291881 2291886) (-1195 "bookvol10.2.pamphlet" 2289333 2289342 2289391 2289406) (-1194 "bookvol10.4.pamphlet" 2287983 2287998 2289323 2289328) (-1193 "bookvol10.3.pamphlet" 2286886 2286897 2287938 2287943) (-1192 "bookvol10.4.pamphlet" 2283720 2283729 2286876 2286881) (-1191 "bookvol10.3.pamphlet" 2282376 2282393 2283710 2283715) (-1190 "bookvol10.3.pamphlet" 2280965 2280981 2281941 2282038) (-1189 "bookvol10.2.pamphlet" 2268275 2268292 2280921 2280960) (-1188 NIL 2255583 2255602 2268231 2268236) (-1187 "bookvol10.4.pamphlet" 2249949 2249966 2255289 2255294) (-1186 "bookvol10.4.pamphlet" 2248908 2248933 2249939 2249944) (-1185 "bookvol10.4.pamphlet" 2247425 2247442 2248898 2248903) (-1184 "bookvol10.2.pamphlet" 2246937 2246946 2247415 2247420) (-1183 NIL 2246447 2246458 2246927 2246932) (-1182 "bookvol10.3.pamphlet" 2244496 2244507 2246277 2246304) (-1181 "bookvol10.2.pamphlet" 2244327 2244336 2244486 2244491) (-1180 NIL 2244156 2244167 2244317 2244322) (-1179 "bookvol10.4.pamphlet" 2243830 2243839 2244146 2244151) (-1178 "bookvol10.4.pamphlet" 2243493 2243504 2243820 2243825) (-1177 "bookvol10.3.pamphlet" 2242050 2242059 2243483 2243488) (-1176 "bookvol10.3.pamphlet" 2239067 2239076 2242040 2242045) (-1175 "bookvol10.4.pamphlet" 2238623 2238634 2239057 2239062) (-1174 "bookvol10.4.pamphlet" 2238178 2238187 2238613 2238618) (-1173 "bookvol10.4.pamphlet" 2236271 2236294 2238168 2238173) (-1172 "bookvol10.2.pamphlet" 2235118 2235141 2236239 2236266) (-1171 NIL 2233985 2234010 2235108 2235113) (-1170 "bookvol10.4.pamphlet" 2233361 2233372 2233975 2233980) (-1169 "bookvol10.3.pamphlet" 2232334 2232357 2232604 2232631) (-1168 "bookvol10.3.pamphlet" 2231830 2231841 2232324 2232329) (-1167 "bookvol10.4.pamphlet" 2228682 2228693 2231820 2231825) (-1166 "bookvol10.4.pamphlet" 2225275 2225286 2228672 2228677) (-1165 "bookvol10.3.pamphlet" 2223328 2223337 2225265 2225270) (-1164 "bookvol10.3.pamphlet" 2219313 2219322 2223318 2223323) (-1163 "bookvol10.3.pamphlet" 2218320 2218331 2218402 2218529) (-1162 "bookvol10.4.pamphlet" 2217795 2217806 2218310 2218315) (-1161 "bookvol10.3.pamphlet" 2215123 2215132 2217785 2217790) (-1160 "bookvol10.3.pamphlet" 2211879 2211888 2215113 2215118) (-1159 "bookvol10.3.pamphlet" 2208886 2208914 2210346 2210443) (-1158 "bookvol10.3.pamphlet" 2206008 2206036 2207018 2207167) (-1157 "bookvol10.3.pamphlet" 2202691 2202702 2203558 2203711) (-1156 "bookvol10.4.pamphlet" 2201811 2201829 2202681 2202686) (-1155 "bookvol10.3.pamphlet" 2199255 2199266 2199324 2199477) (-1154 "bookvol10.4.pamphlet" 2198645 2198658 2199245 2199250) (-1153 "bookvol10.4.pamphlet" 2197123 2197134 2198635 2198640) (-1152 "bookvol10.4.pamphlet" 2196749 2196766 2197113 2197118) (-1151 "bookvol10.3.pamphlet" 2187396 2187424 2188394 2188823) (-1150 "bookvol10.3.pamphlet" 2187076 2187091 2187386 2187391) (-1149 "bookvol10.3.pamphlet" 2179047 2179062 2187066 2187071) (-1148 "bookvol10.4.pamphlet" 2178219 2178233 2179003 2179008) (-1147 "bookvol10.4.pamphlet" 2174318 2174334 2178209 2178214) (-1146 "bookvol10.4.pamphlet" 2170786 2170802 2174308 2174313) (-1145 "bookvol10.4.pamphlet" 2163186 2163197 2170667 2170672) (-1144 "bookvol10.3.pamphlet" 2162265 2162282 2162414 2162441) (-1143 "bookvol10.3.pamphlet" 2161648 2161657 2161746 2161773) (-1142 "bookvol10.2.pamphlet" 2161424 2161433 2161604 2161643) (-1141 "bookvol10.3.pamphlet" 2156372 2156383 2161172 2161187) (-1140 "bookvol10.4.pamphlet" 2155583 2155598 2156362 2156367) (-1139 "bookvol10.4.pamphlet" 2153792 2153805 2155573 2155578) (-1138 "bookvol10.4.pamphlet" 2153216 2153227 2153782 2153787) (-1137 "bookvol10.4.pamphlet" 2152122 2152138 2153206 2153211) (-1136 "bookvol10.2.pamphlet" 2151328 2151337 2152112 2152117) (-1135 "bookvol10.3.pamphlet" 2150416 2150444 2150583 2150598) (-1134 "bookvol10.2.pamphlet" 2149473 2149484 2150396 2150411) (-1133 NIL 2148538 2148551 2149463 2149468) (-1132 "bookvol10.3.pamphlet" 2144163 2144174 2148368 2148395) (-1131 "bookvol10.3.pamphlet" 2142206 2142223 2143865 2143892) (-1130 "bookvol10.4.pamphlet" 2140933 2140953 2142196 2142201) (-1129 "bookvol10.2.pamphlet" 2135976 2135985 2140889 2140928) (-1128 NIL 2131051 2131062 2135966 2135971) (-1127 "bookvol10.3.pamphlet" 2128731 2128749 2129639 2129726) (-1126 "bookvol10.3.pamphlet" 2123598 2123611 2128482 2128509) (-1125 "bookvol10.3.pamphlet" 2120138 2120151 2123588 2123593) (-1124 "bookvol10.2.pamphlet" 2118915 2118924 2120128 2120133) (-1123 "bookvol10.4.pamphlet" 2117480 2117489 2118905 2118910) (-1122 "bookvol10.2.pamphlet" 2101307 2101318 2117470 2117475) (-1121 "bookvol10.3.pamphlet" 2101083 2101094 2101297 2101302) (-1120 "bookvol10.4.pamphlet" 2100628 2100641 2101039 2101044) (-1119 "bookvol10.4.pamphlet" 2098221 2098232 2100618 2100623) (-1118 "bookvol10.4.pamphlet" 2096786 2096797 2098211 2098216) (-1117 "bookvol10.4.pamphlet" 2090213 2090224 2096776 2096781) (-1116 "bookvol10.4.pamphlet" 2088633 2088651 2090203 2090208) (-1115 "bookvol10.2.pamphlet" 2088400 2088417 2088589 2088628) (-1114 "bookvol10.3.pamphlet" 2086516 2086542 2087965 2088062) (-1113 "bookvol10.3.pamphlet" 2083970 2083990 2084345 2084472) (-1112 "bookvol10.4.pamphlet" 2082813 2082838 2083960 2083965) (-1111 "bookvol10.2.pamphlet" 2080911 2080941 2082745 2082808) (-1110 NIL 2078953 2078985 2080789 2080794) (-1109 "bookvol10.2.pamphlet" 2077391 2077402 2078909 2078948) (-1108 "bookvol10.3.pamphlet" 2075756 2075765 2077257 2077386) (-1107 "bookvol10.4.pamphlet" 2075499 2075508 2075746 2075751) (-1106 "bookvol10.4.pamphlet" 2074607 2074618 2075489 2075494) (-1105 "bookvol10.4.pamphlet" 2073876 2073893 2074597 2074602) (-1104 "bookvol10.4.pamphlet" 2071746 2071761 2073832 2073837) (-1103 "bookvol10.3.pamphlet" 2063459 2063486 2063961 2064092) (-1102 "bookvol10.2.pamphlet" 2062694 2062703 2063449 2063454) (-1101 NIL 2061927 2061938 2062684 2062689) (-1100 "bookvol10.4.pamphlet" 2054953 2054962 2061917 2061922) (-1099 "bookvol10.2.pamphlet" 2054432 2054449 2054909 2054948) (-1098 "bookvol10.4.pamphlet" 2054131 2054151 2054422 2054427) (-1097 "bookvol10.4.pamphlet" 2049456 2049476 2054121 2054126) (-1096 "bookvol10.3.pamphlet" 2048891 2048905 2049446 2049451) (-1095 "bookvol10.3.pamphlet" 2048734 2048774 2048881 2048886) (-1094 "bookvol10.3.pamphlet" 2048626 2048635 2048724 2048729) (-1093 "bookvol10.2.pamphlet" 2045715 2045755 2048616 2048621) (-1092 "bookvol10.3.pamphlet" 2044025 2044036 2045192 2045231) (-1091 "bookvol10.3.pamphlet" 2042443 2042460 2044015 2044020) (-1090 "bookvol10.2.pamphlet" 2041925 2041934 2042433 2042438) (-1089 NIL 2041405 2041416 2041915 2041920) (-1088 "bookvol10.2.pamphlet" 2041294 2041303 2041395 2041400) (-1087 "bookvol10.2.pamphlet" 2037782 2037793 2041262 2041289) (-1086 NIL 2034290 2034303 2037772 2037777) (-1085 "bookvol10.2.pamphlet" 2033402 2033415 2034270 2034285) (-1084 "bookvol10.3.pamphlet" 2033215 2033226 2033321 2033326) (-1083 "bookvol10.2.pamphlet" 2032021 2032032 2033195 2033210) (-1082 "bookvol10.3.pamphlet" 2031093 2031104 2031976 2031981) (-1081 "bookvol10.4.pamphlet" 2030789 2030802 2031083 2031088) (-1080 "bookvol10.4.pamphlet" 2030214 2030227 2030745 2030750) (-1079 "bookvol10.3.pamphlet" 2029490 2029501 2030204 2030209) (-1078 "bookvol10.3.pamphlet" 2026892 2026903 2027171 2027298) (-1077 "bookvol10.4.pamphlet" 2024971 2024982 2026882 2026887) (-1076 "bookvol10.4.pamphlet" 2023852 2023863 2024961 2024966) (-1075 "bookvol10.3.pamphlet" 2023724 2023733 2023842 2023847) (-1074 "bookvol10.4.pamphlet" 2023437 2023457 2023714 2023719) (-1073 "bookvol10.3.pamphlet" 2021558 2021574 2022223 2022358) (-1072 "bookvol10.4.pamphlet" 2021259 2021279 2021548 2021553) (-1071 "bookvol10.4.pamphlet" 2018945 2018961 2021249 2021254) (-1070 "bookvol10.3.pamphlet" 2018347 2018371 2018935 2018940) (-1069 "bookvol10.3.pamphlet" 2016691 2016715 2018337 2018342) (-1068 "bookvol10.3.pamphlet" 2016543 2016556 2016681 2016686) (-1067 "bookvol10.4.pamphlet" 2013611 2013631 2016533 2016538) (-1066 "bookvol10.2.pamphlet" 2004071 2004088 2013567 2013606) (-1065 NIL 1994563 1994582 2004061 2004066) (-1064 "bookvol10.4.pamphlet" 1993197 1993217 1994553 1994558) (-1063 "bookvol10.2.pamphlet" 1991581 1991611 1993187 1993192) (-1062 NIL 1989963 1989995 1991571 1991576) (-1061 "bookvol10.2.pamphlet" 1969279 1969294 1989831 1989958) (-1060 NIL 1948309 1948326 1968863 1968868) (-1059 "bookvol10.3.pamphlet" 1944754 1944763 1947538 1947565) (-1058 "bookvol10.3.pamphlet" 1944001 1944010 1944620 1944749) (-1057 NIL 1943081 1943113 1943991 1943996) (-1056 "bookvol10.2.pamphlet" 1941984 1941993 1942983 1943076) (-1055 NIL 1940973 1940984 1941974 1941979) (-1054 "bookvol10.2.pamphlet" 1940495 1940504 1940963 1940968) (-1053 "bookvol10.2.pamphlet" 1939972 1939983 1940485 1940490) (-1052 "bookvol10.4.pamphlet" 1939380 1939437 1939962 1939967) (-1051 "bookvol10.3.pamphlet" 1938115 1938134 1938603 1938642) (-1050 "bookvol10.2.pamphlet" 1933632 1933663 1938059 1938110) (-1049 NIL 1929051 1929084 1933480 1933485) (-1048 "bookvol10.4.pamphlet" 1928939 1928959 1929041 1929046) (-1047 "bookvol10.2.pamphlet" 1928292 1928301 1928919 1928934) (-1046 NIL 1927653 1927664 1928282 1928287) (-1045 "bookvol10.4.pamphlet" 1926547 1926556 1927643 1927648) (-1044 "bookvol10.3.pamphlet" 1925212 1925228 1926107 1926134) (-1043 "bookvol10.4.pamphlet" 1923254 1923265 1925202 1925207) (-1042 "bookvol10.4.pamphlet" 1920868 1920879 1923244 1923249) (-1041 "bookvol10.4.pamphlet" 1920330 1920341 1920858 1920863) (-1040 "bookvol10.4.pamphlet" 1920065 1920077 1920320 1920325) (-1039 "bookvol10.4.pamphlet" 1919053 1919062 1920055 1920060) (-1038 "bookvol10.4.pamphlet" 1918470 1918483 1919043 1919048) (-1037 "bookvol10.2.pamphlet" 1917819 1917830 1918460 1918465) (-1036 NIL 1917166 1917179 1917809 1917814) (-1035 "bookvol10.3.pamphlet" 1915808 1915817 1916395 1916422) (-1034 "bookvol10.3.pamphlet" 1915155 1915202 1915746 1915803) (-1033 "bookvol10.4.pamphlet" 1914479 1914490 1915145 1915150) (-1032 "bookvol10.4.pamphlet" 1914208 1914219 1914469 1914474) (-1031 "bookvol10.4.pamphlet" 1911760 1911769 1914198 1914203) (-1030 "bookvol10.4.pamphlet" 1911465 1911476 1911750 1911755) (-1029 "bookvol10.4.pamphlet" 1900907 1900918 1911307 1911312) (-1028 "bookvol10.4.pamphlet" 1894883 1894894 1900857 1900862) (-1027 "bookvol10.3.pamphlet" 1892974 1892991 1894585 1894612) (-1026 "bookvol10.3.pamphlet" 1892318 1892329 1892929 1892934) (-1025 "bookvol10.4.pamphlet" 1891494 1891511 1892308 1892313) (-1024 "bookvol10.4.pamphlet" 1889791 1889808 1891449 1891454) (-1023 "bookvol10.3.pamphlet" 1888574 1888594 1889278 1889371) (-1022 "bookvol10.4.pamphlet" 1887029 1887038 1888564 1888569) (-1021 "bookvol10.2.pamphlet" 1886901 1886910 1887019 1887024) (-1020 "bookvol10.4.pamphlet" 1884198 1884213 1886891 1886896) (-1019 "bookvol10.4.pamphlet" 1881041 1881056 1884188 1884193) (-1018 "bookvol10.4.pamphlet" 1880786 1880811 1881031 1881036) (-1017 "bookvol10.4.pamphlet" 1880349 1880360 1880776 1880781) (-1016 "bookvol10.4.pamphlet" 1879249 1879267 1880339 1880344) (-1015 "bookvol10.4.pamphlet" 1877454 1877472 1879239 1879244) (-1014 "bookvol10.4.pamphlet" 1876679 1876696 1877444 1877449) (-1013 "bookvol10.4.pamphlet" 1875829 1875846 1876669 1876674) (-1012 "bookvol10.2.pamphlet" 1873012 1873021 1875731 1875824) (-1011 NIL 1870281 1870292 1873002 1873007) (-1010 "bookvol10.2.pamphlet" 1868190 1868201 1870261 1870276) (-1009 NIL 1866036 1866049 1868109 1868114) (-1008 "bookvol10.4.pamphlet" 1865453 1865464 1866026 1866031) (-1007 "bookvol10.4.pamphlet" 1864637 1864649 1865443 1865448) (-1006 "bookvol10.4.pamphlet" 1863994 1864003 1864627 1864632) (-1005 "bookvol10.4.pamphlet" 1863748 1863757 1863984 1863989) (-1004 "bookvol10.3.pamphlet" 1860533 1860547 1862215 1862308) (-1003 "bookvol10.3.pamphlet" 1858946 1858983 1859065 1859221) (-1002 "bookvol10.2.pamphlet" 1858539 1858548 1858936 1858941) (-1001 NIL 1858130 1858141 1858529 1858534) (-1000 "bookvol10.3.pamphlet" 1853519 1853530 1857960 1857987) (-999 "bookvol10.3.pamphlet" 1852146 1852156 1852443 1852508) (-998 "bookvol10.4.pamphlet" 1851469 1851487 1852136 1852141) (-997 "bookvol10.2.pamphlet" 1849630 1849640 1851399 1851464) (-996 NIL 1847542 1847554 1849313 1849318) (-995 "bookvol10.2.pamphlet" 1846348 1846358 1847498 1847537) (-994 "bookvol10.3.pamphlet" 1845811 1845825 1846338 1846343) (-993 "bookvol10.2.pamphlet" 1844502 1844512 1845701 1845806) (-992 NIL 1842796 1842808 1843997 1844002) (-991 "bookvol10.4.pamphlet" 1842487 1842503 1842786 1842791) (-990 "bookvol10.3.pamphlet" 1842044 1842052 1842477 1842482) (-989 "bookvol10.4.pamphlet" 1837446 1837465 1842034 1842039) (-988 "bookvol10.3.pamphlet" 1833521 1833553 1837360 1837365) (-987 "bookvol10.4.pamphlet" 1831517 1831535 1833511 1833516) (-986 "bookvol10.4.pamphlet" 1828827 1828848 1831507 1831512) (-985 "bookvol10.4.pamphlet" 1828154 1828173 1828817 1828822) (-984 "bookvol10.2.pamphlet" 1824280 1824290 1828144 1828149) (-983 "bookvol10.4.pamphlet" 1821364 1821374 1824270 1824275) (-982 "bookvol10.4.pamphlet" 1821181 1821195 1821354 1821359) (-981 "bookvol10.2.pamphlet" 1820263 1820273 1821137 1821176) (-980 "bookvol10.4.pamphlet" 1819570 1819594 1820253 1820258) (-979 "bookvol10.4.pamphlet" 1818428 1818438 1819560 1819565) (-978 "bookvol10.4.pamphlet" 1803829 1803845 1818306 1818311) (-977 "bookvol10.2.pamphlet" 1797722 1797745 1803797 1803824) (-976 NIL 1791601 1791626 1797678 1797683) (-975 "bookvol10.2.pamphlet" 1790584 1790592 1791591 1791596) (-974 "bookvol10.2.pamphlet" 1789347 1789376 1790482 1790579) (-973 NIL 1788200 1788231 1789337 1789342) (-972 "bookvol10.3.pamphlet" 1787015 1787023 1788190 1788195) (-971 "bookvol10.2.pamphlet" 1784348 1784358 1787005 1787010) (-970 "bookvol10.4.pamphlet" 1774493 1774510 1784304 1784309) (-969 "bookvol10.2.pamphlet" 1773912 1773922 1774449 1774488) (-968 "bookvol10.3.pamphlet" 1773794 1773810 1773902 1773907) (-967 "bookvol10.3.pamphlet" 1773682 1773692 1773784 1773789) (-966 "bookvol10.3.pamphlet" 1773570 1773580 1773672 1773677) (-965 "bookvol10.3.pamphlet" 1770971 1770983 1771536 1771591) (-964 "bookvol10.3.pamphlet" 1769357 1769369 1770062 1770189) (-963 "bookvol10.4.pamphlet" 1768561 1768600 1769347 1769352) (-962 "bookvol10.4.pamphlet" 1768313 1768321 1768551 1768556) (-961 "bookvol10.4.pamphlet" 1766556 1766566 1768303 1768308) (-960 "bookvol10.4.pamphlet" 1764529 1764543 1766546 1766551) (-959 "bookvol10.2.pamphlet" 1764152 1764160 1764519 1764524) (-958 "bookvol10.3.pamphlet" 1763395 1763405 1763558 1763585) (-957 "bookvol10.4.pamphlet" 1761287 1761299 1763385 1763390) (-956 "bookvol10.4.pamphlet" 1760659 1760671 1761277 1761282) (-955 "bookvol10.2.pamphlet" 1759796 1759804 1760649 1760654) (-954 "bookvol10.4.pamphlet" 1758568 1758590 1759752 1759757) (-953 "bookvol10.3.pamphlet" 1755880 1755890 1756382 1756509) (-952 "bookvol10.4.pamphlet" 1755141 1755164 1755870 1755875) (-951 "bookvol10.4.pamphlet" 1753205 1753227 1755131 1755136) (-950 "bookvol10.2.pamphlet" 1746607 1746628 1753073 1753200) (-949 NIL 1739311 1739334 1745779 1745784) (-948 "bookvol10.4.pamphlet" 1738759 1738773 1739301 1739306) (-947 "bookvol10.4.pamphlet" 1738369 1738381 1738749 1738754) (-946 "bookvol10.4.pamphlet" 1737310 1737339 1738325 1738330) (-945 "bookvol10.4.pamphlet" 1736058 1736073 1737300 1737305) (-944 "bookvol10.3.pamphlet" 1735119 1735129 1735206 1735233) (-943 "bookvol10.4.pamphlet" 1731759 1731767 1735109 1735114) (-942 "bookvol10.4.pamphlet" 1730516 1730530 1731749 1731754) (-941 "bookvol10.4.pamphlet" 1730061 1730071 1730506 1730511) (-940 "bookvol10.4.pamphlet" 1729648 1729662 1730051 1730056) (-939 "bookvol10.4.pamphlet" 1729174 1729188 1729638 1729643) (-938 "bookvol10.4.pamphlet" 1728675 1728697 1729164 1729169) (-937 "bookvol10.4.pamphlet" 1727745 1727763 1728607 1728612) (-936 "bookvol10.4.pamphlet" 1727326 1727340 1727735 1727740) (-935 "bookvol10.4.pamphlet" 1726893 1726905 1727316 1727321) (-934 "bookvol10.4.pamphlet" 1726469 1726479 1726883 1726888) (-933 "bookvol10.4.pamphlet" 1726042 1726060 1726459 1726464) (-932 "bookvol10.4.pamphlet" 1725324 1725338 1726032 1726037) (-931 "bookvol10.4.pamphlet" 1724393 1724401 1725314 1725319) (-930 "bookvol10.4.pamphlet" 1723419 1723435 1724383 1724388) (-929 "bookvol10.4.pamphlet" 1722317 1722355 1723409 1723414) (-928 "bookvol10.4.pamphlet" 1722097 1722105 1722307 1722312) (-927 "bookvol10.3.pamphlet" 1716769 1716777 1722087 1722092) (-926 "bookvol10.3.pamphlet" 1713171 1713179 1716759 1716764) (-925 "bookvol10.4.pamphlet" 1712304 1712314 1713161 1713166) (-924 "bookvol10.4.pamphlet" 1698261 1698288 1712294 1712299) (-923 "bookvol10.3.pamphlet" 1698168 1698182 1698251 1698256) (-922 "bookvol10.3.pamphlet" 1698079 1698089 1698158 1698163) (-921 "bookvol10.3.pamphlet" 1697990 1698000 1698069 1698074) (-920 "bookvol10.2.pamphlet" 1697018 1697032 1697980 1697985) (-919 "bookvol10.4.pamphlet" 1696634 1696653 1697008 1697013) (-918 "bookvol10.4.pamphlet" 1696416 1696432 1696624 1696629) (-917 "bookvol10.3.pamphlet" 1696038 1696046 1696390 1696411) (-916 "bookvol10.2.pamphlet" 1694994 1695002 1695964 1696033) (-915 "bookvol10.4.pamphlet" 1694723 1694733 1694984 1694989) (-914 "bookvol10.4.pamphlet" 1693335 1693349 1694713 1694718) (-913 "bookvol10.4.pamphlet" 1684701 1684709 1693325 1693330) (-912 "bookvol10.4.pamphlet" 1683251 1683268 1684691 1684696) (-911 "bookvol10.4.pamphlet" 1682266 1682276 1683241 1683246) (-910 "bookvol10.3.pamphlet" 1677634 1677644 1682168 1682261) (-909 "bookvol10.4.pamphlet" 1676989 1677005 1677624 1677629) (-908 "bookvol10.4.pamphlet" 1675024 1675053 1676979 1676984) (-907 "bookvol10.4.pamphlet" 1674394 1674412 1675014 1675019) (-906 "bookvol10.4.pamphlet" 1673813 1673840 1674384 1674389) (-905 "bookvol10.3.pamphlet" 1673480 1673492 1673618 1673711) (-904 "bookvol10.2.pamphlet" 1671146 1671154 1673406 1673475) (-903 NIL 1668840 1668850 1671102 1671107) (-902 "bookvol10.4.pamphlet" 1666725 1666737 1668830 1668835) (-901 "bookvol10.4.pamphlet" 1664325 1664348 1666715 1666720) (-900 "bookvol10.3.pamphlet" 1659311 1659321 1664155 1664170) (-899 "bookvol10.3.pamphlet" 1654001 1654011 1659301 1659306) (-898 "bookvol10.2.pamphlet" 1652554 1652564 1653981 1653996) (-897 "bookvol10.4.pamphlet" 1651217 1651231 1652544 1652549) (-896 "bookvol10.3.pamphlet" 1650487 1650497 1651069 1651074) (-895 "bookvol10.2.pamphlet" 1648781 1648791 1650467 1650482) (-894 NIL 1647083 1647095 1648771 1648776) (-893 "bookvol10.3.pamphlet" 1645188 1645196 1647073 1647078) (-892 "bookvol10.4.pamphlet" 1638980 1638988 1645178 1645183) (-891 "bookvol10.4.pamphlet" 1638280 1638297 1638970 1638975) (-890 "bookvol10.2.pamphlet" 1636424 1636432 1638270 1638275) (-889 "bookvol10.4.pamphlet" 1636113 1636126 1636414 1636419) (-888 "bookvol10.3.pamphlet" 1634755 1634772 1636103 1636108) (-887 "bookvol10.3.pamphlet" 1629186 1629196 1634745 1634750) (-886 "bookvol10.4.pamphlet" 1628923 1628935 1629176 1629181) (-885 "bookvol10.4.pamphlet" 1627213 1627229 1628913 1628918) (-884 "bookvol10.3.pamphlet" 1624752 1624764 1627203 1627208) (-883 "bookvol10.4.pamphlet" 1624406 1624420 1624742 1624747) (-882 "bookvol10.4.pamphlet" 1622563 1622594 1624114 1624119) (-881 "bookvol10.2.pamphlet" 1621988 1621998 1622553 1622558) (-880 "bookvol10.3.pamphlet" 1621072 1621086 1621978 1621983) (-879 "bookvol10.2.pamphlet" 1620836 1620846 1621062 1621067) (-878 "bookvol10.4.pamphlet" 1618198 1618206 1620826 1620831) (-877 "bookvol10.3.pamphlet" 1617626 1617654 1618188 1618193) (-876 "bookvol10.4.pamphlet" 1617417 1617433 1617616 1617621) (-875 "bookvol10.3.pamphlet" 1616845 1616873 1617407 1617412) (-874 "bookvol10.4.pamphlet" 1616630 1616646 1616835 1616840) (-873 "bookvol10.3.pamphlet" 1616088 1616116 1616620 1616625) (-872 "bookvol10.4.pamphlet" 1615873 1615889 1616078 1616083) (-871 "bookvol10.4.pamphlet" 1614664 1614713 1615863 1615868) (-870 "bookvol10.4.pamphlet" 1614076 1614084 1614654 1614659) (-869 "bookvol10.3.pamphlet" 1613046 1613054 1614066 1614071) (-868 "bookvol10.4.pamphlet" 1607429 1607452 1613002 1613007) (-867 "bookvol10.4.pamphlet" 1601248 1601271 1607378 1607383) (-866 "bookvol10.3.pamphlet" 1598578 1598596 1599753 1599846) (-865 "bookvol10.3.pamphlet" 1596593 1596605 1596814 1596907) (-864 "bookvol10.3.pamphlet" 1596288 1596300 1596519 1596588) (-863 "bookvol10.2.pamphlet" 1594844 1594856 1596214 1596283) (-862 "bookvol10.4.pamphlet" 1593773 1593792 1594834 1594839) (-861 "bookvol10.4.pamphlet" 1592754 1592770 1593763 1593768) (-860 "bookvol10.3.pamphlet" 1591355 1591363 1592425 1592518) (-859 "bookvol10.2.pamphlet" 1590105 1590113 1591257 1591350) (-858 "bookvol10.2.pamphlet" 1588168 1588176 1590007 1590100) (-857 "bookvol10.3.pamphlet" 1586893 1586903 1587964 1588057) (-856 "bookvol10.2.pamphlet" 1585646 1585654 1586795 1586888) (-855 "bookvol10.3.pamphlet" 1583951 1583971 1585036 1585129) (-854 "bookvol10.2.pamphlet" 1582693 1582701 1583853 1583946) (-853 "bookvol10.3.pamphlet" 1581677 1581707 1582551 1582618) (-852 "bookvol10.3.pamphlet" 1581458 1581481 1581667 1581672) (-851 "bookvol10.4.pamphlet" 1580542 1580550 1581448 1581453) (-850 "bookvol10.3.pamphlet" 1569956 1569964 1580532 1580537) (-849 "bookvol10.3.pamphlet" 1569545 1569553 1569946 1569951) (-848 "bookvol10.4.pamphlet" 1568006 1568016 1569462 1569467) (-847 "bookvol10.3.pamphlet" 1567364 1567392 1567686 1567725) (-846 "bookvol10.3.pamphlet" 1566663 1566687 1567044 1567083) (-845 "bookvol10.4.pamphlet" 1564497 1564509 1566583 1566588) (-844 "bookvol10.2.pamphlet" 1558643 1558653 1564453 1564492) (-843 NIL 1552679 1552691 1558491 1558496) (-842 "bookvol10.2.pamphlet" 1551845 1551853 1552669 1552674) (-841 NIL 1551009 1551019 1551835 1551840) (-840 "bookvol10.2.pamphlet" 1550343 1550351 1550989 1551004) (-839 NIL 1549685 1549695 1550333 1550338) (-838 "bookvol10.2.pamphlet" 1549439 1549447 1549675 1549680) (-837 "bookvol10.4.pamphlet" 1548580 1548596 1549429 1549434) (-836 "bookvol10.2.pamphlet" 1548514 1548522 1548570 1548575) (-835 "bookvol10.3.pamphlet" 1547000 1547010 1548061 1548090) (-834 "bookvol10.4.pamphlet" 1546340 1546352 1546990 1546995) (-833 "bookvol10.3.pamphlet" 1544024 1544032 1546330 1546335) (-832 "bookvol10.4.pamphlet" 1536208 1536216 1544014 1544019) (-831 "bookvol10.2.pamphlet" 1533674 1533682 1536198 1536203) (-830 "bookvol10.4.pamphlet" 1533223 1533231 1533664 1533669) (-829 "bookvol10.3.pamphlet" 1532965 1532975 1533045 1533112) (-828 "bookvol10.3.pamphlet" 1531739 1531749 1532512 1532541) (-827 "bookvol10.4.pamphlet" 1531212 1531224 1531729 1531734) (-826 "bookvol10.4.pamphlet" 1530214 1530222 1531202 1531207) (-825 "bookvol10.2.pamphlet" 1529990 1530000 1530158 1530209) (-824 "bookvol10.4.pamphlet" 1528602 1528610 1529980 1529985) (-823 "bookvol10.2.pamphlet" 1527567 1527575 1528592 1528597) (-822 "bookvol10.3.pamphlet" 1526992 1527004 1527453 1527492) (-821 "bookvol10.4.pamphlet" 1526826 1526836 1526982 1526987) (-820 "bookvol10.3.pamphlet" 1526369 1526377 1526816 1526821) (-819 "bookvol10.3.pamphlet" 1525403 1525411 1526359 1526364) (-818 "bookvol10.3.pamphlet" 1524747 1524755 1525393 1525398) (-817 "bookvol10.3.pamphlet" 1519036 1519044 1524737 1524742) (-816 "bookvol10.3.pamphlet" 1518445 1518453 1519026 1519031) (-815 "bookvol10.2.pamphlet" 1518220 1518228 1518371 1518440) (-814 "bookvol10.3.pamphlet" 1511591 1511601 1518210 1518215) (-813 "bookvol10.3.pamphlet" 1510852 1510862 1511581 1511586) (-812 "bookvol10.3.pamphlet" 1510300 1510326 1510664 1510813) (-811 "bookvol10.3.pamphlet" 1507658 1507668 1507986 1508113) (-810 "bookvol10.3.pamphlet" 1499515 1499535 1499873 1500004) (-809 "bookvol10.4.pamphlet" 1498094 1498113 1499505 1499510) (-808 "bookvol10.4.pamphlet" 1495744 1495761 1498084 1498089) (-807 "bookvol10.4.pamphlet" 1491687 1491704 1495701 1495706) (-806 "bookvol10.4.pamphlet" 1491074 1491098 1491677 1491682) (-805 "bookvol10.4.pamphlet" 1488640 1488657 1491064 1491069) (-804 "bookvol10.4.pamphlet" 1485531 1485553 1488630 1488635) (-803 "bookvol10.3.pamphlet" 1484117 1484125 1485521 1485526) (-802 "bookvol10.4.pamphlet" 1481421 1481443 1484107 1484112) (-801 "bookvol10.4.pamphlet" 1480797 1480821 1481411 1481416) (-800 "bookvol10.4.pamphlet" 1467159 1467167 1480787 1480792) (-799 "bookvol10.4.pamphlet" 1466590 1466606 1467149 1467154) (-798 "bookvol10.3.pamphlet" 1463985 1463993 1466580 1466585) (-797 "bookvol10.4.pamphlet" 1459352 1459368 1463975 1463980) (-796 "bookvol10.4.pamphlet" 1458871 1458889 1459342 1459347) (-795 "bookvol10.2.pamphlet" 1457256 1457264 1458861 1458866) (-794 "bookvol10.3.pamphlet" 1455392 1455402 1456110 1456149) (-793 "bookvol10.4.pamphlet" 1455028 1455049 1455382 1455387) (-792 "bookvol10.2.pamphlet" 1452802 1452812 1454984 1455023) (-791 NIL 1450301 1450313 1452485 1452490) (-790 "bookvol10.2.pamphlet" 1450149 1450157 1450291 1450296) (-789 "bookvol10.2.pamphlet" 1449897 1449905 1450139 1450144) (-788 "bookvol10.2.pamphlet" 1449189 1449197 1449887 1449892) (-787 "bookvol10.2.pamphlet" 1449050 1449058 1449179 1449184) (-786 "bookvol10.2.pamphlet" 1448912 1448920 1449040 1449045) (-785 "bookvol10.4.pamphlet" 1448635 1448651 1448902 1448907) (-784 "bookvol10.4.pamphlet" 1436952 1436960 1448625 1448630) (-783 "bookvol10.4.pamphlet" 1427711 1427719 1436942 1436947) (-782 "bookvol10.2.pamphlet" 1425050 1425058 1427701 1427706) (-781 "bookvol10.4.pamphlet" 1423890 1423898 1425040 1425045) (-780 "bookvol10.4.pamphlet" 1415962 1415972 1423695 1423700) (-779 "bookvol10.2.pamphlet" 1415259 1415275 1415918 1415957) (-778 "bookvol10.4.pamphlet" 1414804 1414814 1415176 1415181) (-777 "bookvol10.3.pamphlet" 1407793 1407803 1412354 1412507) (-776 "bookvol10.4.pamphlet" 1407185 1407197 1407783 1407788) (-775 "bookvol10.3.pamphlet" 1403380 1403399 1403688 1403815) (-774 "bookvol10.3.pamphlet" 1401904 1401914 1401981 1402074) (-773 "bookvol10.4.pamphlet" 1400276 1400290 1401894 1401899) (-772 "bookvol10.4.pamphlet" 1400168 1400197 1400266 1400271) (-771 "bookvol10.4.pamphlet" 1399414 1399434 1400158 1400163) (-770 "bookvol10.3.pamphlet" 1399302 1399316 1399394 1399409) (-769 "bookvol10.4.pamphlet" 1398896 1398935 1399292 1399297) (-768 "bookvol10.4.pamphlet" 1397430 1397449 1398886 1398891) (-767 "bookvol10.4.pamphlet" 1397118 1397144 1397420 1397425) (-766 "bookvol10.3.pamphlet" 1396859 1396867 1397108 1397113) (-765 "bookvol10.4.pamphlet" 1396535 1396545 1396849 1396854) (-764 "bookvol10.4.pamphlet" 1396004 1396020 1396525 1396530) (-763 "bookvol10.3.pamphlet" 1394894 1394902 1395978 1395999) (-762 "bookvol10.4.pamphlet" 1393516 1393526 1394884 1394889) (-761 "bookvol10.3.pamphlet" 1391114 1391122 1393506 1393511) (-760 "bookvol10.4.pamphlet" 1388574 1388591 1391104 1391109) (-759 "bookvol10.4.pamphlet" 1387827 1387841 1388564 1388569) (-758 "bookvol10.4.pamphlet" 1385939 1385955 1387817 1387822) (-757 "bookvol10.4.pamphlet" 1385596 1385610 1385929 1385934) (-756 "bookvol10.4.pamphlet" 1383756 1383770 1385586 1385591) (-755 "bookvol10.2.pamphlet" 1383352 1383360 1383746 1383751) (-754 NIL 1382946 1382956 1383342 1383347) (-753 "bookvol10.2.pamphlet" 1382232 1382240 1382936 1382941) (-752 NIL 1381516 1381526 1382222 1382227) (-751 "bookvol10.4.pamphlet" 1380589 1380597 1381506 1381511) (-750 "bookvol10.4.pamphlet" 1370155 1370163 1380579 1380584) (-749 "bookvol10.4.pamphlet" 1368591 1368599 1370145 1370150) (-748 "bookvol10.4.pamphlet" 1362765 1362773 1368581 1368586) (-747 "bookvol10.4.pamphlet" 1356509 1356517 1362755 1362760) (-746 "bookvol10.4.pamphlet" 1352131 1352139 1356499 1356504) (-745 "bookvol10.4.pamphlet" 1345505 1345513 1352121 1352126) (-744 "bookvol10.4.pamphlet" 1335900 1335908 1345495 1345500) (-743 "bookvol10.4.pamphlet" 1331827 1331835 1335890 1335895) (-742 "bookvol10.4.pamphlet" 1329702 1329710 1331817 1331822) (-741 "bookvol10.4.pamphlet" 1322148 1322156 1329692 1329697) (-740 "bookvol10.4.pamphlet" 1316304 1316312 1322138 1322143) (-739 "bookvol10.4.pamphlet" 1312134 1312142 1316294 1316299) (-738 "bookvol10.4.pamphlet" 1310646 1310654 1312124 1312129) (-737 "bookvol10.4.pamphlet" 1309944 1309952 1310636 1310641) (-736 "bookvol10.2.pamphlet" 1309450 1309460 1309912 1309939) (-735 NIL 1308976 1308988 1309440 1309445) (-734 "bookvol10.3.pamphlet" 1306197 1306211 1306526 1306679) (-733 "bookvol10.3.pamphlet" 1304316 1304330 1304388 1304608) (-732 "bookvol10.4.pamphlet" 1301300 1301317 1304306 1304311) (-731 "bookvol10.4.pamphlet" 1300698 1300715 1301290 1301295) (-730 "bookvol10.2.pamphlet" 1298732 1298753 1300596 1300693) (-729 "bookvol10.4.pamphlet" 1298389 1298399 1298722 1298727) (-728 "bookvol10.4.pamphlet" 1297829 1297837 1298379 1298384) (-727 "bookvol10.3.pamphlet" 1295834 1295844 1297591 1297630) (-726 "bookvol10.2.pamphlet" 1295667 1295677 1295790 1295829) (-725 "bookvol10.3.pamphlet" 1292620 1292632 1295375 1295442) (-724 "bookvol10.4.pamphlet" 1292180 1292194 1292610 1292615) (-723 "bookvol10.4.pamphlet" 1291741 1291758 1292170 1292175) (-722 "bookvol10.4.pamphlet" 1289786 1289805 1291731 1291736) (-721 "bookvol10.3.pamphlet" 1287236 1287251 1287580 1287707) (-720 "bookvol10.4.pamphlet" 1286515 1286534 1287226 1287231) (-719 "bookvol10.4.pamphlet" 1286323 1286366 1286505 1286510) (-718 "bookvol10.4.pamphlet" 1286067 1286103 1286313 1286318) (-717 "bookvol10.4.pamphlet" 1284402 1284419 1286057 1286062) (-716 "bookvol10.2.pamphlet" 1283266 1283274 1284392 1284397) (-715 NIL 1282128 1282138 1283256 1283261) (-714 "bookvol10.2.pamphlet" 1280874 1280887 1281988 1282123) (-713 NIL 1279642 1279657 1280758 1280763) (-712 "bookvol10.2.pamphlet" 1277648 1277656 1279632 1279637) (-711 NIL 1275652 1275662 1277638 1277643) (-710 "bookvol10.2.pamphlet" 1274796 1274804 1275642 1275647) (-709 NIL 1273938 1273948 1274786 1274791) (-708 "bookvol10.3.pamphlet" 1272617 1272631 1273918 1273933) (-707 "bookvol10.2.pamphlet" 1272298 1272308 1272585 1272612) (-706 NIL 1271999 1272011 1272288 1272293) (-705 "bookvol10.3.pamphlet" 1271312 1271351 1271979 1271994) (-704 "bookvol10.3.pamphlet" 1269954 1269966 1271134 1271201) (-703 "bookvol10.3.pamphlet" 1269465 1269483 1269944 1269949) (-702 "bookvol10.3.pamphlet" 1266125 1266141 1266943 1267096) (-701 "bookvol10.3.pamphlet" 1265486 1265525 1266027 1266120) (-700 "bookvol10.3.pamphlet" 1264273 1264281 1265476 1265481) (-699 "bookvol10.4.pamphlet" 1264013 1264047 1264263 1264268) (-698 "bookvol10.2.pamphlet" 1262455 1262465 1263969 1264008) (-697 "bookvol10.4.pamphlet" 1261027 1261044 1262445 1262450) (-696 "bookvol10.4.pamphlet" 1260497 1260515 1261017 1261022) (-695 "bookvol10.4.pamphlet" 1260083 1260096 1260487 1260492) (-694 "bookvol10.4.pamphlet" 1259398 1259408 1260073 1260078) (-693 "bookvol10.4.pamphlet" 1258291 1258301 1259388 1259393) (-692 "bookvol10.3.pamphlet" 1258067 1258077 1258281 1258286) (-691 "bookvol10.4.pamphlet" 1257528 1257546 1258057 1258062) (-690 "bookvol10.3.pamphlet" 1256967 1256975 1257430 1257523) (-689 "bookvol10.4.pamphlet" 1255606 1255616 1256957 1256962) (-688 "bookvol10.3.pamphlet" 1254050 1254058 1255496 1255601) (-687 "bookvol10.4.pamphlet" 1253450 1253472 1254040 1254045) (-686 "bookvol10.4.pamphlet" 1251312 1251320 1253440 1253445) (-685 "bookvol10.4.pamphlet" 1249553 1249563 1251302 1251307) (-684 "bookvol10.2.pamphlet" 1248828 1248838 1249521 1249548) (-683 "bookvol10.3.pamphlet" 1244801 1244809 1245415 1245616) (-682 "bookvol10.4.pamphlet" 1244009 1244021 1244791 1244796) (-681 "bookvol10.4.pamphlet" 1241117 1241143 1243999 1244004) (-680 "bookvol10.4.pamphlet" 1238393 1238403 1241107 1241112) (-679 "bookvol10.3.pamphlet" 1237284 1237294 1237768 1237795) (-678 "bookvol10.4.pamphlet" 1234610 1234634 1237168 1237173) (-677 "bookvol10.2.pamphlet" 1219821 1219843 1234566 1234605) (-676 NIL 1204880 1204904 1219627 1219632) (-675 "bookvol10.4.pamphlet" 1204148 1204196 1204870 1204875) (-674 "bookvol10.4.pamphlet" 1202868 1202880 1204138 1204143) (-673 "bookvol10.4.pamphlet" 1201767 1201781 1202858 1202863) (-672 "bookvol10.4.pamphlet" 1201101 1201113 1201757 1201762) (-671 "bookvol10.4.pamphlet" 1199919 1199929 1201091 1201096) (-670 "bookvol10.4.pamphlet" 1199727 1199741 1199909 1199914) (-669 "bookvol10.4.pamphlet" 1199492 1199504 1199717 1199722) (-668 "bookvol10.4.pamphlet" 1199122 1199132 1199482 1199487) (-667 "bookvol10.3.pamphlet" 1197066 1197083 1199112 1199117) (-666 "bookvol10.3.pamphlet" 1194985 1194995 1196667 1196672) (-665 "bookvol10.2.pamphlet" 1190441 1190451 1194965 1194980) (-664 NIL 1185905 1185917 1190431 1190436) (-663 "bookvol10.3.pamphlet" 1182711 1182728 1185895 1185900) (-662 "bookvol10.3.pamphlet" 1180969 1180983 1181391 1181442) (-661 "bookvol10.4.pamphlet" 1180502 1180519 1180959 1180964) (-660 "bookvol10.4.pamphlet" 1179342 1179370 1180492 1180497) (-659 "bookvol10.4.pamphlet" 1177146 1177160 1179332 1179337) (-658 "bookvol10.2.pamphlet" 1176803 1176813 1177102 1177141) (-657 NIL 1176492 1176504 1176793 1176798) (-656 "bookvol10.3.pamphlet" 1175506 1175525 1176348 1176417) (-655 "bookvol10.4.pamphlet" 1174763 1174773 1175496 1175501) (-654 "bookvol10.4.pamphlet" 1173208 1173257 1174753 1174758) (-653 "bookvol10.4.pamphlet" 1171847 1171857 1173198 1173203) (-652 "bookvol10.3.pamphlet" 1171248 1171262 1171781 1171808) (-651 "bookvol10.2.pamphlet" 1170850 1170858 1171238 1171243) (-650 NIL 1170450 1170460 1170840 1170845) (-649 "bookvol10.4.pamphlet" 1169368 1169380 1170440 1170445) (-648 "bookvol10.3.pamphlet" 1168755 1168771 1169048 1169087) (-647 "bookvol10.4.pamphlet" 1167799 1167816 1168712 1168717) (-646 "bookvol10.2.pamphlet" 1166416 1166426 1167755 1167794) (-645 NIL 1165031 1165043 1166372 1166377) (-644 "bookvol10.3.pamphlet" 1164307 1164319 1164711 1164750) (-643 "bookvol10.3.pamphlet" 1163710 1163720 1163987 1164026) (-642 "bookvol10.4.pamphlet" 1162482 1162500 1163700 1163705) (-641 "bookvol10.2.pamphlet" 1160857 1160867 1162384 1162477) (-640 "bookvol10.2.pamphlet" 1156605 1156615 1160837 1160852) (-639 NIL 1152327 1152339 1156561 1156566) (-638 "bookvol10.3.pamphlet" 1149063 1149080 1152317 1152322) (-637 "bookvol10.2.pamphlet" 1148546 1148556 1149053 1149058) (-636 "bookvol10.3.pamphlet" 1147646 1147656 1148320 1148347) (-635 "bookvol10.4.pamphlet" 1147077 1147091 1147636 1147641) (-634 "bookvol10.3.pamphlet" 1145018 1145028 1146447 1146474) (-633 "bookvol10.4.pamphlet" 1144309 1144323 1145008 1145013) (-632 "bookvol10.4.pamphlet" 1142949 1142961 1144299 1144304) (-631 "bookvol10.4.pamphlet" 1139822 1139834 1142939 1142944) (-630 "bookvol10.2.pamphlet" 1139254 1139264 1139802 1139817) (-629 "bookvol10.4.pamphlet" 1138031 1138043 1139166 1139171) (-628 "bookvol10.4.pamphlet" 1135945 1135955 1138021 1138026) (-627 "bookvol10.4.pamphlet" 1134828 1134841 1135935 1135940) (-626 "bookvol10.3.pamphlet" 1132842 1132854 1134118 1134263) (-625 "bookvol10.2.pamphlet" 1132367 1132377 1132768 1132837) (-624 NIL 1131920 1131932 1132323 1132328) (-623 "bookvol10.3.pamphlet" 1130453 1130461 1131161 1131176) (-622 "bookvol10.4.pamphlet" 1127821 1127840 1130443 1130448) (-621 "bookvol10.4.pamphlet" 1126740 1126756 1127811 1127816) (-620 "bookvol10.2.pamphlet" 1125759 1125767 1126730 1126735) (-619 "bookvol10.4.pamphlet" 1121411 1121426 1125749 1125754) (-618 "bookvol10.3.pamphlet" 1119474 1119501 1121391 1121406) (-617 "bookvol10.4.pamphlet" 1117858 1117875 1119464 1119469) (-616 "bookvol10.4.pamphlet" 1116916 1116938 1117848 1117853) (-615 "bookvol10.3.pamphlet" 1115688 1115701 1116509 1116578) (-614 "bookvol10.4.pamphlet" 1115261 1115277 1115678 1115683) (-613 "bookvol10.3.pamphlet" 1114701 1114715 1115183 1115222) (-612 "bookvol10.2.pamphlet" 1114477 1114487 1114681 1114696) (-611 NIL 1114261 1114273 1114467 1114472) (-610 "bookvol10.4.pamphlet" 1112974 1112991 1114251 1114256) (-609 "bookvol10.2.pamphlet" 1112696 1112706 1112964 1112969) (-608 "bookvol10.2.pamphlet" 1112433 1112443 1112686 1112691) (-607 "bookvol10.3.pamphlet" 1110968 1110978 1112217 1112222) (-606 "bookvol10.4.pamphlet" 1110671 1110683 1110958 1110963) (-605 "bookvol10.2.pamphlet" 1109762 1109784 1110639 1110666) (-604 NIL 1108873 1108897 1109752 1109757) (-603 "bookvol10.3.pamphlet" 1107495 1107511 1108220 1108247) (-602 "bookvol10.3.pamphlet" 1105472 1105484 1106785 1106930) (-601 "bookvol10.2.pamphlet" 1103554 1103578 1105452 1105467) (-600 NIL 1101501 1101527 1103401 1103406) (-599 "bookvol10.3.pamphlet" 1100509 1100524 1100649 1100676) (-598 "bookvol10.3.pamphlet" 1099669 1099679 1100499 1100504) (-597 "bookvol10.4.pamphlet" 1098480 1098499 1099659 1099664) (-596 "bookvol10.4.pamphlet" 1097974 1097988 1098470 1098475) (-595 "bookvol10.4.pamphlet" 1097704 1097716 1097964 1097969) (-594 "bookvol10.3.pamphlet" 1095496 1095511 1097540 1097665) (-593 "bookvol10.3.pamphlet" 1087922 1087937 1094470 1094567) (-592 "bookvol10.4.pamphlet" 1087405 1087421 1087912 1087917) (-591 "bookvol10.3.pamphlet" 1086635 1086648 1086801 1086828) (-590 "bookvol10.4.pamphlet" 1085715 1085734 1086625 1086630) (-589 "bookvol10.4.pamphlet" 1083679 1083687 1085705 1085710) (-588 "bookvol10.4.pamphlet" 1082202 1082212 1083635 1083640) (-587 "bookvol10.4.pamphlet" 1081803 1081814 1082192 1082197) (-586 "bookvol10.4.pamphlet" 1080149 1080159 1081793 1081798) (-585 "bookvol10.3.pamphlet" 1077894 1077908 1080004 1080031) (-584 "bookvol10.4.pamphlet" 1077030 1077046 1077884 1077889) (-583 "bookvol10.4.pamphlet" 1076171 1076187 1077020 1077025) (-582 "bookvol10.4.pamphlet" 1075931 1075939 1076161 1076166) (-581 "bookvol10.3.pamphlet" 1075624 1075636 1075736 1075829) (-580 "bookvol10.3.pamphlet" 1075385 1075411 1075550 1075619) (-579 "bookvol10.4.pamphlet" 1074994 1075010 1075375 1075380) (-578 "bookvol10.4.pamphlet" 1068240 1068257 1074984 1074989) (-577 "bookvol10.4.pamphlet" 1066099 1066115 1067814 1067819) (-576 "bookvol10.4.pamphlet" 1065405 1065413 1066089 1066094) (-575 "bookvol10.3.pamphlet" 1065181 1065191 1065319 1065400) (-574 "bookvol10.4.pamphlet" 1063545 1063559 1065171 1065176) (-573 "bookvol10.4.pamphlet" 1063034 1063044 1063535 1063540) (-572 "bookvol10.4.pamphlet" 1061679 1061696 1063024 1063029) (-571 "bookvol10.4.pamphlet" 1060042 1060058 1061322 1061327) (-570 "bookvol10.4.pamphlet" 1057769 1057787 1059974 1059979) (-569 "bookvol10.4.pamphlet" 1047876 1047884 1057759 1057764) (-568 "bookvol10.3.pamphlet" 1047237 1047245 1047730 1047871) (-567 "bookvol10.4.pamphlet" 1046503 1046520 1047227 1047232) (-566 "bookvol10.4.pamphlet" 1046168 1046192 1046493 1046498) (-565 "bookvol10.4.pamphlet" 1042569 1042577 1046158 1046163) (-564 "bookvol10.4.pamphlet" 1035949 1035967 1042501 1042506) (-563 "bookvol10.3.pamphlet" 1029947 1029955 1035939 1035944) (-562 "bookvol10.4.pamphlet" 1029047 1029104 1029937 1029942) (-561 "bookvol10.4.pamphlet" 1028121 1028131 1029037 1029042) (-560 "bookvol10.4.pamphlet" 1027989 1028013 1028111 1028116) (-559 "bookvol10.4.pamphlet" 1026303 1026319 1027979 1027984) (-558 "bookvol10.2.pamphlet" 1024927 1024935 1026229 1026298) (-557 NIL 1023613 1023623 1024917 1024922) (-556 "bookvol10.4.pamphlet" 1022743 1022830 1023603 1023608) (-555 "bookvol10.2.pamphlet" 1021206 1021216 1022657 1022738) (-554 "bookvol10.4.pamphlet" 1020709 1020717 1021196 1021201) (-553 "bookvol10.4.pamphlet" 1019891 1019918 1020699 1020704) (-552 "bookvol10.4.pamphlet" 1019383 1019399 1019881 1019886) (-551 "bookvol10.3.pamphlet" 1018463 1018494 1018626 1018653) (-550 "bookvol10.2.pamphlet" 1015859 1015867 1018365 1018458) (-549 NIL 1013341 1013351 1015849 1015854) (-548 "bookvol10.4.pamphlet" 1012775 1012788 1013331 1013336) (-547 "bookvol10.4.pamphlet" 1011841 1011860 1012765 1012770) (-546 "bookvol10.4.pamphlet" 1010899 1010923 1011831 1011836) (-545 "bookvol10.4.pamphlet" 1009885 1009902 1010889 1010894) (-544 "bookvol10.4.pamphlet" 1009032 1009062 1009875 1009880) (-543 "bookvol10.4.pamphlet" 1007317 1007339 1009022 1009027) (-542 "bookvol10.4.pamphlet" 1006367 1006386 1007307 1007312) (-541 "bookvol10.3.pamphlet" 1003411 1003419 1006357 1006362) (-540 "bookvol10.4.pamphlet" 1003036 1003046 1003401 1003406) (-539 "bookvol10.4.pamphlet" 1002624 1002632 1003026 1003031) (-538 "bookvol10.3.pamphlet" 1002005 1002068 1002614 1002619) (-537 "bookvol10.3.pamphlet" 1001411 1001434 1001995 1002000) (-536 "bookvol10.2.pamphlet" 1000034 1000097 1001401 1001406) (-535 "bookvol10.4.pamphlet" 998566 998588 1000024 1000029) (-534 "bookvol10.3.pamphlet" 998472 998489 998556 998561) (-533 "bookvol10.4.pamphlet" 997893 997903 998462 998467) (-532 "bookvol10.4.pamphlet" 993659 993670 997883 997888) (-531 "bookvol10.3.pamphlet" 992791 992817 993303 993330) (-530 "bookvol10.4.pamphlet" 991881 991925 992747 992752) (-529 "bookvol10.4.pamphlet" 990486 990510 991837 991842) (-528 "bookvol10.3.pamphlet" 989365 989380 989892 989919) (-527 "bookvol10.3.pamphlet" 989090 989128 989195 989222) (-526 "bookvol10.3.pamphlet" 988500 988516 988771 988864) (-525 "bookvol10.3.pamphlet" 985571 985586 987906 987933) (-524 "bookvol10.3.pamphlet" 985409 985426 985527 985532) (-523 "bookvol10.2.pamphlet" 984798 984810 985399 985404) (-522 NIL 984185 984199 984788 984793) (-521 "bookvol10.3.pamphlet" 983998 984010 984175 984180) (-520 "bookvol10.3.pamphlet" 983769 983781 983988 983993) (-519 "bookvol10.3.pamphlet" 983504 983516 983759 983764) (-518 "bookvol10.2.pamphlet" 982438 982450 983494 983499) (-517 "bookvol10.3.pamphlet" 982198 982210 982428 982433) (-516 "bookvol10.3.pamphlet" 981960 981972 982188 982193) (-515 "bookvol10.4.pamphlet" 979212 979230 981950 981955) (-514 "bookvol10.3.pamphlet" 974146 974185 979147 979152) (-513 "bookvol10.3.pamphlet" 973567 973590 974136 974141) (-512 "bookvol10.4.pamphlet" 972718 972734 973557 973562) (-511 "bookvol10.3.pamphlet" 971941 971949 972708 972713) (-510 "bookvol10.4.pamphlet" 970564 970581 971931 971936) (-509 "bookvol10.3.pamphlet" 969842 969855 970258 970285) (-508 "bookvol10.4.pamphlet" 966717 966736 969832 969837) (-507 "bookvol10.4.pamphlet" 965605 965620 966707 966712) (-506 "bookvol10.3.pamphlet" 965336 965362 965435 965462) (-505 "bookvol10.3.pamphlet" 964649 964664 964742 964769) (-504 "bookvol10.3.pamphlet" 962862 962870 964465 964558) (-503 "bookvol10.4.pamphlet" 962417 962450 962852 962857) (-502 "bookvol10.2.pamphlet" 961841 961849 962407 962412) (-501 NIL 961263 961273 961831 961836) (-500 "bookvol10.3.pamphlet" 960063 960071 961253 961258) (-499 "bookvol10.2.pamphlet" 957313 957323 960043 960058) (-498 NIL 954404 954416 957136 957141) (-497 "bookvol10.3.pamphlet" 952273 952281 952871 952964) (-496 "bookvol10.4.pamphlet" 951127 951138 952263 952268) (-495 "bookvol10.3.pamphlet" 950717 950741 951117 951122) (-494 "bookvol10.3.pamphlet" 946440 946450 950547 950574) (-493 "bookvol10.3.pamphlet" 938293 938309 938655 938786) (-492 "bookvol10.3.pamphlet" 935484 935499 936087 936214) (-491 "bookvol10.4.pamphlet" 934024 934032 935474 935479) (-490 "bookvol10.3.pamphlet" 933056 933087 933267 933294) (-489 "bookvol10.3.pamphlet" 932641 932649 932958 933051) (-488 "bookvol10.4.pamphlet" 918518 918530 932631 932636) (-487 "bookvol10.4.pamphlet" 918263 918271 918363 918368) (-486 "bookvol10.4.pamphlet" 902336 902372 918133 918138) (-485 "bookvol10.4.pamphlet" 902097 902105 902195 902200) (-484 "bookvol10.4.pamphlet" 901918 901932 902031 902036) (-483 "bookvol10.4.pamphlet" 901795 901809 901908 901913) (-482 "bookvol10.4.pamphlet" 901628 901636 901728 901733) (-481 "bookvol10.3.pamphlet" 900820 900836 901330 901357) (-480 "bookvol10.3.pamphlet" 899901 899936 900075 900090) (-479 "bookvol10.3.pamphlet" 897068 897095 898033 898182) (-478 "bookvol10.2.pamphlet" 896034 896042 897048 897063) (-477 NIL 895008 895018 896024 896029) (-476 "bookvol10.4.pamphlet" 893591 893612 894998 895003) (-475 "bookvol10.2.pamphlet" 892169 892181 893581 893586) (-474 NIL 890745 890759 892159 892164) (-473 "bookvol10.3.pamphlet" 883350 883358 890735 890740) (-472 "bookvol10.4.pamphlet" 881729 881737 883340 883345) (-471 "bookvol10.4.pamphlet" 880172 880180 881719 881724) (-470 "bookvol10.2.pamphlet" 879226 879238 880162 880167) (-469 NIL 878278 878292 879216 879221) (-468 "bookvol10.3.pamphlet" 877788 877811 878016 878043) (-467 "bookvol10.4.pamphlet" 872478 872565 877744 877749) (-466 "bookvol10.4.pamphlet" 871739 871757 872468 872473) (-465 "bookvol10.3.pamphlet" 867687 867695 871729 871734) (-464 "bookvol10.4.pamphlet" 865270 865278 867677 867682) (-463 "bookvol10.3.pamphlet" 864377 864404 865238 865265) (-462 "bookvol10.4.pamphlet" 863487 863501 864367 864372) (-461 "bookvol10.4.pamphlet" 859588 859601 863477 863482) (-460 "bookvol10.4.pamphlet" 859192 859202 859578 859583) (-459 "bookvol10.4.pamphlet" 858776 858793 859182 859187) (-458 "bookvol10.4.pamphlet" 858243 858262 858766 858771) (-457 "bookvol10.4.pamphlet" 856233 856246 858233 858238) (-456 "bookvol10.4.pamphlet" 854490 854498 856223 856228) (-455 "bookvol10.3.pamphlet" 851523 851540 852284 852411) (-454 "bookvol10.3.pamphlet" 845418 845445 851317 851384) (-453 "bookvol10.2.pamphlet" 844346 844354 845344 845413) (-452 NIL 843336 843346 844336 844341) (-451 "bookvol10.4.pamphlet" 837117 837155 843292 843297) (-450 "bookvol10.4.pamphlet" 833215 833253 837107 837112) (-449 "bookvol10.4.pamphlet" 828281 828319 833205 833210) (-448 "bookvol10.4.pamphlet" 824536 824574 828271 828276) (-447 "bookvol10.4.pamphlet" 823833 823841 824526 824531) (-446 "bookvol10.4.pamphlet" 822155 822165 823789 823794) (-445 "bookvol10.4.pamphlet" 820614 820627 822145 822150) (-444 "bookvol10.4.pamphlet" 818779 818798 820604 820609) (-443 "bookvol10.4.pamphlet" 809045 809056 818769 818774) (-442 "bookvol10.2.pamphlet" 806058 806066 809025 809040) (-441 "bookvol10.2.pamphlet" 805100 805108 806038 806053) (-440 "bookvol10.3.pamphlet" 804949 804961 805090 805095) (-439 NIL 803161 803169 804939 804944) (-438 "bookvol10.3.pamphlet" 802324 802332 803151 803156) (-437 "bookvol10.4.pamphlet" 801366 801385 802260 802265) (-436 "bookvol10.3.pamphlet" 799452 799460 801356 801361) (-435 "bookvol10.4.pamphlet" 798874 798890 799442 799447) (-434 "bookvol10.4.pamphlet" 797682 797698 798831 798836) (-433 "bookvol10.4.pamphlet" 794954 794970 797672 797677) (-432 "bookvol10.2.pamphlet" 788988 788998 794717 794949) (-431 NIL 782812 782824 788543 788548) (-430 "bookvol10.4.pamphlet" 782434 782450 782802 782807) (-429 "bookvol10.3.pamphlet" 781742 781754 782254 782353) (-428 "bookvol10.4.pamphlet" 781016 781032 781732 781737) (-427 "bookvol10.2.pamphlet" 780117 780127 780960 781011) (-426 NIL 779192 779204 780037 780042) (-425 "bookvol10.4.pamphlet" 777879 777895 779182 779187) (-424 "bookvol10.4.pamphlet" 772268 772302 777869 777874) (-423 "bookvol10.4.pamphlet" 771878 771894 772258 772263) (-422 "bookvol10.4.pamphlet" 771001 771024 771868 771873) (-421 "bookvol10.4.pamphlet" 769943 769953 770991 770996) (-420 "bookvol10.3.pamphlet" 761367 761377 768967 769036) (-419 "bookvol10.2.pamphlet" 756446 756456 761309 761362) (-418 NIL 751537 751549 756402 756407) (-417 "bookvol10.4.pamphlet" 750983 751001 751527 751532) (-416 "bookvol10.3.pamphlet" 750377 750407 750914 750919) (-415 "bookvol10.3.pamphlet" 749572 749593 750357 750372) (-414 "bookvol10.4.pamphlet" 749308 749340 749562 749567) (-413 "bookvol10.2.pamphlet" 748972 748982 749298 749303) (-412 NIL 748502 748514 748830 748835) (-411 "bookvol10.2.pamphlet" 746830 746843 748458 748497) (-410 NIL 745190 745205 746820 746825) (-409 "bookvol10.3.pamphlet" 742289 742299 742692 742865) (-408 "bookvol10.4.pamphlet" 741892 741904 742279 742284) (-407 "bookvol10.4.pamphlet" 741226 741238 741882 741887) (-406 "bookvol10.2.pamphlet" 738196 738204 741116 741221) (-405 NIL 735194 735204 738116 738121) (-404 "bookvol10.2.pamphlet" 734238 734246 735096 735189) (-403 NIL 733368 733378 734228 734233) (-402 "bookvol10.2.pamphlet" 733120 733130 733348 733363) (-401 "bookvol10.3.pamphlet" 731896 731913 733110 733115) (-400 NIL 730381 730430 731886 731891) (-399 "bookvol10.4.pamphlet" 729310 729318 730371 730376) (-398 "bookvol10.2.pamphlet" 726470 726478 729290 729305) (-397 "bookvol10.2.pamphlet" 726144 726152 726450 726465) (-396 "bookvol10.3.pamphlet" 723482 723490 726134 726139) (-395 "bookvol10.4.pamphlet" 722961 722971 723472 723477) (-394 "bookvol10.4.pamphlet" 722742 722766 722951 722956) (-393 "bookvol10.4.pamphlet" 721943 721951 722732 722737) (-392 "bookvol10.3.pamphlet" 721365 721387 721911 721938) (-391 "bookvol10.2.pamphlet" 719693 719701 721355 721360) (-390 "bookvol10.3.pamphlet" 719585 719593 719683 719688) (-389 "bookvol10.2.pamphlet" 719383 719391 719511 719580) (-388 "bookvol10.3.pamphlet" 716438 716448 719339 719344) (-387 "bookvol10.3.pamphlet" 716133 716145 716372 716399) (-386 "bookvol10.2.pamphlet" 713153 713161 716113 716128) (-385 "bookvol10.2.pamphlet" 712195 712203 713133 713148) (-384 "bookvol10.2.pamphlet" 709899 709917 712163 712190) (-383 "bookvol10.3.pamphlet" 709359 709371 709833 709860) (-382 "bookvol10.4.pamphlet" 707095 707109 709349 709354) (-381 "bookvol10.3.pamphlet" 700516 700524 706961 707090) (-380 "bookvol10.4.pamphlet" 697948 697962 700506 700511) (-379 "bookvol10.2.pamphlet" 697660 697670 697928 697943) (-378 NIL 697326 697338 697596 697601) (-377 "bookvol10.4.pamphlet" 696576 696588 697316 697321) (-376 "bookvol10.2.pamphlet" 694281 694300 696502 696571) (-375 "bookvol10.2.pamphlet" 691279 691289 694249 694276) (-374 NIL 688190 688202 691162 691167) (-373 "bookvol10.4.pamphlet" 686859 686875 688180 688185) (-372 "bookvol10.2.pamphlet" 684892 684905 686815 686854) (-371 NIL 682851 682866 684776 684781) (-370 "bookvol10.2.pamphlet" 682003 682011 682841 682846) (-369 "bookvol10.2.pamphlet" 670932 670942 681945 681998) (-368 NIL 659873 659885 670888 670893) (-367 "bookvol10.3.pamphlet" 659456 659466 659863 659868) (-366 "bookvol10.2.pamphlet" 657885 657902 659446 659451) (-365 "bookvol10.2.pamphlet" 657203 657211 657787 657880) (-364 NIL 656607 656617 657193 657198) (-363 "bookvol10.3.pamphlet" 655216 655226 656587 656602) (-362 "bookvol10.4.pamphlet" 654031 654046 655206 655211) (-361 "bookvol10.3.pamphlet" 653450 653465 653747 653840) (-360 "bookvol10.4.pamphlet" 653315 653332 653440 653445) (-359 "bookvol10.4.pamphlet" 652804 652825 653305 653310) (-358 "bookvol10.4.pamphlet" 644083 644094 652794 652799) (-357 "bookvol10.4.pamphlet" 643129 643146 644073 644078) (-356 "bookvol10.3.pamphlet" 642615 642635 642845 642938) (-355 "bookvol10.3.pamphlet" 642063 642079 642296 642389) (-354 "bookvol10.3.pamphlet" 640581 640601 641779 641872) (-353 "bookvol10.3.pamphlet" 639091 639108 640297 640390) (-352 "bookvol10.3.pamphlet" 637602 637623 638772 638865) (-351 "bookvol10.4.pamphlet" 634964 634983 637592 637597) (-350 "bookvol10.2.pamphlet" 632538 632546 634866 634959) (-349 NIL 630198 630208 632528 632533) (-348 "bookvol10.4.pamphlet" 628943 628960 630188 630193) (-347 "bookvol10.4.pamphlet" 626358 626369 628933 628938) (-346 "bookvol10.4.pamphlet" 619566 619582 626348 626353) (-345 "bookvol10.4.pamphlet" 618181 618200 619556 619561) (-344 "bookvol10.4.pamphlet" 617590 617607 618171 618176) (-343 "bookvol10.3.pamphlet" 616443 616463 617306 617399) (-342 "bookvol10.3.pamphlet" 615338 615358 616159 616252) (-341 "bookvol10.3.pamphlet" 614137 614158 615019 615112) (-340 "bookvol10.2.pamphlet" 602768 602790 613976 614132) (-339 NIL 591478 591502 602688 602693) (-338 "bookvol10.4.pamphlet" 591223 591263 591468 591473) (-337 "bookvol10.3.pamphlet" 583853 583899 590979 591018) (-336 "bookvol10.2.pamphlet" 583559 583569 583843 583848) (-335 NIL 583050 583062 583336 583341) (-334 "bookvol10.3.pamphlet" 582483 582507 583040 583045) (-333 "bookvol10.2.pamphlet" 580525 580549 582473 582478) (-332 NIL 578565 578591 580515 580520) (-331 "bookvol10.4.pamphlet" 578309 578349 578555 578560) (-330 "bookvol10.4.pamphlet" 576830 576838 578299 578304) (-329 "bookvol10.3.pamphlet" 576359 576369 576820 576825) (-328 NIL 566184 566192 576349 576354) (-327 "bookvol10.2.pamphlet" 559057 559071 566086 566179) (-326 NIL 551982 551998 559013 559018) (-325 "bookvol10.3.pamphlet" 550396 550406 551388 551415) (-324 "bookvol10.2.pamphlet" 548516 548528 550294 550391) (-323 NIL 546620 546634 548400 548405) (-322 "bookvol10.4.pamphlet" 546170 546192 546610 546615) (-321 "bookvol10.3.pamphlet" 545820 545830 546124 546129) (-320 "bookvol10.2.pamphlet" 544011 544023 545810 545815) (-319 "bookvol10.3.pamphlet" 543617 543627 543907 543934) (-318 "bookvol10.4.pamphlet" 541813 541830 543607 543612) (-317 "bookvol10.4.pamphlet" 541695 541705 541803 541808) (-316 "bookvol10.4.pamphlet" 540871 540881 541685 541690) (-315 "bookvol10.4.pamphlet" 540753 540763 540861 540866) (-314 "bookvol10.3.pamphlet" 537586 537609 538885 539034) (-313 "bookvol10.4.pamphlet" 534950 534958 537576 537581) (-312 "bookvol10.4.pamphlet" 534852 534881 534940 534945) (-311 "bookvol10.4.pamphlet" 531660 531676 534842 534847) (-310 "bookvol10.3.pamphlet" 526909 526919 527649 528056) (-309 "bookvol10.4.pamphlet" 522969 522982 526899 526904) (-308 "bookvol10.4.pamphlet" 522729 522741 522959 522964) (-307 "bookvol10.3.pamphlet" 519667 519692 520301 520394) (-306 "bookvol10.4.pamphlet" 519520 519528 519657 519662) (-305 "bookvol10.3.pamphlet" 519187 519195 519510 519515) (-304 "bookvol10.4.pamphlet" 518677 518691 519177 519182) (-303 "bookvol10.2.pamphlet" 518241 518251 518667 518672) (-302 NIL 517803 517815 518231 518236) (-301 "bookvol10.2.pamphlet" 515337 515345 517729 517798) (-300 NIL 512933 512943 515327 515332) (-299 "bookvol10.4.pamphlet" 504773 504781 512923 512928) (-298 "bookvol10.4.pamphlet" 504358 504372 504763 504768) (-297 "bookvol10.4.pamphlet" 504035 504046 504348 504353) (-296 "bookvol10.2.pamphlet" 496582 496590 504025 504030) (-295 NIL 489035 489045 496480 496485) (-294 "bookvol10.4.pamphlet" 485808 485816 489025 489030) (-293 "bookvol10.4.pamphlet" 485549 485561 485798 485803) (-292 "bookvol10.4.pamphlet" 485044 485060 485539 485544) (-291 "bookvol10.4.pamphlet" 484610 484626 485034 485039) (-290 "bookvol10.4.pamphlet" 481984 481992 484600 484605) (-289 "bookvol10.3.pamphlet" 481018 481040 481227 481254) (-288 "bookvol10.3.pamphlet" 475876 475886 478691 478803) (-287 "bookvol10.4.pamphlet" 475592 475604 475866 475871) (-286 "bookvol10.4.pamphlet" 471906 471916 475582 475587) (-285 "bookvol10.2.pamphlet" 471448 471456 471850 471901) (-284 "bookvol10.3.pamphlet" 470628 470669 471374 471443) (-283 "bookvol10.2.pamphlet" 468882 468901 470618 470623) (-282 NIL 467100 467121 468838 468843) (-281 "bookvol10.2.pamphlet" 466564 466582 467090 467095) (-280 "bookvol10.4.pamphlet" 465943 465962 466554 466559) (-279 "bookvol10.2.pamphlet" 465632 465640 465933 465938) (-278 NIL 465319 465329 465622 465627) (-277 "bookvol10.2.pamphlet" 463023 463033 465287 465314) (-276 NIL 460676 460688 462942 462947) (-275 "bookvol10.4.pamphlet" 457467 457497 460632 460637) (-274 "bookvol10.4.pamphlet" 454318 454341 457423 457428) (-273 "bookvol10.4.pamphlet" 452273 452289 454308 454313) (-272 "bookvol10.4.pamphlet" 447039 447055 452263 452268) (-271 "bookvol10.3.pamphlet" 445315 445323 447029 447034) (-270 "bookvol10.3.pamphlet" 444851 444859 445305 445310) (-269 "bookvol10.3.pamphlet" 444428 444436 444841 444846) (-268 "bookvol10.3.pamphlet" 444008 444016 444418 444423) (-267 "bookvol10.3.pamphlet" 443544 443552 443998 444003) (-266 "bookvol10.3.pamphlet" 443080 443088 443534 443539) (-265 "bookvol10.3.pamphlet" 442616 442624 443070 443075) (-264 "bookvol10.3.pamphlet" 442152 442160 442606 442611) (-263 "bookvol10.4.pamphlet" 437768 437776 442142 442147) (-262 "bookvol10.2.pamphlet" 434449 434459 437758 437763) (-261 NIL 431128 431140 434439 434444) (-260 "bookvol10.4.pamphlet" 428108 428195 431118 431123) (-259 "bookvol10.3.pamphlet" 427278 427288 427938 427965) (-258 "bookvol10.2.pamphlet" 426866 426876 427234 427273) (-257 "bookvol10.3.pamphlet" 424309 424323 424602 424729) (-256 "bookvol10.3.pamphlet" 418254 418262 424299 424304) (-255 "bookvol10.4.pamphlet" 417915 417925 418244 418249) (-254 "bookvol10.4.pamphlet" 412740 412748 417905 417910) (-253 "bookvol10.4.pamphlet" 410895 410903 412730 412735) (-252 "bookvol10.4.pamphlet" 403495 403508 410885 410890) (-251 "bookvol10.4.pamphlet" 402748 402758 403485 403490) (-250 "bookvol10.4.pamphlet" 400103 400111 402738 402743) (-249 "bookvol10.4.pamphlet" 399640 399655 400093 400098) (-248 "bookvol10.4.pamphlet" 388812 388820 399630 399635) (-247 "bookvol10.2.pamphlet" 386964 386974 388768 388807) (-246 "bookvol10.2.pamphlet" 382305 382321 386832 386959) (-245 NIL 377732 377750 382261 382266) (-244 "bookvol10.3.pamphlet" 371091 371107 371229 371530) (-243 "bookvol10.3.pamphlet" 364463 364481 364588 364889) (-242 "bookvol10.3.pamphlet" 361700 361715 362257 362384) (-241 "bookvol10.4.pamphlet" 361044 361054 361690 361695) (-240 "bookvol10.3.pamphlet" 359679 359689 360450 360477) (-239 "bookvol10.2.pamphlet" 358072 358082 359659 359674) (-238 "bookvol10.2.pamphlet" 357519 357527 358016 358067) (-237 NIL 357010 357020 357509 357514) (-236 "bookvol10.3.pamphlet" 356863 356873 356942 356969) (-235 "bookvol10.2.pamphlet" 355622 355632 356831 356858) (-234 "bookvol10.4.pamphlet" 353802 353810 355612 355617) (-233 "bookvol10.3.pamphlet" 353094 353109 353638 353763) (-232 "bookvol10.3.pamphlet" 344684 344700 345309 345440) (-231 "bookvol10.4.pamphlet" 343507 343525 344674 344679) (-230 "bookvol10.2.pamphlet" 342669 342685 343359 343502) (-229 NIL 341572 341590 342264 342269) (-228 "bookvol10.4.pamphlet" 340375 340383 341562 341567) (-227 "bookvol10.2.pamphlet" 339347 339357 340343 340370) (-226 NIL 338305 338317 339303 339308) (-225 "bookvol10.2.pamphlet" 337418 337426 338285 338300) (-224 NIL 336539 336549 337408 337413) (-223 "bookvol10.2.pamphlet" 335698 335708 336519 336534) (-222 NIL 334774 334786 335597 335602) (-221 "bookvol10.2.pamphlet" 334392 334402 334742 334769) (-220 NIL 334030 334042 334382 334387) (-219 "bookvol10.3.pamphlet" 332238 332248 333674 333701) (-218 "bookvol10.3.pamphlet" 330966 330974 331362 331389) (-217 "bookvol10.4.pamphlet" 322208 322216 330956 330961) (-216 "bookvol10.3.pamphlet" 321411 321419 321840 321867) (-215 "bookvol10.3.pamphlet" 317688 317696 321301 321406) (-214 "bookvol10.4.pamphlet" 315897 315913 317678 317683) (-213 "bookvol10.3.pamphlet" 313807 313839 315877 315892) (-212 "bookvol10.3.pamphlet" 307481 307491 313637 313664) (-211 "bookvol10.4.pamphlet" 307094 307108 307471 307476) (-210 "bookvol10.4.pamphlet" 304575 304585 307084 307089) (-209 "bookvol10.4.pamphlet" 303071 303087 304565 304570) (-208 "bookvol10.3.pamphlet" 300952 300960 301538 301631) (-207 "bookvol10.4.pamphlet" 298803 298820 300942 300947) (-206 "bookvol10.4.pamphlet" 298401 298425 298793 298798) (-205 "bookvol10.3.pamphlet" 296988 296998 298391 298396) (-204 "bookvol10.3.pamphlet" 296816 296824 296978 296983) (-203 "bookvol10.3.pamphlet" 296636 296644 296806 296811) (-202 "bookvol10.4.pamphlet" 295575 295583 296626 296631) (-201 "bookvol10.3.pamphlet" 295037 295045 295565 295570) (-200 "bookvol10.3.pamphlet" 294515 294523 295027 295032) (-199 "bookvol10.3.pamphlet" 294005 294013 294505 294510) (-198 "bookvol10.3.pamphlet" 293495 293503 293995 294000) (-197 "bookvol10.4.pamphlet" 288337 288345 293485 293490) (-196 "bookvol10.4.pamphlet" 286656 286664 288327 288332) (-195 "bookvol10.3.pamphlet" 286633 286641 286646 286651) (-194 "bookvol10.3.pamphlet" 286155 286163 286623 286628) (-193 "bookvol10.3.pamphlet" 285677 285685 286145 286150) (-192 "bookvol10.3.pamphlet" 285145 285153 285667 285672) (-191 "bookvol10.3.pamphlet" 284630 284638 285135 285140) (-190 "bookvol10.3.pamphlet" 284054 284062 284620 284625) (-189 "bookvol10.3.pamphlet" 283548 283556 284044 284049) (-188 "bookvol10.3.pamphlet" 283058 283066 283538 283543) (-187 "bookvol10.3.pamphlet" 282598 282606 283048 283053) (-186 "bookvol10.3.pamphlet" 282124 282132 282588 282593) (-185 "bookvol10.3.pamphlet" 281647 281655 282114 282119) (-184 "bookvol10.4.pamphlet" 277706 277714 281637 281642) (-183 "bookvol10.4.pamphlet" 277210 277218 277696 277701) (-182 "bookvol10.4.pamphlet" 274027 274035 277200 277205) (-181 "bookvol10.4.pamphlet" 273442 273452 274017 274022) (-180 "bookvol10.4.pamphlet" 271932 271948 273432 273437) (-179 "bookvol10.4.pamphlet" 270601 270614 271922 271927) (-178 "bookvol10.4.pamphlet" 264428 264441 270591 270596) (-177 "bookvol10.4.pamphlet" 263467 263477 264418 264423) (-176 "bookvol10.4.pamphlet" 262967 262982 263392 263397) (-175 "bookvol10.4.pamphlet" 262672 262691 262957 262962) (-174 "bookvol10.4.pamphlet" 257565 257575 262662 262667) (-173 "bookvol10.3.pamphlet" 253300 253310 257467 257560) (-172 "bookvol10.2.pamphlet" 252975 252983 253238 253295) (-171 "bookvol10.3.pamphlet" 252471 252479 252965 252970) (-170 "bookvol10.4.pamphlet" 252238 252253 252461 252466) (-169 "bookvol10.3.pamphlet" 246262 246272 246505 246766) (-168 "bookvol10.4.pamphlet" 245975 245987 246252 246257) (-167 "bookvol10.4.pamphlet" 245771 245785 245965 245970) (-166 "bookvol10.2.pamphlet" 243827 243837 245493 245766) (-165 NIL 241587 241599 243255 243260) (-164 "bookvol10.4.pamphlet" 241333 241351 241577 241582) (-163 "bookvol10.4.pamphlet" 240866 240874 241323 241328) (-162 "bookvol10.3.pamphlet" 240673 240681 240856 240861) (-161 "bookvol10.2.pamphlet" 239578 239586 240663 240668) (-160 "bookvol10.4.pamphlet" 238076 238086 239568 239573) (-159 "bookvol10.4.pamphlet" 235336 235352 238066 238071) (-158 "bookvol10.3.pamphlet" 234173 234181 235326 235331) (-157 "bookvol10.4.pamphlet" 233505 233522 234163 234168) (-156 "bookvol10.4.pamphlet" 229569 229577 233495 233500) (-155 "bookvol10.3.pamphlet" 228222 228238 229525 229564) (-154 "bookvol10.2.pamphlet" 224493 224503 228202 228217) (-153 NIL 220645 220657 224356 224361) (-152 "bookvol10.4.pamphlet" 219970 219983 220635 220640) (-151 "bookvol10.4.pamphlet" 218048 218070 219960 219965) (-150 "bookvol10.2.pamphlet" 217963 217971 218028 218043) (-149 "bookvol10.4.pamphlet" 217471 217481 217953 217958) (-148 "bookvol10.2.pamphlet" 217224 217232 217451 217466) (-147 "bookvol10.3.pamphlet" 212724 212732 217214 217219) (-146 "bookvol10.2.pamphlet" 211905 211913 212714 212719) (-145 "bookvol10.3.pamphlet" 210142 210150 210843 210870) (-144 "bookvol10.3.pamphlet" 209260 209268 209698 209725) (-143 "bookvol10.4.pamphlet" 208418 208432 209250 209255) (-142 "bookvol10.3.pamphlet" 206781 206789 207887 207926) (-141 "bookvol10.3.pamphlet" 196438 196462 206771 206776) (-140 "bookvol10.4.pamphlet" 195824 195851 196428 196433) (-139 "bookvol10.3.pamphlet" 192160 192168 195798 195819) (-138 "bookvol10.2.pamphlet" 191782 191790 192150 192155) (-137 "bookvol10.2.pamphlet" 191293 191301 191772 191777) (-136 "bookvol10.3.pamphlet" 190311 190321 191123 191150) (-135 "bookvol10.3.pamphlet" 189505 189515 190141 190168) (-134 "bookvol10.2.pamphlet" 188869 188879 189461 189500) (-133 NIL 188265 188277 188859 188864) (-132 "bookvol10.2.pamphlet" 187330 187338 188221 188260) (-131 NIL 186427 186437 187320 187325) (-130 "bookvol10.3.pamphlet" 184947 184957 186257 186284) (-129 "bookvol10.4.pamphlet" 183710 183721 184937 184942) (-128 "bookvol10.2.pamphlet" 182624 182634 183690 183705) (-127 NIL 181512 181524 182580 182585) (-126 "bookvol10.3.pamphlet" 179493 179505 179748 179841) (-125 "bookvol10.3.pamphlet" 179157 179169 179419 179488) (-124 "bookvol10.4.pamphlet" 178813 178830 179147 179152) (-123 "bookvol10.3.pamphlet" 174205 174213 178803 178808) (-122 "bookvol10.4.pamphlet" 171583 171593 174161 174166) (-121 "bookvol10.3.pamphlet" 170477 170485 171573 171578) (-120 "bookvol10.2.pamphlet" 170135 170147 170445 170472) (-119 "bookvol10.4.pamphlet" 168341 168377 170125 170130) (-118 "bookvol10.3.pamphlet" 168231 168239 168306 168336) (-117 "bookvol10.2.pamphlet" 168208 168216 168221 168226) (-116 "bookvol10.3.pamphlet" 168100 168108 168175 168203) (-115 "bookvol10.5.pamphlet" 165464 165472 168090 168095) (-114 "bookvol10.3.pamphlet" 164941 164949 165158 165185) (-113 "bookvol10.3.pamphlet" 164284 164292 164931 164936) (-112 "bookvol10.3.pamphlet" 162124 162132 162751 162844) (-111 "bookvol10.2.pamphlet" 161309 161319 162092 162119) (-110 NIL 160514 160526 161299 161304) (-109 "bookvol10.3.pamphlet" 159935 159943 160494 160509) (-108 "bookvol10.4.pamphlet" 159069 159096 159885 159890) (-107 "bookvol10.4.pamphlet" 156390 156400 159059 159064) (-106 "bookvol10.3.pamphlet" 151452 151462 156220 156247) (-105 "bookvol10.2.pamphlet" 151124 151132 151442 151447) (-104 NIL 150794 150804 151114 151119) (-103 "bookvol10.4.pamphlet" 150233 150246 150784 150789) (-102 "bookvol10.4.pamphlet" 150093 150101 150223 150228) (-101 "bookvol10.3.pamphlet" 149539 149549 150073 150088) (-100 "bookvol10.2.pamphlet" 146136 146144 149279 149534) (-99 "bookvol10.3.pamphlet" 142171 142178 146116 146131) (-98 "bookvol10.2.pamphlet" 141641 141648 142161 142166) (-97 NIL 141109 141118 141631 141636) (-96 "bookvol10.3.pamphlet" 136401 136410 140939 140966) (-95 "bookvol10.4.pamphlet" 135201 135212 136357 136362) (-94 "bookvol10.3.pamphlet" 134272 134285 135191 135196) (-93 "bookvol10.3.pamphlet" 132761 132774 134262 134267) (-92 "bookvol10.3.pamphlet" 131881 131894 132751 132756) (-91 "bookvol10.3.pamphlet" 130849 130862 131871 131876) (-90 "bookvol10.3.pamphlet" 130224 130237 130839 130844) (-89 "bookvol10.3.pamphlet" 129429 129442 130214 130219) (-88 "bookvol10.3.pamphlet" 128082 128095 129419 129424) (-87 "bookvol10.3.pamphlet" 127173 127186 128072 128077) (-86 "bookvol10.3.pamphlet" 125295 125308 127163 127168) (-85 "bookvol10.3.pamphlet" 123012 123025 125285 125290) (-84 "bookvol10.3.pamphlet" 119204 119217 123002 123007) (-83 "bookvol10.3.pamphlet" 118345 118358 119194 119199) (-82 "bookvol10.3.pamphlet" 116982 116995 118335 118340) (-81 "bookvol10.3.pamphlet" 114334 114373 116972 116977) (-80 "bookvol10.3.pamphlet" 112008 112047 114324 114329) (-79 "bookvol10.3.pamphlet" 110645 110658 111998 112003) (-78 "bookvol10.3.pamphlet" 109384 109397 110635 110640) (-77 "bookvol10.3.pamphlet" 108898 108911 109374 109379) (-76 "bookvol10.3.pamphlet" 107694 107707 108888 108893) (-75 "bookvol10.3.pamphlet" 105698 105711 107684 107689) (-74 "bookvol10.3.pamphlet" 105008 105021 105688 105693) (-73 "bookvol10.3.pamphlet" 92049 92062 104998 105003) (-72 "bookvol10.3.pamphlet" 90155 90168 92039 92044) (-71 "bookvol10.3.pamphlet" 88878 88891 90145 90150) (-70 "bookvol10.3.pamphlet" 87729 87742 88868 88873) (-69 "bookvol10.3.pamphlet" 87043 87056 87719 87724) (-68 "bookvol10.3.pamphlet" 77536 77549 87033 87038) (-67 "bookvol10.3.pamphlet" 76838 76851 77526 77531) (-66 "bookvol10.3.pamphlet" 75953 75966 76828 76833) (-65 "bookvol10.3.pamphlet" 75551 75560 75783 75810) (-64 "bookvol10.3.pamphlet" 74439 74448 74957 74984) (-63 "bookvol10.4.pamphlet" 72262 72273 74429 74434) (-62 "bookvol10.2.pamphlet" 64788 64809 72218 72257) (-61 NIL 57346 57369 64778 64783) (-60 "bookvol10.4.pamphlet" 56590 56612 57336 57341) (-59 "bookvol10.4.pamphlet" 56205 56218 56580 56585) (-58 "bookvol10.4.pamphlet" 55592 55599 56195 56200) (-57 "bookvol10.3.pamphlet" 53934 53941 55582 55587) (-56 "bookvol10.4.pamphlet" 53005 53014 53924 53929) (-55 "bookvol10.3.pamphlet" 51444 51460 52985 53000) (-54 "bookvol10.3.pamphlet" 51357 51364 51434 51439) (-53 "bookvol10.3.pamphlet" 49658 49665 51173 51266) (-52 "bookvol10.2.pamphlet" 47837 47848 49556 49653) (-51 NIL 45853 45866 47574 47579) (-50 "bookvol10.3.pamphlet" 43897 43918 44247 44274) (-49 "bookvol10.3.pamphlet" 43020 43046 43769 43822) (-48 "bookvol10.4.pamphlet" 38807 38818 42976 42981) (-47 "bookvol10.4.pamphlet" 37996 38010 38797 38802) (-46 "bookvol10.4.pamphlet" 35416 35431 37793 37798) (-45 "bookvol10.3.pamphlet" 33730 33757 33948 34104) (-44 "bookvol10.4.pamphlet" 32843 32853 33720 33725) (-43 "bookvol10.2.pamphlet" 32295 32304 32799 32838) (-42 NIL 31779 31790 32285 32290) (-41 "bookvol10.2.pamphlet" 31277 31298 31735 31774) (-40 "bookvol10.2.pamphlet" 30658 30665 31267 31272) (-39 "bookvol10.2.pamphlet" 28939 28946 30638 30653) (-38 NIL 27194 27203 28895 28900) (-37 "bookvol10.2.pamphlet" 24922 24931 27184 27189) 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1969356) (-1059 "bookvol10.3.pamphlet" 1945242 1945251 1948026 1948053) (-1058 "bookvol10.3.pamphlet" 1944489 1944498 1945108 1945237) (-1057 NIL 1943569 1943601 1944479 1944484) (-1056 "bookvol10.2.pamphlet" 1942472 1942481 1943471 1943564) (-1055 NIL 1941461 1941472 1942462 1942467) (-1054 "bookvol10.2.pamphlet" 1940983 1940992 1941451 1941456) (-1053 "bookvol10.2.pamphlet" 1940460 1940471 1940973 1940978) (-1052 "bookvol10.4.pamphlet" 1939868 1939925 1940450 1940455) (-1051 "bookvol10.3.pamphlet" 1938603 1938622 1939091 1939130) (-1050 "bookvol10.2.pamphlet" 1934120 1934151 1938547 1938598) (-1049 NIL 1929539 1929572 1933968 1933973) (-1048 "bookvol10.4.pamphlet" 1929427 1929447 1929529 1929534) (-1047 "bookvol10.2.pamphlet" 1928780 1928789 1929407 1929422) (-1046 NIL 1928141 1928152 1928770 1928775) (-1045 "bookvol10.4.pamphlet" 1927035 1927044 1928131 1928136) (-1044 "bookvol10.3.pamphlet" 1925700 1925716 1926595 1926622) (-1043 "bookvol10.4.pamphlet" 1923742 1923753 1925690 1925695) (-1042 "bookvol10.4.pamphlet" 1921356 1921367 1923732 1923737) (-1041 "bookvol10.4.pamphlet" 1920818 1920829 1921346 1921351) (-1040 "bookvol10.4.pamphlet" 1920553 1920565 1920808 1920813) (-1039 "bookvol10.4.pamphlet" 1919541 1919550 1920543 1920548) (-1038 "bookvol10.4.pamphlet" 1918958 1918971 1919531 1919536) (-1037 "bookvol10.2.pamphlet" 1918307 1918318 1918948 1918953) (-1036 NIL 1917654 1917667 1918297 1918302) (-1035 "bookvol10.3.pamphlet" 1916296 1916305 1916883 1916910) (-1034 "bookvol10.3.pamphlet" 1915643 1915690 1916234 1916291) (-1033 "bookvol10.4.pamphlet" 1914967 1914978 1915633 1915638) (-1032 "bookvol10.4.pamphlet" 1914696 1914707 1914957 1914962) (-1031 "bookvol10.4.pamphlet" 1912248 1912257 1914686 1914691) (-1030 "bookvol10.4.pamphlet" 1911953 1911964 1912238 1912243) (-1029 "bookvol10.4.pamphlet" 1901395 1901406 1911795 1911800) (-1028 "bookvol10.4.pamphlet" 1895371 1895382 1901345 1901350) (-1027 "bookvol10.3.pamphlet" 1893462 1893479 1895073 1895100) (-1026 "bookvol10.3.pamphlet" 1892806 1892817 1893417 1893422) (-1025 "bookvol10.4.pamphlet" 1891982 1891999 1892796 1892801) (-1024 "bookvol10.4.pamphlet" 1890279 1890296 1891937 1891942) (-1023 "bookvol10.3.pamphlet" 1889062 1889082 1889766 1889859) (-1022 "bookvol10.4.pamphlet" 1887517 1887526 1889052 1889057) (-1021 "bookvol10.2.pamphlet" 1887389 1887398 1887507 1887512) (-1020 "bookvol10.4.pamphlet" 1884686 1884701 1887379 1887384) (-1019 "bookvol10.4.pamphlet" 1881529 1881544 1884676 1884681) (-1018 "bookvol10.4.pamphlet" 1881274 1881299 1881519 1881524) (-1017 "bookvol10.4.pamphlet" 1880837 1880848 1881264 1881269) (-1016 "bookvol10.4.pamphlet" 1879737 1879755 1880827 1880832) (-1015 "bookvol10.4.pamphlet" 1877942 1877960 1879727 1879732) (-1014 "bookvol10.4.pamphlet" 1877167 1877184 1877932 1877937) (-1013 "bookvol10.4.pamphlet" 1876317 1876334 1877157 1877162) (-1012 "bookvol10.2.pamphlet" 1873500 1873509 1876219 1876312) (-1011 NIL 1870769 1870780 1873490 1873495) (-1010 "bookvol10.2.pamphlet" 1868678 1868689 1870749 1870764) (-1009 NIL 1866524 1866537 1868597 1868602) (-1008 "bookvol10.4.pamphlet" 1865941 1865952 1866514 1866519) (-1007 "bookvol10.4.pamphlet" 1865125 1865137 1865931 1865936) (-1006 "bookvol10.4.pamphlet" 1864482 1864491 1865115 1865120) (-1005 "bookvol10.4.pamphlet" 1864236 1864245 1864472 1864477) (-1004 "bookvol10.3.pamphlet" 1861021 1861035 1862703 1862796) (-1003 "bookvol10.3.pamphlet" 1859434 1859471 1859553 1859709) (-1002 "bookvol10.2.pamphlet" 1859027 1859036 1859424 1859429) (-1001 NIL 1858618 1858629 1859017 1859022) (-1000 "bookvol10.3.pamphlet" 1854007 1854018 1858448 1858475) (-999 "bookvol10.3.pamphlet" 1852634 1852644 1852931 1852996) (-998 "bookvol10.4.pamphlet" 1851957 1851975 1852624 1852629) (-997 "bookvol10.2.pamphlet" 1850118 1850128 1851887 1851952) (-996 NIL 1848030 1848042 1849801 1849806) (-995 "bookvol10.2.pamphlet" 1846836 1846846 1847986 1848025) (-994 "bookvol10.3.pamphlet" 1846299 1846313 1846826 1846831) (-993 "bookvol10.2.pamphlet" 1844990 1845000 1846189 1846294) (-992 NIL 1843284 1843296 1844485 1844490) (-991 "bookvol10.4.pamphlet" 1842975 1842991 1843274 1843279) (-990 "bookvol10.3.pamphlet" 1842532 1842540 1842965 1842970) (-989 "bookvol10.4.pamphlet" 1837934 1837953 1842522 1842527) (-988 "bookvol10.3.pamphlet" 1834009 1834041 1837848 1837853) (-987 "bookvol10.4.pamphlet" 1832005 1832023 1833999 1834004) (-986 "bookvol10.4.pamphlet" 1829315 1829336 1831995 1832000) (-985 "bookvol10.4.pamphlet" 1828642 1828661 1829305 1829310) (-984 "bookvol10.2.pamphlet" 1824768 1824778 1828632 1828637) (-983 "bookvol10.4.pamphlet" 1821852 1821862 1824758 1824763) (-982 "bookvol10.4.pamphlet" 1821669 1821683 1821842 1821847) (-981 "bookvol10.2.pamphlet" 1820751 1820761 1821625 1821664) (-980 "bookvol10.4.pamphlet" 1820058 1820082 1820741 1820746) (-979 "bookvol10.4.pamphlet" 1818916 1818926 1820048 1820053) (-978 "bookvol10.4.pamphlet" 1804317 1804333 1818794 1818799) (-977 "bookvol10.2.pamphlet" 1798210 1798233 1804285 1804312) (-976 NIL 1792089 1792114 1798166 1798171) (-975 "bookvol10.2.pamphlet" 1791072 1791080 1792079 1792084) (-974 "bookvol10.2.pamphlet" 1789835 1789864 1790970 1791067) (-973 NIL 1788688 1788719 1789825 1789830) (-972 "bookvol10.3.pamphlet" 1787503 1787511 1788678 1788683) (-971 "bookvol10.2.pamphlet" 1784836 1784846 1787493 1787498) (-970 "bookvol10.4.pamphlet" 1774981 1774998 1784792 1784797) (-969 "bookvol10.2.pamphlet" 1774400 1774410 1774937 1774976) (-968 "bookvol10.3.pamphlet" 1774282 1774298 1774390 1774395) (-967 "bookvol10.3.pamphlet" 1774170 1774180 1774272 1774277) (-966 "bookvol10.3.pamphlet" 1774058 1774068 1774160 1774165) (-965 "bookvol10.3.pamphlet" 1771459 1771471 1772024 1772079) (-964 "bookvol10.3.pamphlet" 1769845 1769857 1770550 1770677) (-963 "bookvol10.4.pamphlet" 1769049 1769088 1769835 1769840) (-962 "bookvol10.4.pamphlet" 1768801 1768809 1769039 1769044) (-961 "bookvol10.4.pamphlet" 1767044 1767054 1768791 1768796) (-960 "bookvol10.4.pamphlet" 1765017 1765031 1767034 1767039) (-959 "bookvol10.2.pamphlet" 1764640 1764648 1765007 1765012) (-958 "bookvol10.3.pamphlet" 1763883 1763893 1764046 1764073) (-957 "bookvol10.4.pamphlet" 1761775 1761787 1763873 1763878) (-956 "bookvol10.4.pamphlet" 1761147 1761159 1761765 1761770) (-955 "bookvol10.2.pamphlet" 1760284 1760292 1761137 1761142) (-954 "bookvol10.4.pamphlet" 1759056 1759078 1760240 1760245) (-953 "bookvol10.3.pamphlet" 1756368 1756378 1756870 1756997) (-952 "bookvol10.4.pamphlet" 1755629 1755652 1756358 1756363) (-951 "bookvol10.4.pamphlet" 1753693 1753715 1755619 1755624) (-950 "bookvol10.2.pamphlet" 1747095 1747116 1753561 1753688) (-949 NIL 1739799 1739822 1746267 1746272) (-948 "bookvol10.4.pamphlet" 1739247 1739261 1739789 1739794) (-947 "bookvol10.4.pamphlet" 1738857 1738869 1739237 1739242) (-946 "bookvol10.4.pamphlet" 1737798 1737827 1738813 1738818) (-945 "bookvol10.4.pamphlet" 1736546 1736561 1737788 1737793) (-944 "bookvol10.3.pamphlet" 1735607 1735617 1735694 1735721) (-943 "bookvol10.4.pamphlet" 1732247 1732255 1735597 1735602) (-942 "bookvol10.4.pamphlet" 1731004 1731018 1732237 1732242) (-941 "bookvol10.4.pamphlet" 1730549 1730559 1730994 1730999) (-940 "bookvol10.4.pamphlet" 1730136 1730150 1730539 1730544) (-939 "bookvol10.4.pamphlet" 1729662 1729676 1730126 1730131) (-938 "bookvol10.4.pamphlet" 1729163 1729185 1729652 1729657) (-937 "bookvol10.4.pamphlet" 1728233 1728251 1729095 1729100) (-936 "bookvol10.4.pamphlet" 1727814 1727828 1728223 1728228) (-935 "bookvol10.4.pamphlet" 1727381 1727393 1727804 1727809) (-934 "bookvol10.4.pamphlet" 1726957 1726967 1727371 1727376) (-933 "bookvol10.4.pamphlet" 1726530 1726548 1726947 1726952) (-932 "bookvol10.4.pamphlet" 1725812 1725826 1726520 1726525) (-931 "bookvol10.4.pamphlet" 1724881 1724889 1725802 1725807) (-930 "bookvol10.4.pamphlet" 1723907 1723923 1724871 1724876) (-929 "bookvol10.4.pamphlet" 1722805 1722843 1723897 1723902) (-928 "bookvol10.4.pamphlet" 1722585 1722593 1722795 1722800) (-927 "bookvol10.3.pamphlet" 1717257 1717265 1722575 1722580) (-926 "bookvol10.3.pamphlet" 1713659 1713667 1717247 1717252) (-925 "bookvol10.4.pamphlet" 1712792 1712802 1713649 1713654) (-924 "bookvol10.4.pamphlet" 1698749 1698776 1712782 1712787) (-923 "bookvol10.3.pamphlet" 1698656 1698670 1698739 1698744) (-922 "bookvol10.3.pamphlet" 1698567 1698577 1698646 1698651) (-921 "bookvol10.3.pamphlet" 1698478 1698488 1698557 1698562) (-920 "bookvol10.2.pamphlet" 1697506 1697520 1698468 1698473) (-919 "bookvol10.4.pamphlet" 1697122 1697141 1697496 1697501) (-918 "bookvol10.4.pamphlet" 1696904 1696920 1697112 1697117) (-917 "bookvol10.3.pamphlet" 1696526 1696534 1696878 1696899) (-916 "bookvol10.2.pamphlet" 1695482 1695490 1696452 1696521) (-915 "bookvol10.4.pamphlet" 1695211 1695221 1695472 1695477) (-914 "bookvol10.4.pamphlet" 1693823 1693837 1695201 1695206) (-913 "bookvol10.4.pamphlet" 1685189 1685197 1693813 1693818) (-912 "bookvol10.4.pamphlet" 1683739 1683756 1685179 1685184) (-911 "bookvol10.4.pamphlet" 1682754 1682764 1683729 1683734) (-910 "bookvol10.3.pamphlet" 1678122 1678132 1682656 1682749) (-909 "bookvol10.4.pamphlet" 1677477 1677493 1678112 1678117) (-908 "bookvol10.4.pamphlet" 1675512 1675541 1677467 1677472) (-907 "bookvol10.4.pamphlet" 1674882 1674900 1675502 1675507) (-906 "bookvol10.4.pamphlet" 1674301 1674328 1674872 1674877) (-905 "bookvol10.3.pamphlet" 1673968 1673980 1674106 1674199) (-904 "bookvol10.2.pamphlet" 1671634 1671642 1673894 1673963) (-903 NIL 1669328 1669338 1671590 1671595) (-902 "bookvol10.4.pamphlet" 1667213 1667225 1669318 1669323) (-901 "bookvol10.4.pamphlet" 1664813 1664836 1667203 1667208) (-900 "bookvol10.3.pamphlet" 1659799 1659809 1664643 1664658) (-899 "bookvol10.3.pamphlet" 1654489 1654499 1659789 1659794) (-898 "bookvol10.2.pamphlet" 1653042 1653052 1654469 1654484) (-897 "bookvol10.4.pamphlet" 1651705 1651719 1653032 1653037) (-896 "bookvol10.3.pamphlet" 1650975 1650985 1651557 1651562) (-895 "bookvol10.2.pamphlet" 1649269 1649279 1650955 1650970) (-894 NIL 1647571 1647583 1649259 1649264) (-893 "bookvol10.3.pamphlet" 1645676 1645684 1647561 1647566) (-892 "bookvol10.4.pamphlet" 1639468 1639476 1645666 1645671) (-891 "bookvol10.4.pamphlet" 1638768 1638785 1639458 1639463) (-890 "bookvol10.2.pamphlet" 1636912 1636920 1638758 1638763) (-889 "bookvol10.4.pamphlet" 1636601 1636614 1636902 1636907) (-888 "bookvol10.3.pamphlet" 1635243 1635260 1636591 1636596) (-887 "bookvol10.3.pamphlet" 1629674 1629684 1635233 1635238) (-886 "bookvol10.4.pamphlet" 1629411 1629423 1629664 1629669) (-885 "bookvol10.4.pamphlet" 1627701 1627717 1629401 1629406) (-884 "bookvol10.3.pamphlet" 1625240 1625252 1627691 1627696) (-883 "bookvol10.4.pamphlet" 1624894 1624908 1625230 1625235) (-882 "bookvol10.4.pamphlet" 1623051 1623082 1624602 1624607) (-881 "bookvol10.2.pamphlet" 1622476 1622486 1623041 1623046) (-880 "bookvol10.3.pamphlet" 1621560 1621574 1622466 1622471) (-879 "bookvol10.2.pamphlet" 1621324 1621334 1621550 1621555) (-878 "bookvol10.4.pamphlet" 1618686 1618694 1621314 1621319) (-877 "bookvol10.3.pamphlet" 1618114 1618142 1618676 1618681) (-876 "bookvol10.4.pamphlet" 1617905 1617921 1618104 1618109) (-875 "bookvol10.3.pamphlet" 1617333 1617361 1617895 1617900) (-874 "bookvol10.4.pamphlet" 1617118 1617134 1617323 1617328) (-873 "bookvol10.3.pamphlet" 1616576 1616604 1617108 1617113) (-872 "bookvol10.4.pamphlet" 1616361 1616377 1616566 1616571) (-871 "bookvol10.4.pamphlet" 1615152 1615201 1616351 1616356) (-870 "bookvol10.4.pamphlet" 1614564 1614572 1615142 1615147) (-869 "bookvol10.3.pamphlet" 1613534 1613542 1614554 1614559) (-868 "bookvol10.4.pamphlet" 1607917 1607940 1613490 1613495) (-867 "bookvol10.4.pamphlet" 1601736 1601759 1607866 1607871) (-866 "bookvol10.3.pamphlet" 1599066 1599084 1600241 1600334) (-865 "bookvol10.3.pamphlet" 1597081 1597093 1597302 1597395) (-864 "bookvol10.3.pamphlet" 1596776 1596788 1597007 1597076) (-863 "bookvol10.2.pamphlet" 1595332 1595344 1596702 1596771) (-862 "bookvol10.4.pamphlet" 1594261 1594280 1595322 1595327) (-861 "bookvol10.4.pamphlet" 1593242 1593258 1594251 1594256) (-860 "bookvol10.3.pamphlet" 1591843 1591851 1592913 1593006) (-859 "bookvol10.2.pamphlet" 1590593 1590601 1591745 1591838) (-858 "bookvol10.2.pamphlet" 1588656 1588664 1590495 1590588) (-857 "bookvol10.3.pamphlet" 1587381 1587391 1588452 1588545) (-856 "bookvol10.2.pamphlet" 1586134 1586142 1587283 1587376) (-855 "bookvol10.3.pamphlet" 1584439 1584459 1585524 1585617) (-854 "bookvol10.2.pamphlet" 1583181 1583189 1584341 1584434) (-853 "bookvol10.3.pamphlet" 1582165 1582195 1583039 1583106) (-852 "bookvol10.3.pamphlet" 1581946 1581969 1582155 1582160) (-851 "bookvol10.4.pamphlet" 1581030 1581038 1581936 1581941) (-850 "bookvol10.3.pamphlet" 1570444 1570452 1581020 1581025) (-849 "bookvol10.3.pamphlet" 1570033 1570041 1570434 1570439) (-848 "bookvol10.4.pamphlet" 1568494 1568504 1569950 1569955) (-847 "bookvol10.3.pamphlet" 1567852 1567880 1568174 1568213) (-846 "bookvol10.3.pamphlet" 1567151 1567175 1567532 1567571) (-845 "bookvol10.4.pamphlet" 1564985 1564997 1567071 1567076) (-844 "bookvol10.2.pamphlet" 1559131 1559141 1564941 1564980) (-843 NIL 1553167 1553179 1558979 1558984) (-842 "bookvol10.2.pamphlet" 1552333 1552341 1553157 1553162) (-841 NIL 1551497 1551507 1552323 1552328) (-840 "bookvol10.2.pamphlet" 1550831 1550839 1551477 1551492) (-839 NIL 1550173 1550183 1550821 1550826) (-838 "bookvol10.2.pamphlet" 1549927 1549935 1550163 1550168) (-837 "bookvol10.4.pamphlet" 1549068 1549084 1549917 1549922) (-836 "bookvol10.2.pamphlet" 1549002 1549010 1549058 1549063) (-835 "bookvol10.3.pamphlet" 1547488 1547498 1548549 1548578) (-834 "bookvol10.4.pamphlet" 1546828 1546840 1547478 1547483) (-833 "bookvol10.3.pamphlet" 1544512 1544520 1546818 1546823) (-832 "bookvol10.4.pamphlet" 1536696 1536704 1544502 1544507) (-831 "bookvol10.2.pamphlet" 1534162 1534170 1536686 1536691) (-830 "bookvol10.4.pamphlet" 1533711 1533719 1534152 1534157) (-829 "bookvol10.3.pamphlet" 1533453 1533463 1533533 1533600) (-828 "bookvol10.3.pamphlet" 1532227 1532237 1533000 1533029) (-827 "bookvol10.4.pamphlet" 1531700 1531712 1532217 1532222) (-826 "bookvol10.4.pamphlet" 1530702 1530710 1531690 1531695) (-825 "bookvol10.2.pamphlet" 1530478 1530488 1530646 1530697) (-824 "bookvol10.4.pamphlet" 1529090 1529098 1530468 1530473) (-823 "bookvol10.2.pamphlet" 1528055 1528063 1529080 1529085) (-822 "bookvol10.3.pamphlet" 1527480 1527492 1527941 1527980) (-821 "bookvol10.4.pamphlet" 1527314 1527324 1527470 1527475) (-820 "bookvol10.3.pamphlet" 1526857 1526865 1527304 1527309) (-819 "bookvol10.3.pamphlet" 1525891 1525899 1526847 1526852) (-818 "bookvol10.3.pamphlet" 1525235 1525243 1525881 1525886) (-817 "bookvol10.3.pamphlet" 1519524 1519532 1525225 1525230) (-816 "bookvol10.3.pamphlet" 1518933 1518941 1519514 1519519) (-815 "bookvol10.2.pamphlet" 1518708 1518716 1518859 1518928) (-814 "bookvol10.3.pamphlet" 1512079 1512089 1518698 1518703) (-813 "bookvol10.3.pamphlet" 1511340 1511350 1512069 1512074) (-812 "bookvol10.3.pamphlet" 1510788 1510814 1511152 1511301) (-811 "bookvol10.3.pamphlet" 1508146 1508156 1508474 1508601) (-810 "bookvol10.3.pamphlet" 1500003 1500023 1500361 1500492) (-809 "bookvol10.4.pamphlet" 1498582 1498601 1499993 1499998) (-808 "bookvol10.4.pamphlet" 1496232 1496249 1498572 1498577) (-807 "bookvol10.4.pamphlet" 1492175 1492192 1496189 1496194) (-806 "bookvol10.4.pamphlet" 1491562 1491586 1492165 1492170) (-805 "bookvol10.4.pamphlet" 1489128 1489145 1491552 1491557) (-804 "bookvol10.4.pamphlet" 1486019 1486041 1489118 1489123) (-803 "bookvol10.3.pamphlet" 1484605 1484613 1486009 1486014) (-802 "bookvol10.4.pamphlet" 1481909 1481931 1484595 1484600) (-801 "bookvol10.4.pamphlet" 1481285 1481309 1481899 1481904) (-800 "bookvol10.4.pamphlet" 1467647 1467655 1481275 1481280) (-799 "bookvol10.4.pamphlet" 1467078 1467094 1467637 1467642) (-798 "bookvol10.3.pamphlet" 1464473 1464481 1467068 1467073) (-797 "bookvol10.4.pamphlet" 1459840 1459856 1464463 1464468) (-796 "bookvol10.4.pamphlet" 1459359 1459377 1459830 1459835) (-795 "bookvol10.2.pamphlet" 1457744 1457752 1459349 1459354) (-794 "bookvol10.3.pamphlet" 1455880 1455890 1456598 1456637) (-793 "bookvol10.4.pamphlet" 1455516 1455537 1455870 1455875) (-792 "bookvol10.2.pamphlet" 1453290 1453300 1455472 1455511) (-791 NIL 1450789 1450801 1452973 1452978) (-790 "bookvol10.2.pamphlet" 1450637 1450645 1450779 1450784) (-789 "bookvol10.2.pamphlet" 1450385 1450393 1450627 1450632) (-788 "bookvol10.2.pamphlet" 1449677 1449685 1450375 1450380) (-787 "bookvol10.2.pamphlet" 1449538 1449546 1449667 1449672) (-786 "bookvol10.2.pamphlet" 1449400 1449408 1449528 1449533) (-785 "bookvol10.4.pamphlet" 1449123 1449139 1449390 1449395) (-784 "bookvol10.4.pamphlet" 1437440 1437448 1449113 1449118) (-783 "bookvol10.4.pamphlet" 1428199 1428207 1437430 1437435) (-782 "bookvol10.2.pamphlet" 1425538 1425546 1428189 1428194) (-781 "bookvol10.4.pamphlet" 1424378 1424386 1425528 1425533) (-780 "bookvol10.4.pamphlet" 1416450 1416460 1424183 1424188) (-779 "bookvol10.2.pamphlet" 1415747 1415763 1416406 1416445) (-778 "bookvol10.4.pamphlet" 1415292 1415302 1415664 1415669) (-777 "bookvol10.3.pamphlet" 1408281 1408291 1412842 1412995) (-776 "bookvol10.4.pamphlet" 1407673 1407685 1408271 1408276) (-775 "bookvol10.3.pamphlet" 1403868 1403887 1404176 1404303) (-774 "bookvol10.3.pamphlet" 1402392 1402402 1402469 1402562) (-773 "bookvol10.4.pamphlet" 1400764 1400778 1402382 1402387) (-772 "bookvol10.4.pamphlet" 1400656 1400685 1400754 1400759) (-771 "bookvol10.4.pamphlet" 1399902 1399922 1400646 1400651) (-770 "bookvol10.3.pamphlet" 1399790 1399804 1399882 1399897) (-769 "bookvol10.4.pamphlet" 1399384 1399423 1399780 1399785) (-768 "bookvol10.4.pamphlet" 1397918 1397937 1399374 1399379) (-767 "bookvol10.4.pamphlet" 1397606 1397632 1397908 1397913) (-766 "bookvol10.3.pamphlet" 1397347 1397355 1397596 1397601) (-765 "bookvol10.4.pamphlet" 1397023 1397033 1397337 1397342) (-764 "bookvol10.4.pamphlet" 1396492 1396508 1397013 1397018) (-763 "bookvol10.3.pamphlet" 1395382 1395390 1396466 1396487) (-762 "bookvol10.4.pamphlet" 1394004 1394014 1395372 1395377) (-761 "bookvol10.3.pamphlet" 1391602 1391610 1393994 1393999) (-760 "bookvol10.4.pamphlet" 1389062 1389079 1391592 1391597) (-759 "bookvol10.4.pamphlet" 1388315 1388329 1389052 1389057) (-758 "bookvol10.4.pamphlet" 1386427 1386443 1388305 1388310) (-757 "bookvol10.4.pamphlet" 1386084 1386098 1386417 1386422) (-756 "bookvol10.4.pamphlet" 1384244 1384258 1386074 1386079) (-755 "bookvol10.2.pamphlet" 1383840 1383848 1384234 1384239) (-754 NIL 1383434 1383444 1383830 1383835) (-753 "bookvol10.2.pamphlet" 1382720 1382728 1383424 1383429) (-752 NIL 1382004 1382014 1382710 1382715) (-751 "bookvol10.4.pamphlet" 1381077 1381085 1381994 1381999) (-750 "bookvol10.4.pamphlet" 1370643 1370651 1381067 1381072) (-749 "bookvol10.4.pamphlet" 1369079 1369087 1370633 1370638) (-748 "bookvol10.4.pamphlet" 1363253 1363261 1369069 1369074) (-747 "bookvol10.4.pamphlet" 1356997 1357005 1363243 1363248) (-746 "bookvol10.4.pamphlet" 1352619 1352627 1356987 1356992) (-745 "bookvol10.4.pamphlet" 1345993 1346001 1352609 1352614) (-744 "bookvol10.4.pamphlet" 1336388 1336396 1345983 1345988) (-743 "bookvol10.4.pamphlet" 1332315 1332323 1336378 1336383) (-742 "bookvol10.4.pamphlet" 1330190 1330198 1332305 1332310) (-741 "bookvol10.4.pamphlet" 1322636 1322644 1330180 1330185) (-740 "bookvol10.4.pamphlet" 1316792 1316800 1322626 1322631) (-739 "bookvol10.4.pamphlet" 1312622 1312630 1316782 1316787) (-738 "bookvol10.4.pamphlet" 1311134 1311142 1312612 1312617) (-737 "bookvol10.4.pamphlet" 1310432 1310440 1311124 1311129) (-736 "bookvol10.2.pamphlet" 1309938 1309948 1310400 1310427) (-735 NIL 1309464 1309476 1309928 1309933) (-734 "bookvol10.3.pamphlet" 1306685 1306699 1307014 1307167) (-733 "bookvol10.3.pamphlet" 1304804 1304818 1304876 1305096) (-732 "bookvol10.4.pamphlet" 1301788 1301805 1304794 1304799) (-731 "bookvol10.4.pamphlet" 1301186 1301203 1301778 1301783) (-730 "bookvol10.2.pamphlet" 1299220 1299241 1301084 1301181) (-729 "bookvol10.4.pamphlet" 1298877 1298887 1299210 1299215) (-728 "bookvol10.4.pamphlet" 1298317 1298325 1298867 1298872) (-727 "bookvol10.3.pamphlet" 1296322 1296332 1298079 1298118) (-726 "bookvol10.2.pamphlet" 1296155 1296165 1296278 1296317) (-725 "bookvol10.3.pamphlet" 1293108 1293120 1295863 1295930) (-724 "bookvol10.4.pamphlet" 1292668 1292682 1293098 1293103) (-723 "bookvol10.4.pamphlet" 1292229 1292246 1292658 1292663) (-722 "bookvol10.4.pamphlet" 1290274 1290293 1292219 1292224) (-721 "bookvol10.3.pamphlet" 1287724 1287739 1288068 1288195) (-720 "bookvol10.4.pamphlet" 1287003 1287022 1287714 1287719) (-719 "bookvol10.4.pamphlet" 1286811 1286854 1286993 1286998) (-718 "bookvol10.4.pamphlet" 1286555 1286591 1286801 1286806) (-717 "bookvol10.4.pamphlet" 1284890 1284907 1286545 1286550) (-716 "bookvol10.2.pamphlet" 1283754 1283762 1284880 1284885) (-715 NIL 1282616 1282626 1283744 1283749) (-714 "bookvol10.2.pamphlet" 1281362 1281375 1282476 1282611) (-713 NIL 1280130 1280145 1281246 1281251) (-712 "bookvol10.2.pamphlet" 1278136 1278144 1280120 1280125) (-711 NIL 1276140 1276150 1278126 1278131) (-710 "bookvol10.2.pamphlet" 1275284 1275292 1276130 1276135) (-709 NIL 1274426 1274436 1275274 1275279) (-708 "bookvol10.3.pamphlet" 1273105 1273119 1274406 1274421) (-707 "bookvol10.2.pamphlet" 1272786 1272796 1273073 1273100) (-706 NIL 1272487 1272499 1272776 1272781) (-705 "bookvol10.3.pamphlet" 1271800 1271839 1272467 1272482) (-704 "bookvol10.3.pamphlet" 1270442 1270454 1271622 1271689) (-703 "bookvol10.3.pamphlet" 1269953 1269971 1270432 1270437) (-702 "bookvol10.3.pamphlet" 1266613 1266629 1267431 1267584) (-701 "bookvol10.3.pamphlet" 1265974 1266013 1266515 1266608) (-700 "bookvol10.3.pamphlet" 1264761 1264769 1265964 1265969) (-699 "bookvol10.4.pamphlet" 1264501 1264535 1264751 1264756) (-698 "bookvol10.2.pamphlet" 1262943 1262953 1264457 1264496) (-697 "bookvol10.4.pamphlet" 1261515 1261532 1262933 1262938) (-696 "bookvol10.4.pamphlet" 1260985 1261003 1261505 1261510) (-695 "bookvol10.4.pamphlet" 1260571 1260584 1260975 1260980) (-694 "bookvol10.4.pamphlet" 1259886 1259896 1260561 1260566) (-693 "bookvol10.4.pamphlet" 1258779 1258789 1259876 1259881) (-692 "bookvol10.3.pamphlet" 1258555 1258565 1258769 1258774) (-691 "bookvol10.4.pamphlet" 1258016 1258034 1258545 1258550) (-690 "bookvol10.3.pamphlet" 1257455 1257463 1257918 1258011) (-689 "bookvol10.4.pamphlet" 1256094 1256104 1257445 1257450) (-688 "bookvol10.3.pamphlet" 1254538 1254546 1255984 1256089) (-687 "bookvol10.4.pamphlet" 1253938 1253960 1254528 1254533) (-686 "bookvol10.4.pamphlet" 1251800 1251808 1253928 1253933) (-685 "bookvol10.4.pamphlet" 1250041 1250051 1251790 1251795) (-684 "bookvol10.2.pamphlet" 1249316 1249326 1250009 1250036) (-683 "bookvol10.3.pamphlet" 1245289 1245297 1245903 1246104) (-682 "bookvol10.4.pamphlet" 1244497 1244509 1245279 1245284) (-681 "bookvol10.4.pamphlet" 1241605 1241631 1244487 1244492) (-680 "bookvol10.4.pamphlet" 1238881 1238891 1241595 1241600) (-679 "bookvol10.3.pamphlet" 1237772 1237782 1238256 1238283) (-678 "bookvol10.4.pamphlet" 1235098 1235122 1237656 1237661) (-677 "bookvol10.2.pamphlet" 1220309 1220331 1235054 1235093) (-676 NIL 1205368 1205392 1220115 1220120) (-675 "bookvol10.4.pamphlet" 1204636 1204684 1205358 1205363) (-674 "bookvol10.4.pamphlet" 1203356 1203368 1204626 1204631) (-673 "bookvol10.4.pamphlet" 1202255 1202269 1203346 1203351) (-672 "bookvol10.4.pamphlet" 1201589 1201601 1202245 1202250) (-671 "bookvol10.4.pamphlet" 1200407 1200417 1201579 1201584) (-670 "bookvol10.4.pamphlet" 1200215 1200229 1200397 1200402) (-669 "bookvol10.4.pamphlet" 1199980 1199992 1200205 1200210) (-668 "bookvol10.4.pamphlet" 1199610 1199620 1199970 1199975) (-667 "bookvol10.3.pamphlet" 1197554 1197571 1199600 1199605) (-666 "bookvol10.3.pamphlet" 1195473 1195483 1197155 1197160) (-665 "bookvol10.2.pamphlet" 1190929 1190939 1195453 1195468) (-664 NIL 1186393 1186405 1190919 1190924) (-663 "bookvol10.3.pamphlet" 1183199 1183216 1186383 1186388) (-662 "bookvol10.3.pamphlet" 1181457 1181471 1181879 1181930) (-661 "bookvol10.4.pamphlet" 1180990 1181007 1181447 1181452) (-660 "bookvol10.4.pamphlet" 1179830 1179858 1180980 1180985) (-659 "bookvol10.4.pamphlet" 1177634 1177648 1179820 1179825) (-658 "bookvol10.2.pamphlet" 1177291 1177301 1177590 1177629) (-657 NIL 1176980 1176992 1177281 1177286) (-656 "bookvol10.3.pamphlet" 1175994 1176013 1176836 1176905) (-655 "bookvol10.4.pamphlet" 1175251 1175261 1175984 1175989) (-654 "bookvol10.4.pamphlet" 1173696 1173745 1175241 1175246) (-653 "bookvol10.4.pamphlet" 1172335 1172345 1173686 1173691) (-652 "bookvol10.3.pamphlet" 1171736 1171750 1172269 1172296) (-651 "bookvol10.2.pamphlet" 1171338 1171346 1171726 1171731) (-650 NIL 1170938 1170948 1171328 1171333) (-649 "bookvol10.4.pamphlet" 1169856 1169868 1170928 1170933) (-648 "bookvol10.3.pamphlet" 1169243 1169259 1169536 1169575) (-647 "bookvol10.4.pamphlet" 1168287 1168304 1169200 1169205) (-646 "bookvol10.2.pamphlet" 1166904 1166914 1168243 1168282) (-645 NIL 1165519 1165531 1166860 1166865) (-644 "bookvol10.3.pamphlet" 1164795 1164807 1165199 1165238) (-643 "bookvol10.3.pamphlet" 1164198 1164208 1164475 1164514) (-642 "bookvol10.4.pamphlet" 1162970 1162988 1164188 1164193) (-641 "bookvol10.2.pamphlet" 1161345 1161355 1162872 1162965) (-640 "bookvol10.2.pamphlet" 1157093 1157103 1161325 1161340) (-639 NIL 1152815 1152827 1157049 1157054) (-638 "bookvol10.3.pamphlet" 1149551 1149568 1152805 1152810) (-637 "bookvol10.2.pamphlet" 1149034 1149044 1149541 1149546) (-636 "bookvol10.3.pamphlet" 1148134 1148144 1148808 1148835) (-635 "bookvol10.4.pamphlet" 1147565 1147579 1148124 1148129) (-634 "bookvol10.3.pamphlet" 1145506 1145516 1146935 1146962) (-633 "bookvol10.4.pamphlet" 1144797 1144811 1145496 1145501) (-632 "bookvol10.4.pamphlet" 1143437 1143449 1144787 1144792) (-631 "bookvol10.4.pamphlet" 1140310 1140322 1143427 1143432) (-630 "bookvol10.2.pamphlet" 1139742 1139752 1140290 1140305) (-629 "bookvol10.4.pamphlet" 1138519 1138531 1139654 1139659) (-628 "bookvol10.4.pamphlet" 1136433 1136443 1138509 1138514) (-627 "bookvol10.4.pamphlet" 1135316 1135329 1136423 1136428) (-626 "bookvol10.3.pamphlet" 1133330 1133342 1134606 1134751) (-625 "bookvol10.2.pamphlet" 1132855 1132865 1133256 1133325) (-624 NIL 1132408 1132420 1132811 1132816) (-623 "bookvol10.3.pamphlet" 1130941 1130949 1131649 1131664) (-622 "bookvol10.4.pamphlet" 1128309 1128328 1130931 1130936) (-621 "bookvol10.4.pamphlet" 1127052 1127068 1128299 1128304) (-620 "bookvol10.2.pamphlet" 1125759 1125767 1127042 1127047) (-619 "bookvol10.4.pamphlet" 1121411 1121426 1125749 1125754) (-618 "bookvol10.3.pamphlet" 1119474 1119501 1121391 1121406) (-617 "bookvol10.4.pamphlet" 1117858 1117875 1119464 1119469) (-616 "bookvol10.4.pamphlet" 1116916 1116938 1117848 1117853) (-615 "bookvol10.3.pamphlet" 1115688 1115701 1116509 1116578) (-614 "bookvol10.4.pamphlet" 1115261 1115277 1115678 1115683) (-613 "bookvol10.3.pamphlet" 1114701 1114715 1115183 1115222) (-612 "bookvol10.2.pamphlet" 1114477 1114487 1114681 1114696) (-611 NIL 1114261 1114273 1114467 1114472) (-610 "bookvol10.4.pamphlet" 1112974 1112991 1114251 1114256) (-609 "bookvol10.2.pamphlet" 1112696 1112706 1112964 1112969) (-608 "bookvol10.2.pamphlet" 1112433 1112443 1112686 1112691) (-607 "bookvol10.3.pamphlet" 1110968 1110978 1112217 1112222) (-606 "bookvol10.4.pamphlet" 1110671 1110683 1110958 1110963) (-605 "bookvol10.2.pamphlet" 1109762 1109784 1110639 1110666) (-604 NIL 1108873 1108897 1109752 1109757) (-603 "bookvol10.3.pamphlet" 1107495 1107511 1108220 1108247) (-602 "bookvol10.3.pamphlet" 1105472 1105484 1106785 1106930) (-601 "bookvol10.2.pamphlet" 1103554 1103578 1105452 1105467) (-600 NIL 1101501 1101527 1103401 1103406) (-599 "bookvol10.3.pamphlet" 1100509 1100524 1100649 1100676) (-598 "bookvol10.3.pamphlet" 1099669 1099679 1100499 1100504) (-597 "bookvol10.4.pamphlet" 1098480 1098499 1099659 1099664) (-596 "bookvol10.4.pamphlet" 1097974 1097988 1098470 1098475) (-595 "bookvol10.4.pamphlet" 1097704 1097716 1097964 1097969) (-594 "bookvol10.3.pamphlet" 1095496 1095511 1097540 1097665) (-593 "bookvol10.3.pamphlet" 1087922 1087937 1094470 1094567) (-592 "bookvol10.4.pamphlet" 1087405 1087421 1087912 1087917) (-591 "bookvol10.3.pamphlet" 1086635 1086648 1086801 1086828) (-590 "bookvol10.4.pamphlet" 1085715 1085734 1086625 1086630) (-589 "bookvol10.4.pamphlet" 1083679 1083687 1085705 1085710) (-588 "bookvol10.4.pamphlet" 1082202 1082212 1083635 1083640) (-587 "bookvol10.4.pamphlet" 1081803 1081814 1082192 1082197) (-586 "bookvol10.4.pamphlet" 1080149 1080159 1081793 1081798) (-585 "bookvol10.3.pamphlet" 1077894 1077908 1080004 1080031) (-584 "bookvol10.4.pamphlet" 1077030 1077046 1077884 1077889) (-583 "bookvol10.4.pamphlet" 1076171 1076187 1077020 1077025) (-582 "bookvol10.4.pamphlet" 1075931 1075939 1076161 1076166) (-581 "bookvol10.3.pamphlet" 1075624 1075636 1075736 1075829) (-580 "bookvol10.3.pamphlet" 1075385 1075411 1075550 1075619) (-579 "bookvol10.4.pamphlet" 1074994 1075010 1075375 1075380) (-578 "bookvol10.4.pamphlet" 1068240 1068257 1074984 1074989) (-577 "bookvol10.4.pamphlet" 1066099 1066115 1067814 1067819) (-576 "bookvol10.4.pamphlet" 1065405 1065413 1066089 1066094) (-575 "bookvol10.3.pamphlet" 1065181 1065191 1065319 1065400) (-574 "bookvol10.4.pamphlet" 1063545 1063559 1065171 1065176) (-573 "bookvol10.4.pamphlet" 1063034 1063044 1063535 1063540) (-572 "bookvol10.4.pamphlet" 1061679 1061696 1063024 1063029) (-571 "bookvol10.4.pamphlet" 1060042 1060058 1061322 1061327) (-570 "bookvol10.4.pamphlet" 1057769 1057787 1059974 1059979) (-569 "bookvol10.4.pamphlet" 1047876 1047884 1057759 1057764) (-568 "bookvol10.3.pamphlet" 1047237 1047245 1047730 1047871) (-567 "bookvol10.4.pamphlet" 1046503 1046520 1047227 1047232) (-566 "bookvol10.4.pamphlet" 1046168 1046192 1046493 1046498) (-565 "bookvol10.4.pamphlet" 1042569 1042577 1046158 1046163) (-564 "bookvol10.4.pamphlet" 1035949 1035967 1042501 1042506) (-563 "bookvol10.3.pamphlet" 1029947 1029955 1035939 1035944) (-562 "bookvol10.4.pamphlet" 1029047 1029104 1029937 1029942) (-561 "bookvol10.4.pamphlet" 1028121 1028131 1029037 1029042) (-560 "bookvol10.4.pamphlet" 1027989 1028013 1028111 1028116) (-559 "bookvol10.4.pamphlet" 1026303 1026319 1027979 1027984) (-558 "bookvol10.2.pamphlet" 1024927 1024935 1026229 1026298) (-557 NIL 1023613 1023623 1024917 1024922) (-556 "bookvol10.4.pamphlet" 1022743 1022830 1023603 1023608) (-555 "bookvol10.2.pamphlet" 1021206 1021216 1022657 1022738) (-554 "bookvol10.4.pamphlet" 1020709 1020717 1021196 1021201) (-553 "bookvol10.4.pamphlet" 1019891 1019918 1020699 1020704) (-552 "bookvol10.4.pamphlet" 1019383 1019399 1019881 1019886) (-551 "bookvol10.3.pamphlet" 1018463 1018494 1018626 1018653) (-550 "bookvol10.2.pamphlet" 1015859 1015867 1018365 1018458) (-549 NIL 1013341 1013351 1015849 1015854) (-548 "bookvol10.4.pamphlet" 1012775 1012788 1013331 1013336) (-547 "bookvol10.4.pamphlet" 1011841 1011860 1012765 1012770) (-546 "bookvol10.4.pamphlet" 1010899 1010923 1011831 1011836) (-545 "bookvol10.4.pamphlet" 1009885 1009902 1010889 1010894) (-544 "bookvol10.4.pamphlet" 1009032 1009062 1009875 1009880) (-543 "bookvol10.4.pamphlet" 1007317 1007339 1009022 1009027) (-542 "bookvol10.4.pamphlet" 1006367 1006386 1007307 1007312) (-541 "bookvol10.3.pamphlet" 1003411 1003419 1006357 1006362) (-540 "bookvol10.4.pamphlet" 1003036 1003046 1003401 1003406) (-539 "bookvol10.4.pamphlet" 1002624 1002632 1003026 1003031) (-538 "bookvol10.3.pamphlet" 1002005 1002068 1002614 1002619) (-537 "bookvol10.3.pamphlet" 1001411 1001434 1001995 1002000) (-536 "bookvol10.2.pamphlet" 1000034 1000097 1001401 1001406) (-535 "bookvol10.4.pamphlet" 998566 998588 1000024 1000029) (-534 "bookvol10.3.pamphlet" 998472 998489 998556 998561) (-533 "bookvol10.4.pamphlet" 997893 997903 998462 998467) (-532 "bookvol10.4.pamphlet" 993659 993670 997883 997888) (-531 "bookvol10.3.pamphlet" 992791 992817 993303 993330) (-530 "bookvol10.4.pamphlet" 991881 991925 992747 992752) (-529 "bookvol10.4.pamphlet" 990486 990510 991837 991842) (-528 "bookvol10.3.pamphlet" 989365 989380 989892 989919) (-527 "bookvol10.3.pamphlet" 989090 989128 989195 989222) (-526 "bookvol10.3.pamphlet" 988500 988516 988771 988864) (-525 "bookvol10.3.pamphlet" 985571 985586 987906 987933) (-524 "bookvol10.3.pamphlet" 985409 985426 985527 985532) (-523 "bookvol10.2.pamphlet" 984798 984810 985399 985404) (-522 NIL 984185 984199 984788 984793) (-521 "bookvol10.3.pamphlet" 983998 984010 984175 984180) (-520 "bookvol10.3.pamphlet" 983769 983781 983988 983993) (-519 "bookvol10.3.pamphlet" 983504 983516 983759 983764) (-518 "bookvol10.2.pamphlet" 982438 982450 983494 983499) (-517 "bookvol10.3.pamphlet" 982198 982210 982428 982433) (-516 "bookvol10.3.pamphlet" 981960 981972 982188 982193) (-515 "bookvol10.4.pamphlet" 979212 979230 981950 981955) (-514 "bookvol10.3.pamphlet" 974146 974185 979147 979152) (-513 "bookvol10.3.pamphlet" 973567 973590 974136 974141) (-512 "bookvol10.4.pamphlet" 972718 972734 973557 973562) (-511 "bookvol10.3.pamphlet" 971941 971949 972708 972713) (-510 "bookvol10.4.pamphlet" 970564 970581 971931 971936) (-509 "bookvol10.3.pamphlet" 969842 969855 970258 970285) (-508 "bookvol10.4.pamphlet" 966717 966736 969832 969837) (-507 "bookvol10.4.pamphlet" 965605 965620 966707 966712) (-506 "bookvol10.3.pamphlet" 965336 965362 965435 965462) (-505 "bookvol10.3.pamphlet" 964649 964664 964742 964769) (-504 "bookvol10.3.pamphlet" 962862 962870 964465 964558) (-503 "bookvol10.4.pamphlet" 962417 962450 962852 962857) (-502 "bookvol10.2.pamphlet" 961841 961849 962407 962412) (-501 NIL 961263 961273 961831 961836) (-500 "bookvol10.3.pamphlet" 960063 960071 961253 961258) (-499 "bookvol10.2.pamphlet" 957313 957323 960043 960058) (-498 NIL 954404 954416 957136 957141) (-497 "bookvol10.3.pamphlet" 952273 952281 952871 952964) (-496 "bookvol10.4.pamphlet" 951127 951138 952263 952268) (-495 "bookvol10.3.pamphlet" 950717 950741 951117 951122) (-494 "bookvol10.3.pamphlet" 946440 946450 950547 950574) (-493 "bookvol10.3.pamphlet" 938293 938309 938655 938786) (-492 "bookvol10.3.pamphlet" 935484 935499 936087 936214) (-491 "bookvol10.4.pamphlet" 934024 934032 935474 935479) (-490 "bookvol10.3.pamphlet" 933056 933087 933267 933294) (-489 "bookvol10.3.pamphlet" 932641 932649 932958 933051) (-488 "bookvol10.4.pamphlet" 918518 918530 932631 932636) (-487 "bookvol10.4.pamphlet" 918263 918271 918363 918368) (-486 "bookvol10.4.pamphlet" 902336 902372 918133 918138) (-485 "bookvol10.4.pamphlet" 902097 902105 902195 902200) (-484 "bookvol10.4.pamphlet" 901918 901932 902031 902036) (-483 "bookvol10.4.pamphlet" 901795 901809 901908 901913) (-482 "bookvol10.4.pamphlet" 901628 901636 901728 901733) (-481 "bookvol10.3.pamphlet" 900820 900836 901330 901357) (-480 "bookvol10.3.pamphlet" 899901 899936 900075 900090) (-479 "bookvol10.3.pamphlet" 897068 897095 898033 898182) (-478 "bookvol10.2.pamphlet" 896034 896042 897048 897063) (-477 NIL 895008 895018 896024 896029) (-476 "bookvol10.4.pamphlet" 893591 893612 894998 895003) (-475 "bookvol10.2.pamphlet" 892169 892181 893581 893586) (-474 NIL 890745 890759 892159 892164) (-473 "bookvol10.3.pamphlet" 883350 883358 890735 890740) (-472 "bookvol10.4.pamphlet" 881729 881737 883340 883345) (-471 "bookvol10.4.pamphlet" 880172 880180 881719 881724) (-470 "bookvol10.2.pamphlet" 879226 879238 880162 880167) (-469 NIL 878278 878292 879216 879221) (-468 "bookvol10.3.pamphlet" 877788 877811 878016 878043) (-467 "bookvol10.4.pamphlet" 872478 872565 877744 877749) (-466 "bookvol10.4.pamphlet" 871739 871757 872468 872473) (-465 "bookvol10.3.pamphlet" 867687 867695 871729 871734) (-464 "bookvol10.4.pamphlet" 865270 865278 867677 867682) (-463 "bookvol10.3.pamphlet" 864377 864404 865238 865265) (-462 "bookvol10.4.pamphlet" 863487 863501 864367 864372) (-461 "bookvol10.4.pamphlet" 859588 859601 863477 863482) (-460 "bookvol10.4.pamphlet" 859192 859202 859578 859583) (-459 "bookvol10.4.pamphlet" 858776 858793 859182 859187) (-458 "bookvol10.4.pamphlet" 858243 858262 858766 858771) (-457 "bookvol10.4.pamphlet" 856233 856246 858233 858238) (-456 "bookvol10.4.pamphlet" 854490 854498 856223 856228) (-455 "bookvol10.3.pamphlet" 851523 851540 852284 852411) (-454 "bookvol10.3.pamphlet" 845418 845445 851317 851384) (-453 "bookvol10.2.pamphlet" 844346 844354 845344 845413) (-452 NIL 843336 843346 844336 844341) (-451 "bookvol10.4.pamphlet" 837117 837155 843292 843297) (-450 "bookvol10.4.pamphlet" 833215 833253 837107 837112) (-449 "bookvol10.4.pamphlet" 828281 828319 833205 833210) (-448 "bookvol10.4.pamphlet" 824536 824574 828271 828276) (-447 "bookvol10.4.pamphlet" 823833 823841 824526 824531) (-446 "bookvol10.4.pamphlet" 822155 822165 823789 823794) (-445 "bookvol10.4.pamphlet" 820614 820627 822145 822150) (-444 "bookvol10.4.pamphlet" 818779 818798 820604 820609) (-443 "bookvol10.4.pamphlet" 809045 809056 818769 818774) (-442 "bookvol10.2.pamphlet" 806058 806066 809025 809040) (-441 "bookvol10.2.pamphlet" 805100 805108 806038 806053) (-440 "bookvol10.3.pamphlet" 804949 804961 805090 805095) (-439 NIL 803161 803169 804939 804944) (-438 "bookvol10.3.pamphlet" 802324 802332 803151 803156) (-437 "bookvol10.4.pamphlet" 801366 801385 802260 802265) (-436 "bookvol10.3.pamphlet" 799452 799460 801356 801361) (-435 "bookvol10.4.pamphlet" 798874 798890 799442 799447) (-434 "bookvol10.4.pamphlet" 797682 797698 798831 798836) (-433 "bookvol10.4.pamphlet" 794954 794970 797672 797677) (-432 "bookvol10.2.pamphlet" 788988 788998 794717 794949) (-431 NIL 782812 782824 788543 788548) (-430 "bookvol10.4.pamphlet" 782434 782450 782802 782807) (-429 "bookvol10.3.pamphlet" 781742 781754 782254 782353) (-428 "bookvol10.4.pamphlet" 781016 781032 781732 781737) (-427 "bookvol10.2.pamphlet" 780117 780127 780960 781011) (-426 NIL 779192 779204 780037 780042) (-425 "bookvol10.4.pamphlet" 777879 777895 779182 779187) (-424 "bookvol10.4.pamphlet" 772268 772302 777869 777874) (-423 "bookvol10.4.pamphlet" 771878 771894 772258 772263) (-422 "bookvol10.4.pamphlet" 771001 771024 771868 771873) (-421 "bookvol10.4.pamphlet" 769943 769953 770991 770996) (-420 "bookvol10.3.pamphlet" 761367 761377 768967 769036) (-419 "bookvol10.2.pamphlet" 756446 756456 761309 761362) (-418 NIL 751537 751549 756402 756407) (-417 "bookvol10.4.pamphlet" 750983 751001 751527 751532) (-416 "bookvol10.3.pamphlet" 750377 750407 750914 750919) (-415 "bookvol10.3.pamphlet" 749572 749593 750357 750372) (-414 "bookvol10.4.pamphlet" 749308 749340 749562 749567) (-413 "bookvol10.2.pamphlet" 748972 748982 749298 749303) (-412 NIL 748502 748514 748830 748835) (-411 "bookvol10.2.pamphlet" 746830 746843 748458 748497) (-410 NIL 745190 745205 746820 746825) (-409 "bookvol10.3.pamphlet" 742289 742299 742692 742865) (-408 "bookvol10.4.pamphlet" 741892 741904 742279 742284) (-407 "bookvol10.4.pamphlet" 741226 741238 741882 741887) (-406 "bookvol10.2.pamphlet" 738196 738204 741116 741221) (-405 NIL 735194 735204 738116 738121) (-404 "bookvol10.2.pamphlet" 734238 734246 735096 735189) (-403 NIL 733368 733378 734228 734233) (-402 "bookvol10.2.pamphlet" 733120 733130 733348 733363) (-401 "bookvol10.3.pamphlet" 731896 731913 733110 733115) (-400 NIL 730381 730430 731886 731891) (-399 "bookvol10.4.pamphlet" 729310 729318 730371 730376) (-398 "bookvol10.2.pamphlet" 726470 726478 729290 729305) (-397 "bookvol10.2.pamphlet" 726144 726152 726450 726465) (-396 "bookvol10.3.pamphlet" 723482 723490 726134 726139) (-395 "bookvol10.4.pamphlet" 722961 722971 723472 723477) (-394 "bookvol10.4.pamphlet" 722742 722766 722951 722956) (-393 "bookvol10.4.pamphlet" 721943 721951 722732 722737) (-392 "bookvol10.3.pamphlet" 721365 721387 721911 721938) (-391 "bookvol10.2.pamphlet" 719693 719701 721355 721360) (-390 "bookvol10.3.pamphlet" 719585 719593 719683 719688) (-389 "bookvol10.2.pamphlet" 719383 719391 719511 719580) (-388 "bookvol10.3.pamphlet" 716438 716448 719339 719344) (-387 "bookvol10.3.pamphlet" 716133 716145 716372 716399) (-386 "bookvol10.2.pamphlet" 713153 713161 716113 716128) (-385 "bookvol10.2.pamphlet" 712195 712203 713133 713148) (-384 "bookvol10.2.pamphlet" 709899 709917 712163 712190) (-383 "bookvol10.3.pamphlet" 709359 709371 709833 709860) (-382 "bookvol10.4.pamphlet" 707095 707109 709349 709354) (-381 "bookvol10.3.pamphlet" 700516 700524 706961 707090) (-380 "bookvol10.4.pamphlet" 697948 697962 700506 700511) (-379 "bookvol10.2.pamphlet" 697660 697670 697928 697943) (-378 NIL 697326 697338 697596 697601) (-377 "bookvol10.4.pamphlet" 696576 696588 697316 697321) (-376 "bookvol10.2.pamphlet" 694281 694300 696502 696571) (-375 "bookvol10.2.pamphlet" 691279 691289 694249 694276) (-374 NIL 688190 688202 691162 691167) (-373 "bookvol10.4.pamphlet" 686859 686875 688180 688185) (-372 "bookvol10.2.pamphlet" 684892 684905 686815 686854) (-371 NIL 682851 682866 684776 684781) (-370 "bookvol10.2.pamphlet" 682003 682011 682841 682846) (-369 "bookvol10.2.pamphlet" 670932 670942 681945 681998) (-368 NIL 659873 659885 670888 670893) (-367 "bookvol10.3.pamphlet" 659456 659466 659863 659868) (-366 "bookvol10.2.pamphlet" 657885 657902 659446 659451) (-365 "bookvol10.2.pamphlet" 657203 657211 657787 657880) (-364 NIL 656607 656617 657193 657198) (-363 "bookvol10.3.pamphlet" 655216 655226 656587 656602) (-362 "bookvol10.4.pamphlet" 654031 654046 655206 655211) (-361 "bookvol10.3.pamphlet" 653450 653465 653747 653840) (-360 "bookvol10.4.pamphlet" 653315 653332 653440 653445) (-359 "bookvol10.4.pamphlet" 652804 652825 653305 653310) (-358 "bookvol10.4.pamphlet" 644083 644094 652794 652799) (-357 "bookvol10.4.pamphlet" 643129 643146 644073 644078) (-356 "bookvol10.3.pamphlet" 642615 642635 642845 642938) (-355 "bookvol10.3.pamphlet" 642063 642079 642296 642389) (-354 "bookvol10.3.pamphlet" 640581 640601 641779 641872) (-353 "bookvol10.3.pamphlet" 639091 639108 640297 640390) (-352 "bookvol10.3.pamphlet" 637602 637623 638772 638865) (-351 "bookvol10.4.pamphlet" 634964 634983 637592 637597) (-350 "bookvol10.2.pamphlet" 632538 632546 634866 634959) (-349 NIL 630198 630208 632528 632533) (-348 "bookvol10.4.pamphlet" 628943 628960 630188 630193) (-347 "bookvol10.4.pamphlet" 626358 626369 628933 628938) (-346 "bookvol10.4.pamphlet" 619566 619582 626348 626353) (-345 "bookvol10.4.pamphlet" 618181 618200 619556 619561) (-344 "bookvol10.4.pamphlet" 617590 617607 618171 618176) (-343 "bookvol10.3.pamphlet" 616443 616463 617306 617399) (-342 "bookvol10.3.pamphlet" 615338 615358 616159 616252) (-341 "bookvol10.3.pamphlet" 614137 614158 615019 615112) (-340 "bookvol10.2.pamphlet" 602768 602790 613976 614132) (-339 NIL 591478 591502 602688 602693) (-338 "bookvol10.4.pamphlet" 591223 591263 591468 591473) (-337 "bookvol10.3.pamphlet" 583853 583899 590979 591018) (-336 "bookvol10.2.pamphlet" 583559 583569 583843 583848) (-335 NIL 583050 583062 583336 583341) (-334 "bookvol10.3.pamphlet" 582483 582507 583040 583045) (-333 "bookvol10.2.pamphlet" 580525 580549 582473 582478) (-332 NIL 578565 578591 580515 580520) (-331 "bookvol10.4.pamphlet" 578309 578349 578555 578560) (-330 "bookvol10.4.pamphlet" 576830 576838 578299 578304) (-329 "bookvol10.3.pamphlet" 576359 576369 576820 576825) (-328 NIL 566184 566192 576349 576354) (-327 "bookvol10.2.pamphlet" 559057 559071 566086 566179) (-326 NIL 551982 551998 559013 559018) (-325 "bookvol10.3.pamphlet" 550396 550406 551388 551415) (-324 "bookvol10.2.pamphlet" 548516 548528 550294 550391) (-323 NIL 546620 546634 548400 548405) (-322 "bookvol10.4.pamphlet" 546170 546192 546610 546615) (-321 "bookvol10.3.pamphlet" 545820 545830 546124 546129) (-320 "bookvol10.2.pamphlet" 544011 544023 545810 545815) (-319 "bookvol10.3.pamphlet" 543617 543627 543907 543934) (-318 "bookvol10.4.pamphlet" 541813 541830 543607 543612) (-317 "bookvol10.4.pamphlet" 541695 541705 541803 541808) (-316 "bookvol10.4.pamphlet" 540871 540881 541685 541690) (-315 "bookvol10.4.pamphlet" 540753 540763 540861 540866) (-314 "bookvol10.3.pamphlet" 537586 537609 538885 539034) (-313 "bookvol10.4.pamphlet" 534950 534958 537576 537581) (-312 "bookvol10.4.pamphlet" 534852 534881 534940 534945) (-311 "bookvol10.4.pamphlet" 531660 531676 534842 534847) (-310 "bookvol10.3.pamphlet" 526909 526919 527649 528056) (-309 "bookvol10.4.pamphlet" 522969 522982 526899 526904) (-308 "bookvol10.4.pamphlet" 522729 522741 522959 522964) (-307 "bookvol10.3.pamphlet" 519667 519692 520301 520394) (-306 "bookvol10.4.pamphlet" 519520 519528 519657 519662) (-305 "bookvol10.3.pamphlet" 519187 519195 519510 519515) (-304 "bookvol10.4.pamphlet" 518677 518691 519177 519182) (-303 "bookvol10.2.pamphlet" 518241 518251 518667 518672) (-302 NIL 517803 517815 518231 518236) (-301 "bookvol10.2.pamphlet" 515337 515345 517729 517798) (-300 NIL 512933 512943 515327 515332) (-299 "bookvol10.4.pamphlet" 504773 504781 512923 512928) (-298 "bookvol10.4.pamphlet" 504358 504372 504763 504768) (-297 "bookvol10.4.pamphlet" 504035 504046 504348 504353) (-296 "bookvol10.2.pamphlet" 496582 496590 504025 504030) (-295 NIL 489035 489045 496480 496485) (-294 "bookvol10.4.pamphlet" 485808 485816 489025 489030) (-293 "bookvol10.4.pamphlet" 485549 485561 485798 485803) (-292 "bookvol10.4.pamphlet" 485044 485060 485539 485544) (-291 "bookvol10.4.pamphlet" 484610 484626 485034 485039) (-290 "bookvol10.4.pamphlet" 481984 481992 484600 484605) (-289 "bookvol10.3.pamphlet" 481018 481040 481227 481254) (-288 "bookvol10.3.pamphlet" 475876 475886 478691 478803) (-287 "bookvol10.4.pamphlet" 475592 475604 475866 475871) (-286 "bookvol10.4.pamphlet" 471906 471916 475582 475587) (-285 "bookvol10.2.pamphlet" 471448 471456 471850 471901) (-284 "bookvol10.3.pamphlet" 470628 470669 471374 471443) (-283 "bookvol10.2.pamphlet" 468882 468901 470618 470623) (-282 NIL 467100 467121 468838 468843) (-281 "bookvol10.2.pamphlet" 466564 466582 467090 467095) (-280 "bookvol10.4.pamphlet" 465943 465962 466554 466559) (-279 "bookvol10.2.pamphlet" 465632 465640 465933 465938) (-278 NIL 465319 465329 465622 465627) (-277 "bookvol10.2.pamphlet" 463023 463033 465287 465314) (-276 NIL 460676 460688 462942 462947) (-275 "bookvol10.4.pamphlet" 457467 457497 460632 460637) (-274 "bookvol10.4.pamphlet" 454318 454341 457423 457428) (-273 "bookvol10.4.pamphlet" 452273 452289 454308 454313) (-272 "bookvol10.4.pamphlet" 447039 447055 452263 452268) (-271 "bookvol10.3.pamphlet" 445315 445323 447029 447034) (-270 "bookvol10.3.pamphlet" 444851 444859 445305 445310) (-269 "bookvol10.3.pamphlet" 444428 444436 444841 444846) (-268 "bookvol10.3.pamphlet" 444008 444016 444418 444423) (-267 "bookvol10.3.pamphlet" 443544 443552 443998 444003) (-266 "bookvol10.3.pamphlet" 443080 443088 443534 443539) (-265 "bookvol10.3.pamphlet" 442616 442624 443070 443075) (-264 "bookvol10.3.pamphlet" 442152 442160 442606 442611) (-263 "bookvol10.4.pamphlet" 437768 437776 442142 442147) (-262 "bookvol10.2.pamphlet" 434449 434459 437758 437763) (-261 NIL 431128 431140 434439 434444) (-260 "bookvol10.4.pamphlet" 428108 428195 431118 431123) (-259 "bookvol10.3.pamphlet" 427278 427288 427938 427965) (-258 "bookvol10.2.pamphlet" 426866 426876 427234 427273) (-257 "bookvol10.3.pamphlet" 424309 424323 424602 424729) (-256 "bookvol10.3.pamphlet" 418254 418262 424299 424304) (-255 "bookvol10.4.pamphlet" 417915 417925 418244 418249) (-254 "bookvol10.4.pamphlet" 412740 412748 417905 417910) (-253 "bookvol10.4.pamphlet" 410895 410903 412730 412735) (-252 "bookvol10.4.pamphlet" 403495 403508 410885 410890) (-251 "bookvol10.4.pamphlet" 402748 402758 403485 403490) (-250 "bookvol10.4.pamphlet" 400103 400111 402738 402743) (-249 "bookvol10.4.pamphlet" 399640 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T)) (((|#1|) . T)) (|has| |#2| (-904)) ((((-1143) (-57)) . T)) ((((-568)) |has| (-409 |#2|) (-630 (-568))) (((-409 |#2|)) . T)) ((((-541)) . T) (((-215)) . T) (((-381)) . T) (((-887 (-381))) . T)) ((((-850)) . T)) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) (((|#1|) |has| |#1| (-172))) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) @@ -282,14 +282,14 @@ (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-1090)) (((|#1|) . 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T)) (((|#1| (-972)) . T)) ((((-864 |#1|) $) |has| (-864 |#1|) (-281 (-864 |#1|) (-864 |#1|)))) @@ -299,7 +299,7 @@ (((|#2| |#2|) . T)) (|has| |#1| (-1136)) (((|#1| (-763) (-1075)) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) (|has| (-1229 |#1| |#2| |#3| |#4|) (-148)) (|has| (-1229 |#1| |#2| |#3| |#4|) (-150)) (|has| |#1| (-148)) @@ -318,20 +318,20 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1047))) ((((-850)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) (((|#1|) . 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T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($ $) -2199 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((($) . T)) ((($) . T)) ((($) . T)) -((($) -2198 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-850)) . T)) ((((-850)) . T)) (|has| (-1228 |#2| |#3| |#4|) (-150)) @@ -342,16 +342,16 @@ ((((-850)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) (((|#1|) . T)) ((((-568) |#1|) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-840))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-840))) ((((-850)) |has| |#1| (-1090))) -(-2198 (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-150)) (|has| |#1| (-148)) ((((-905 |#1|)) . T)) @@ -366,7 +366,7 @@ ((((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-558))) (|has| |#1| (-15 * (|#1| (-763) |#1|))) (|has| |#1| (-365)) -(-2198 (-12 (|has| (-1235 |#1| |#2| |#3|) (-225)) (|has| |#1| (-365))) (|has| |#1| (-15 * (|#1| (-568) |#1|)))) +(-2199 (-12 (|has| (-1235 |#1| |#2| |#3|) (-225)) (|has| |#1| (-365))) (|has| |#1| (-15 * (|#1| (-568) |#1|)))) (|has| |#1| (-15 * (|#1| (-409 (-568)) |#1|))) ((((-568)) . T)) (|has| |#1| (-365)) @@ -378,10 +378,10 @@ (((|#1|) . T)) ((((-568) |#1|) . T)) (((|#2|) . T)) -(-2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) ((((-2 (|:| |k| (-568)) (|:| |c| |#1|))) . 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T)) ((((-850)) . T)) ((((-850)) . T)) @@ -717,22 +717,22 @@ (|has| |#1| (-1090)) (((|#2|) . T)) ((((-541)) |has| |#2| (-609 (-541))) (((-887 (-381))) |has| |#2| (-609 (-887 (-381)))) (((-887 (-568))) |has| |#2| (-609 (-887 (-568))))) -(((|#4|) -2198 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2198 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2199 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2199 (|has| |#3| (-172)) (|has| |#3| (-365)))) ((((-850)) . T)) (((|#1|) . T)) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-904))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) ((($ $) . T) (((-1161) $) |has| |#1| (-225)) (((-1161) |#1|) |has| |#1| (-225)) (((-813 (-1161)) |#1|) . T) (((-813 (-1161)) $) . 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T)) (|has| (-409 |#2|) (-150)) (|has| (-409 |#2|) (-148)) @@ -745,22 +745,22 @@ (|has| |#1| (-558)) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-850)) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) (|has| |#1| (-43 (-409 (-568)))) -((((-390) (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-390) (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) (|has| |#1| (-43 (-409 (-568)))) (|has| |#2| (-1136)) (|has| |#1| (-558)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (((|#1|) . T)) ((((-390) (-1143)) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-558)) ((((-125 |#1|)) . T)) ((((-568) |#1|) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (((|#2|) . T)) ((((-850)) . T)) (((|#2|) |has| |#2| (-1047)) (((-568)) -12 (|has| |#2| (-630 (-568))) (|has| |#2| (-1047)))) @@ -774,7 +774,7 @@ (((|#1|) |has| |#1| (-172))) ((((-850)) . T)) ((((-541)) |has| |#1| (-609 (-541)))) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) (((|#2|) |has| |#2| (-303 |#2|))) ((((-568) (-568)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) (((|#1|) . T)) @@ -784,7 +784,7 @@ ((((-568) (-568)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) ((($) . T) (((-568)) . T) (((-409 (-568))) . T)) (|has| |#2| (-370)) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) (((|#1|) . T) (((-409 (-568))) . T) (($) . T)) (((|#1|) . T) (((-409 (-568))) . T) (($) . T)) (((|#1|) . 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T)) (|has| |#1| (-558)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-558)) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) @@ -932,7 +932,7 @@ (|has| |#1| (-150)) (|has| |#1| (-148)) (|has| |#4| (-840)) -(((|#2| (-232 (-1697 |#1|) (-763)) (-852 |#1|)) . T)) +(((|#2| (-232 (-1699 |#1|) (-763)) (-852 |#1|)) . T)) (|has| |#3| (-840)) (((|#1| (-534 |#3|) |#3|) . T)) (|has| |#1| (-150)) @@ -946,22 +946,22 @@ (|has| |#1| (-148)) ((((-409 (-568))) |has| |#2| (-365)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-350)) (|has| |#1| (-370))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-350)) (|has| |#1| (-370))) ((((-1127 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-225)) (|has| |#2| (-1047))) -(((|#2|) . T) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -(-2198 (|has| |#3| (-788)) (|has| |#3| (-840))) -(-2198 (|has| |#3| (-788)) (|has| |#3| (-840))) +(((|#2|) . T) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +(-2199 (|has| |#3| (-788)) (|has| |#3| (-840))) +(-2199 (|has| |#3| (-788)) (|has| |#3| (-840))) ((((-850)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-688)) . T)) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (|has| |#1| (-558)) (((|#1|) . T)) (((|#1|) . T)) @@ -983,10 +983,10 @@ (((|#1| (-409 (-568))) . T)) (((|#3|) . T) (((-607 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-409 (-568))) . T) (($) . T)) ((((-1159 |#1| |#2| |#3|) (-1159 |#1| |#2| |#3|)) -12 (|has| (-1159 |#1| |#2| |#3|) (-303 (-1159 |#1| |#2| |#3|))) (|has| |#1| (-365))) (((-1161) (-1159 |#1| |#2| |#3|)) -12 (|has| (-1159 |#1| |#2| |#3|) (-523 (-1161) (-1159 |#1| |#2| |#3|))) (|has| |#1| (-365)))) @@ -994,8 +994,8 @@ ((((-850)) . T)) ((((-850)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) -(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) |has| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (-303 (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))))) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) +(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) |has| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (-303 (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))))) ((((-850)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1006,10 +1006,10 @@ ((($ $) . T) (((-852 |#1|) $) . T) (((-852 |#1|) |#2|) . T)) (|has| |#1| (-823)) (|has| |#1| (-1090)) -(((|#2| |#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($ $) |has| |#2| (-172))) -(((|#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)))) -((((-568) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($) |has| |#2| (-172))) +(((|#2| |#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($ $) |has| |#2| (-172))) +(((|#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)))) +((((-568) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($) |has| |#2| (-172))) ((((-763)) . T)) ((((-568)) . T)) (|has| |#1| (-558)) @@ -1023,34 +1023,34 @@ (((|#1| (-568) (-1075)) . T)) (((|#1|) . T)) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-303 |#1|))) (|has| |#1| (-370)) @@ -1101,32 +1101,32 @@ ((((-1161) $) |has| |#1| (-523 (-1161) $)) (($ $) |has| |#1| (-303 $)) ((|#1| |#1|) |has| |#1| (-303 |#1|)) (((-1161) |#1|) |has| |#1| (-523 (-1161) |#1|))) (|has| |#2| (-558)) ((((-1161)) |has| |#1| (-895 (-1161)))) -(-2198 (-12 (|has| |#1| (-225)) (|has| |#1| (-365))) (|has| |#1| (-350))) +(-2199 (-12 (|has| |#1| (-225)) (|has| |#1| (-365))) (|has| |#1| (-350))) ((((-390) (-1108)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-390) |#1|) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-1090)) ((((-850)) . T)) ((((-850)) . T)) ((((-905 |#1|)) . 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T)) -(-2198 (|has| |#2| (-788)) (|has| |#2| (-840))) -(-2198 (|has| |#2| (-788)) (|has| |#2| (-840))) +(-2199 (|has| |#2| (-788)) (|has| |#2| (-840))) +(-2199 (|has| |#2| (-788)) (|has| |#2| (-840))) (-12 (|has| |#1| (-788)) (|has| |#2| (-788))) (((|#1|) . T)) (-12 (|has| |#1| (-788)) (|has| |#2| (-788))) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#1| (-1181)) ((((-568) (-568)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) ((((-409 (-568))) . T) (($) . T)) @@ -1144,7 +1144,7 @@ (((|#1|) . T) (($) . T) (((-409 (-568))) . T)) (((|#1|) . T) (($) . T) (((-409 (-568))) . T)) (((|#1|) . T)) -((($ $) . T) (((-409 (-568)) (-409 (-568))) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1| |#1|) . T)) +((($ $) . T) (((-409 (-568)) (-409 (-568))) -2199 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1| |#1|) . T)) ((((-850)) . T)) (((|#1|) . T)) ((((-541)) |has| |#3| (-609 (-541)))) @@ -1152,16 +1152,16 @@ (((|#1| |#2|) . T)) (|has| |#1| (-840)) (|has| |#1| (-840)) -((($) . T) (((-409 (-568))) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1|) . T)) +((($) . T) (((-409 (-568))) -2199 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1|) . T)) ((((-568) |#3|) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-558))) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) |has| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (-303 (-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-558))) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) |has| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (-303 (-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))))) ((($) . T)) ((((-409 $) (-409 $)) |has| |#2| (-558)) (($ $) . T) ((|#2| |#2|) . T)) ((((-169 (-215))) . T)) ((((-215)) . T)) (((|#2|) |has| |#2| (-1090))) -((((-850)) -2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((-1244 |#2|)) . T)) +((((-850)) -2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((-1244 |#2|)) . T)) (|has| |#2| (-842)) (|has| |#1| (-842)) (|has| |#1| (-842)) @@ -1171,10 +1171,10 @@ ((((-850)) . T)) ((((-568)) |has| (-409 |#2|) (-630 (-568))) (((-409 |#2|)) . T)) ((((-568) (-147)) . T)) -((((-568) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T) ((|#1| |#2|) . T)) +((((-568) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T) ((|#1| |#2|) . T)) ((((-409 (-568))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-850)) . T)) ((((-905 |#1|)) . T)) (|has| |#1| (-365)) @@ -1200,31 +1200,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-172))) -((((-568) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T) ((|#1| |#2|) . T)) +((((-568) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) |has| |#1| (-172)) (($) -2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904)))) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) |has| |#1| (-172)) (($) -2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904)))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1|) . T)) (((|#1|) . T)) ((((-541)) |has| |#1| (-609 (-541))) (((-887 (-381))) |has| |#1| (-609 (-887 (-381)))) (((-887 (-568))) |has| |#1| (-609 (-887 (-568))))) ((((-850)) . T)) -(((|#2|) . T) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#2| (-840)) (-12 (|has| |#2| (-225)) (|has| |#2| (-1047))) (|has| |#1| (-558)) (|has| |#1| (-1136)) ((((-1143) |#1|) . T)) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) -((((-409 (-568)) (-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($ $) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1| |#1|) . T)) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +((((-409 (-568)) (-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($ $) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1| |#1|) . T)) ((((-409 (-568))) |has| |#1| (-1037 (-568))) (((-568)) |has| |#1| (-1037 (-568))) (((-1161)) |has| |#1| (-1037 (-1161))) ((|#1|) . T)) ((((-568) |#2|) . T)) ((((-409 (-568))) |has| |#1| (-1037 (-409 (-568)))) (((-568)) |has| |#1| (-1037 (-568))) ((|#1|) . T)) ((((-568)) |has| |#1| (-881 (-568))) (((-381)) |has| |#1| (-881 (-381)))) -((((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) +((((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) (((|#1|) . T)) ((((-634 |#4|)) . T) (((-850)) . T)) ((((-541)) |has| |#4| (-609 (-541)))) @@ -1238,17 +1238,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1161)) |has| (-409 |#2|) (-895 (-1161)))) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-850)) -2198 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) (((-1244 |#3|)) . T)) +((((-850)) -2199 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) (((-1244 |#3|)) . T)) ((((-568) |#2|) . T)) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) -(((|#2| |#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($ $) |has| |#2| (-172))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(((|#2| |#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($ $) |has| |#2| (-172))) ((((-850)) . T)) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T) ((|#2|) . T)) ((((-850)) . T)) ((((-850)) . T)) ((((-1143) (-1161) (-568) (-215) (-850)) . T)) @@ -1284,7 +1284,7 @@ ((((-850)) . T)) ((((-541)) |has| |#1| (-609 (-541)))) ((((-850)) |has| |#1| (-1090))) -(((|#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($) |has| |#2| (-172))) +(((|#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1047))) (($) |has| |#2| (-172))) (|has| $ (-150)) ((((-409 |#2|)) . T)) ((((-409 (-568))) |has| (-409 |#2|) (-1037 (-409 (-568)))) (((-568)) |has| (-409 |#2|) (-1037 (-568))) (((-409 |#2|)) . T)) @@ -1295,18 +1295,18 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-150)) (|has| |#1| (-148)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-225)) ((((-1161) (-57)) . T)) ((((-850)) . T)) -(-2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) (((|#1| |#1|) . T)) ((((-1161)) |has| |#2| (-895 (-1161)))) ((((-568) (-121)) . T)) @@ -1331,7 +1331,7 @@ ((((-999 |#1|)) . T) ((|#1|) . T)) ((((-850)) . T)) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-409 (-568))) . T) (((-409 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1157 |#1|)) . T)) ((((-568)) . T) (($) . T) (((-409 (-568))) . T)) @@ -1339,7 +1339,7 @@ (|has| |#1| (-842)) (((|#2|) . T)) ((((-568)) . T) (($) . T) (((-409 (-568))) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) ((((-568) |#2|) . T)) ((((-850)) |has| |#1| (-1090))) (((|#2|) . T)) @@ -1356,7 +1356,7 @@ (|has| |#1| (-43 (-409 (-568)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) (((|#2| |#2|) . T)) (((|#2|) . T)) (|has| |#2| (-365)) @@ -1367,7 +1367,7 @@ (((|#2|) |has| |#2| (-172))) ((((-568) |#3|) . T)) ((((-568) (-147)) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((((-147)) . T)) ((((-850)) . T)) (|has| |#1| (-904)) @@ -1394,20 +1394,20 @@ (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#2|) . T)) ((((-568) (-147)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) -((($) -2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +((($) -2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (|has| |#1| (-842)) (((|#2| (-763) (-1075)) . T)) (((|#1| |#2|) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-558))) (|has| |#1| (-786)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2198 (|has| |#1| (-150)) (-12 (|has| |#1| (-365)) (|has| |#2| (-150)))) -(-2198 (|has| |#1| (-148)) (-12 (|has| |#1| (-365)) (|has| |#2| (-148)))) +(-2199 (|has| |#1| (-150)) (-12 (|has| |#1| (-365)) (|has| |#2| (-150)))) +(-2199 (|has| |#1| (-148)) (-12 (|has| |#1| (-365)) (|has| |#2| (-148)))) (((|#4|) . T)) (|has| |#1| (-148)) ((((-1143) |#1|) . T)) @@ -1420,7 +1420,7 @@ (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (((|#3|) . T)) ((((-1235 |#1| |#2| |#3|)) |has| |#1| (-365))) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) (((|#1|) . T)) ((((-850)) |has| |#1| (-1090))) ((((-850)) |has| |#1| (-1090)) (((-958 |#1|)) . T)) @@ -1434,11 +1434,11 @@ (((|#3| |#3|) -12 (|has| |#3| (-303 |#3|)) (|has| |#3| (-1090)))) (((|#2| (-888 |#1|)) . T)) ((($) . T)) -((($) -2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) ((|#2|) |has| |#2| (-172)) (((-409 (-568))) |has| |#2| (-43 (-409 (-568))))) +((($) -2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) ((|#2|) |has| |#2| (-172)) (((-409 (-568))) |has| |#2| (-43 (-409 (-568))))) ((((-390) (-1143)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) -((((-850)) -2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((-1244 |#2|)) . T)) -((((-57)) . T) (((-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))) . T)) +((((-850)) -2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((-1244 |#2|)) . T)) +((((-57)) . T) (((-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))) . T)) (((|#1|) . T)) ((((-850)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) @@ -1446,7 +1446,7 @@ (|has| |#2| (-148)) (|has| |#2| (-150)) (|has| |#1| (-478)) -(-2198 (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) +(-2199 (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) (|has| |#1| (-365)) ((((-850)) . T)) (|has| |#1| (-43 (-409 (-568)))) @@ -1457,8 +1457,8 @@ (|has| |#1| (-840)) ((((-850)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) -((((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2198 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1235 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2198 (|has| |#1| (-365)) (|has| |#1| (-558)))) +((((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1235 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) -2199 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1| |#2|) . T)) ((((-1161)) |has| |#1| (-895 (-1161)))) @@ -1466,7 +1466,7 @@ ((((-850)) . T)) ((((-850)) . T)) (|has| |#1| (-1090)) -(((|#2| (-493 (-1697 |#1|) (-763)) (-852 |#1|)) . T)) +(((|#2| (-493 (-1699 |#1|) (-763)) (-852 |#1|)) . T)) ((((-409 (-568))) |has| |#2| (-365)) (($) |has| |#2| (-365))) (((|#1| (-534 (-1161)) (-1161)) . T)) (((|#1|) . T)) @@ -1486,17 +1486,17 @@ (|has| |#1| (-150)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8| |#9|) . T)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) ((((-1159 |#1| |#2| |#3|)) |has| |#1| (-365))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-1161) (-57)) . T)) ((($ $) . T)) (((|#1| (-568)) . T)) ((((-905 |#1|)) . T)) -(((|#1|) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047))) (($) -2198 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)))) +(((|#1|) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047))) (($) -2199 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)))) (((|#1|) . T) (((-568)) |has| |#1| (-1037 (-568))) (((-409 (-568))) |has| |#1| (-1037 (-409 (-568))))) (|has| |#1| (-842)) (|has| |#1| (-842)) @@ -1511,14 +1511,14 @@ (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1090)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1090)))) -(((|#3|) -2198 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#3|) -2199 (|has| |#3| (-172)) (|has| |#3| (-365)))) (|has| |#2| (-842)) (|has| |#1| (-842)) -(-2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-904))) (((|#1|) . T)) ((($ $) . T) (((-409 (-568)) (-409 (-568))) . T)) ((((-568) |#2|) . T)) -(((|#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)))) (|has| |#1| (-350)) (((|#3| |#3|) -12 (|has| |#3| (-303 |#3|)) (|has| |#3| (-1090)))) ((($) . T) (((-409 (-568))) . T)) @@ -1526,7 +1526,7 @@ (|has| |#1| (-815)) (|has| |#1| (-815)) (((|#1|) . T)) -(-2198 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-840)) (|has| |#1| (-840)) (|has| |#1| (-840)) @@ -1535,14 +1535,14 @@ ((((-568)) . T) (($) . T) (((-409 (-568))) . T)) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-1161)) |has| |#1| (-895 (-1161))) (((-1075)) . T)) (((|#1|) . T)) (|has| |#1| (-840)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))) |has| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (-303 (-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))))) +((((-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))) |has| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (-303 (-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))))) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (|has| |#1| (-1090)) (((|#1|) . T)) @@ -1560,7 +1560,7 @@ (((|#1|) . T)) ((((-147)) . T)) (((|#2|) |has| |#2| (-172))) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((|#1|) . T)) (|has| |#1| (-148)) (|has| |#1| (-150)) @@ -1582,32 +1582,32 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) |has| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (-303 (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))))) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-904))) +(((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) |has| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (-303 (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-904))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -2198 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#3|) -2199 (|has| |#3| (-172)) (|has| |#3| (-365)))) (|has| |#1| (-842)) (|has| |#1| (-558)) ((((-581 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-2198 (-12 (|has| |#1| (-365)) (|has| |#2| (-815))) (-12 (|has| |#1| (-365)) (|has| |#2| (-842)))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (-12 (|has| |#1| (-365)) (|has| |#2| (-815))) (-12 (|has| |#1| (-365)) (|has| |#2| (-842)))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-905 |#1|)) . T)) (((|#1| (-505 |#1| |#3|) (-505 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-763)) . 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T)) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) ((((-409 |#2|)) . T) (((-409 (-568))) . T) (($) . T)) ((((-663 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1615,17 +1615,17 @@ ((((-850)) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) ((((-850)) . T)) -((((-409 (-568))) |has| |#2| (-43 (-409 (-568)))) ((|#2|) |has| |#2| (-172)) (($) -2198 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904)))) +((((-409 (-568))) |has| |#2| (-43 (-409 (-568)))) ((|#2|) |has| |#2| (-172)) (($) -2199 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904)))) ((((-850)) . T)) ((((-850)) . T)) ((((-850)) . T)) (((|#2|) . T)) -(-2198 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) ((((-409 (-568))) |has| |#1| (-1037 (-409 (-568)))) (((-568)) |has| |#1| (-1037 (-568))) ((|#1|) . T)) (|has| |#1| (-1181)) (|has| |#1| (-1181)) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (|has| |#1| (-1181)) (|has| |#1| (-1181)) (((|#3| |#3|) . T)) @@ -1638,37 +1638,37 @@ (((|#1|) . T) (((-409 (-568))) . T) (($) . T)) ((((-1143) (-57)) . T)) (|has| |#1| (-1090)) -(-2198 (|has| |#2| (-815)) (|has| |#2| (-842))) +(-2199 (|has| |#2| (-815)) (|has| |#2| (-842))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) (((-409 (-568))) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1|) . 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T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-904))) (|has| |#2| (-904)) (|has| |#1| (-365)) (((|#2|) |has| |#2| (-1090))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((($) . T) ((|#2|) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) ((((-541)) . T) (((-409 (-1157 (-568)))) . T) (((-215)) . T) (((-381)) . T)) ((((-381)) . T) (((-215)) . T) (((-850)) . T)) (|has| |#1| (-904)) (|has| |#1| (-904)) (|has| |#1| (-904)) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) (|has| (-169 (-215)) (-842)) ((($ $) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#1| (-365)) ((($ $) . T)) ((((-568) (-121)) . T)) @@ -1676,7 +1676,7 @@ (|has| |#2| (-558)) (((|#1|) . T)) ((((-121)) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-568)) . T)) (((|#1| (-568)) . T)) ((($) . T)) @@ -1698,7 +1698,7 @@ (((|#1| (-1235 |#1| |#2| |#3|)) . T)) (((|#1|) . T)) (((|#1| (-409 (-568))) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-850)) . T)) (((|#1| (-1207 |#1| |#2| |#3|)) . T)) (|has| |#1| (-1090)) @@ -1720,18 +1720,18 @@ (((|#1|) . T)) ((((-568)) . T)) ((((-850)) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-350))) (|has| |#1| (-150)) ((((-850)) . T)) (((|#3|) . T)) -(-2198 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047))) +(-2199 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047))) ((((-850)) . T)) ((((-1228 |#2| |#3| |#4|)) . T) (((-1229 |#1| |#2| |#3| |#4|)) . T)) ((((-850)) . T)) -((((-53)) -12 (|has| |#1| (-558)) (|has| |#1| (-1037 (-568)))) (((-607 $)) . T) ((|#1|) . T) (((-568)) |has| |#1| (-1037 (-568))) (((-409 (-568))) -2198 (-12 (|has| |#1| (-558)) (|has| |#1| (-1037 (-568)))) (|has| |#1| (-1037 (-409 (-568))))) (((-409 (-953 |#1|))) |has| |#1| (-558)) (((-953 |#1|)) |has| |#1| (-1047)) (((-1161)) . T)) +((((-53)) -12 (|has| |#1| (-558)) (|has| |#1| (-1037 (-568)))) (((-607 $)) . T) ((|#1|) . T) (((-568)) |has| |#1| (-1037 (-568))) (((-409 (-568))) -2199 (-12 (|has| |#1| (-558)) (|has| |#1| (-1037 (-568)))) (|has| |#1| (-1037 (-409 (-568))))) (((-409 (-953 |#1|))) |has| |#1| (-558)) (((-953 |#1|)) |has| |#1| (-1047)) (((-1161)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-763)) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-303 |#1|))) ((((-1229 |#1| |#2| |#3| |#4|)) . T)) ((((-568)) |has| |#1| (-881 (-568))) (((-381)) |has| |#1| (-881 (-381)))) @@ -1739,7 +1739,7 @@ (|has| |#1| (-558)) (((|#1|) . T)) ((((-850)) . T)) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) @@ -1747,7 +1747,7 @@ ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-763) |#1|))) (|has| |#1| (-895 (-1161))))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1090))) -(((|#2|) -2198 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2199 (|has| |#2| (-172)) (|has| |#2| (-365)))) ((((-1228 |#2| |#3| |#4|)) . T)) ((((-121)) . T)) (|has| |#1| (-815)) @@ -1757,8 +1757,8 @@ (|has| |#1| (-840)) (|has| |#1| (-840)) (((|#1| (-763) (-1075)) . T)) -(-2198 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(-2199 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-1161)) . T)) (((|#1| (-568) (-1075)) . T)) (((|#1| (-409 (-568)) (-1075)) . T)) @@ -1778,34 +1778,34 @@ (|has| |#1| (-1090)) ((((-568)) -12 (|has| |#1| (-365)) (|has| |#2| (-630 (-568)))) ((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#2| (-1047))) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) ((((-850)) . T)) (|has| |#3| (-840)) ((((-850)) . T)) ((((-1228 |#2| |#3| |#4|) (-314 |#2| |#3| |#4|)) . T)) ((((-850)) . T)) -(((|#1| |#1|) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047)))) +(((|#1| |#1|) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047)))) (((|#1|) . T)) ((((-568)) . T)) ((((-850)) . T)) ((((-568)) . T)) -((((-734 |#1| |#2|)) . T) (((-607 $)) . T) ((|#2|) . T) (((-568)) . T) (((-409 (-568))) -2198 (-12 (|has| |#2| (-558)) (|has| |#2| (-1037 (-568)))) (|has| |#2| (-1037 (-409 (-568))))) (((-409 (-953 |#2|))) |has| |#2| (-558)) (((-953 |#2|)) |has| |#2| (-1047)) (((-1161)) . T)) -(((|#1|) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047)))) +((((-734 |#1| |#2|)) . T) (((-607 $)) . T) ((|#2|) . T) (((-568)) . T) (((-409 (-568))) -2199 (-12 (|has| |#2| (-558)) (|has| |#2| (-1037 (-568)))) (|has| |#2| (-1037 (-409 (-568))))) (((-409 (-953 |#2|))) |has| |#2| (-558)) (((-953 |#2|)) |has| |#2| (-1047)) (((-1161)) . T)) +(((|#1|) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1047)))) (((|#2|) |has| |#2| (-365))) ((((-568)) |has| |#2| (-881 (-568))) (((-381)) |has| |#2| (-881 (-381)))) (((|#2|) . T)) (|has| |#1| (-842)) ((($) . T) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-365))) (((|#2|) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1| (-763)) . T)) (((|#2|) . T)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) |has| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (-303 (-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-904))) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) |has| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (-303 (-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-904))) (((|#2|) . T) (((-568)) |has| |#2| (-630 (-568)))) ((((-850)) . T)) ((((-850)) . T)) @@ -1839,7 +1839,7 @@ (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) (((|#1|) . T)) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) ((((-850)) . T)) (((|#1|) . T) (((-409 (-568))) . T) (($) . T)) @@ -1850,7 +1850,7 @@ (|has| (-409 |#2|) (-225)) (|has| |#1| (-904)) (((|#2|) |has| |#2| (-1047))) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) (|has| |#1| (-365)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1877,7 +1877,7 @@ (((|#1| (-409 (-568)) (-1075)) . T)) (((|#1| (-763) (-1075)) . T)) ((((-409 |#2|) (-409 |#2|)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) -(((|#1|) . T) (((-568)) -2198 (|has| (-409 (-568)) (-1037 (-568))) (|has| |#1| (-1037 (-568)))) (((-409 (-568))) . T)) +(((|#1|) . T) (((-568)) -2199 (|has| (-409 (-568)) (-1037 (-568))) (|has| |#1| (-1037 (-568)))) (((-409 (-568))) . T)) (((|#1| (-599 |#1| |#3|) (-599 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1886,7 +1886,7 @@ ((((-409 |#2|)) . T) (((-409 (-568))) . T) (($) . T)) (|has| |#2| (-225)) (((|#2| (-534 (-852 |#1|)) (-852 |#1|)) . T)) -((($) -2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) ((|#2|) |has| |#2| (-172)) (((-409 (-568))) |has| |#2| (-43 (-409 (-568))))) +((($) -2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) ((|#2|) |has| |#2| (-172)) (((-409 (-568))) |has| |#2| (-43 (-409 (-568))))) ((((-850)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-850)) . T)) @@ -1898,10 +1898,10 @@ ((((-688)) . T)) (((|#2|) |has| |#2| (-172))) (|has| |#2| (-840)) -((((-121)) |has| |#1| (-1090)) (((-850)) -2198 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090)))) +((((-121)) |has| |#1| (-1090)) (((-850)) -2199 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))) . T)) ((((-850)) . T)) ((((-850)) . T)) ((((-850)) . T)) @@ -1909,15 +1909,15 @@ ((((-688)) . T) (((-409 (-568))) . T) (((-568)) . T)) (((|#2|) . T)) (((|#1| |#1|) |has| |#1| (-172))) -(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) ((((-381)) . T)) ((((-688)) . T)) ((((-409 (-568))) |has| |#2| (-365)) (($) |has| |#2| (-365))) (((|#1|) |has| |#1| (-172))) ((((-409 (-953 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((($) . T)) (((|#2|) . T)) (|has| |#2| (-842)) @@ -1928,7 +1928,7 @@ (|has| |#1| (-842)) ((((-1161)) |has| |#2| (-895 (-1161)))) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-409 (-568))) . T) (($) . T)) (|has| |#1| (-478)) (|has| |#1| (-370)) @@ -1936,7 +1936,7 @@ (|has| |#1| (-370)) (|has| |#1| (-365)) ((((-850)) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-478)) (|has| |#1| (-558)) (|has| |#1| (-1047)) (|has| |#1| (-1102))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-478)) (|has| |#1| (-558)) (|has| |#1| (-1047)) (|has| |#1| (-1102))) ((((-125 |#1|)) . T)) ((((-125 |#1|)) . T)) ((((-147)) . T)) @@ -1961,14 +1961,14 @@ (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-842)) (|has| |#1| (-43 (-409 (-568)))) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) (((|#1| |#2|) . T)) (|has| |#1| (-150)) (|has| |#1| (-148)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)))) ((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)))) ((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) (((|#2|) . T)) (((|#1|) . T)) (((|#3|) . T)) @@ -1989,11 +1989,11 @@ ((((-541)) |has| |#1| (-609 (-541))) (((-887 (-568))) |has| |#1| (-609 (-887 (-568)))) (((-887 (-381))) |has| |#1| (-609 (-887 (-381)))) (((-381)) |has| |#1| (-1021)) (((-215)) |has| |#1| (-1021))) (((|#1|) |has| |#1| (-365))) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((($ $) . T) (((-607 $) $) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) ((($) . T) (((-1229 |#1| |#2| |#3| |#4|)) . T) (((-409 (-568))) . T)) -((($) -2198 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1047))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-558))) +((($) -2199 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1047))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-365)) (|has| |#1| (-365)) @@ -2004,7 +2004,7 @@ ((((-381)) . T)) (((|#3|) -12 (|has| |#3| (-303 |#3|)) (|has| |#3| (-1090)))) ((((-850)) . T)) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-904))) (((|#1|) . T)) (|has| |#1| (-842)) (|has| |#1| (-842)) @@ -2018,16 +2018,16 @@ (|has| |#1| (-148)) (|has| |#1| (-150)) ((((-568)) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-1228 |#2| |#3| |#4|)) . T) (((-409 (-568))) |has| (-1228 |#2| |#3| |#4|) (-43 (-409 (-568)))) (($) . T)) ((((-568)) . T)) (|has| |#2| (-478)) (|has| |#1| (-150)) (|has| |#1| (-148)) (|has| |#1| (-365)) -(-2198 (-12 (|has| (-1235 |#1| |#2| |#3|) (-150)) (|has| |#1| (-365))) (|has| |#1| (-150))) -(-2198 (-12 (|has| (-1235 |#1| |#2| |#3|) (-148)) (|has| |#1| (-365))) (|has| |#1| (-148))) +(-2199 (-12 (|has| (-1235 |#1| |#2| |#3|) (-150)) (|has| |#1| (-365))) (|has| |#1| (-150))) +(-2199 (-12 (|has| (-1235 |#1| |#2| |#3|) (-148)) (|has| |#1| (-365))) (|has| |#1| (-148))) (|has| |#1| (-365)) (|has| |#1| (-148)) (|has| |#1| (-225)) @@ -2047,19 +2047,19 @@ ((((-215)) . T)) (((|#1|) . T) (((-568)) |has| |#1| (-630 (-568)))) (((|#3|) |has| |#3| (-172))) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) ((((-568)) . T)) (((|#1| $) |has| |#1| (-281 |#1| |#1|))) ((((-409 (-568))) . T) (($) . T) (((-409 |#1|)) . T) ((|#1|) . T)) ((((-850)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2198 (|has| |#1| (-285)) (|has| |#1| (-365))) (((-409 (-568)) (-409 (-568))) |has| |#1| (-365))) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +(((|#1| |#1|) . T) (($ $) -2199 (|has| |#1| (-285)) (|has| |#1| (-365))) (((-409 (-568)) (-409 (-568))) |has| |#1| (-365))) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) ((($) . T)) ((($) . T) ((|#2|) |has| |#2| (-172)) (((-409 (-568))) |has| |#2| (-558))) ((((-568) |#1|) . T)) ((((-1161)) |has| (-409 |#2|) (-895 (-1161)))) -(((|#1|) . T) (($) -2198 (|has| |#1| (-285)) (|has| |#1| (-365))) (((-409 (-568))) |has| |#1| (-365))) +(((|#1|) . T) (($) -2199 (|has| |#1| (-285)) (|has| |#1| (-365))) (((-409 (-568))) |has| |#1| (-365))) ((((-541)) |has| |#2| (-609 (-541)))) ((((-679 |#2|)) . T) (((-850)) . T)) (((|#1|) . T)) @@ -2067,8 +2067,8 @@ (((|#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1090)))) ((((-864 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) -(-2198 (|has| |#4| (-788)) (|has| |#4| (-840))) -(-2198 (|has| |#3| (-788)) (|has| |#3| (-840))) +(-2199 (|has| |#4| (-788)) (|has| |#4| (-840))) +(-2199 (|has| |#3| (-788)) (|has| |#3| (-840))) ((((-850)) . T)) ((((-850)) . T)) (((|#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1090)))) @@ -2084,7 +2084,7 @@ ((((-409 (-568))) . T) (($) . T)) ((((-409 (-568))) . T) (($) . T)) ((((-409 (-568))) . T) (($) . T)) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-1199))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-1199))) ((($) . T)) ((((-409 (-568))) |has| (-409 |#2|) (-1037 (-409 (-568)))) (((-568)) |has| (-409 |#2|) (-1037 (-568))) (((-409 |#2|)) . T)) (((|#2|) . T) (((-568)) |has| |#2| (-630 (-568)))) @@ -2092,8 +2092,8 @@ (|has| |#1| (-842)) (((|#1|) . T) (((-568)) |has| |#1| (-630 (-568)))) ((((-568)) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) (((-409 (-568))) -2198 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1|) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))) |has| (-2 (|:| -3649 (-1143)) (|:| -4083 (-57))) (-303 (-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (((-409 (-568))) -2199 (|has| |#1| (-365)) (|has| |#1| (-350))) ((|#1|) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))) |has| (-2 (|:| -3651 (-1143)) (|:| -4085 (-57))) (-303 (-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))))) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (|has| |#1| (-840)) (|has| |#1| (-43 (-409 (-568)))) @@ -2123,11 +2123,11 @@ ((((-850)) |has| |#1| (-1090))) (|has| |#1| (-1181)) (((|#1|) . T)) -(-2198 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) +(-2199 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-370)) (|has| |#3| (-716)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047)) (|has| |#3| (-1090))) ((((-1161) |#1|) |has| |#1| (-523 (-1161) |#1|))) (((|#2|) . T)) -((($ $) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) -((($) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($ $) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-905 |#1|)) . T)) ((($) . T)) ((((-409 (-953 |#1|))) . T)) @@ -2135,10 +2135,10 @@ ((((-541)) |has| |#4| (-609 (-541)))) ((((-850)) . T) (((-634 |#4|)) . T)) (|has| |#1| (-840)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#1| (-1090)) (((|#1|) . T)) -(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) |has| (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|)) (-303 (-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))))) +(((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) |has| (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|)) (-303 (-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))))) (((|#2|) . T)) (|has| |#1| (-365)) (|has| |#1| (-842)) @@ -2146,11 +2146,11 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-409 (-568))) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-148)) (|has| |#1| (-150)) -(-2198 (-12 (|has| (-1159 |#1| |#2| |#3|) (-150)) (|has| |#1| (-365))) (|has| |#1| (-150))) -(-2198 (-12 (|has| (-1159 |#1| |#2| |#3|) (-148)) (|has| |#1| (-365))) (|has| |#1| (-148))) +(-2199 (-12 (|has| (-1159 |#1| |#2| |#3|) (-150)) (|has| |#1| (-365))) (|has| |#1| (-150))) +(-2199 (-12 (|has| (-1159 |#1| |#2| |#3|) (-148)) (|has| |#1| (-365))) (|has| |#1| (-148))) (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-150)) @@ -2180,9 +2180,9 @@ ((((-850)) . T)) ((((-850)) . T)) ((((-541)) |has| |#1| (-609 (-541)))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-1161) |#1|) |has| |#1| (-523 (-1161) |#1|)) ((|#1| |#1|) |has| |#1| (-303 |#1|))) -(((|#1|) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)))) ((((-310 |#1|)) . T)) (((|#2|) |has| |#2| (-365))) (((|#2|) . T)) @@ -2203,13 +2203,13 @@ (|has| |#1| (-148)) (|has| |#1| (-150)) ((($ $) . T)) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) (|has| |#1| (-558)) (((|#2|) . T)) ((((-568)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1047))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1047))) ((((-581 |#1|)) . T)) ((($) . T)) (((|#1| (-64 |#1|) (-64 |#1|)) . T)) @@ -2218,7 +2218,7 @@ ((($) . T)) (((|#1|) . T)) ((((-850)) . T)) -(((|#2|) |has| |#2| (-6 (-4521 "*")))) +(((|#2|) |has| |#2| (-6 (-4523 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2236,11 +2236,11 @@ ((((-1161) |#1|) . T)) (((|#4|) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) ((((-409 (-568))) |has| |#1| (-1037 (-409 (-568)))) (((-568)) |has| |#1| (-1037 (-568))) ((|#1|) . T)) ((((-1161) (-57)) . T)) ((((-850)) . T)) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-716)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047)) (|has| |#2| (-1090))) ((($) . T) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-1228 |#2| |#3| |#4|) (-314 |#2| |#3| |#4|)) . T)) ((((-1229 |#1| |#2| |#3| |#4|) (-1229 |#1| |#2| |#3| |#4|)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) @@ -2262,16 +2262,16 @@ ((((-1161)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) -(-2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-904))) (((|#2| |#3|) . T)) -(-2198 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#2| (-365)) (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) (((|#1| (-534 |#2|)) . T)) (((|#1| (-763)) . T)) (((|#1| (-534 (-1079 (-1161)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-904)) -(-2198 (|has| |#2| (-788)) (|has| |#2| (-840))) +(-2199 (|has| |#2| (-788)) (|has| |#2| (-840))) ((((-850)) . T)) ((($ $) . T) (((-1228 |#2| |#3| |#4|) (-1228 |#2| |#3| |#4|)) . T) (((-409 (-568)) (-409 (-568))) |has| (-1228 |#2| |#3| |#4|) (-43 (-409 (-568))))) ((((-905 |#1|)) . T)) @@ -2280,14 +2280,14 @@ ((($) . T)) ((($) . T)) (|has| |#1| (-365)) -(-2198 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350)) (|has| |#1| (-558))) (|has| |#1| (-365)) ((($) . T) (((-1228 |#2| |#3| |#4|)) . T) (((-409 (-568))) |has| (-1228 |#2| |#3| |#4|) (-43 (-409 (-568))))) (((|#1| |#2|) . T)) (|has| |#2| (-558)) ((((-1159 |#1| |#2| |#3|)) |has| |#1| (-365))) -(-2198 (-12 (|has| |#1| (-301)) (|has| |#1| (-904))) (|has| |#1| (-365)) (|has| |#1| (-350))) -(-2198 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) +(-2199 (-12 (|has| |#1| (-301)) (|has| |#1| (-904))) (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047))) ((((-568)) |has| |#1| (-630 (-568))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-850)) . T)) @@ -2295,12 +2295,12 @@ ((((-121)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((($ $) -2198 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($ $) -2199 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-409 |#2|)) . T) (((-409 (-568))) . T) (($) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| (-534 (-852 |#2|)) (-852 |#2|) (-775 |#1| (-852 |#2|))) . T)) (|has| |#2| (-365)) -((($) -2198 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (|has| |#1| (-842)) (((|#1|) . T)) (((|#1|) . T)) @@ -2323,21 +2323,21 @@ (((|#1|) |has| |#1| (-172))) ((((-850)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-303 |#4|)) (|has| |#4| (-1090)))) -(((|#2|) -2198 (|has| |#2| (-6 (-4521 "*"))) (|has| |#2| (-172)))) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(((|#2|) -2199 (|has| |#2| (-6 (-4523 "*"))) (|has| |#2| (-172)))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (|has| |#2| (-842)) (|has| |#2| (-904)) (|has| |#1| (-904)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-1235 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-850)) . T)) ((((-850)) . T)) ((((-541)) . T) (((-568)) . T) (((-887 (-568))) . T) (((-381)) . T) (((-215)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 (-57)))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 (-57)))) . T)) (((|#1|) . T)) ((((-860)) . T) (((-568)) . T) (((-409 (-568))) . T)) ((((-409 (-568))) . T) (((-568)) . T)) @@ -2346,7 +2346,7 @@ (((|#1| |#2|) . T)) (((|#1| (-409 (-568))) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-285)) (|has| |#1| (-365))) +(-2199 (|has| |#1| (-285)) (|has| |#1| (-365))) ((((-147)) . T)) ((((-409 |#2|)) . T) (((-409 (-568))) . T) (($) . T)) (|has| |#1| (-840)) @@ -2362,7 +2362,7 @@ ((((-409 (-568))) . T) (($) . T)) ((((-850)) . T)) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-850)) . T)) ((((-850)) . T)) @@ -2373,7 +2373,7 @@ (((|#1|) . T)) ((((-850)) . T)) ((((-634 (-147))) . T) (((-1143)) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) ((((-1161) |#1|) |has| |#1| (-523 (-1161) |#1|)) ((|#1| |#1|) |has| |#1| (-303 |#1|))) (|has| |#1| (-842)) ((((-850)) . T)) @@ -2385,16 +2385,16 @@ ((((-850)) . T) (((-634 |#4|)) . T)) (((|#2|) . T)) ((((-905 |#1|)) . T) (((-409 (-568))) . T) (($) . T)) -(-2198 (|has| |#4| (-172)) (|has| |#4| (-716)) (|has| |#4| (-840)) (|has| |#4| (-1047))) -(-2198 (|has| |#3| (-172)) (|has| |#3| (-716)) (|has| |#3| (-840)) (|has| |#3| (-1047))) +(-2199 (|has| |#4| (-172)) (|has| |#4| (-716)) (|has| |#4| (-840)) (|has| |#4| (-1047))) +(-2199 (|has| |#3| (-172)) (|has| |#3| (-716)) (|has| |#3| (-840)) (|has| |#3| (-1047))) ((((-1161) (-57)) . T)) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2198 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-25)) (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (|has| |#1| (-904)) (|has| |#1| (-904)) ((((-2 (|:| |k| (-568)) (|:| |c| |#1|))) . T)) @@ -2411,7 +2411,7 @@ (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (|has| |#1| (-815)) ((((-850)) |has| |#1| (-1090))) ((((-905 |#1|) (-905 |#1|)) . T) (($ $) . T) (((-409 (-568)) (-409 (-568))) . T)) @@ -2430,11 +2430,11 @@ (|has| |#1| (-150)) (|has| |#1| (-148)) (((|#2|) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) -((((-57)) . T) (((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) +((((-57)) . T) (((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) (|has| |#1| (-350)) ((((-568)) . T)) ((((-850)) . T)) @@ -2443,14 +2443,14 @@ ((((-1229 |#1| |#2| |#3| |#4|) $) |has| (-1229 |#1| |#2| |#3| |#4|) (-281 (-1229 |#1| |#2| |#3| |#4|) (-1229 |#1| |#2| |#3| |#4|)))) (|has| |#1| (-365)) ((((-1075) |#1|) . T) (((-1075) $) . T) (($ $) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) ((((-409 (-568)) (-409 (-568))) . T) (((-688) (-688)) . T) (($ $) . T)) ((((-310 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-409 (-568))) |has| |#1| (-365))) (|has| |#1| (-1090)) (((|#1|) . T)) -(((|#1|) -2198 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) -(((|#1|) -2198 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2199 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2199 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) (((|#2|) . T)) ((((-409 (-568))) . T) (((-688)) . T) (($) . T)) (|has| |#1| (-43 (-409 (-568)))) @@ -2471,7 +2471,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-568)) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (((|#2|) . T) (((-568)) |has| |#2| (-630 (-568)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2509,20 +2509,20 @@ (|has| |#2| (-1021)) ((($) . T)) (|has| |#1| (-904)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -((($ $) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +((($ $) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1| |#1|) . T) (((-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-568)) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1|) . T) (($) . T)) ((($) . T)) (|has| |#1| (-365)) ((((-905 |#1|)) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((($ $) . T) (((-409 (-568)) (-409 (-568))) . T)) -(-2198 (|has| |#1| (-370)) (|has| |#1| (-842))) +(-2199 (|has| |#1| (-370)) (|has| |#1| (-842))) (((|#1|) . T)) ((((-850)) . T)) ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-409 (-568)) |#1|))) (|has| |#1| (-895 (-1161))))) @@ -2530,15 +2530,15 @@ ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-568) |#1|))) (|has| |#1| (-895 (-1161))))) ((($) . T) (((-409 (-568))) . T)) ((((-763) |#1|) . T)) -(((|#2| (-232 (-1697 |#1|) (-763))) . T)) +(((|#2| (-232 (-1699 |#1|) (-763))) . T)) (((|#1| (-534 |#3|)) . T)) ((((-409 (-568))) . T)) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((((-850)) . T)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) |has| (-2 (|:| -3649 (-1161)) (|:| -4083 (-57))) (-303 (-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))))) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) |has| (-2 (|:| -3651 (-1161)) (|:| -4085 (-57))) (-303 (-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))))) (|has| |#1| (-904)) (|has| |#2| (-365)) -(-2198 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (((|#1|) . T)) ((((-169 (-381))) . T) (((-215)) . T) (((-381)) . T)) ((((-850)) . T)) @@ -2557,11 +2557,11 @@ (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-43 (-409 (-568)))) -(-2198 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-301)) (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-43 (-409 (-568)))) (-12 (|has| |#1| (-550)) (|has| |#1| (-823))) ((((-850)) . T)) -((((-1161)) -2198 (-12 (|has| |#1| (-15 * (|#1| (-568) |#1|))) (|has| |#1| (-895 (-1161)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-895 (-1161)))))) +((((-1161)) -2199 (-12 (|has| |#1| (-15 * (|#1| (-568) |#1|))) (|has| |#1| (-895 (-1161)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-895 (-1161)))))) (|has| |#1| (-365)) ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-409 (-568)) |#1|))) (|has| |#1| (-895 (-1161))))) (|has| |#1| (-365)) @@ -2573,7 +2573,7 @@ (((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#1| (-365))) ((((-850)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2599,9 +2599,9 @@ ((((-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-881 (-381)))) (((-568)) -12 (|has| |#1| (-365)) (|has| |#2| (-881 (-568))))) (|has| |#1| (-365)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-558)) (|has| |#1| (-558)) @@ -2609,22 +2609,22 @@ (((|#3|) . T)) (((|#1|) . T)) (|has| |#2| (-842)) -(-2198 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) (((|#2|) . T)) (((|#2|) . T)) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-716)) (|has| |#2| (-840)) (|has| |#2| (-1047))) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-716)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#1| (-43 (-409 (-568)))) (((|#1| |#2|) . T)) (|has| |#1| (-43 (-409 (-568)))) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) ((((-1143) |#1|) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-370))) (|has| |#1| (-150)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2634,7 +2634,7 @@ (|has| |#1| (-43 (-409 (-568)))) ((((-860)) . T) (((-409 (-568))) . T) (($) . T)) ((($) . T) (((-409 (-568))) . T)) -(-2198 (|has| |#1| (-148)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-148)) (|has| |#1| (-350))) (|has| |#1| (-150)) ((((-409 |#2|) (-409 |#2|)) . T) (((-409 (-568)) (-409 (-568))) . T) (($ $) . T)) ((((-409 (-568))) |has| |#2| (-1037 (-568))) (((-568)) |has| |#2| (-1037 (-568))) (((-1161)) |has| |#2| (-1037 (-1161))) ((|#2|) . T)) @@ -2661,7 +2661,7 @@ (|has| |#1| (-786)) ((((-850)) . T)) ((((-541)) |has| |#1| (-609 (-541)))) -((((-850)) -2198 (|has| |#1| (-842)) (|has| |#1| (-1090)))) +((((-850)) -2199 (|has| |#1| (-842)) (|has| |#1| (-1090)))) ((((-123)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2675,7 +2675,7 @@ ((((-850)) . T)) ((((-905 |#1|) (-905 |#1|)) . T) (($ $) . T) (((-409 (-568)) (-409 (-568))) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-558))) (((|#1|) . T)) ((((-905 |#1|)) . T) (($) . T) (((-409 (-568))) . T)) (|has| |#1| (-365)) @@ -2683,7 +2683,7 @@ ((((-568)) . T)) ((((-2 (|:| |k| (-568)) (|:| |c| |#1|))) . T)) ((((-568)) . T)) -(-2198 (|has| |#2| (-788)) (|has| |#2| (-840))) +(-2199 (|has| |#2| (-788)) (|has| |#2| (-840))) ((((-169 (-381))) . T) (((-215)) . T) (((-381)) . T)) ((((-850)) . T)) ((((-850)) . T)) @@ -2697,7 +2697,7 @@ (|has| |#1| (-365)) ((((-850)) |has| |#1| (-1090))) ((((-850)) |has| |#1| (-1090))) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-478)) (|has| |#1| (-716)) (|has| |#1| (-895 (-1161))) (|has| |#1| (-1047)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) (|has| |#1| (-1136)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-568) |#1|) . T)) @@ -2721,18 +2721,18 @@ (((|#2|) |has| |#2| (-172)) (($) . T) (((-409 (-568))) |has| |#2| (-558))) ((((-409 |#2|)) . T) (((-409 (-568))) . T) (($) . T)) (|has| |#1| (-558)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-381)) . 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T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (|has| |#2| (-904)) (|has| |#1| (-904)) -((($) -2198 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-172)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((((-568) (-568)) . T)) (((|#1|) . T)) -((((-2 (|:| -3649 (-1143)) (|:| -4083 |#1|))) . T)) +((((-2 (|:| -3651 (-1143)) (|:| -4085 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2809,16 +2809,16 @@ (((|#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090)))) ((((-409 (-568)) (-409 (-568))) . T)) ((((-409 (-568))) . 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T) (($) -2198 (|has| |#1| (-172)) (|has| |#1| (-558)))) +((((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) . T) (($) -2199 (|has| |#1| (-172)) (|has| |#1| (-558)))) (|has| |#1| (-558)) (((|#1|) |has| |#1| (-365))) ((((-568)) . T)) @@ -2849,16 +2849,16 @@ ((((-568) (-763)) . T) ((|#3| (-763)) . T)) ((((-1075) |#1|) . T) (((-1075) $) . T) (($ $) . T)) (((|#1|) . T)) -(((|#1| |#2| (-242 |#2| |#1|) (-232 (-1697 |#2|) (-763)) (-966 |#1|) (-774 |#1|) (-921 |#1|) (-236 (-921 |#1|)) |#3|) . T)) +(((|#1| |#2| (-242 |#2| |#1|) (-232 (-1699 |#2|) (-763)) (-966 |#1|) (-774 |#1|) (-921 |#1|) (-236 (-921 |#1|)) |#3|) . T)) (((|#2|) . T)) (((|#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) ((((-850)) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) -((((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +((((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) (((|#1|) . T) (((-568)) |has| |#1| (-1037 (-568))) (((-409 (-568))) |has| |#1| (-1037 (-409 (-568))))) -(((|#1|) . T) (((-409 (-568))) -2198 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) . T)) +(((|#1|) . T) (((-409 (-568))) -2199 (|has| |#1| (-43 (-409 (-568)))) (|has| |#1| (-365))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) ((((-568)) |has| |#1| (-881 (-568))) (((-381)) |has| |#1| (-881 (-381)))) (((|#1|) . T)) @@ -2883,15 +2883,15 @@ (((|#2| (-763)) . T)) ((((-1161)) . T)) ((((-864 |#1|)) . T)) -(-2198 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047))) -(-2198 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-840)) (|has| |#3| (-1047))) +(-2199 (|has| |#3| (-25)) (|has| |#3| (-137)) (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-788)) (|has| |#3| (-840)) (|has| |#3| (-1047))) +(-2199 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-840)) (|has| |#3| (-1047))) ((((-850)) . T)) (((|#1|) . T)) -(-2198 (|has| |#2| (-788)) (|has| |#2| (-840))) -(-2198 (-12 (|has| |#1| (-788)) (|has| |#2| (-788))) (-12 (|has| |#1| (-842)) (|has| |#2| (-842)))) +(-2199 (|has| |#2| (-788)) (|has| |#2| (-840))) +(-2199 (-12 (|has| |#1| (-788)) (|has| |#2| (-788))) (-12 (|has| |#1| (-842)) (|has| |#2| (-842)))) ((((-864 |#1|)) . T)) (((|#1|) . T)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) (|has| |#1| (-370)) (|has| |#1| (-370)) (|has| |#1| (-370)) @@ -2920,7 +2920,7 @@ (((|#1|) . T)) ((((-850)) . T)) (|has| |#2| (-904)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) ((((-541)) |has| |#2| (-609 (-541))) (((-887 (-381))) |has| |#2| (-609 (-887 (-381)))) (((-887 (-568))) |has| |#2| (-609 (-887 (-568))))) ((((-850)) . T)) ((((-850)) . T)) @@ -2942,7 +2942,7 @@ ((((-850)) . T)) (((|#1|) . T)) ((((-850)) . T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#1|) |has| |#1| (-172)) (($) . T)) ((((-568)) . T) (((-409 (-568))) . T)) (((|#1|) |has| |#1| (-303 |#1|))) @@ -2955,12 +2955,12 @@ ((((-409 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1090)) -(((|#2| (-493 (-1697 |#1|) (-763))) . T)) +(((|#2| (-493 (-1699 |#1|) (-763))) . T)) ((((-568) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-534 (-1161))) . T)) ((((-2 (|:| |k| (-568)) (|:| |c| |#1|))) . 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T)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((($) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) . T)) ((($) . T)) -((($) -2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (|has| |#2| (-904)) (|has| |#1| (-904)) (((|#1|) . T)) @@ -3248,11 +3248,11 @@ ((((-409 (-568))) . T) (($) . T)) (((|#1| (-568)) . T)) ((((-850)) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-365)) (|has| |#1| (-365)) -(-2198 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-172)) (|has| |#1| (-558))) (((|#1| (-763)) . T)) (((|#1| (-568)) . T)) (((|#1| (-409 (-568))) . T)) @@ -3270,16 +3270,16 @@ ((((-887 (-381))) . T) (((-887 (-568))) . T) (((-1161)) . T) (((-541)) . T)) (((|#1|) . T)) ((((-850)) . T)) -(-2198 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) -(-2198 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-137)) (|has| |#2| (-137))) (-12 (|has| |#1| (-788)) (|has| |#2| (-788)))) +(-2199 (|has| |#2| (-137)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-788)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-137)) (|has| |#2| (-137))) (-12 (|has| |#1| (-788)) (|has| |#2| (-788)))) ((((-568)) . T)) ((((-568)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2198 (|has| |#2| (-172)) (|has| |#2| (-716)) (|has| |#2| (-840)) (|has| |#2| (-1047))) +(-2199 (|has| |#2| (-172)) (|has| |#2| (-716)) (|has| |#2| (-840)) (|has| |#2| (-1047))) ((((-1161)) -12 (|has| |#2| (-895 (-1161))) (|has| |#2| (-1047)))) -(-2198 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-716)) (|has| |#2| (-716)))) +(-2199 (-12 (|has| |#1| (-478)) (|has| |#2| (-478))) (-12 (|has| |#1| (-716)) (|has| |#2| (-716)))) (|has| |#1| (-148)) (|has| |#1| (-150)) (|has| |#1| (-365)) @@ -3307,7 +3307,7 @@ (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((|#1|) |has| |#1| (-172)) (($) |has| |#1| (-558))) -(-2198 (|has| |#1| (-350)) (|has| |#1| (-370))) +(-2199 (|has| |#1| (-350)) (|has| |#1| (-370))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T)) @@ -3316,7 +3316,7 @@ ((($) . T) ((|#1|) . T) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) (((|#2|) |has| |#2| (-1090)) (((-568)) -12 (|has| |#2| (-1037 (-568))) (|has| |#2| (-1090))) (((-409 (-568))) -12 (|has| |#2| (-1037 (-409 (-568)))) (|has| |#2| (-1090)))) ((((-541)) |has| |#1| (-609 (-541)))) -((((-850)) -2198 (|has| |#1| (-842)) (|has| |#1| (-1090)))) +((((-850)) -2199 (|has| |#1| (-842)) (|has| |#1| (-1090)))) ((($) . T) (((-409 (-568))) . T)) (|has| |#1| (-904)) (|has| |#1| (-904)) @@ -3325,10 +3325,10 @@ ((((-850)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-172))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-840))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-840))) (((|#2|) . T)) -(-2198 (|has| |#1| (-21)) (|has| |#1| (-840))) +(-2199 (|has| |#1| (-21)) (|has| |#1| (-840))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) @@ -3343,17 +3343,17 @@ (((|#1|) . T) (((-409 (-568))) . T) (((-568)) . T) (($) . T)) ((((-568) (-568)) . T)) ((($) . T) (((-409 (-568))) . T)) -(-2198 (|has| |#4| (-172)) (|has| |#4| (-840)) (|has| |#4| (-1047)) SEQ) -(-2198 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047)) SEQ) +(-2199 (|has| |#4| (-172)) (|has| |#4| (-840)) (|has| |#4| (-1047)) SEQ) +(-2199 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047)) SEQ) (|has| |#4| (-788)) -(-2198 (|has| |#4| (-788)) (|has| |#4| (-840))) +(-2199 (|has| |#4| (-788)) (|has| |#4| (-840))) (|has| |#4| (-840)) (|has| |#3| (-788)) -(-2198 (|has| |#3| (-788)) (|has| |#3| (-840))) +(-2199 (|has| |#3| (-788)) (|has| |#3| (-840))) (|has| |#3| (-840)) ((((-568)) . T)) (((|#2|) . T)) -((((-1161)) -2198 (-12 (|has| (-1159 |#1| |#2| |#3|) (-895 (-1161))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-568) |#1|))) (|has| |#1| (-895 (-1161)))))) +((((-1161)) -2199 (-12 (|has| (-1159 |#1| |#2| |#3|) (-895 (-1161))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-568) |#1|))) (|has| |#1| (-895 (-1161)))))) ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-409 (-568)) |#1|))) (|has| |#1| (-895 (-1161))))) (((|#1|) |has| |#1| (-172)) (($) . T)) ((((-1161)) -12 (|has| |#1| (-15 * (|#1| (-763) |#1|))) (|has| |#1| (-895 (-1161))))) @@ -3372,11 +3372,11 @@ ((((-1159 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1159 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1125 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +(((|#2|) . T) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) ((($) . T)) (|has| |#1| (-1021)) -(((|#2|) . T) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) ((((-850)) . T)) ((((-541)) |has| |#2| (-609 (-541))) (((-887 (-568))) |has| |#2| (-609 (-887 (-568)))) (((-887 (-381))) |has| |#2| (-609 (-887 (-381)))) (((-381)) |has| |#2| (-1021)) (((-215)) |has| |#2| (-1021))) ((((-1161) (-57)) . T)) @@ -3398,8 +3398,8 @@ (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-365)) -(((|#3|) . T) ((|#2|) . T) (($) -2198 (|has| |#4| (-172)) (|has| |#4| (-840)) (|has| |#4| (-1047))) ((|#4|) -2198 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1047)))) -(((|#2|) . T) (($) -2198 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047))) ((|#3|) -2198 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1047)))) +(((|#3|) . T) ((|#2|) . T) (($) -2199 (|has| |#4| (-172)) (|has| |#4| (-840)) (|has| |#4| (-1047))) ((|#4|) -2199 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1047)))) +(((|#2|) . T) (($) -2199 (|has| |#3| (-172)) (|has| |#3| (-840)) (|has| |#3| (-1047))) ((|#3|) -2199 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1047)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) @@ -3422,21 +3422,21 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-281 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-904))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) ((((-850)) . T)) ((((-850)) . T)) ((((-850)) . T)) (((|#1| (-534 |#2|)) . T)) -((((-2 (|:| -3649 (-1161)) (|:| -4083 (-57)))) . T)) +((((-2 (|:| -3651 (-1161)) (|:| -4085 (-57)))) . T)) (((|#1| (-568)) . T)) (((|#1| (-409 (-568))) . T)) (((|#1| (-763)) . T)) (((|#1| (-763)) . T)) (((|#1|) . T)) ((((-125 |#1|)) . T) (($) . T) (((-409 (-568))) . T)) -(-2198 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) -(-2198 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) +(-2199 (|has| |#2| (-453)) (|has| |#2| (-558)) (|has| |#2| (-904))) +(-2199 (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((($) . T)) (((|#2| (-534 (-852 |#1|))) . T)) ((((-2 (|:| |k| (-568)) (|:| |c| |#1|))) . T)) @@ -3448,22 +3448,22 @@ (((|#1| |#2|) . T)) ((((-1143) |#1|) . T)) ((((-409 |#2|)) . T)) -((((-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) . T)) +((((-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) . T)) (|has| |#1| (-558)) (|has| |#1| (-558)) -((($) -2198 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) +((($) -2199 (|has| |#1| (-365)) (|has| |#1| (-453)) (|has| |#1| (-558)) (|has| |#1| (-904))) ((|#1|) |has| |#1| (-172)) (((-409 (-568))) |has| |#1| (-43 (-409 (-568))))) ((($) . T) ((|#2|) . T)) (((|#1|) . T)) (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-281 |#2| |#2|))) (((|#1| (-634 |#1|)) |has| |#1| (-840))) -(-2198 (|has| |#1| (-225)) (|has| |#1| (-350))) -(-2198 (|has| |#1| (-365)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-225)) (|has| |#1| (-350))) +(-2199 (|has| |#1| (-365)) (|has| |#1| (-350))) (|has| |#1| (-1090)) (((|#1|) . T)) (|has| |#1| (-1136)) ((((-409 (-568))) . T) (($) . T)) -((((-999 |#1|)) . T) ((|#1|) . T) (((-568)) -2198 (|has| (-999 |#1|) (-1037 (-568))) (|has| |#1| (-1037 (-568)))) (((-409 (-568))) -2198 (|has| (-999 |#1|) (-1037 (-409 (-568)))) (|has| |#1| (-1037 (-409 (-568)))))) +((((-999 |#1|)) . T) ((|#1|) . T) (((-568)) -2199 (|has| (-999 |#1|) (-1037 (-568))) (|has| |#1| (-1037 (-568)))) (((-409 (-568))) -2199 (|has| (-999 |#1|) (-1037 (-409 (-568)))) (|has| |#1| (-1037 (-409 (-568)))))) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#1|) -12 (|has| |#1| (-303 |#1|)) (|has| |#1| (-1090)))) @@ -3478,9 +3478,9 @@ ((((-215)) . T)) (((|#1| |#2| |#3| |#4|) . T)) ((((-1125 |#1| |#2|) (-1125 |#1| |#2|)) |has| (-1125 |#1| |#2|) (-303 (-1125 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))) |has| (-2 (|:| -3649 |#1|) (|:| -4083 |#2|)) (-303 (-2 (|:| -3649 |#1|) (|:| -4083 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))) |has| (-2 (|:| -3651 |#1|) (|:| -4085 |#2|)) (-303 (-2 (|:| -3651 |#1|) (|:| -4085 |#2|))))) ((((-125 |#1|)) |has| (-125 |#1|) (-303 (-125 |#1|)))) -(-2198 (|has| |#1| (-842)) (|has| |#1| (-1090))) +(-2199 (|has| |#1| (-842)) (|has| |#1| (-1090))) ((($ $) . T)) ((($ $) . T) (((-852 |#1|) $) . T) (((-852 |#1|) |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-225)) ((|#2| |#1|) |has| |#1| (-225)) ((|#3| |#1|) . T) ((|#3| $) . T)) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 8d7f0e0..c6e8fa3 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,3 +1,3 @@ -(30 . 3487447478) -(4522 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| |AlgebraicallyClosedField&| |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgebraicFunction| |AffineSpaceCategory| |Aggregate&| |Aggregate| |ArcHyperbolicFunctionCategory| 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|Database| |DoubleResultantPackage| |DistinctDegreeFactorize| |DecimalExpansion| |ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration| |DegreeReductionPackage| |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatSpecialFunctions| |DoubleFloatVector| |DenavitHartenbergMatrix| |Dictionary&| |Dictionary| |DifferentialExtension&| |DifferentialExtension| |DifferentialRing&| |DifferentialRing| |DictionaryOperations&| |DictionaryOperations| |DiophantineSolutionPackage| |DirectProductCategory&| |DirectProductCategory| |DirectProductFunctions2| |DirectProduct| |DirichletRing| |DisplayPackage| |DivisorCategory| |Divisor| |DivisionRing&| |DivisionRing| |DoublyLinkedAggregate| |DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| |DrawOptionFunctions1| |DrawOption| |DifferentialSparseMultivariatePolynomial| |DesingTreeCategory| |DesingTree| |DesingTreePackage| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| |EntireRing| |EigenPackage| |EquationFunctions2| |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| |Export3D| |ExponentialExpansion| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries| |Expression| |ExpressionSpaceODESolver| |ExpressionSolve| |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactoredFunctions| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRingFunctions2| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| |FortranCodePackage1| |FiniteDivisorFunctions2| |FiniteDivisorCategory&| |FiniteDivisorCategory| |FiniteDivisor| |FullyEvalableOver&| |FullyEvalableOver| |FortranExpression| |FunctionFieldCategoryFunctions2| |FunctionFieldCategory&| |FunctionFieldCategory| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FractionFreeFastGaussianFractions| |FractionFreeFastGaussian| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldNormalBasisExtension| |FiniteField| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteFieldExtension| |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregate&| |FiniteLinearAggregate| |FreeLieAlgebra| |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |FloatingComplexPackage| |Float| |FloatingRealPackage| |FreeModule1| |FreeModuleCat| |FortranMatrixCategory| |FortranMatrixFunctionCategory| |FreeModule| |FreeMonoid| |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat1| |ScriptFormulaFormat| |FortranProgramCategory| |FortranFunctionCategory| |FortranPackage| |FortranProgram| |FullPartialFractionExpansion| |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| |FactoredFunctions2| |FractionFunctions2| |Fraction| |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdealFunctions2| |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebra| |Factored| |FactoredFunctionUtilities| |FunctionSpaceToExponentialExpansion| |FunctionSpaceFunctions2| |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregateFunctions2| |FiniteSetAggregate&| |FiniteSetAggregate| |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| |FunctionSpace&| |FunctionSpace| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| |FunctionSpaceUnivariatePolynomialFactor| |FortranTemplate| |FortranType| |FunctionCalled| |FortranVectorCategory| |FortranVectorFunctionCategory| |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GcdDomain&| |GcdDomain| |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| |GnuDraw| |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| |GeneralModulePolynomial| |GuessOptionFunctions0| |GuessOption| |GosperSummationMethod| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| |GuessAlgebraicNumber| |GuessFiniteFunctions| |GuessFinite| |GuessInteger| |Guess| |GuessPolynomial| |GuessUnivariatePolynomial| |Pi| |HashTable| |HallBasis| |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousAggregate| |HTMLFormat| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| |InnerCommonDenominator| |InfClsPt| |PolynomialIdeals| |IdealDecompositionPackage| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |InnerNormalBasisFieldFunctions| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InfinitlyClosePoint| |Infinity| |InputFormFunctions1| |InputForm| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| |IntegerNumberSystem| |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| |IntersectionDivisorPackage| |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| |InterfaceGroebnerPackage| |IntegerFactorizationPackage| |InterpolateFormsPackage| |IntegrationFunctionsTable| |GenusZeroIntegration| |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| |Integer| |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| |TranscendentalIntegration| |InverseLaplaceTransform| |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| |IntegrationResultToFunction| |IntegrationResultFunctions2| |IntegrationResult| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| |InternalRationalUnivariateRepresentationPackage| |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| |CoercibleTo| |ConvertibleTo| |Kovacic| |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| |ListFunctions3| |List| |LinearSystemFromPowerSeriesPackage| |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| |LinearAggregate| |LocalPowerSeriesCategory| |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| |LinesOpPack| |LocalParametrizationOfSimplePointPackage| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| |ListAggregate| |LinearSystemMatrixPackage1| |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| |LieSquareMatrix| |LyndonWord| |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| |Magma| |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingPackage1| |MappingPackage2| |MappingPackage3| |MappingPackage4| |MatrixCategoryFunctions2| |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| |MathMLFormat| |ModularField| |ModMonic| |ModuleMonomial| |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |MultisetAggregate| |Multiset| |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| |MultivariateFactorize| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| |NumericComplexEigenPackage| |NumericContinuedFraction| |NonCommutativeOperatorDivision| |NewtonInterpolation| |NumberFieldIntegralBasis| |NumericalIntegrationProblem| |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| |NoneFunctions1| |None| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NottinghamGroup| |NPCoef| |NewtonPolygon| |NumericRealEigenPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OrderedCancellationAbelianMonoid| |OctonionCategory&| |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| |OrderedIntegralDomain| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| |OpenMathErrorKind| |OpenMathError| |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMath| |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| |OnePointCompletionFunctions2| |OnePointCompletion| |Operator| |OperationsQuery| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrdSetInts| |OutputForm| |OutputPackage| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteFieldCategory| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfPerfectFieldCategory| |PseudoAlgebraicClosureOfRationalNumberCategory| |PseudoAlgebraicClosureOfRationalNumber| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForAlgebraicFunctionField| |Palette| |PolynomialAN2Expression| |ParametrizationPackage| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResultFunctions2| |PatternMatchResult| |PatternFunctions1| |PatternFunctions2| |Pattern| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PackageForPoly| |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| |PlacesCategory| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |Plcs| |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| |PlotTools| |PolynomialPackageForCurve| |FunctionSpaceAssertions| |PatternMatchAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |FunctionSpaceAttachPredicates| |AttachPredicates| |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |ProjectiveAlgebraicSetPackage| |PolynomialRing| |Product| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PriorityQueueAggregate| |PseudoRemainderSequence| |ProjectiveSpaceCategory| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| |PushVariables| |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategoryFunctions2| |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| |QueueAggregate| |QuaternionCategory&| |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| |RandomNumberSource| |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| |RealSolvePackage| |RealClosure| |RecurrenceOperator| |ReductionOfOrder| |Reference| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RandomFloatDistributions| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunction| |RootsFindingPackage| |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| |RegularTriangularSetGcdPackage| |RuleCalled| |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| |SimpleAlgebraicExtensionAlgFactor| |SimpleAlgebraicExtension| |SAERationalFunctionAlgFactor| |SingletonAsOrderedSet| |SortedCache| |StructuralConstantsPackage| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |SegmentFunctions2| |SegmentBindingFunctions2| |SegmentBinding| |SegmentCategory| |Segment| |SegmentExpansionCategory| |SetAggregate&| |SetAggregate| |SetCategoryWithDegree| |SetCategory&| |SetCategory| |SetOfMIntegersInOneToN| |Set| |SExpressionCategory| |SExpression| |SExpressionOf| |SimpleFortranProgram| |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage| |SquareFreeRegularTriangularSetCategory| |SymmetricGroupCombinatoricFunctions| |SemiGroup&| |SemiGroup| |SplitHomogeneousDirectProduct| |SturmHabichtPackage| |ElementaryFunctionSign| |RationalFunctionSign| |SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |Stream| |StringCategory| |String| |StringTable| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctionsNonCommutative| |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| |SuchThat| |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePolynomialExpressions| |SupFractionFactorizer| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |SystemSolvePackage| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| |TriangularMatrixOperations| |TranscendentalManipulations| |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UnivariateFormalPowerSeriesFunctions| |UnivariateFormalPowerSeries| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| |UnivariateTaylorSeriesODESolver| |UTSodetools| |TaylorSolve| |UnivariateTaylorSeriesCZero| |Variable| |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| |TwoDimensionalViewport| |ThreeDimensionalViewport| |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record| |Union| |Category| |mapmult| |printInfo| |supDimElseRittWu?| |pointDominateBy| |semiResultantEuclidean2| |reduced?| |prinb| |positiveRemainder| |cExp| |setTower!| |mathieu22| |iter| |setFoundPlacesToEmpty| |rdHack1| |collectUpper| |legendre| |setFormula!| |leftDivide| |generalCoefficient| |wrregime| |nonSingularModel| |extendedSubResultantGcd| |poisson| |nullary?| |inverseIntegralMatrixAtInfinity| |degreeOfMinimalForm| |coefficients| |polygamma| |numericalIntegration| |variable| |nextPrimitivePoly| |rk4f| |hermite| |rightUnits| |stoseInvertibleSetreg| |leadingSupport| |OMUnknownSymbol?| |basisOfMiddleNucleus| |subMultV| |extract!| |Frobenius| |removeCosSq| |genericLeftNorm| |any?| |dimensionOfIrreducibleRepresentation| |axesColorDefault| |lazyIrreducibleFactors| |internalIntegrate0| |iiBeta| |delta| |setAdaptive3D| |LagrangeInterpolation| |euclideanGroebner| |redpps| |reducedDiscriminant| |reducedForm| |numerator| |OMputEndAttr| |bubbleSort!| |symmetric?| |modularGcd| |rewriteSetByReducingWithParticularGenerators| |range| |eval| |showAll?| |mainCharacterization| |changeMeasure| |plotPolar| |generateIrredPoly| |semiSubResultantGcdEuclidean2| |flexible?| |merge| |lfextlimint| |algDsolve| |moduleSum| |xRange| |fullDisplay| |zeroVector| |primextendedint| |solveLinearPolynomialEquationByRecursion| |OMencodingXML| |palglimint| |insertRoot!| |heap| |fortranLogical| |matrixDimensions| |normalized?| |qqq| |listYoungTableaus| |extractIndex| |associatedSystem| |polynomial| |explicitlyEmpty?| |besselJ| |rdregime| |rightMinimalPolynomial| |doubleResultant| |startTable!| |center| |placesOfDegree| |viewWriteAvailable| |initials| |chartV| |ord| |fortranInteger| |OMputInteger| |leftQuotient| |enqueue!| |times| |factorList| |replace| |every?| |pushuconst| |subscript| |coshIfCan| |cLog| |predicate| |rowEchWoZeroLinesWOVectorise| |unitVector| |doublyTransitive?| |zeroDim?| |rangeIsFinite| |setcurve!| |prefixRagits| |birth| |dcabs1| |variableName| |datalist| |iiasec| |cfirst| |writeLine!| |measure2Result| |maxint| |traverse| |fullParamInit| |rootOfIrreduciblePoly| |groebner?| |seed| |guessRat| |initiallyReduced?| |rightRank| |binaryTournament| |factorsOfCyclicGroupSize| |region| |makingStats?| |toseInvertible?| |linearAssociatedLog| |hMonic| |bombieriNorm| |overset?| |laplacian| |numberOfFractionalTerms| |unravel| |removeZeroes| |whileLoop| |sincos| |mainVariables| |isAbsolutelyIrreducible?| |oneDimensionalArray| |probablyZeroDim?| |argscript| 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|PseudoAlgebraicClosureOfFiniteFieldCategory| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfPerfectFieldCategory| |PseudoAlgebraicClosureOfRationalNumberCategory| |PseudoAlgebraicClosureOfRationalNumber| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForAlgebraicFunctionField| |Palette| |PolynomialAN2Expression| |ParametrizationPackage| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResultFunctions2| |PatternMatchResult| |PatternFunctions1| |PatternFunctions2| |Pattern| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PackageForPoly| |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| |PlacesCategory| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |Plcs| |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| |PlotTools| |PolynomialPackageForCurve| |FunctionSpaceAssertions| |PatternMatchAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |FunctionSpaceAttachPredicates| |AttachPredicates| |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |ProjectiveAlgebraicSetPackage| |PolynomialRing| |Product| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PriorityQueueAggregate| |PseudoRemainderSequence| |ProjectiveSpaceCategory| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| |PushVariables| |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategoryFunctions2| |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| |QueueAggregate| |QuaternionCategory&| |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| |RandomNumberSource| |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| |RealSolvePackage| |RealClosure| |RecurrenceOperator| |ReductionOfOrder| |Reference| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RandomFloatDistributions| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunction| |RootsFindingPackage| |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| 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|SimplifyAlgebraicNumberConvertPackage| |SingleInteger| |StackAggregate| |SquareMatrixCategory&| |SquareMatrixCategory| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| |SortPackage| |ThreeSpace| |ThreeSpaceCategory| |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |Stream| |StringCategory| |String| |StringTable| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctionsNonCommutative| |StreamTranscendentalFunctions| |SubResultantPackage| |SubSpace| |SuchThat| |SparseUnivariateLaurentSeries| |FunctionSpaceSum| |RationalFunctionSum| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePolynomialExpressions| |SupFractionFactorizer| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| |TheSymbolTable| |SymbolTable| |SystemSolvePackage| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| |TopLevelThreeSpace| |TranscendentalFunctionCategory&| |TranscendentalFunctionCategory| |Tree| |TrigonometricFunctionCategory&| |TrigonometricFunctionCategory| |TrigonometricManipulations| |TriangularMatrixOperations| |TranscendentalManipulations| |TriangularSetCategory&| |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |Type| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| |UniqueFactorizationDomain| |UnivariateFormalPowerSeriesFunctions| |UnivariateFormalPowerSeries| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeries| |UnivariateFactorize| |UniversalSegmentFunctions2| |UniversalSegment| |UnivariatePolynomialFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomial| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategory| |UnivariatePowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnaryRecursiveAggregate&| |UnaryRecursiveAggregate| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeries| |UnivariateTaylorSeriesODESolver| |UTSodetools| |TaylorSolve| |UnivariateTaylorSeriesCZero| |Variable| |VectorCategory&| |VectorCategory| |VectorFunctions2| |Vector| |TwoDimensionalViewport| |ThreeDimensionalViewport| |ViewDefaultsPackage| |ViewportPackage| |Void| |VectorSpace&| |VectorSpace| |WeierstrassPreparation| |WildFunctionFieldIntegralBasis| |WeightedPolynomials| |WuWenTsunTriangularSet| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |ExtensionField&| |ExtensionField| |XPBWPolynomial| |XPolynomialsCat| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| 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|hasHi| |supDimElseRittWu?| |rational?| |eval| |possiblyInfinite?| |mindeg| |linearDependenceOverZ| |minColIndex| |shellSort| |pointDominateBy| |resetAttributeButtons| |subHeight| |leviCivitaSymbol| |exists?| |showTheFTable| |euclideanNormalForm| |semiResultantEuclidean2| |submod| |leftFactorIfCan| |univariate?| |outputArgs| |nextsousResultant2| |Ei2| |reduced?| |multinomial| |foundZeroes| |stirling1| |difference| |content| |midpoint| |knownInfBasis| |OMgetEndAtp| |representationType| |chiSquare| |tube| |desingTreeWoFullParam| |patternMatchTimes| |degOneCoef| |center| |deriv| |startStats!| |removeDuplicates!| |tubeRadiusDefault| |safetyMargin| |halfExtendedResultant1| |ridHack1| |largest| |f2df| |drawComplex| |balancedFactorisation| |nextSubsetGray| |factorSFBRlcUnit| |shade| |setEpilogue!| |setScreenResolution| |derivationCoordinates| |initTable!| |modifyPoint| |SturmHabichtCoefficients| |has?| |ratDenom| |basisOfLeftAnnihilator| |createNormalElement| |basisOfInterpolateForms| 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|stronglyReduce| |prefix?| |hessian| |float| |d02bbf| |qqq| |bat1| |useSingleFactorBound| |zeroMatrix| |OMgetAttr| |pseudoDivide| |removeSuperfluousQuasiComponents| |basisOfRightNucloid| |e02ahf| |listYoungTableaus| |iisqrt2| |generalPosition| |trunc| |stop| |lowerCase?| |hypergeometric0F1| |localUnquote| |associatedSystem| |extractIndex| |more?| |cCot| |baseRDEsys| |translateToOrigin| |constDsolve| |less?| |reindex| |alphabetic?| |rootPoly| |transcendenceDegree| |toroidal| |combineFeatureCompatibility| |viewport3D| |lSpaceBasis| |divideExponents| |cup| |dioSolve| |polynomial| |weierstrass| |tubeRadius| |sqfrFactor| |bivariate?| |setSingularPoints| |basisOfInterpolateFormsForFact| |declare!| |d03faf| |explicitlyEmpty?| |someBasis| |clearTheIFTable| |decomposeFunc| |iilog| |critMTonD1| |complexNumeric| |binaryFunction| |d03eef| |besselJ| |optpair| |apply| |primes| |rightZero| |bandedHessian| |kernels| |extendedEuclidean| |d03edf| |rdregime| |OMreceive| |dAndcExp| |goto| |rightMinimalPolynomial| |univariate| |internal?| |operator| |coefChoose| |torsionIfCan| |phiCoord| |brace| |quasiAlgebraicSet| |externalList| |getOrder| |factor| |doubleResultant| |identification| |copy!| |An| |paren| |cons| |indicialEquations| |removeRedundantFactors| |real| |sncndn| |primlimintfrac| |startTable!| |squareFreePolynomial| |irreducibleFactors| |copy| |quoByVar| |bat| |imag| |placesOfDegree| |dmpToHdmp| |setLegalFortranSourceExtensions| |scanOneDimSubspaces| |child?| |setRow!| |sumOfKthPowerDivisors| |viewWriteAvailable| |first| |invertibleSet| |addPointLast| |pToDmp| |printInfo!| |initials| |compiledFunction| |fortranReal| |indexName| |palgextint| |expandTrigProducts| |chartV| |stoseInvertible?| |makeprod| |nsqfree| |setright!| |semiResultantEuclideannaif| |ord| |recolor| |realEigenvectors| |list| |makeResult| |represents| |changeNameToObjf| |fortranInteger| |addPoint2| |cycleTail| |repSq| |getBadValues| |yCoord| |OMputInteger| |eigenvalues| |pair?| |is?| |antiCommutator| |rowEchelon| |false| |leftQuotient| |guessHP| |hex| |extDegree| |zeroDimPrimary?| |flush| |enqueue!| |OMUnknownCD?| |expressIdealMember| |maxrank| |distribute| |binomThmExpt| |removeDuplicates| |times| |youngGroup| |att2Result| |listVariable| |cycle| |UnVectorise| |highCommonTerms| |c05nbf| |factorList| |rest| |idealSimplify| |rectangularMatrix| |stoseIntegralLastSubResultant| |explogs2trigs| |cyclotomicDecomposition| |c05adf| |replace| |updatF| |reverse| |decompose| |removeCoshSq| |indices| |polyPart| |c06gsf| |every?| |checkRur| |dec| |setDifference| |po| |iFTable| |divisor| |c06gqf| |pushuconst| |getVariableOrder| |OMputApp| |setIntersection| |select!| |associative?| |c06gcf| |subscript| |randomLC| |allPairsAmong| |fortranDoubleComplex| |getOp| |numberOfMonomials| |simplifyPower| |nil| |c06gbf| |coshIfCan| |createRandomElement| |setUnion| |lineColorDefault| |cotIfCan| |iidprod| |cLog| |c06fuf| |anticoord| |getCurve| |commutator| |size| |superscript| |separant| |substitute| |c06frf| |predicate| |hadamard| |rewriteIdealWithRemainder| |numericalOptimization| |cschIfCan| |getMultiplicationMatrix| |rowEchWoZeroLinesWOVectorise| |c06fqf| |approximate| |alphanumeric?| |mvar| |cyclicEntries| |hexDigit?| |imagI| |complex| |c06fpf| |unitVector| |atanhIfCan| |airyAi| |coerceL| |iicoth| |decimal| |say| |c06ekf| |doublyTransitive?| |asechIfCan| |showClipRegion| |horizConcat| |symmetricTensors| |objectOf| |debug| |zeroDim?| |c06ecf| |BasicMethod| |hash| |boundOfCauchy| |OMputEndError| |OMgetEndApp| |cTan| |c06ebf| |delete!| |firstDenom| |semiIndiceSubResultantEuclidean| |repeating?| |back| |c06eaf| |title| |LazardQuotient2| |minGbasis| |asecIfCan| |dn| |s17def| |setsubMatrix!| |heapSort| |bipolarCylindrical| |parametric?| |getButtonValue| |s17dcf| |explicitlyFinite?| |rightOne| |inGroundField?| |setnext!| |space| |s17akf| |tubePoints| |integralLastSubResultant| |generators| |numberOfIrreduciblePoly| |bfEntry| |s17ajf| |maxPower| |perfectNthRoot| |columnSpace| |makeSeries| |match?| |qShiftC| |s17ahf| |calcRanges| |subst| |iicsch| |stoseLastSubResultant| |f2st| |s17agf| |bag| |zoom| |dimensions| |branchPointAtInfinity?| |s17aff| |factorset| |dequeue!| |leaves| |setchart!| |changeVar| |equality| |entry| |s17aef| |sechIfCan| |optimize| |transpose| |acoshIfCan| |pointLists| |noLinearFactor?| |s17adf| |close| |OMputError| |charpol| |divisors| |point| |lowerPolynomial| |s17acf| |symbolTable| |testDim| |quatern| |super| |divOfZero| |pushFortranOutputStack| |s15aef| |ScanRoman| |evenlambert| |partialDenominators| |cot2tan| |oblateSpheroidal| |filename| |s15adf| |floor| |create| |pquo| |seriesToOutputForm| |cscIfCan| |popFortranOutputStack| |rowEch| |s14baf| |genusTreeNeg| |insert| |stoseInvertible?sqfreg| |queue| |display| |sylvesterMatrix| |s14abf| |outputAsFortran| |common| |closeComponent| |coerceListOfPairs| |leftTraceMatrix| |cond| |s14aaf| |rightExtendedGcd| |fortranCharacter| |integerBound| |sizePascalTriangle| |trivialIdeal?| |s13adf| |modifyPointData| |components| BY |halfExtendedSubResultantGcd2| |rationalPower| |OMputSymbol| |s13acf| |leftLcm| |ratpart| |lfinfieldint| |expr| |projectivePoint| |inRadical?| |depth| |s13aaf| |points| |flagFactor| |wreath| |shrinkable| |makeViewport3D| |elColumn2!| |last| |s01eaf| |localReal?| |nthFactor| |multiplyExponents| |generalInfiniteProduct| |count| |ellipticCylindrical| |s21bdf| |imagK| |inconsistent?| F2FG |s21bcf| |sturmVariationsOf| |partitions| |truncate| |fortranLiteralLine| |hdmpToDmp| |reshape| |s21bbf| |stFunc2| |conjugates| |move| |rename| |primitiveElement| |s21baf| |lexGroebner| |differentiate| |perspective| |sts2stst| |op| |OMputVariable| |iipolygamma| |rootRadius| |s20adf| |linearPolynomials| |limitPlus| |hyperelliptic| |leftPower| |upperCase?| |e02agf| |linearMatrix| |constantOpIfCan| |alternating| |selectFiniteRoutines| |elementary| |s20acf| |vector| |getZechTable| |graeffe| |iiperm| |makeSin| |d01aqf| |symmetricDifference| |FormatArabic| |normalizedAssociate| |integerDecode| |noncommutativeJordanAlgebra?| |s19adf| |completeSmith| |setTopPredicate| |controlPanel| |triangularSystems| |d01apf| |prologue| |failed?| |desingTreeAtPoint| |stronglyReduced?| |tValues| |singularitiesOf| |s19acf| |genericRightDiscriminant| |lllp| |setLabelValue| |badValues| |constantOperator| |d01anf| |basisOfNucleus| |rquo| |simpsono| |prepareSubResAlgo| |cartesian| |d01amf| |fullDesTree| |adaptive3D?| |iomode| |realRoots| |rischNormalize| |d01alf| |keys| |factorSquareFree| SEGMENT |label| |viewWriteDefault| |nilFactor| |s19abf| |partialNumerators| |iiBesselJ| |permutations| |newReduc| |d01akf| |lazyPseudoQuotient| |invertible?| |child| |selectPDERoutines| |s19aaf| |hasoln| |minimumExponent| |normalForm| |thetaCoord| |functionIsFracPolynomial?| |setClipValue| |monomialIntPoly| |d01ajf| |cTanh| |sturmSequence| |convert| |newton| |replaceDiffs| |s18def| |placesAbove| |flatten| |fibonacci| |imagJ| |localPointV| |construct| |plus| |s18dcf| |OMencodingUnknown| |real?| |identity| |fullOutput| |s18aff| |asimpson| |generalizedEigenvectors| |affinePoint| |OMlistSymbols| |monicLeftDivide| |s18aef| |magnitude| |updateStatus!| |viewport2D| |OMgetAtp| |modularFactor| |weight| |s18adf| |mapUnivariate| |wordsForStrongGenerators| |associatedEquations| |leadingBasisTerm| |ideal| |s18acf| |squareFreeFactors| |makeUnit| |drawCurves| |colorDef| |f04qaf| |extensionDegree| |diagonal?| |showTheIFTable| |fortranLiteral| |medialSet| |guessBinRat| |f04mcf| |resultantEuclidean| |goodnessOfFit| |remove| |complex?| |collect| |basisOfRightAnnihilator| |f04mbf| |qPot| |factorSqFree| |createGenericMatrix| |B1solve| |integralDerivationMatrix| |f04maf| |moebiusMu| |infRittWu?| |eyeDistance| |setMinPoints| |algintegrate| |f04jgf| |singular?| |doubleComplex?| |cosIfCan| |multMonom| |f04faf| |dmp2rfi| |bfKeys| |yCoordinates| |iiBesselY| |polygon| |index| |fglmIfCan| |f04axf| |radicalEigenvector| |OMputBVar| |isTimes| |composite| |f04atf| |pattern| |Ei| |insertMatch| |ShiftAction| |tab1| |iiacot| |f04asf| |subresultantVector| |cyclic| |mulmod| |innerSolve| |ShiftC| |useEisensteinCriterion?| |goodPoint| |read!| |OMputFloat| |f04arf| |roughUnitIdeal?| |powern| |multisect| |univariateSolve| |basisOfCenter| |cyclicParents| |infiniteProduct| |cycleRagits| |leftNorm| |recoverAfterFail| |collectQuasiMonic| |nlde| |factorSquareFreeByRecursion| |endSubProgram| |outputSpacing| |input| |applyRules| |Vectorise| |lepol| |iisech| |pow| |test| |quotValuation| |tanintegrate| |members| |digit?| |anfactor| |quotient| |OMencodingSGML| |setVariableOrder| |ldf2vmf| |exptMod| |getMatch| |atanIfCan| |htrigs| |norm| |log| |aLinear| |screenResolution| |numberOfComposites| |principalIdeal| |central?| |cycleEntry| |cyclicGroup| |unit?| |closedCurve| |guessHolo| |closed?| |normDeriv2| |errorKind| |padicallyExpand| |nthExponent| |recur| |constantToUnaryFunction| |init| |intPatternMatch| |findCoef| |match| |minimize| |accuracyIF| |computeCycleLength| |complexExpand| |monomial2series| |nand| |split| |beauzamyBound| |isobaric?| |brillhartIrreducible?| |orbit| |uncouplingMatrices| |reverse!| |affineAlgSet| |interpolateForms| |node| |quotientByP| |exprHasWeightCosWXorSinWX| |complexEigenvectors| |ffactor| |Hausdorff| |sbt| ** |lieAlgebra?| E1 |OMreadStr| |hdmpToP| |squareTop| |safety| |basisOfCentroid| |affineRationalPoints| |tracePowMod| |rowEchLocal| |rowEchWoZeroLines| |numFunEvals| |interval| |semiDegreeSubResultantEuclidean| |chebyshevT| |countRealRootsMultiple| |primintegrate| |rootSimp| |coerceS| |shiftRoots| |groebnerIdeal| |Aleph| |rootPower| |vertConcat| |integerIfCan| |computeBasis| |chvar| |sample| |changeName| |euler| |musserTrials| |createLowComplexityNormalBasis| |isPower| |merge!| |asinIfCan| |univcase| |lowerCase| |deepExpand| |OMsend| |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/index.kaf b/src/share/algebra/dependents.daase/index.kaf index fce8e8c..e935ec4 100755 --- a/src/share/algebra/dependents.daase/index.kaf +++ b/src/share/algebra/dependents.daase/index.kaf @@ -1,7 +1,8 @@ -67647 (|AbelianGroup&| |FourierSeries| |FreeAbelianGroup| |IndexedDirectProductAbelianGroup| |QuadraticForm|) -(|AbelianMonoid&| |CardinalNumber| |EuclideanModularRing| |GradedAlgebra| |GradedAlgebra&| |GradedModule| |GradedModule&| |IndexedDirectProductAbelianMonoid| |ListMonoidOps| |ModularField| |ModularRing|) -(|AbelianMonoidRing&|) +76844 (|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|) @@ -14,36 +15,43 @@ (|BagAggregate&|) (|BalancedPAdicRational|) (|ModuleOperator| |Operator|) -(|BasicType&| |IVField| |IVValue| |Timer|) +(|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| |InventorDataSink| |LieSquareMatrix| |MakeCachableSet| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |Pi| |QuasiAlgebraicSet| |QueryEquation| |RectangularMatrix| |SquareMatrix| |Switch| |SymbolTable| |TheSymbolTable| |Tuple| |Variable|) +(|AssociatedJordanAlgebra| |AssociatedLieAlgebra| |Float| |FortranScalarType| |InfiniteTuple| |LieSquareMatrix| |MakeCachableSet| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |Pi| |QuasiAlgebraicSet| |QueryEquation| |RectangularMatrix| |SquareMatrix| |Switch| |SymbolTable| |TheSymbolTable| |Tuple| |Variable|) (|Collection&|) -(|FunctionSpaceSum|) -(|Algebra| |Algebra&| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |CartesianTensor| |CartesianTensorFunctions2| |CharacteristicPolynomialInMonogenicalAlgebra| |CharacteristicPolynomialPackage| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory| |ComplexCategory&| |ComplexFunctions2| |ComplexPattern| |ComplexPatternMatch| |EuclideanModularRing| |FiniteRankAlgebra| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra| |FiniteRankNonAssociativeAlgebra&| |FourierSeries| |FramedAlgebra| |FramedAlgebra&| |FramedNonAssociativeAlgebra| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeLieAlgebra| |FreeNilpotentLie| |GeneralModulePolynomial| |GenericNonAssociativeAlgebra| |GradedAlgebra| |GradedAlgebra&| |GradedModule| |GradedModule&| |IntegerMod| |LieAlgebra| |LieAlgebra&| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LocalAlgebra| |Localize| |MatrixLinearAlgebraFunctions| |ModularField| |ModularRing| |Module| |Module&| |MonogenicAlgebra| |MonogenicAlgebra&| |NonAssociativeAlgebra| |NonAssociativeAlgebra&| |NumberTheoreticPolynomialFunctions| |Octonion| |OctonionCategory| |OctonionCategory&| |OctonionCategoryFunctions2| |OrthogonalPolynomialFunctions| |PackedHermitianSequence| |Quaternion| |QuaternionCategory| |QuaternionCategory&| |QuaternionCategoryFunctions2| |ResidueRing| |SimpleAlgebraicExtension| |XPBWPolynomial|) -(|AlgebraicNumber| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |InnerAlgebraicNumber| |InnerTrigonometricManipulations|) +(|FunctionSpaceSum| |Guess| |MyExpression| |RecurrenceOperator|) +(|Algebra| |Algebra&| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |CartesianTensor| |CartesianTensorFunctions2| |CharacteristicPolynomialInMonogenicalAlgebra| |CharacteristicPolynomialPackage| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory| |ComplexCategory&| |ComplexFunctions2| |ComplexPattern| |ComplexPatternMatch| |EuclideanModularRing| |FiniteRankAlgebra| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra| |FiniteRankNonAssociativeAlgebra&| |FourierSeries| |FramedAlgebra| |FramedAlgebra&| |FramedNonAssociativeAlgebra| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeLieAlgebra| |FreeNilpotentLie| |GeneralModulePolynomial| |GenericNonAssociativeAlgebra| |GradedAlgebra| |GradedAlgebra&| |GradedModule| |GradedModule&| |IntegerMod| |LieAlgebra| |LieAlgebra&| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LocalAlgebra| |Localize| |MatrixLinearAlgebraFunctions| |ModularField| |ModularRing| |Module| |Module&| |MonogenicAlgebra| |MonogenicAlgebra&| |NonAssociativeAlgebra| |NonAssociativeAlgebra&| |NumberTheoreticPolynomialFunctions| |Octonion| |OctonionCategory| |OctonionCategory&| |OctonionCategoryFunctions2| |OrthogonalPolynomialFunctions| |Quaternion| |QuaternionCategory| |QuaternionCategory&| |QuaternionCategoryFunctions2| |ResidueRing| |SimpleAlgebraicExtension| |XPBWPolynomial|) +(|AlgebraicNumber| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |InnerAlgebraicNumber| |InnerTrigonometricManipulations|) (|Complex| |ComplexCategory&| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPattern| |ComplexPatternMatch| |MachineComplex|) -(|AlgebraicNumber| |ApplyRules| |Boolean| |CharacterClass| |ComplexPattern| |DoubleFloat| |DrawNumericHack| |ExpressionSpaceODESolver| |Float| |FullPartialFractionExpansion| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerAlgebraicNumber| |InnerPrimeField| |InputForm| |Integer| |IntegerMod| |LaurentPolynomial| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |Numeric| |OrderedVariableList| |ParametricLinearEquations| |Partition| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchQuotientFieldCategory| |PatternMatchTools| |Pi| |PlotFunctions1| |PrimeField| |RewriteRule| |Ruleset| |Symbol| |TopLevelDrawFunctions|) +(|ComplexDoubleFloatMatrix|) +(|AlgebraicNumber| |ApplyRules| |Boolean| |CharacterClass| |ComplexPattern| |DoubleFloat| |DrawNumericHack| |ExpressionSolve| |ExpressionSpaceODESolver| |Float| |FullPartialFractionExpansion| |GuessFinite| |GuessFiniteFunctions| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerAlgebraicNumber| |InnerPrimeField| |InputForm| |Integer| |IntegerMod| |LaurentPolynomial| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |Numeric| |OrderedVariableList| |ParametricLinearEquations| |Partition| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchQuotientFieldCategory| |PatternMatchTools| |Pi| |PlotFunctions1| |PrimeField| |RecurrenceOperator| |RewriteRule| |Ruleset| |Symbol| |TopLevelDrawFunctions|) (|Dequeue|) +(|DesingTree| |DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |IntersectionDivisorPackage|) (|Dictionary&|) (|DictionaryOperations&|) (|DifferentialExtension&| |Factored| |LaurentPolynomial|) (|DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |OrderlyDifferentialPolynomial| |SequentialDifferentialPolynomial|) (|AlgebraicNumber| |DifferentialRing&| |DoubleFloat| |Float| |InnerAlgebraicNumber| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |OrdinaryDifferentialRing|) (|DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |OrderlyDifferentialVariable| |SequentialDifferentialVariable|) -(|DirectProductMatrixModule| |DistributedMultivariatePolynomial| |LieSquareMatrix| |RectangularMatrix| |SquareMatrix|) -(|DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |HomogeneousDirectProduct| |OrderedDirectProduct| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |SplitHomogeneousDirectProduct| |SquareMatrixCategory| |SquareMatrixCategory&|) +(|DirectProductMatrixModule| |DistributedMultivariatePolynomial| |InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |LieSquareMatrix| |RectangularMatrix| |SquareMatrix|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |BlowUpPackage| |DesingTreePackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |HomogeneousDirectProduct| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |NewtonPolygon| |OrderedDirectProduct| |PackageForPoly| |ParametrizationPackage| |PolynomialPackageForCurve| |ProjectiveAlgebraicSetPackage| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |SplitHomogeneousDirectProduct| |SquareMatrixCategory| |SquareMatrixCategory&|) +(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) (|DivisionRing&|) -(|ExpertSystemContinuityPackage1| |Float| |InputForm| |Pi| |SExpression|) +(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) +(|DesingTreePackage| |Divisor| |GeneralPackageForAlgebraicFunctionField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage|) +(|ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |DoubleFloatMatrix| |DoubleFloatVector| |ExpertSystemContinuityPackage1| |Float| |InputForm| |Pi| |SExpression|) +(|DoubleFloatMatrix|) (|ElementaryFunctionCategory&| |GaloisGroupFactorizationUtilities|) -(|Automorphism| |LinearOrdinaryDifferentialOperator2| |ModuleOperator| |Operator| |RewriteRule| |Ruleset|) +(|Automorphism| |DirichletRing| |LinearOrdinaryDifferentialOperator2| |ModuleOperator| |Operator| |RewriteRule| |Ruleset|) (|EltableAggregate&|) (|RewriteRule|) (|CRApackage| |ComplexFactorization| |ConstantLODE| |ContinuedFraction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |EuclideanDomain&| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule| |FunctionFieldIntegralBasis| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenExEuclid| |GenUFactorize| |GeneralHenselPackage| |GroebnerFactorizationPackage| |InnerModularGcd| |InnerMultFact| |IntegralBasisTools| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |LaplaceTransform| |LeadingCoefDetermination| |MPolyCatPolyFactorizer| |MRationalFactorize| |ModularHermitianRowReduction| |MultivariateFactorize| |MultivariateLifting| |MultivariateSquareFree| |NPCoef| |NonLinearFirstOrderODESolver| |ODEIntegration| |ParametricLinearEquations| |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionFactorizer| |RationalUnivariateRepresentationPackage| |SmithNormalForm| |TransSolvePackage| |ZeroDimensionalSolvePackage|) @@ -52,17 +60,17 @@ (|DeRhamComplex|) (|AlgebraicManipulations| |AlgebraicNumber| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |FortranExpression| |InnerAlgebraicNumber|) (|ExtensibleLinearAggregate&| |FlexibleArray| |IndexedFlexibleArray|) -(|ExtensionField&|) -(|AlgebraGivenByStructuralConstants| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicManipulations| |BoundIntegerRoots| |CliffordAlgebra| |ComplexRootFindingPackage| |ComplexRootPackage| |ContinuedFraction| |CoordinateSystems| |DenavitHartenbergMatrix| |DoubleResultantPackage| |EllipticFunctionsUnivariateTaylorSeries| |ExponentialOfUnivariatePuiseuxSeries| |ExtensionField| |ExtensionField&| |Field&| |FindOrderFinite| |FiniteAlgebraicExtensionField| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FloatingComplexPackage| |FloatingRealPackage| |FormalFraction| |FullPartialFractionExpansion| |FunctionSpaceToUnivariatePowerSeries| |GaloisGroupFactorizationUtilities| |GosperSummationMethod| |HyperellipticFiniteDivisor| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerAlgFactor| |InnerMatrixLinearAlgebraFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |IntegrationResult| |IntegrationResultFunctions2| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |MachineFloat| |ModularField| |MoebiusTransform| |MonomialExtensionTools| |NonCommutativeOperatorDivision| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODETools| |PadeApproximantPackage| |PadeApproximants| |PartialFraction| |Pi| |PolynomialCategoryQuotientFunctions| |PolynomialDecomposition| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| |PolynomialRoots| |PolynomialSolveByFormulas| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |PseudoLinearNormalForm| |PureAlgebraicLODE| |QuadraticForm| |RationalIntegration| |RationalLODE| |RationalRicDE| |RealClosure| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory| |RealRootCharacterizationCategory&| |ReduceLODE| |ReducedDivisor| |ReductionOfOrder| |ResidueRing| |RightOpenIntervalRootCharacterization| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StructuralConstantsPackage| |SystemODESolver| |TangentExpansions| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |VectorSpace| |VectorSpace&| |WeierstrassPreparation|) +(|ExtensionField&| |PseudoAlgebraicClosureOfFiniteField|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffineSpace| |AffineSpaceCategory| |AlgebraGivenByStructuralConstants| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicManipulations| |BlowUpPackage| |BoundIntegerRoots| |CliffordAlgebra| |ComplexRootFindingPackage| |ComplexRootPackage| |ContinuedFraction| |CoordinateSystems| |DenavitHartenbergMatrix| |DesingTreePackage| |DoubleResultantPackage| |EllipticFunctionsUnivariateTaylorSeries| |ExponentialOfUnivariatePuiseuxSeries| |ExtensionField| |ExtensionField&| |Field&| |FindOrderFinite| |FiniteAlgebraicExtensionField| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FloatingComplexPackage| |FloatingRealPackage| |FullPartialFractionExpansion| |FunctionSpaceToUnivariatePowerSeries| |GaloisGroupFactorizationUtilities| |GeneralPackageForAlgebraicFunctionField| |GosperSummationMethod| |Guess| |HyperellipticFiniteDivisor| |InfClsPt| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InnerAlgFactor| |InnerMatrixLinearAlgebraFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |IntegrationResult| |IntegrationResultFunctions2| |InterfaceGroebnerPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinesOpPack| |LocalParametrizationOfSimplePointPackage| |LocalPowerSeriesCategory| |MachineFloat| |ModularField| |MoebiusTransform| |MonomialExtensionTools| |NeitherSparseOrDensePowerSeries| |NonCommutativeOperatorDivision| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODETools| |PackageForAlgebraicFunctionField| |PadeApproximantPackage| |PadeApproximants| |ParametrizationPackage| |PartialFraction| |Pi| |Places| |PlacesCategory| |Plcs| |PolynomialCategoryQuotientFunctions| |PolynomialDecomposition| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| |PolynomialPackageForCurve| |PolynomialRoots| |PolynomialSolveByFormulas| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectiveSpace| |ProjectiveSpaceCategory| |PseudoLinearNormalForm| |PureAlgebraicLODE| |QuadraticForm| |RationalIntegration| |RationalInterpolation| |RationalLODE| |RationalRicDE| |RealClosure| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory| |RealRootCharacterizationCategory&| |ReduceLODE| |ReducedDivisor| |ReductionOfOrder| |ResidueRing| |RightOpenIntervalRootCharacterization| |RootsFindingPackage| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StructuralConstantsPackage| |SystemODESolver| |TangentExpansions| |TaylorSolve| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |VectorSpace| |VectorSpace&| |WeierstrassPreparation|) (|FieldOfPrimeCharacteristic&| |FiniteFieldPolynomialPackage2|) (|BinaryFile| |File| |FortranTemplate| |KeyedAccessFile| |TextFile|) (|BinaryFile| |File| |FortranTemplate| |KeyedAccessFile| |TextFile|) (|FileName|) (|Boolean| |DiscreteLogarithmPackage| |FindOrderFinite| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |IntegerMod| |ReducedDivisor| |SetOfMIntegersInOneToN|) -(|FiniteAbelianMonoidRing&| |PolynomialRing| |SymmetricPolynomial| |UnivariatePuiseuxSeriesWithExponentialSingularity|) +(|BlowUpPackage| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRingFunctions2| |FractionFreeFastGaussianFractions| |NewtonPolygon| |PackageForPoly| |PolynomialPackageForCurve| |PolynomialRing| |SymmetricPolynomial| |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |InnerFiniteField| |InnerPrimeField| |NormRetractPackage| |PrimeField|) (|FiniteDivisor| |FiniteDivisorCategory&| |HyperellipticFiniteDivisor|) -(|ChineseRemainderToolsForIntegralBases| |DistinctDegreeFactorize| |FiniteFieldCategory&| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |InnerNormalBasisFieldFunctions| |InnerPrimeField| |IrredPolyOverFiniteField| |MultFiniteFactorize| |NormRetractPackage| |PAdicWildFunctionFieldIntegralBasis| |PrimeField| |TwoFactorize| |WildFunctionFieldIntegralBasis|) +(|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |ChineseRemainderToolsForIntegralBases| |DistinctDegreeFactorize| |FiniteFieldCategory&| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |GuessFinite| |GuessFiniteFunctions| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerNormalBasisFieldFunctions| |InnerPrimeField| |IrredPolyOverFiniteField| |MultFiniteFactorize| |NormRetractPackage| |NottinghamGroup| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionFieldOverFiniteField| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PrimeField| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfFiniteField| |TwoFactorize| |WildFunctionFieldIntegralBasis|) (|BezoutMatrix| |CommonDenominator| |FiniteLinearAggregate&| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregateSort| |InnerCommonDenominator| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |LinearSystemMatrixPackage| |MatrixCategory| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |MultiVariableCalculusFunctions| |SmithNormalForm| |TriangularMatrixOperations| |TwoDimensionalArrayCategory| |TwoDimensionalArrayCategory&|) (|FiniteRankAlgebra&|) (|FiniteRankNonAssociativeAlgebra&|) @@ -77,7 +85,7 @@ (|FortranProgram|) (|Asp8|) (|Asp10| |Asp19| |Asp31| |Asp35| |Asp41| |Asp42| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp78|) -(|AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |BoundIntegerRoots| |ChangeOfVariable| |ContinuedFraction| |DoubleResultantPackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EvaluateCycleIndicators| |FindOrderFinite| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FormalFraction| |FourierSeries| |FullPartialFractionExpansion| |FunctionFieldCategory| |FunctionFieldCategory&| |FunctionFieldCategoryFunctions2| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |HyperellipticFiniteDivisor| |InnerAlgebraicNumber| |IntegrationResult| |Kovacic| |LaurentPolynomial| |LieExponentials| |LinearOrdinaryDifferentialOperatorFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineFloat| |MultipleMap| |Pi| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicLODE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealZeroPackageQ| |ReducedDivisor| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesODESolver| |XExponentialPackage|) +(|AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |BoundIntegerRoots| |ChangeOfVariable| |ContinuedFraction| |DoubleResultantPackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EvaluateCycleIndicators| |FindOrderFinite| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FourierSeries| |FractionFreeFastGaussianFractions| |FullPartialFractionExpansion| |FunctionFieldCategory| |FunctionFieldCategory&| |FunctionFieldCategoryFunctions2| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |HyperellipticFiniteDivisor| |InnerAlgebraicNumber| |IntegrationResult| |Kovacic| |LaurentPolynomial| |LieExponentials| |LinearOrdinaryDifferentialOperatorFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineFloat| |MultipleMap| |Pi| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicLODE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealZeroPackageQ| |ReducedDivisor| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesODESolver| |XExponentialPackage|) (|FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra&| |FramedModule| |FunctionFieldIntegralBasis| |IntegralBasisTools| |NumberFieldIntegralBasis| |WildFunctionFieldIntegralBasis|) (|AlgebraGivenByStructuralConstants| |AlgebraPackage| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |GenericNonAssociativeAlgebra| |LieSquareMatrix|) (|FreeAbelianGroup| |FreeAbelianMonoid| |InnerFreeAbelianMonoid|) @@ -87,44 +95,44 @@ (|FullyLinearlyExplicitRingOver&|) (|Factored| |FullyRetractableTo&| |LaurentPolynomial| |Octonion| |OnePointCompletion| |OrderedCompletion| |RealClosure|) (|AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |DoubleResultantPackage| |FindOrderFinite| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FunctionFieldCategory&| |FunctionFieldCategoryFunctions2| |HyperellipticFiniteDivisor| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PureAlgebraicLODE| |RadicalFunctionField| |ReducedDivisor|) -(|AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |ApplyRules| |CombinatorialFunction| |ComplexTrigonometricManipulations| |ElementaryFunction| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |Expression| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |InnerTrigonometricManipulations| |IntegrationTools| |LiouvillianFunction| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |RewriteRule| |Ruleset| |SimpleFortranProgram| |TopLevelDrawFunctionsForAlgebraicCurves| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|BalancedFactorisation| |DefiniteIntegrationTools| |EigenPackage| |ElementaryFunctionSign| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FGLMIfCanPackage| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GcdDomain&| |GenusZeroIntegration| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |InnerNumericFloatSolvePackage| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |LazardSetSolvingPackage| |LexTriangularPackage| |LinGroebnerPackage| |NormInMonogenicAlgebra| |NormalizationPackage| |NormalizedTriangularSetCategory| |PatternMatchIntegration| |PolyGroebner| |PolynomialSquareFree| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |QuasiAlgebraicSet| |QuasiComponentPackage| |RationalFunctionLimitPackage| |RationalFunctionSign| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) +(|AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |ApplyRules| |CombinatorialFunction| |ComplexTrigonometricManipulations| |ElementaryFunction| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |Expression| |ExpressionSolve| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |Guess| |InnerTrigonometricManipulations| |IntegrationTools| |LiouvillianFunction| |MyExpression| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |RecurrenceOperator| |RewriteRule| |Ruleset| |SimpleFortranProgram| |TopLevelDrawFunctionsForAlgebraicCurves| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) +(|BalancedFactorisation| |DefiniteIntegrationTools| |EigenPackage| |ElementaryFunctionSign| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FGLMIfCanPackage| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GcdDomain&| |GenusZeroIntegration| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Guess| |InnerNumericFloatSolvePackage| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |LazardSetSolvingPackage| |LexTriangularPackage| |LinGroebnerPackage| |NormInMonogenicAlgebra| |NormalizationPackage| |NormalizedTriangularSetCategory| |PatternMatchIntegration| |PolyGroebner| |PolynomialSquareFree| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |QuasiAlgebraicSet| |QuasiComponentPackage| |RationalFunctionLimitPackage| |RationalFunctionSign| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|CartesianTensor| |GradedAlgebra&|) (|CartesianTensor| |GradedModule&|) -(|Automorphism| |FractionalIdeal| |FreeGroup| |Group&| |LieExponentials| |MoebiusTransform|) +(|Automorphism| |FractionalIdeal| |FreeGroup| |Group&| |LieExponentials| |MoebiusTransform| |NottinghamGroup|) (|HomogeneousAggregate&| |ThreeDimensionalMatrix|) (|HomogeneousDistributedMultivariatePolynomial|) (|HyperbolicFunctionCategory&|) -(|IVBaseColor| |IVCoordinate3| |IVCoordinate4| |IVFaceSet| |IVIndexedLineSet| |IVPointSet| |IVQuadMesh|) -(|IVBasicNode| |IVGroup| |IVNodeObject| |IVSeparator|) (|IndexedAggregate&| |SortPackage|) (|FreeModule| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents|) (|DifferentialSparseMultivariatePolynomial| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |OrderlyDifferentialPolynomial| |Polynomial| |RegularChain| |SequentialDifferentialPolynomial| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries|) (|IndexedTwoDimensionalArray|) (|IndexedMatrix|) +(|DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |IntersectionDivisorPackage|) (|InnerEvalable&|) (|InnerFiniteField|) -(|Boolean| |DoubleFloat| |ExpressionSpaceODESolver| |Float| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |OrderedVariableList| |Pi| |PlotFunctions1| |Symbol| |TopLevelDrawFunctions|) -(|AlgebraicIntegrate| |AlgebraicNumber| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |BrillhartTests| |CartesianTensor| |CartesianTensorFunctions2| |ComplexRootPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |DecimalExpansion| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EvaluateCycleIndicators| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FourierSeries| |FreeAbelianGroup| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |HeuGcd| |HexadecimalExpansion| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerAlgebraicNumber| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InputForm| |IntegerLinearDependence| |IntegerMod| |IntegerRetractions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LieExponentials| |LinearOrdinaryDifferentialOperatorFactorizer| |MachineFloat| |ModularDistinctDegreeFactorizer| |NonLinearFirstOrderODESolver| |NumberFieldIntegralBasis| |ODEIntegration| |OrderedVariableList| |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Partition| |PatternMatchIntegration| |Pi| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RadixExpansion| |RationalFactorize| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionIntegration| |RationalFunctionSum| |RationalIntegration| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealZeroPackage| |RealZeroPackageQ| |SAERationalFunctionAlgFactor| |SExpression| |SimpleAlgebraicExtensionAlgFactor| |SortPackage| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |Symbol| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |TrigonometricManipulations| |UnivariateFactorize| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateTaylorSeriesODESolver| |XExponentialPackage|) +(|Boolean| |DoubleFloat| |ExpressionSolve| |ExpressionSpaceODESolver| |Float| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |OrderedVariableList| |Pi| |PlotFunctions1| |RecurrenceOperator| |Symbol| |TopLevelDrawFunctions|) +(|AlgebraicIntegrate| |AlgebraicNumber| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |BrillhartTests| |CartesianTensor| |CartesianTensorFunctions2| |ComplexRootPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |DecimalExpansion| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EvaluateCycleIndicators| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FourierSeries| |FreeAbelianGroup| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |Guess| |GuessFinite| |GuessFiniteFunctions| |HeuGcd| |HexadecimalExpansion| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerAlgebraicNumber| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InputForm| |IntegerLinearDependence| |IntegerMod| |IntegerRetractions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LieExponentials| |LinearOrdinaryDifferentialOperatorFactorizer| |MachineFloat| |ModularDistinctDegreeFactorizer| |MyExpression| |NeitherSparseOrDensePowerSeries| |NonLinearFirstOrderODESolver| |NumberFieldIntegralBasis| |ODEIntegration| |OrderedVariableList| |PAdicInteger| |PAdicIntegerCategory| |PAdicRational| |PAdicRationalConstructor| |Partition| |PatternMatchIntegration| |Pi| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RadixExpansion| |RationalFactorize| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionIntegration| |RationalFunctionSum| |RationalIntegration| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealZeroPackage| |RealZeroPackageQ| |RecurrenceOperator| |SAERationalFunctionAlgFactor| |SExpression| |SimpleAlgebraicExtensionAlgFactor| |SortPackage| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |Symbol| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |TrigonometricManipulations| |UnivariateFactorize| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateTaylorSeriesODESolver| |XExponentialPackage|) (|ComplexIntegerSolveLinearPolynomialEquation| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerNumberSystem&| |IntegerPrimesPackage| |IntegerRoots| |MachineInteger| |PatternMatchIntegerNumberSystem| |RomanNumeral| |SingleInteger|) -(|AlgebraPackage| |AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicallyClosedFunctionSpace| |AlgebraicallyClosedFunctionSpace&| |AssociatedEquations| |CombinatorialFunction| |CommonDenominator| |ComplexTrigonometricManipulations| |DegreeReductionPackage| |DrawNumericHack| |ElementaryFunction| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ExpressionSpaceODESolver| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |FormalFraction| |Fraction| |FractionFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GenerateUnivariatePowerSeries| |GosperSummationMethod| |InfiniteProductCharacteristicZero| |InnerCommonDenominator| |InnerMatrixQuotientFieldFunctions| |InnerPolySum| |InnerTrigonometricManipulations| |IntegralDomain&| |LaurentPolynomial| |LinearDependence| |LinearSystemPolynomialPackage| |LiouvillianFunction| |MPolyCatRationalFunctionFactorizer| |MatrixCommonDenominator| |MultipleMap| |NonLinearSolvePackage| |PatternMatchFunctionSpace| |PatternMatchQuotientFieldCategory| |PiCoercions| |PointsOfFiniteOrder| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PrecomputedAssociatedEquations| |PseudoRemainderSequence| |QuotientFieldCategory| |QuotientFieldCategory&| |QuotientFieldCategoryFunctions2| |RationalFunction| |RationalFunctionIntegration| |RationalFunctionSum| |RetractSolvePackage| |StreamInfiniteProduct| |SubResultantPackage| |SystemSolvePackage| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackageService| |TriangularMatrixOperations| |TriangularSetCategory| |TriangularSetCategory&| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesWithExponentialSingularity| |WuWenTsunTriangularSet|) +(|AlgebraPackage| |AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicallyClosedFunctionSpace| |AlgebraicallyClosedFunctionSpace&| |AssociatedEquations| |CombinatorialFunction| |CommonDenominator| |ComplexTrigonometricManipulations| |DegreeReductionPackage| |DrawNumericHack| |ElementaryFunction| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ExpressionSolve| |ExpressionSpaceODESolver| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GenerateUnivariatePowerSeries| |GosperSummationMethod| |Guess| |InfiniteProductCharacteristicZero| |InnerCommonDenominator| |InnerMatrixQuotientFieldFunctions| |InnerPolySum| |InnerTrigonometricManipulations| |IntegralDomain&| |LaurentPolynomial| |LinearDependence| |LinearSystemPolynomialPackage| |LiouvillianFunction| |MPolyCatRationalFunctionFactorizer| |MatrixCommonDenominator| |MultipleMap| |MyExpression| |NewtonInterpolation| |NonLinearSolvePackage| |PatternMatchFunctionSpace| |PatternMatchQuotientFieldCategory| |PiCoercions| |PointsOfFiniteOrder| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PrecomputedAssociatedEquations| |PseudoRemainderSequence| |QuotientFieldCategory| |QuotientFieldCategory&| |QuotientFieldCategoryFunctions2| |RationalFunction| |RationalFunctionIntegration| |RationalFunctionSum| |RecurrenceOperator| |RetractSolvePackage| |StreamInfiniteProduct| |SubResultantPackage| |SystemSolvePackage| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackageService| |TriangularMatrixOperations| |TriangularSetCategory| |TriangularSetCategory&| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesWithExponentialSingularity| |WuWenTsunTriangularSet|) (|Interval|) (|PatternMatchFunctionSpace| |PatternMatchKernel|) (|KeyedDictionary&|) -(|CyclicStreamTools| |LazyStreamAggregate&| |Stream|) +(|CyclicStreamTools| |LazyStreamAggregate&| |NeitherSparseOrDensePowerSeries| |Stream|) (|AntiSymm| |DeRhamComplex| |LeftAlgebra&|) (|AlgebraGivenByStructuralConstants| |ApplyUnivariateSkewPolynomial| |DirectProductMatrixModule| |DirectProductModule| |GenericNonAssociativeAlgebra| |LinearOrdinaryDifferentialOperator2| |ModuleOperator|) (|LieAlgebra&|) -(|LinearAggregate&| |PackedHermitianSequence|) +(|LinearAggregate&|) (|AssociatedEquations| |ConstantLODE| |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorsOps| |ODETools| |PrecomputedAssociatedEquations| |PrimitiveRatDE| |PrimitiveRatRicDE| |ReduceLODE| |ReductionOfOrder| |SystemODESolver| |UTSodetools|) (|AlgebraicNumber| |ConstantLODE| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |InnerAlgebraicNumber| |IntegerLinearDependence| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |InverseLaplaceTransform| |LaplaceTransform| |LinearDependence| |NonLinearFirstOrderODESolver| |ODEIntegration| |PatternMatchIntegration| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |RationalFunctionDefiniteIntegration| |TransSolvePackage| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|AlgebraGivenByStructuralConstants| |AntiSymm| |CharacterClass| |DeRhamComplex| |DistributedMultivariatePolynomial| |FGLMIfCanPackage| |FiniteFieldNormalBasisExtensionByPolynomial| |FortranExpression| |FortranProgram| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GenericNonAssociativeAlgebra| |GroebnerSolve| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |LexTriangularPackage| |LinGroebnerPackage| |MultivariatePolynomial| |OrderedVariableList| |OrdinaryWeightedPolynomials| |Partition| |PolToPol| |QuasiAlgebraicSet2| |RationalUnivariateRepresentationPackage| |RegularChain| |ResidueRing| |WeightedPolynomials| |ZeroDimensionalSolvePackage|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraGivenByStructuralConstants| |AntiSymm| |BlowUpPackage| |CharacterClass| |DeRhamComplex| |DesingTreePackage| |DistributedMultivariatePolynomial| |FGLMIfCanPackage| |FiniteFieldNormalBasisExtensionByPolynomial| |FortranExpression| |FortranProgram| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GenericNonAssociativeAlgebra| |GroebnerSolve| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InterfaceGroebnerPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LexTriangularPackage| |LinGroebnerPackage| |LocalParametrizationOfSimplePointPackage| |MultivariatePolynomial| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |ParametrizationPackage| |Partition| |PolToPol| |ProjectiveAlgebraicSetPackage| |QuasiAlgebraicSet2| |RationalUnivariateRepresentationPackage| |RegularChain| |ResidueRing| |WeightedPolynomials| |ZeroDimensionalSolvePackage|) (|DataList| |IndexedList| |List| |ListAggregate&| |PatternMatchListAggregate| |PatternMatchListResult|) +(|DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LinearSystemFromPowerSeriesPackage| |LocalParametrizationOfSimplePointPackage| |NeitherSparseOrDensePowerSeries| |ParametrizationPackage| |PlacesCategory| |Plcs|) (|Boolean| |Logic&| |SingleInteger|) (|LiePolynomial| |PoincareBirkhoffWittLyndonBasis|) (|MachineComplex|) (|AlgebraGivenByStructuralConstants| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |RectangularMatrix| |SquareMatrix|) -(|BezoutMatrix| |DenavitHartenbergMatrix| |IndexedMatrix| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |LinearSystemMatrixPackage| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |SmithNormalForm| |TriangularMatrixOperations|) +(|BezoutMatrix| |ComplexDoubleFloatMatrix| |DenavitHartenbergMatrix| |DoubleFloatMatrix| |IndexedMatrix| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |LinearSystemMatrixPackage| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |SmithNormalForm| |TriangularMatrixOperations|) (|FreeAbelianGroup| |GeneralModulePolynomial| |IntegrationResult| |LieExponentials| |Localize| |Module&| |XExponentialPackage|) (|Monad&|) (|MonadWithUnit&|) @@ -134,54 +142,67 @@ (|ListMultiDictionary|) (|Multiset|) (|SparseMultivariateTaylorSeries| |TaylorSeries|) +(|MyExpression|) +(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField|) (|RegularChain|) (|AssociatedJordanAlgebra| |AssociatedLieAlgebra| |FreeNilpotentLie| |NonAssociativeAlgebra&|) (|NonAssociativeRing&|) (|NonAssociativeRng&|) -(|CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| |DirectProduct| |DirectProductCategory| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductModule| |DistributedMultivariatePolynomial| |FreeAbelianMonoid| |FreeNilpotentLie| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |IndexedExponents| |InnerModularGcd| |OrderedDirectProduct| |OrderingFunctions| |OrdinaryWeightedPolynomials| |QuasiAlgebraicSet2| |RadicalFunctionField| |RectangularMatrix| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory| |SquareMatrixCategory&| |WeightedPolynomials|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffineSpace| |BlowUpPackage| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| |DesingTreePackage| |DirectProduct| |DirectProductCategory| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductModule| |DistributedMultivariatePolynomial| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FreeAbelianMonoid| |FreeNilpotentLie| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |IndexedExponents| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerModularGcd| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |NewtonPolygon| |OrderedDirectProduct| |OrderingFunctions| |OrdinaryWeightedPolynomials| |PackageForPoly| |ParametrizationPackage| |PolynomialPackageForCurve| |ProjectiveAlgebraicSetPackage| |ProjectiveSpace| |QuasiAlgebraicSet2| |RadicalFunctionField| |RectangularMatrix| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory| |SquareMatrixCategory&| |WeightedPolynomials|) (|d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType|) (|e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|Octonion| |OctonionCategory&| |OctonionCategoryFunctions2|) (|TwoDimensionalArray|) (|FlexibleArray| |IndexedFlexibleArray| |IndexedOneDimensionalArray| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |PrimitiveArray|) (|DoubleFloat| |ExpressionToOpenMath| |Float| |Integer| |SingleInteger| |Symbol|) -(|AbelianMonoidRing| |AbelianMonoidRing&| |ExponentialOfUnivariatePuiseuxSeries| |FiniteAbelianMonoidRing| |FiniteAbelianMonoidRing&| |IndexedDirectProductOrderedAbelianMonoid| |OrderingFunctions| |PolynomialRing| |PowerSeriesCategory| |PowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePowerSeriesCategory&|) -(|AlgebraicMultFact| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |EuclideanGroebnerBasisPackage| |FactoringUtilities| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |HomogeneousDirectProduct| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |InnerMultFact| |InnerPolySum| |InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LinearSystemPolynomialPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariateSquareFree| |NPCoef| |NonNegativeInteger| |NormalizationPackage| |NormalizedTriangularSetCategory| |OrderedDirectProduct| |ParametricLinearEquations| |PatternMatchPolynomialCategory| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSquareFree| |PushVariables| |QuasiAlgebraicSet| |QuasiComponentPackage| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |ResidueRing| |SplitHomogeneousDirectProduct| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |TriangularSetCategory| |TriangularSetCategory&| |WeightedPolynomials| |WuWenTsunTriangularSet|) +(|AbelianMonoidRing| |AbelianMonoidRing&| |ExponentialOfUnivariatePuiseuxSeries| |FiniteAbelianMonoidRing| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRingFunctions2| |IndexedDirectProductOrderedAbelianMonoid| |OrderingFunctions| |PolynomialRing| |PowerSeriesCategory| |PowerSeriesCategory&| |UnivariatePowerSeriesCategory| |UnivariatePowerSeriesCategory&|) +(|AlgebraicMultFact| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |EuclideanGroebnerBasisPackage| |FactoringUtilities| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |HomogeneousDirectProduct| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |InnerMultFact| |InnerPolySum| |InterfaceGroebnerPackage| |InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LinearSystemPolynomialPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariateSquareFree| |NPCoef| |NonNegativeInteger| |NormalizationPackage| |NormalizedTriangularSetCategory| |OrderedDirectProduct| |ParametricLinearEquations| |PatternMatchPolynomialCategory| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSquareFree| |PushVariables| |QuasiAlgebraicSet| |QuasiComponentPackage| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |ResidueRing| |SplitHomogeneousDirectProduct| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |TriangularSetCategory| |TriangularSetCategory&| |WeightedPolynomials| |WuWenTsunTriangularSet|) (|Partition|) (|Character| |OrderedVariableList|) (|XDistributedPolynomial|) (|SturmHabichtPackage|) (|OrderedFreeMonoid| |XPolynomialRing|) (|ComplexRootFindingPackage| |ComplexRootPackage| |ExpertSystemToolsPackage1| |FloatingComplexPackage| |FloatingRealPackage| |FunctionSpaceToUnivariatePowerSeries| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrderedRing&| |RealClosure| |RealRootCharacterizationCategory| |RealRootCharacterizationCategory&| |RightOpenIntervalRootCharacterization| |SegmentExpansionCategory| |ZeroDimensionalSolvePackage|) -(|AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicMultFact| |AlgebraicallyClosedFunctionSpace| |AlgebraicallyClosedFunctionSpace&| |ApplyRules| |BasicOperator| |BinarySearchTree| |BinaryTournament| |Boolean| |CardinalNumber| |CombinatorialFunction| |ComplexTrigonometricManipulations| |ConstantLODE| |DataList| |Database| |DeRhamComplex| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory| |DifferentialVariableCategory&| |DrawNumericHack| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EuclideanGroebnerBasisPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExtAlgBasis| |FactoringUtilities| |FourierComponent| |FourierSeries| |FreeLieAlgebra| |FreeModule| |FreeModule1| |FunctionSpace| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceFunctions2| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GeneralModulePolynomial| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |Heap| |IndexCard| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |InnerMultFact| |InnerPolySum| |InnerTrigonometricManipulations| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |Kernel| |KernelFunctions2| |LaplaceTransform| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LieExponentials| |LiePolynomial| |LinearSystemPolynomialPackage| |LiouvillianFunction| |LyndonWord| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |Magma| |MergeThing| |ModuleMonomial| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariateSquareFree| |MultivariateTaylorSeriesCategory| |NPCoef| |NewSparseMultivariatePolynomial| |NonLinearFirstOrderODESolver| |NormalizationPackage| |NormalizedTriangularSetCategory| |ODEIntegration| |OrdSetInts| |OrderedFreeMonoid| |OrderedMultisetAggregate| |OrderedSet&| |OrderlyDifferentialVariable| |ParametricLinearEquations| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchTools| |PiCoercions| |PoincareBirkhoffWittLyndonBasis| |PointsOfFiniteOrder| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSquareFree| |PositiveInteger| |PowerSeriesCategory| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PriorityQueueAggregate| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet| |QuasiComponentPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |ResidueRing| |RewriteRule| |Ruleset| |SequentialDifferentialVariable| |SimpleFortranProgram| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |Symbol| |TableauxBumpers| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TriangularSetCategory| |TriangularSetCategory&| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity| |WeightedPolynomials| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |XPBWPolynomial| |XPolynomialsCat| |XRecursivePolynomial|) -(|DistributedMultivariatePolynomial| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |HomogeneousDistributedMultivariatePolynomial| |MultivariatePolynomial| |RegularChain|) +(|AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicMultFact| |AlgebraicallyClosedFunctionSpace| |AlgebraicallyClosedFunctionSpace&| |ApplyRules| |BasicOperator| |BinarySearchTree| |BinaryTournament| |Boolean| |CardinalNumber| |CombinatorialFunction| |ComplexTrigonometricManipulations| |ConstantLODE| |DataList| |Database| |DeRhamComplex| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory| |DifferentialVariableCategory&| |DrawNumericHack| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EuclideanGroebnerBasisPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionFunctions2| |ExpressionSolve| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExtAlgBasis| |FactoringUtilities| |FourierComponent| |FourierSeries| |FreeLieAlgebra| |FreeModule| |FreeModule1| |FunctionSpace| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceFunctions2| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GeneralModulePolynomial| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralTriangularSet| |GeneralizedMultivariateFactorize| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |Guess| |Heap| |IndexCard| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |InnerMultFact| |InnerPolySum| |InnerTrigonometricManipulations| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InterfaceGroebnerPackage| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |Kernel| |KernelFunctions2| |LaplaceTransform| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LieExponentials| |LiePolynomial| |LinearSystemPolynomialPackage| |LiouvillianFunction| |LyndonWord| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |Magma| |MergeThing| |ModuleMonomial| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariateSquareFree| |MultivariateTaylorSeriesCategory| |MyExpression| |NPCoef| |NewSparseMultivariatePolynomial| |NonLinearFirstOrderODESolver| |NormalizationPackage| |NormalizedTriangularSetCategory| |ODEIntegration| |OrdSetInts| |OrderedFreeMonoid| |OrderedMultisetAggregate| |OrderedSet&| |OrderlyDifferentialVariable| |ParametricLinearEquations| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchTools| |PiCoercions| |PoincareBirkhoffWittLyndonBasis| |PointsOfFiniteOrder| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSquareFree| |PositiveInteger| |PowerSeriesCategory| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PriorityQueueAggregate| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet| |QuasiComponentPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |RecurrenceOperator| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |ResidueRing| |RewriteRule| |Ruleset| |SequentialDifferentialVariable| |SimpleFortranProgram| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |SupFractionFactorizer| |Symbol| |TableauxBumpers| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TriangularSetCategory| |TriangularSetCategory&| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity| |WeightedPolynomials| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |XPBWPolynomial| |XPolynomialsCat| |XRecursivePolynomial|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |DesingTreePackage| |DistributedMultivariatePolynomial| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |HomogeneousDistributedMultivariatePolynomial| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |MultivariatePolynomial| |ParametrizationPackage| |ProjectiveAlgebraicSetPackage| |RegularChain|) (|OrderlyDifferentialPolynomial|) (|d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType|) -(|FortranScalarType| |InfiniteTuple| |InputForm| |InventorDataSink| |QuasiAlgebraicSet| |QueryEquation| |SExpression| |Switch| |SymbolTable| |TheSymbolTable|) +(|FortranScalarType| |InfiniteTuple| |InputForm| |QuasiAlgebraicSet| |QueryEquation| |SExpression| |Switch| |SymbolTable| |TheSymbolTable|) (|PAdicRational|) (|BalancedPAdicInteger| |InnerPAdicInteger| |PAdicInteger| |PAdicRationalConstructor|) (|d03eefAnnaType| |d03fafAnnaType|) -(|FortranExpression| |MultiVariableCalculusFunctions| |OrdinaryDifferentialRing| |PartialDifferentialRing&|) +(|FortranExpression| |Guess| |MultiVariableCalculusFunctions| |MyExpression| |OrdinaryDifferentialRing| |PartialDifferentialRing&| |RecurrenceOperator|) (|ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |FunctionSpaceToUnivariatePowerSeries|) (|SymmetricPolynomial|) (|ApplyRules| |ComplexPattern| |OrderedVariableList| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchQuotientFieldCategory| |PatternMatchTools| |RewriteRule| |Ruleset| |Symbol|) (|ApplyRules| |ComplexPatternMatch| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |RewriteRule| |Ruleset| |Symbol|) (|Kernel|) (|Permutation|) +(|InfClsPt|) +(|DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |ParametrizationPackage| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |Plcs|) +(|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) (|PlaneAlgebraicCurvePlot| |Plot|) (|NumericTubePlot| |Plot3D| |TubePlot|) (|XPBWPolynomial|) (|Point|) (|GenericNonAssociativeAlgebra| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |PushVariables| |RationalFunctionFactor| |SAERationalFunctionAlgFactor|) -(|AlgebraicMultFact| |DistributedMultivariatePolynomial| |EuclideanGroebnerBasisPackage| |FactoringUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPolynomialGcdPackage| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |HomogeneousDistributedMultivariatePolynomial| |InnerMultFact| |InnerPolySum| |LeadingCoefDetermination| |LinearSystemPolynomialPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NPCoef| |ParametricLinearEquations| |PatternMatchPolynomialCategory| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSquareFree| |PushVariables| |QuasiAlgebraicSet| |ResidueRing| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SupFractionFactorizer| |WeightedPolynomials|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraicMultFact| |DesingTreePackage| |DistributedMultivariatePolynomial| |EuclideanGroebnerBasisPackage| |FactoringUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |HomogeneousDistributedMultivariatePolynomial| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InnerMultFact| |InnerPolySum| |InterfaceGroebnerPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LeadingCoefDetermination| |LinearSystemPolynomialPackage| |LocalParametrizationOfSimplePointPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NPCoef| |ParametricLinearEquations| |ParametrizationPackage| |PatternMatchPolynomialCategory| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialRoots| |PolynomialSquareFree| |ProjectiveAlgebraicSetPackage| |PushVariables| |QuasiAlgebraicSet| |ResidueRing| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SupFractionFactorizer| |WeightedPolynomials|) (|GeneralPolynomialGcdPackage| |LinearPolynomialEquationByFractions| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&|) (|GeneralPolynomialSet| |PolynomialSetCategory&|) -(|AlgebraGivenByStructuralConstants| |CliffordAlgebra| |DirectProductMatrixModule| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldExtension| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |GenericNonAssociativeAlgebra| |InnerFiniteField| |InnerPrimeField| |IntegerMod| |LieExponentials| |LieSquareMatrix| |NormRetractPackage| |Permanent| |PrimeField| |QuadraticForm| |SetOfMIntegersInOneToN| |SubSpace|) +(|AlgebraGivenByStructuralConstants| |CliffordAlgebra| |DirectProductMatrixModule| |DirichletRing| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldExtension| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |GenericNonAssociativeAlgebra| |InnerFiniteField| |InnerPrimeField| |IntegerMod| |LieExponentials| |LieSquareMatrix| |NormRetractPackage| |Permanent| |PrimeField| |QuadraticForm| |SetOfMIntegersInOneToN| |SubSpace|) (|PowerSeriesCategory&|) (|FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldNormalBasis|) (|Tuple|) (|ConstantLODE| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |FunctionSpaceIntegration| |InverseLaplaceTransform| |LaplaceTransform| |NonLinearFirstOrderODESolver| |ODEIntegration|) (|Heap|) +(|InfClsPt|) +(|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LocalParametrizationOfSimplePointPackage| |ParametrizationPackage| |PolynomialPackageForCurve| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace|) +(|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber|) +(|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField|) +(|PseudoAlgebraicClosureOfFiniteField|) +(|PseudoAlgebraicClosureOfAlgExtOfRationalNumber|) +(|FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |PseudoAlgebraicClosureOfRationalNumber|) (|CliffordAlgebra|) (|Octonion|) (|Quaternion| |QuaternionCategory&| |QuaternionCategoryFunctions2|) @@ -196,8 +217,8 @@ (|RecursiveAggregate&| |SplittingTree| |Tree|) (|GeneralPolynomialSet| |GeneralTriangularSet| |InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |NewSparseMultivariatePolynomial| |NormalizationPackage| |NormalizedTriangularSetCategory| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |QuasiComponentPackage| |RecursivePolynomialCategory&| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |SquareFreeNormalizedTriangularSetCategory| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetCategory| |SquareFreeRegularTriangularSetGcdPackage| |TriangularSetCategory| |TriangularSetCategory&| |WuWenTsunTriangularSet|) (|LazardSetSolvingPackage| |NormalizationPackage| |QuasiComponentPackage| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage|) -(|AlgebraicIntegrate| |AlgebraicNumber| |AntiSymm| |BoundIntegerRoots| |CardinalNumber| |ComplexTrigonometricManipulations| |ConstantLODE| |DeRhamComplex| |DefiniteIntegrationTools| |DifferentialSparseMultivariatePolynomial| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FortranExpression| |FractionalIdeal| |FractionalIdealFunctions2| |FreeGroup| |FreeMonoid| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |InnerAlgebraicNumber| |IntegerRetractions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LinearOrdinaryDifferentialOperatorFactorizer| |ListMonoidOps| |LyndonWord| |MachineFloat| |Magma| |ModuleOperator| |MonoidRing| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |ODEIntegration| |Operator| |OrderedFreeMonoid| |OrderlyDifferentialPolynomial| |Pattern| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPushDown| |PatternMatchTools| |Pi| |PoincareBirkhoffWittLyndonBasis| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalFunctionSum| |RationalIntegration| |RationalLODE| |RationalRetractions| |RationalRicDE| |RetractSolvePackage| |RetractableTo&| |RewriteRule| |SequentialDifferentialPolynomial| |SparseUnivariatePuiseuxSeries| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |TrigonometricManipulations| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|AbelianMonoidRing| |AbelianMonoidRing&| |AntiSymm| |ApplyRules| |ApplyUnivariateSkewPolynomial| |Automorphism| |BezoutMatrix| |BiModule| |CliffordAlgebra| |CommuteUnivariatePolynomialCategory| |DeRhamComplex| |DegreeReductionPackage| |DifferentialExtension| |DifferentialExtension&| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |ExpertSystemToolsPackage2| |ExpressionToOpenMath| |FactoringUtilities| |FiniteAbelianMonoidRing| |FiniteAbelianMonoidRing&| |FreeModule| |FreeModule1| |FreeModuleCat| |FullyLinearlyExplicitRingOver| |FullyLinearlyExplicitRingOver&| |FunctionSpaceFunctions2| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralUnivariatePowerSeries| |HomogeneousDistributedMultivariatePolynomial| |IndexedMatrix| |InnerPolySign| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |IntegralBasisPolynomialTools| |LeftAlgebra| |LeftAlgebra&| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorCategory&| |LinearlyExplicitRingOver| |MPolyCatFunctions2| |MPolyCatFunctions3| |Matrix| |MatrixCategory| |MatrixCategory&| |MatrixCategoryFunctions2| |ModMonic| |ModularRing| |ModuleOperator| |MonogenicLinearOperator| |MonoidRing| |MonoidRingFunctions2| |MultivariatePolynomial| |MultivariateTaylorSeriesCategory| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |Operator| |OppositeMonogenicLinearOperator| |OrderlyDifferentialPolynomial| |OrdinaryWeightedPolynomials| |PatternMatchPolynomialCategory| |PatternMatchTools| |Permanent| |Point| |PointCategory| |PointFunctions2| |PointPackage| |PolToPol| |Polynomial| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialComposition| |PolynomialFunctions2| |PolynomialRing| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialToUnivariatePolynomial| |PowerSeriesCategory| |PowerSeriesCategory&| |PushVariables| |RectangularMatrix| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RepresentationPackage1| |RepresentationPackage2| |RewriteRule| |Ring&| |Ruleset| |SequentialDifferentialPolynomial| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SquareMatrix| |SquareMatrixCategory| |SquareMatrixCategory&| |StorageEfficientMatrixOperations| |StreamTaylorSeriesOperations| |SubSpace| |SymmetricFunctions| |SymmetricPolynomial| |TaylorSeries| |ThreeSpace| |ThreeSpaceCategory| |ToolsForSign| |UTSodetools| |UnivariateLaurentSeries| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialCategory| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialFunctions2| |UnivariatePolynomialMultiplicationPackage| |UnivariatePowerSeriesCategory| |UnivariatePowerSeriesCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesFunctions2| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |WeightedPolynomials| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |XPolynomial| |XPolynomialRing| |XPolynomialsCat| |XRecursivePolynomial|) +(|AlgebraicIntegrate| |AlgebraicNumber| |AntiSymm| |BoundIntegerRoots| |CardinalNumber| |ComplexTrigonometricManipulations| |ConstantLODE| |DeRhamComplex| |DefiniteIntegrationTools| |DifferentialSparseMultivariatePolynomial| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FortranExpression| |FractionalIdeal| |FractionalIdealFunctions2| |FreeGroup| |FreeMonoid| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |GosperSummationMethod| |Guess| |InnerAlgebraicNumber| |IntegerRetractions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LinearOrdinaryDifferentialOperatorFactorizer| |ListMonoidOps| |LyndonWord| |MachineFloat| |Magma| |ModuleOperator| |MonoidRing| |MyExpression| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |ODEIntegration| |Operator| |OrderedFreeMonoid| |OrderlyDifferentialPolynomial| |Pattern| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPushDown| |PatternMatchTools| |Pi| |PoincareBirkhoffWittLyndonBasis| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalFunctionSum| |RationalIntegration| |RationalLODE| |RationalRetractions| |RationalRicDE| |RecurrenceOperator| |RetractSolvePackage| |RetractableTo&| |RewriteRule| |SequentialDifferentialPolynomial| |SparseUnivariatePuiseuxSeries| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |TrigonometricManipulations| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity|) +(|AbelianMonoidRing| |AbelianMonoidRing&| |AntiSymm| |ApplyRules| |ApplyUnivariateSkewPolynomial| |Automorphism| |Bezier| |BezoutMatrix| |BiModule| |CliffordAlgebra| |CommuteUnivariatePolynomialCategory| |DeRhamComplex| |DegreeReductionPackage| |DifferentialExtension| |DifferentialExtension&| |DifferentialPolynomialCategory| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DistributedMultivariatePolynomial| |ExpertSystemToolsPackage2| |ExpressionToOpenMath| |FactoringUtilities| |FiniteAbelianMonoidRing| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRingFunctions2| |FreeModule| |FreeModule1| |FreeModuleCat| |FullyLinearlyExplicitRingOver| |FullyLinearlyExplicitRingOver&| |FunctionSpaceFunctions2| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralUnivariatePowerSeries| |HomogeneousDistributedMultivariatePolynomial| |IndexedMatrix| |InnerPolySign| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |IntegralBasisPolynomialTools| |LeftAlgebra| |LeftAlgebra&| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorCategory&| |LinearlyExplicitRingOver| |MPolyCatFunctions2| |MPolyCatFunctions3| |MappingPackage4| |Matrix| |MatrixCategory| |MatrixCategory&| |MatrixCategoryFunctions2| |ModMonic| |ModularRing| |ModuleOperator| |MonogenicLinearOperator| |MonoidRing| |MonoidRingFunctions2| |MultivariatePolynomial| |MultivariateTaylorSeriesCategory| |MyExpression| |MyUnivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |NewtonPolygon| |Operator| |OppositeMonogenicLinearOperator| |OrderlyDifferentialPolynomial| |OrdinaryWeightedPolynomials| |PackageForPoly| |PatternMatchPolynomialCategory| |PatternMatchTools| |Permanent| |Point| |PointCategory| |PointFunctions2| |PointPackage| |PolToPol| |Polynomial| |PolynomialCategory| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialComposition| |PolynomialFunctions2| |PolynomialRing| |PolynomialSetCategory| |PolynomialSetCategory&| |PolynomialToUnivariatePolynomial| |PowerSeriesCategory| |PowerSeriesCategory&| |PushVariables| |RectangularMatrix| |RectangularMatrixCategory| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecursivePolynomialCategory| |RecursivePolynomialCategory&| |RepresentationPackage1| |RepresentationPackage2| |RewriteRule| |Ring&| |Ruleset| |SequentialDifferentialPolynomial| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SquareMatrix| |SquareMatrixCategory| |SquareMatrixCategory&| |StorageEfficientMatrixOperations| |StreamTaylorSeriesOperations| |SubSpace| |SymmetricFunctions| |SymmetricPolynomial| |TaylorSeries| |ThreeSpace| |ThreeSpaceCategory| |ToolsForSign| |UTSodetools| |UnivariateFormalPowerSeries| |UnivariateFormalPowerSeriesFunctions| |UnivariateLaurentSeries| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialCategory| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialFunctions2| |UnivariatePolynomialMultiplicationPackage| |UnivariatePowerSeriesCategory| |UnivariatePowerSeriesCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesCategory| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesFunctions2| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |WeightedPolynomials| |XAlgebra| |XDistributedPolynomial| |XExponentialPackage| |XFreeAlgebra| |XPolynomial| |XPolynomialRing| |XPolynomialsCat| |XRecursivePolynomial|) (|LeftModule| |RightModule|) (|InputForm|) (|InputForm| |SExpression| |SExpressionOf|) @@ -205,13 +226,15 @@ (|SemiGroup&|) (|SequentialDifferentialPolynomial|) (|SetAggregate&|) -(|AnonymousFunction| |Any| |ApplyRules| |ArrayStack| |AssociationList| |AssociationListAggregate| |AttributeButtons| |BalancedBinaryTree| |BasicFunctions| |BasicOperatorFunctions1| |BinaryTree| |BinaryTreeCategory| |BinaryTreeCategory&| |CharacterClass| |Commutator| |ComplexPattern| |ComplexPatternMatch| |Database| |Dequeue| |Dictionary| |Dictionary&| |DictionaryOperations| |DictionaryOperations&| |DrawOption| |Eltable| |EltableAggregate| |EltableAggregate&| |EqTable| |Evalable| |Evalable&| |Exit| |File| |FileCategory| |FiniteSetAggregate| |FiniteSetAggregate&| |FiniteSetAggregateFunctions2| |FormalFraction| |FortranCode| |FortranType| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeAbelianMonoidCategory| |FreeGroup| |FreeModuleCat| |FreeMonoid| |FullPartialFractionExpansion| |FullyEvalableOver| |FullyEvalableOver&| |FunctionCalled| |GeneralSparseTable| |GenusZeroIntegration| |GraphImage| |HashTable| |IndexedAggregate| |IndexedAggregate&| |IndexedDirectProductCategory| |IndexedDirectProductObject| |InnerEvalable| |InnerEvalable&| |InnerFreeAbelianMonoid| |InnerTable| |KeyedAccessFile| |KeyedDictionary| |KeyedDictionary&| |ListMonoidOps| |ListMultiDictionary| |ListToMap| |MakeCachableSet| |MappingPackage1| |MappingPackage2| |MappingPackage3| |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |ModuleMonomial| |MultiDictionary| |MultiVariableCalculusFunctions| |Multiset| |MultisetAggregate| |None| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalPDEProblem| |OnePointCompletion| |OnePointCompletionFunctions2| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OrderedCompletion| |OrderedCompletionFunctions2| |OrdinaryDifferentialRing| |OutputForm| |Palette| |PartialDifferentialRing| |PartialDifferentialRing&| |Pattern| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchListResult| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResult| |PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |PatternMatchable| |PendantTree| |Permutation| |PermutationCategory| |PermutationGroup| |PolynomialCategoryLifting| |PolynomialIdeals| |Product| |PureAlgebraicIntegration| |QuasiAlgebraicSet| |Queue| |RandomDistributions| |RepeatedDoubling| |RepeatedSquaring| |RewriteRule| |RuleCalled| |Ruleset| |SExpressionCategory| |SExpressionOf| |ScriptFormulaFormat| |ScriptFormulaFormat1| |Set| |SetAggregate| |SetAggregate&| |SetCategory&| |SparseTable| |SplittingNode| |SplittingTree| |Stack| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Table| |TableAggregate| |TableAggregate&| |Tableau| |TabulatedComputationPackage| |TexFormat| |TexFormat1| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |Tree| |TwoDimensionalViewport| |UserDefinedPartialOrdering| |Variable|) +(|AnonymousFunction| |Any| |ApplyRules| |ArrayStack| |AssociationList| |AssociationListAggregate| |AttributeButtons| |BalancedBinaryTree| |BasicFunctions| |BasicOperatorFunctions1| |BinaryTree| |BinaryTreeCategory| |BinaryTreeCategory&| |CharacterClass| |Commutator| |ComplexPattern| |ComplexPatternMatch| |Database| |Dequeue| |DesingTree| |DesingTreeCategory| |Dictionary| |Dictionary&| |DictionaryOperations| |DictionaryOperations&| |DivisorCategory| |DrawOption| |Eltable| |EltableAggregate| |EltableAggregate&| |EqTable| |Evalable| |Evalable&| |Exit| |File| |FileCategory| |FiniteSetAggregate| |FiniteSetAggregate&| |FiniteSetAggregateFunctions2| |FortranCode| |FortranType| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeAbelianMonoidCategory| |FreeGroup| |FreeModuleCat| |FreeMonoid| |FullPartialFractionExpansion| |FullyEvalableOver| |FullyEvalableOver&| |FunctionCalled| |GeneralSparseTable| |GenusZeroIntegration| |GraphImage| |GuessOption| |GuessOptionFunctions0| |HTMLFormat| |HashTable| |IndexedAggregate| |IndexedAggregate&| |IndexedDirectProductCategory| |IndexedDirectProductObject| |InnerEvalable| |InnerEvalable&| |InnerFreeAbelianMonoid| |InnerTable| |KeyedAccessFile| |KeyedDictionary| |KeyedDictionary&| |ListMonoidOps| |ListMultiDictionary| |ListToMap| |MakeCachableSet| |MappingPackage1| |MappingPackage2| |MappingPackage3| |MappingPackage4| |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MathMLFormat| |ModuleMonomial| |MultiDictionary| |MultiVariableCalculusFunctions| |Multiset| |MultisetAggregate| |None| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalPDEProblem| |OnePointCompletion| |OnePointCompletionFunctions2| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OrderedCompletion| |OrderedCompletionFunctions2| |OrdinaryDifferentialRing| |OutputForm| |Palette| |PartialDifferentialRing| |PartialDifferentialRing&| |Pattern| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchListResult| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResult| |PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |PatternMatchable| |PendantTree| |Permutation| |PermutationCategory| |PermutationGroup| |PolynomialCategoryLifting| |PolynomialIdeals| |Product| |PureAlgebraicIntegration| |QuasiAlgebraicSet| |Queue| |RandomDistributions| |RepeatedDoubling| |RepeatedSquaring| |RewriteRule| |RuleCalled| |Ruleset| |SExpressionCategory| |SExpressionOf| |ScriptFormulaFormat| |ScriptFormulaFormat1| |Set| |SetAggregate| |SetAggregate&| |SetCategory&| |SparseTable| |SplittingNode| |SplittingTree| |Stack| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Table| |TableAggregate| |TableAggregate&| |Tableau| |TabulatedComputationPackage| |TexFormat| |TexFormat1| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |Tree| |TwoDimensionalViewport| |UserDefinedPartialOrdering| |Variable|) +(|Divisor|) (|BinaryFile| |FiniteFieldNormalBasisExtensionByPolynomial|) (|DifferentialSparseMultivariatePolynomial| |NewSparseMultivariatePolynomial| |OrderlyDifferentialPolynomial| |SequentialDifferentialPolynomial|) (|SparseUnivariatePuiseuxSeries|) (|FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasisExtensionByPolynomial| |NewSparseUnivariatePolynomial| |Pi|) +(|ExpressionSolve| |TaylorSolve|) (|SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries|) -(|InverseLaplaceTransform|) +(|DoubleFloat| |InverseLaplaceTransform|) (|SplittingTree|) (|InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet|) (|AlgebraGivenByStructuralConstants| |GenericNonAssociativeAlgebra|) @@ -222,7 +245,7 @@ (|CharacterClass| |Float| |FortranTemplate| |HashTable| |InputForm| |Integer| |KeyedAccessFile| |Library| |SExpression| |StringTable| |TextFile|) (|IndexedString| |StringAggregate&|) (|String|) -(|AlgebraGivenByStructuralConstants| |AntiSymm| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |DeRhamComplex| |DistributedMultivariatePolynomial| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |FGLMIfCanPackage| |FortranExpression| |FortranProgram| |FunctionCalled| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GroebnerSolve| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InputForm| |LexTriangularPackage| |LinGroebnerPackage| |MultivariatePolynomial| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrdinaryWeightedPolynomials| |PadeApproximantPackage| |ParametricLinearEquations| |Pattern| |PolToPol| |Polynomial| |PolynomialInterpolation| |PolynomialToUnivariatePolynomial| |QuasiAlgebraicSet2| |RationalUnivariateRepresentationPackage| |RegularChain| |Result| |RoutinesTable| |RuleCalled| |SExpression| |SequentialDifferentialPolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |SturmHabichtPackage| |Symbol| |TaylorSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialFunctions2| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |Variable| |XPolynomial| |ZeroDimensionalSolvePackage|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraGivenByStructuralConstants| |AntiSymm| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |BlowUpPackage| |DeRhamComplex| |DesingTreePackage| |DistributedMultivariatePolynomial| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |FGLMIfCanPackage| |FortranExpression| |FortranProgram| |FunctionCalled| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GroebnerSolve| |Guess| |GuessUnivariatePolynomial| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InputForm| |InterfaceGroebnerPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |LexTriangularPackage| |LinGroebnerPackage| |LocalParametrizationOfSimplePointPackage| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrdinaryWeightedPolynomials| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PadeApproximantPackage| |ParametricLinearEquations| |ParametrizationPackage| |Pattern| |PolToPol| |Polynomial| |PolynomialInterpolation| |PolynomialToUnivariatePolynomial| |ProjectiveAlgebraicSetPackage| |QuasiAlgebraicSet2| |RationalInterpolation| |RationalUnivariateRepresentationPackage| |RecurrenceOperator| |RegularChain| |Result| |RoutinesTable| |RuleCalled| |SExpression| |SequentialDifferentialPolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |SturmHabichtPackage| |Symbol| |TaylorSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialFunctions2| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |Variable| |XPolynomial| |ZeroDimensionalSolvePackage|) (|FortranProgram|) (|EqTable| |GeneralSparseTable| |HashTable| |InnerTable| |KeyedAccessFile| |Library| |Result| |RoutinesTable| |SparseTable| |StringTable| |Table| |TableAggregate&|) (|ThreeSpace|) @@ -236,7 +259,7 @@ (|UnivariatePuiseuxSeries|) (|ElementaryFunctionsUnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesConstructorCategory| |UnivariatePuiseuxSeriesConstructorCategory&|) (|ElementaryFunctionsUnivariateLaurentSeries| |SparseUnivariateLaurentSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&|) -(|AlgFactor| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |BalancedFactorisation| |BezoutMatrix| |BoundIntegerRoots| |BrillhartTests| |ChangeOfVariable| |CharacteristicPolynomialInMonogenicalAlgebra| |ChineseRemainderToolsForIntegralBases| |CommuteUnivariatePolynomialCategory| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |DistinctDegreeFactorize| |DoubleResultantPackage| |EuclideanModularRing| |FindOrderFinite| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteRankAlgebra| |FiniteRankAlgebra&| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra| |FramedAlgebra&| |FramedModule| |FullPartialFractionExpansion| |FunctionFieldCategory| |FunctionFieldCategory&| |FunctionFieldCategoryFunctions2| |FunctionFieldIntegralBasis| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GenExEuclid| |GeneralHenselPackage| |HeuGcd| |HyperellipticFiniteDivisor| |InfiniteProductFiniteField| |InnerAlgFactor| |InnerModularGcd| |InnerPolySign| |IntegralBasisPolynomialTools| |IntegralBasisTools| |Kovacic| |LaurentPolynomial| |LinearOrdinaryDifferentialOperatorFactorizer| |ModMonic| |ModularDistinctDegreeFactorizer| |MonogenicAlgebra| |MonogenicAlgebra&| |MonomialExtensionTools| |MultipleMap| |NPCoef| |NewSparseUnivariatePolynomial| |NormInMonogenicAlgebra| |NormRetractPackage| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |PadeApproximants| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PolynomialComposition| |PolynomialDecomposition| |PolynomialFactorizationByRecursionUnivariate| |PolynomialInterpolationAlgorithms| |PolynomialSolveByFormulas| |PrimitiveRatDE| |PrimitiveRatRicDE| |PseudoRemainderSequence| |PureAlgebraicLODE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalIntegration| |RationalLODE| |RationalRicDE| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory| |RealRootCharacterizationCategory&| |RealZeroPackage| |RealZeroPackageQ| |ReduceLODE| |ReducedDivisor| |RightOpenIntervalRootCharacterization| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SparseUnivariatePolynomial| |SubResultantPackage| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |UTSodetools| |UnivariateFactorize| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialSquareFree| |WildFunctionFieldIntegralBasis|) +(|AlgFactor| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |BalancedFactorisation| |BezoutMatrix| |BoundIntegerRoots| |BrillhartTests| |ChangeOfVariable| |CharacteristicPolynomialInMonogenicalAlgebra| |ChineseRemainderToolsForIntegralBases| |CommuteUnivariatePolynomialCategory| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |DistinctDegreeFactorize| |DoubleResultantPackage| |EuclideanModularRing| |FindOrderFinite| |FiniteDivisor| |FiniteDivisorCategory| |FiniteDivisorCategory&| |FiniteDivisorFunctions2| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteRankAlgebra| |FiniteRankAlgebra&| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra| |FramedAlgebra&| |FramedModule| |FullPartialFractionExpansion| |FunctionFieldCategory| |FunctionFieldCategory&| |FunctionFieldCategoryFunctions2| |FunctionFieldIntegralBasis| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GenExEuclid| |GeneralHenselPackage| |HeuGcd| |HyperellipticFiniteDivisor| |InfiniteProductFiniteField| |InnerAlgFactor| |InnerModularGcd| |InnerPolySign| |IntegralBasisPolynomialTools| |IntegralBasisTools| |Kovacic| |LaurentPolynomial| |LinearOrdinaryDifferentialOperatorFactorizer| |ModMonic| |ModularDistinctDegreeFactorizer| |MonogenicAlgebra| |MonogenicAlgebra&| |MonomialExtensionTools| |MultipleMap| |MyUnivariatePolynomial| |NPCoef| |NewSparseUnivariatePolynomial| |NormInMonogenicAlgebra| |NormRetractPackage| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |PadeApproximants| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PolynomialComposition| |PolynomialDecomposition| |PolynomialFactorizationByRecursionUnivariate| |PolynomialInterpolationAlgorithms| |PolynomialSolveByFormulas| |PrimitiveRatDE| |PrimitiveRatRicDE| |PseudoRemainderSequence| |PureAlgebraicLODE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalIntegration| |RationalLODE| |RationalRicDE| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory| |RealRootCharacterizationCategory&| |RealZeroPackage| |RealZeroPackageQ| |ReduceLODE| |ReducedDivisor| |RightOpenIntervalRootCharacterization| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SubResultantPackage| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |UTSodetools| |UnivariateFactorize| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialSquareFree| |WildFunctionFieldIntegralBasis|) (|FunctionSpaceToUnivariatePowerSeries| |InnerSparseUnivariatePowerSeries| |UnivariatePowerSeriesCategory&|) (|ExponentialExpansion| |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|ExponentialOfUnivariatePuiseuxSeries| |GeneralUnivariatePowerSeries|) @@ -244,10 +267,10 @@ (|ExponentialExpansion|) (|ApplyUnivariateSkewPolynomial| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps|) (|UnivariateLaurentSeries| |UnivariatePuiseuxSeries|) -(|ElementaryFunctionsUnivariateLaurentSeries| |EllipticFunctionsUnivariateTaylorSeries| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |PadeApproximants| |SparseUnivariateTaylorSeries| |UTSodetools| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesODESolver|) +(|ElementaryFunctionsUnivariateLaurentSeries| |EllipticFunctionsUnivariateTaylorSeries| |ExpressionSolve| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |PadeApproximants| |SparseUnivariateTaylorSeries| |TaylorSolve| |UTSodetools| |UnivariateFormalPowerSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesODESolver|) (|AlgebraGivenByStructuralConstants| |DenavitHartenbergMatrix| |FiniteFieldNormalBasisExtensionByPolynomial| |FramedModule| |GenericNonAssociativeAlgebra| |Matrix| |OrderedDirectProduct|) -(|IndexedVector| |Vector| |VectorCategory&|) +(|ComplexDoubleFloatVector| |DoubleFloatVector| |IndexedVector| |Vector| |VectorCategory&|) (|CliffordAlgebra| |VectorSpace&|) (|XPolynomialRing|) (|XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XRecursivePolynomial|) -(("XPolynomialsCat" 0 67544) ("XAlgebra" 0 67524) ("VectorSpace" 0 67489) ("VectorCategory" 0 67444) ("Vector" 0 67256) ("UnivariateTaylorSeriesCategory" 0 66754) ("UnivariateTaylorSeries" 0 66700) ("UnivariateSkewPolynomialCategory" 0 66532) ("UnivariatePuiseuxSeriesWithExponentialSingularity" 0 66507) ("UnivariatePuiseuxSeriesConstructorCategory" 0 66319) ("UnivariatePuiseuxSeriesCategory" 0 66247) ("UnivariatePuiseuxSeries" 0 66170) ("UnivariatePowerSeriesCategory" 0 66061) ("UnivariatePolynomialCategory" 0 63182) ("UnivariateLaurentSeriesConstructorCategory" 0 62994) ("UnivariateLaurentSeriesCategory" 0 62819) ("UnivariateLaurentSeries" 0 62791) ("UniqueFactorizationDomain" 0 62635) ("UnaryRecursiveAggregate" 0 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T) ((-23) . T) ((-25) . T) ((-43 (-409 (-568))) -2198 (|has| |#1| (-350)) (|has| |#1| (-365))) ((-43 |#1|) . T) ((-43 $) -2198 (|has| |#1| (-558)) (|has| |#1| (-350)) (|has| |#1| (-365)) (|has| |#1| (-301))) ((-40) |has| |#1| (-1181)) ((-98) |has| |#1| (-1181)) ((-105) . T) ((-120 (-409 (-568)) (-409 (-568))) -2198 (|has| |#1| (-350)) (|has| |#1| (-365))) ((-120 |#1| |#1|) . T) ((-120 $ $) . T) ((-137) . T) ((-148) -2198 (|has| |#1| (-350)) (|has| |#1| (-148))) ((-150) |has| |#1| (-150)) ((-608 (-850)) . T) ((-172) . T) ((-609 (-169 (-215))) |has| |#1| (-1021)) ((-609 (-169 (-381))) |has| |#1| (-1021)) ((-609 (-541)) |has| |#1| (-609 (-541))) ((-609 (-887 (-381))) |has| |#1| (-609 (-887 (-381)))) ((-609 (-887 (-568))) |has| |#1| (-609 (-887 (-568)))) ((-609 (-1157 |#1|)) . T) ((-223 |#1|) . 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T) ((-303 |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1047)) ((-413 |#2|) |has| |#2| (-1090)) ((-499 |#2|) . T) ((-601 (-568) |#2|) . 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T) ((-1251 |#2|) |has| |#2| (-365))) -((-2512 (((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 21)) (-3092 ((|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 23)) (-2795 (((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)) 18))) -(((-231 |#1| |#2| |#3|) (-10 -7 (-15 -2512 ((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -3092 (|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2795 ((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)))) (-763) (-1195) (-1195)) (T -231)) -((-2795 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-232 *5 *6)) (-14 *5 (-763)) (-4 *6 (-1195)) (-4 *7 (-1195)) (-5 *2 (-232 *5 *7)) (-5 *1 (-231 *5 *6 *7)))) (-3092 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-232 *5 *6)) (-14 *5 (-763)) (-4 *6 (-1195)) (-4 *2 (-1195)) (-5 *1 (-231 *5 *6 *2)))) (-2512 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-232 *6 *7)) (-14 *6 (-763)) (-4 *7 (-1195)) (-4 *5 (-1195)) (-5 *2 (-232 *6 *5)) (-5 *1 (-231 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-43 |#2|) |has| |#2| (-172)) ((-105) -2199 (|has| |#2| (-1090)) (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-788)) (|has| |#2| (-716)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-137)) (|has| |#2| (-25))) ((-120 |#2| |#2|) -2199 (|has| |#2| (-1047)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-120 $ $) |has| |#2| (-172)) ((-137) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-788)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-137))) ((-608 (-850)) -2199 (|has| |#2| (-1090)) (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-788)) (|has| |#2| (-716)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-137)) (|has| |#2| (-25))) ((-608 (-1244 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-223 |#2|) |has| |#2| (-1047)) ((-225) -12 (|has| |#2| (-225)) (|has| |#2| (-1047))) ((-281 (-568) |#2|) . T) ((-283 (-568) |#2|) . T) ((-303 |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1047)) ((-413 |#2|) |has| |#2| (-1090)) ((-499 |#2|) . T) ((-601 (-568) |#2|) . T) ((-523 |#2| |#2|) -12 (|has| |#2| (-303 |#2|)) (|has| |#2| (-1090))) ((-637 |#2|) -2199 (|has| |#2| (-1047)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-637 $) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-172))) ((-630 (-568)) -12 (|has| |#2| (-630 (-568))) (|has| |#2| (-1047))) ((-630 |#2|) |has| |#2| (-1047)) ((-707 |#2|) -2199 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-716 (SEQ (|:| * (-1 $ |#2| $)) (|exit| 1 (|:| * (-1 $ $ |#2|))))) |has| |#2| (-716)) ((-716) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-172))) ((-786) |has| |#2| (-840)) ((-787) -2199 (|has| |#2| (-840)) (|has| |#2| (-788))) ((-788) |has| |#2| (-788)) ((-789) -2199 (|has| |#2| (-840)) (|has| |#2| (-788))) ((-790) -2199 (|has| |#2| (-840)) (|has| |#2| (-788))) ((-840) |has| |#2| (-840)) ((-842) -2199 (|has| |#2| (-840)) (|has| |#2| (-788))) ((-895 (-1161)) -12 (|has| |#2| (-895 (-1161))) (|has| |#2| (-1047))) ((-1037 (-409 (-568))) -12 (|has| |#2| (-1037 (-409 (-568)))) (|has| |#2| (-1090))) ((-1037 (-568)) -12 (|has| |#2| (-1037 (-568))) (|has| |#2| (-1090))) ((-1037 |#2|) |has| |#2| (-1090)) ((-1053 |#2|) -2199 (|has| |#2| (-1047)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1053 $) |has| |#2| (-172)) ((-1047) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-172))) ((-1054) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-172))) ((-1102) -2199 (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-716)) (|has| |#2| (-172))) ((-1090) -2199 (|has| |#2| (-1090)) (|has| |#2| (-1047)) (|has| |#2| (-840)) (|has| |#2| (-788)) (|has| |#2| (-716)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-137)) (|has| |#2| (-25))) ((-1195) . T) ((-1251 |#2|) |has| |#2| (-365))) +((-1678 (((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 21)) (-3094 ((|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|) 23)) (-2797 (((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)) 18))) +(((-231 |#1| |#2| |#3|) (-10 -7 (-15 -1678 ((-232 |#1| |#3|) (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -3094 (|#3| (-1 |#3| |#2| |#3|) (-232 |#1| |#2|) |#3|)) (-15 -2797 ((-232 |#1| |#3|) (-1 |#3| |#2|) (-232 |#1| |#2|)))) (-763) (-1195) (-1195)) (T -231)) +((-2797 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-232 *5 *6)) (-14 *5 (-763)) (-4 *6 (-1195)) (-4 *7 (-1195)) (-5 *2 (-232 *5 *7)) (-5 *1 (-231 *5 *6 *7)))) (-3094 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-232 *5 *6)) (-14 *5 (-763)) (-4 *6 (-1195)) (-4 *2 (-1195)) (-5 *1 (-231 *5 *6 *2)))) (-1678 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-232 *6 *7)) (-14 *6 (-763)) (-4 *7 (-1195)) (-4 *5 (-1195)) (-5 *2 (-232 *6 *5)) (-5 *1 (-231 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-52 |#1| |#4|) . T) ((-25) . T) ((-43 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-43 |#1|) |has| |#1| (-172)) ((-43 $) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-105) . T) ((-120 (-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-120 |#1| |#1|) . T) ((-120 $ $) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453)) (|has| |#1| (-172))) ((-137) . T) ((-148) |has| |#1| (-148)) ((-150) |has| |#1| (-150)) ((-608 (-850)) . T) ((-172) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453)) (|has| |#1| (-172))) ((-609 (-541)) -12 (|has| |#1| (-609 (-541))) (|has| |#3| (-609 (-541)))) ((-609 (-887 (-381))) -12 (|has| |#1| (-609 (-887 (-381)))) (|has| |#3| (-609 (-887 (-381))))) ((-609 (-887 (-568))) -12 (|has| |#1| (-609 (-887 (-568)))) (|has| |#3| (-609 (-887 (-568))))) ((-223 |#1|) . T) ((-225) |has| |#1| (-225)) ((-285) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-303 $) . T) ((-324 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-453) -2198 (|has| |#1| (-904)) (|has| |#1| (-453))) ((-523 |#2| |#1|) |has| |#1| (-225)) ((-523 |#2| $) |has| |#1| (-225)) ((-523 |#3| |#1|) . T) ((-523 |#3| $) . T) ((-523 $ $) . T) ((-558) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-637 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-637 |#1|) . T) ((-637 $) . T) ((-630 (-568)) |has| |#1| (-630 (-568))) ((-630 |#1|) . T) ((-707 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-707 |#1|) |has| |#1| (-172)) ((-707 $) -2198 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-716) . T) ((-842) |has| |#1| (-842)) ((-895 (-1161)) |has| |#1| (-895 (-1161))) ((-895 |#3|) . T) ((-881 (-381)) -12 (|has| |#1| (-881 (-381))) (|has| |#3| (-881 (-381)))) ((-881 (-568)) -12 (|has| |#1| (-881 (-568))) (|has| |#3| (-881 (-568)))) ((-950 |#1| |#4| |#3|) . 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T) ((-23) . T) ((-52 |#1| |#4|) . T) ((-25) . T) ((-43 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-43 |#1|) |has| |#1| (-172)) ((-43 $) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-105) . T) ((-120 (-409 (-568)) (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-120 |#1| |#1|) . T) ((-120 $ $) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453)) (|has| |#1| (-172))) ((-137) . T) ((-148) |has| |#1| (-148)) ((-150) |has| |#1| (-150)) ((-608 (-850)) . T) ((-172) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453)) (|has| |#1| (-172))) ((-609 (-541)) -12 (|has| |#1| (-609 (-541))) (|has| |#3| (-609 (-541)))) ((-609 (-887 (-381))) -12 (|has| |#1| (-609 (-887 (-381)))) (|has| |#3| (-609 (-887 (-381))))) ((-609 (-887 (-568))) -12 (|has| |#1| (-609 (-887 (-568)))) (|has| |#3| (-609 (-887 (-568))))) ((-223 |#1|) . T) ((-225) |has| |#1| (-225)) ((-285) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-303 $) . T) ((-324 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-453) -2199 (|has| |#1| (-904)) (|has| |#1| (-453))) ((-523 |#2| |#1|) |has| |#1| (-225)) ((-523 |#2| $) |has| |#1| (-225)) ((-523 |#3| |#1|) . T) ((-523 |#3| $) . T) ((-523 $ $) . T) ((-558) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-637 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-637 |#1|) . T) ((-637 $) . T) ((-630 (-568)) |has| |#1| (-630 (-568))) ((-630 |#1|) . T) ((-707 (-409 (-568))) |has| |#1| (-43 (-409 (-568)))) ((-707 |#1|) |has| |#1| (-172)) ((-707 $) -2199 (|has| |#1| (-904)) (|has| |#1| (-558)) (|has| |#1| (-453))) ((-716) . T) ((-842) |has| |#1| (-842)) ((-895 (-1161)) |has| |#1| (-895 (-1161))) ((-895 |#3|) . T) ((-881 (-381)) -12 (|has| |#1| (-881 (-381))) (|has| |#3| (-881 (-381)))) ((-881 (-568)) -12 (|has| |#1| (-881 (-568))) (|has| |#3| (-881 (-568)))) ((-950 |#1| |#4| |#3|) . 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|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")))) (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215))))))) (T -563)) -((-4083 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1141 (-215))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1338 (-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 (-563)))) (-2041 (*1 *2 *1) (-12 (-5 *2 (-634 (-2 (|:| -3649 (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215)))) (|:| -4083 (-2 (|:| |endPointContinuity| (-3 (|:| |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| (-3 (|:| |str| (-1141 (-215))) (|:| |notEvaluated| "Internal singularities not yet 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|upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-563)))) (-1946 (*1 *2 *1) (-12 (-5 *2 (-634 (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215))))) (-5 *1 (-563)))) (-1470 (*1 *2) (-12 (-5 *2 (-1249)) (-5 *1 (-563)))) (-3365 (*1 *1) (-5 *1 (-563)))) -(-10 -8 (-15 -3365 ($)) (-15 -1470 ((-1249))) (-15 -1946 ((-634 (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215)))) $)) (-15 -2803 ($ (-634 (-2 (|:| -3649 (-2 (|:| |var| (-1161)) (|:| |fn| (-310 (-215))) (|:| -1338 (-1084 (-835 (-215)))) (|:| |abserr| (-215)) (|:| |relerr| (-215)))) (|:| -4083 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| 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NIL) (-1170 3228243 3228350 3228495 "TANEXP" 3228748 NIL TANEXP (NIL T) -7 NIL NIL) (-1169 3221756 3228100 3228193 "TABLE" 3228198 NIL TABLE (NIL T T) -8 NIL NIL) (-1168 3221169 3221267 3221405 "TABLEAU" 3221653 NIL TABLEAU (NIL T) -8 NIL NIL) (-1167 3215777 3216997 3218245 "TABLBUMP" 3219955 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1166 3212240 3212935 3213718 "SYSSOLP" 3215028 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1165 3209374 3209982 3210620 "SYMTAB" 3211624 T SYMTAB (NIL) -8 NIL NIL) (-1164 3204623 3205525 3206508 "SYMS" 3208413 T SYMS (NIL) -8 NIL NIL) (-1163 3201855 3204087 3204314 "SYMPOLY" 3204431 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1162 3201372 3201447 3201570 "SYMFUNC" 3201767 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1161 3197350 3198609 3199431 "SYMBOL" 3200572 T SYMBOL (NIL) -8 NIL NIL) (-1160 3190889 3192578 3194298 "SWITCH" 3195652 T SWITCH (NIL) -8 NIL NIL) (-1159 3184115 3189712 3190014 "SUTS" 3190645 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1158 3176001 3183232 3183513 "SUPXS" 3183892 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1157 3167486 3175619 3175745 "SUP" 3175910 NIL SUP (NIL T) -8 NIL NIL) (-1156 3166645 3166772 3166989 "SUPFRACF" 3167354 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1155 3157217 3166447 3166561 "SUPEXPR" 3166566 NIL SUPEXPR (NIL T) -8 NIL NIL) (-1154 3156838 3156897 3157010 "SUP2" 3157152 NIL SUP2 (NIL T T) -7 NIL NIL) (-1153 3155251 3155525 3155888 "SUMRF" 3156537 NIL SUMRF (NIL T) -7 NIL NIL) (-1152 3154565 3154631 3154830 "SUMFS" 3155172 NIL SUMFS (NIL T T) -7 NIL NIL) (-1151 3138489 3153744 3153994 "SULS" 3154373 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1150 3137811 3138014 3138154 "SUCH" 3138397 NIL SUCH (NIL T T) -8 NIL NIL) (-1149 3131705 3132717 3133676 "SUBSPACE" 3136899 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1148 3131137 3131227 3131390 "SUBRESP" 3131594 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1147 3124506 3125802 3127113 "STTF" 3129873 NIL STTF (NIL T) -7 NIL NIL) (-1146 3118679 3119799 3120946 "STTFNC" 3123406 NIL STTFNC (NIL T) -7 NIL NIL) (-1145 3109998 3111865 3113657 "STTAYLOR" 3116922 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1144 3103254 3109862 3109945 "STRTBL" 3109950 NIL STRTBL (NIL T) -8 NIL NIL) (-1143 3098645 3103209 3103240 "STRING" 3103245 T STRING (NIL) -8 NIL NIL) (-1142 3093509 3097987 3098018 "STRICAT" 3098077 T STRICAT (NIL) -9 NIL 3098139) (-1141 3086236 3091036 3091654 "STREAM" 3092926 NIL STREAM (NIL T) -8 NIL NIL) (-1140 3085746 3085823 3085967 "STREAM3" 3086153 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1139 3084728 3084911 3085146 "STREAM2" 3085559 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1138 3084416 3084468 3084561 "STREAM1" 3084670 NIL STREAM1 (NIL T) -7 NIL NIL) (-1137 3083432 3083613 3083844 "STINPROD" 3084232 NIL STINPROD (NIL T) -7 NIL NIL) (-1136 3083009 3083193 3083224 "STEP" 3083304 T STEP (NIL) -9 NIL 3083382) (-1135 3076564 3082908 3082985 "STBL" 3082990 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1134 3071778 3075816 3075860 "STAGG" 3076013 NIL STAGG (NIL T) -9 NIL 3076102) (-1133 3069480 3070082 3070954 "STAGG-" 3070959 NIL STAGG- (NIL T T) -8 NIL NIL) (-1132 3062972 3064541 3065656 "STACK" 3068400 NIL STACK (NIL T) -8 NIL NIL) (-1131 3055697 3061113 3061569 "SREGSET" 3062602 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1130 3048123 3049491 3051004 "SRDCMPK" 3054303 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1129 3041101 3045561 3045592 "SRAGG" 3046895 T SRAGG (NIL) -9 NIL 3047503) (-1128 3040118 3040373 3040752 "SRAGG-" 3040757 NIL SRAGG- (NIL T) -8 NIL NIL) (-1127 3034566 3039041 3039465 "SQMATRIX" 3039741 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1126 3028322 3031284 3032011 "SPLTREE" 3033911 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1125 3024312 3024978 3025624 "SPLNODE" 3027748 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1124 3023358 3023591 3023622 "SPFCAT" 3024066 T SPFCAT (NIL) -9 NIL NIL) (-1123 3022095 3022305 3022569 "SPECOUT" 3023116 T SPECOUT (NIL) -7 NIL NIL) (-1122 3014065 3015812 3015856 "SPACEC" 3020229 NIL SPACEC (NIL T) -9 NIL 3022045) (-1121 3012236 3013997 3014046 "SPACE3" 3014051 NIL SPACE3 (NIL T) -8 NIL NIL) (-1120 3010990 3011161 3011451 "SORTPAK" 3012042 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1119 3009040 3009343 3009762 "SOLVETRA" 3010654 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1118 3008051 3008273 3008547 "SOLVESER" 3008813 NIL SOLVESER (NIL T) -7 NIL NIL) (-1117 3003271 3004152 3005154 "SOLVERAD" 3007103 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1116 2999086 2999695 3000424 "SOLVEFOR" 3002638 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1115 2993389 2998434 2998532 "SNTSCAT" 2998537 NIL SNTSCAT (NIL T T T T) -9 NIL 2998607) (-1114 2987487 2991714 2992104 "SMTS" 2993080 NIL SMTS (NIL T T T) -8 NIL NIL) (-1113 2981891 2987375 2987452 "SMP" 2987457 NIL SMP (NIL T T) -8 NIL NIL) (-1112 2980050 2980351 2980749 "SMITH" 2981588 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1111 2972992 2977190 2977294 "SMATCAT" 2978645 NIL SMATCAT (NIL NIL T T T) -9 NIL 2979192) (-1110 2969932 2970755 2971933 "SMATCAT-" 2971938 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1109 2967685 2969202 2969246 "SKAGG" 2969507 NIL SKAGG (NIL T) -9 NIL 2969642) (-1108 2963743 2966789 2967067 "SINT" 2967429 T SINT (NIL) -8 NIL NIL) (-1107 2963515 2963553 2963619 "SIMPAN" 2963699 T SIMPAN (NIL) -7 NIL NIL) (-1106 2962353 2962574 2962849 "SIGNRF" 2963274 NIL SIGNRF (NIL T) -7 NIL NIL) (-1105 2961158 2961309 2961600 "SIGNEF" 2962182 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1104 2958850 2959304 2959809 "SHP" 2960700 NIL SHP (NIL T NIL) -7 NIL NIL) (-1103 2952674 2958751 2958827 "SHDP" 2958832 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1102 2952162 2952354 2952385 "SGROUP" 2952537 T SGROUP (NIL) -9 NIL 2952624) (-1101 2951932 2951984 2952088 "SGROUP-" 2952093 NIL SGROUP- (NIL T) -8 NIL NIL) (-1100 2948768 2949465 2950188 "SGCF" 2951231 T SGCF (NIL) -7 NIL NIL) (-1099 2943169 2948214 2948312 "SFRTCAT" 2948317 NIL SFRTCAT (NIL T T T T) -9 NIL 2948356) (-1098 2936593 2937608 2938744 "SFRGCD" 2942152 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1097 2929721 2930792 2931978 "SFQCMPK" 2935526 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1096 2929343 2929432 2929542 "SFORT" 2929662 NIL SFORT (NIL T T) -8 NIL NIL) (-1095 2928488 2929183 2929304 "SEXOF" 2929309 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1094 2927622 2928369 2928437 "SEX" 2928442 T SEX (NIL) -8 NIL NIL) (-1093 2922397 2923086 2923182 "SEXCAT" 2926953 NIL SEXCAT (NIL T T T T T) -9 NIL 2927572) (-1092 2919577 2922331 2922379 "SET" 2922384 NIL SET (NIL T) -8 NIL NIL) (-1091 2917828 2918290 2918595 "SETMN" 2919318 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1090 2917433 2917559 2917590 "SETCAT" 2917707 T SETCAT (NIL) -9 NIL 2917792) (-1089 2917213 2917265 2917364 "SETCAT-" 2917369 NIL SETCAT- (NIL T) -8 NIL NIL) (-1088 2916876 2917026 2917057 "SETCATD" 2917116 T SETCATD (NIL) -9 NIL 2917163) (-1087 2913262 2915336 2915380 "SETAGG" 2916250 NIL SETAGG (NIL T) -9 NIL 2916590) (-1086 2912720 2912836 2913073 "SETAGG-" 2913078 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1085 2911923 2912216 2912278 "SEGXCAT" 2912564 NIL SEGXCAT (NIL T T) -9 NIL 2912684) (-1084 2910983 2911593 2911773 "SEG" 2911778 NIL SEG (NIL T) -8 NIL NIL) (-1083 2909889 2910102 2910146 "SEGCAT" 2910728 NIL SEGCAT (NIL T) -9 NIL 2910966) (-1082 2908940 2909270 2909469 "SEGBIND" 2909725 NIL SEGBIND (NIL T) -8 NIL NIL) (-1081 2908561 2908620 2908733 "SEGBIND2" 2908875 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1080 2907782 2907908 2908111 "SEG2" 2908406 NIL SEG2 (NIL T T) -7 NIL NIL) (-1079 2907219 2907717 2907764 "SDVAR" 2907769 NIL SDVAR (NIL T) -8 NIL NIL) (-1078 2899463 2906989 2907119 "SDPOL" 2907124 NIL SDPOL (NIL T) -8 NIL NIL) (-1077 2898056 2898322 2898641 "SCPKG" 2899178 NIL SCPKG (NIL T) -7 NIL NIL) (-1076 2897277 2897410 2897589 "SCACHE" 2897911 NIL SCACHE (NIL T) -7 NIL NIL) (-1075 2896716 2897037 2897122 "SAOS" 2897214 T SAOS (NIL) -8 NIL NIL) (-1074 2896281 2896316 2896489 "SAERFFC" 2896675 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1073 2890170 2896178 2896258 "SAE" 2896263 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1072 2889763 2889798 2889957 "SAEFACT" 2890129 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1071 2888084 2888398 2888799 "RURPK" 2889429 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1070 2886720 2886999 2887311 "RULESET" 2887918 NIL RULESET (NIL T T T) -8 NIL NIL) (-1069 2883907 2884410 2884875 "RULE" 2886401 NIL RULE (NIL T T T) -8 NIL NIL) (-1068 2883546 2883701 2883784 "RULECOLD" 2883859 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1067 2878395 2879189 2880109 "RSETGCD" 2882745 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1066 2867658 2872703 2872801 "RSETCAT" 2876920 NIL RSETCAT (NIL T T T T) -9 NIL 2878017) (-1065 2865585 2866124 2866948 "RSETCAT-" 2866953 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1064 2857972 2859347 2860867 "RSDCMPK" 2864184 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1063 2855976 2856417 2856492 "RRCC" 2857578 NIL RRCC (NIL T T) -9 NIL 2857922) (-1062 2855327 2855501 2855780 "RRCC-" 2855785 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1061 2829474 2839103 2839171 "RPOLCAT" 2849835 NIL RPOLCAT (NIL T T T) -9 NIL 2852983) (-1060 2820974 2823312 2826434 "RPOLCAT-" 2826439 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1059 2812033 2819185 2819667 "ROUTINE" 2820514 T ROUTINE (NIL) -8 NIL NIL) (-1058 2808733 2811584 2811733 "ROMAN" 2811906 T ROMAN (NIL) -8 NIL NIL) (-1057 2807008 2807593 2807853 "ROIRC" 2808538 NIL ROIRC (NIL T T) -8 NIL NIL) (-1056 2803346 2805646 2805677 "RNS" 2805981 T RNS (NIL) -9 NIL 2806255) (-1055 2801855 2802238 2802772 "RNS-" 2802847 NIL RNS- (NIL T) -8 NIL NIL) (-1054 2801277 2801685 2801716 "RNG" 2801721 T RNG (NIL) -9 NIL 2801742) (-1053 2800668 2801030 2801074 "RMODULE" 2801136 NIL RMODULE (NIL T) -9 NIL 2801178) (-1052 2799504 2799598 2799934 "RMCAT2" 2800569 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1051 2796213 2798682 2799005 "RMATRIX" 2799240 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1050 2789159 2791393 2791509 "RMATCAT" 2794868 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2795845) (-1049 2788534 2788681 2788988 "RMATCAT-" 2788993 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1048 2788101 2788176 2788304 "RINTERP" 2788453 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1047 2787144 2787708 2787739 "RING" 2787851 T RING (NIL) -9 NIL 2787946) (-1046 2786936 2786980 2787077 "RING-" 2787082 NIL RING- (NIL T) -8 NIL NIL) (-1045 2785777 2786014 2786272 "RIDIST" 2786700 T RIDIST (NIL) -7 NIL NIL) (-1044 2777093 2785245 2785451 "RGCHAIN" 2785625 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1043 2775893 2776134 2776413 "RFP" 2776848 NIL RFP (NIL T) -7 NIL NIL) (-1042 2772887 2773501 2774171 "RF" 2775257 NIL RF (NIL T) -7 NIL NIL) (-1041 2772533 2772596 2772699 "RFFACTOR" 2772818 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1040 2772258 2772293 2772390 "RFFACT" 2772492 NIL RFFACT (NIL T) -7 NIL NIL) (-1039 2770375 2770739 2771121 "RFDIST" 2771898 T RFDIST (NIL) -7 NIL NIL) (-1038 2769828 2769920 2770083 "RETSOL" 2770277 NIL RETSOL (NIL T T) -7 NIL NIL) (-1037 2769415 2769495 2769539 "RETRACT" 2769732 NIL RETRACT (NIL T) -9 NIL NIL) (-1036 2769264 2769289 2769376 "RETRACT-" 2769381 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1035 2762130 2768917 2769044 "RESULT" 2769159 T RESULT (NIL) -8 NIL NIL) (-1034 2760710 2761399 2761598 "RESRING" 2762033 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1033 2760346 2760395 2760493 "RESLATC" 2760647 NIL RESLATC (NIL T) -7 NIL NIL) (-1032 2760052 2760086 2760193 "REPSQ" 2760305 NIL REPSQ (NIL T) -7 NIL NIL) (-1031 2757474 2758054 2758656 "REP" 2759472 T REP (NIL) -7 NIL NIL) (-1030 2757172 2757206 2757317 "REPDB" 2757433 NIL REPDB (NIL T) -7 NIL NIL) (-1029 2751090 2752469 2753688 "REP2" 2755988 NIL REP2 (NIL T) -7 NIL NIL) (-1028 2747471 2748152 2748958 "REP1" 2750319 NIL REP1 (NIL T) -7 NIL NIL) (-1027 2740197 2745612 2746068 "REGSET" 2747101 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1026 2739012 2739347 2739596 "REF" 2739983 NIL REF (NIL T) -8 NIL NIL) (-1025 2738389 2738492 2738659 "REDORDER" 2738896 NIL REDORDER (NIL T T) -7 NIL NIL) (-1024 2735251 2735717 2736326 "RECOP" 2737923 NIL RECOP (NIL T T) -7 NIL NIL) (-1023 2731191 2734464 2734691 "RECLOS" 2735079 NIL RECLOS (NIL T) -8 NIL NIL) (-1022 2730243 2730424 2730639 "REALSOLV" 2730998 T REALSOLV (NIL) -7 NIL NIL) (-1021 2730088 2730129 2730160 "REAL" 2730165 T REAL (NIL) -9 NIL 2730200) (-1020 2726571 2727373 2728257 "REAL0Q" 2729253 NIL REAL0Q (NIL T) -7 NIL NIL) (-1019 2722172 2723160 2724221 "REAL0" 2725552 NIL REAL0 (NIL T) -7 NIL NIL) (-1018 2721577 2721649 2721856 "RDIV" 2722094 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1017 2720645 2720819 2721032 "RDIST" 2721399 NIL RDIST (NIL T) -7 NIL NIL) (-1016 2719242 2719529 2719901 "RDETRS" 2720353 NIL RDETRS (NIL T T) -7 NIL NIL) (-1015 2717054 2717508 2718046 "RDETR" 2718784 NIL RDETR (NIL T T) -7 NIL NIL) (-1014 2715665 2715943 2716347 "RDEEFS" 2716770 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1013 2714160 2714466 2714898 "RDEEF" 2715353 NIL RDEEF (NIL T T) -7 NIL NIL) (-1012 2708351 2711286 2711317 "RCFIELD" 2712612 T RCFIELD (NIL) -9 NIL 2713343) (-1011 2706415 2706919 2707615 "RCFIELD-" 2707690 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1010 2702773 2704552 2704596 "RCAGG" 2705680 NIL RCAGG (NIL T) -9 NIL 2706143) (-1009 2702401 2702495 2702658 "RCAGG-" 2702663 NIL RCAGG- (NIL T T) -8 NIL NIL) (-1008 2701737 2701848 2702013 "RATRET" 2702285 NIL RATRET (NIL T) -7 NIL NIL) (-1007 2701290 2701357 2701478 "RATFACT" 2701665 NIL RATFACT (NIL T) -7 NIL NIL) (-1006 2700598 2700718 2700870 "RANDSRC" 2701160 T RANDSRC (NIL) -7 NIL NIL) (-1005 2700332 2700376 2700449 "RADUTIL" 2700547 T RADUTIL (NIL) -7 NIL NIL) (-1004 2693320 2699065 2699384 "RADIX" 2700047 NIL RADIX (NIL NIL) -8 NIL NIL) (-1003 2684883 2693162 2693292 "RADFF" 2693297 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-1002 2684529 2684604 2684635 "RADCAT" 2684795 T RADCAT (NIL) -9 NIL NIL) (-1001 2684311 2684359 2684459 "RADCAT-" 2684464 NIL RADCAT- (NIL T) -8 NIL NIL) (-1000 2677558 2679176 2680329 "QUEUE" 2683193 NIL QUEUE (NIL T) -8 NIL NIL) (-999 2674049 2677495 2677540 "QUAT" 2677545 NIL QUAT (NIL T) -8 NIL NIL) (-998 2673687 2673730 2673857 "QUATCT2" 2674000 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-997 2667424 2670808 2670849 "QUATCAT" 2671629 NIL QUATCAT (NIL T) -9 NIL 2672387) (-996 2663568 2664605 2665992 "QUATCAT-" 2666086 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-995 2661128 2662686 2662728 "QUAGG" 2663103 NIL QUAGG (NIL T) -9 NIL 2663278) (-994 2660053 2660526 2660698 "QFORM" 2661000 NIL QFORM (NIL NIL T) -8 NIL NIL) (-993 2651280 2656547 2656588 "QFCAT" 2657246 NIL QFCAT (NIL T) -9 NIL 2658235) (-992 2646852 2648053 2649644 "QFCAT-" 2649738 NIL QFCAT- (NIL T T) -8 NIL NIL) (-991 2646490 2646533 2646660 "QFCAT2" 2646803 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-990 2645950 2646060 2646190 "QEQUAT" 2646380 T QEQUAT (NIL) -8 NIL NIL) (-989 2639098 2640169 2641353 "QCMPACK" 2644883 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-988 2636678 2637099 2637525 "QALGSET" 2638755 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-987 2635923 2636097 2636329 "QALGSET2" 2636498 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-986 2634614 2634837 2635154 "PWFFINTB" 2635696 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-985 2632796 2632964 2633318 "PUSHVAR" 2634428 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-984 2628713 2629767 2629809 "PTRANFN" 2631693 NIL PTRANFN (NIL T) -9 NIL NIL) (-983 2627115 2627406 2627728 "PTPACK" 2628424 NIL PTPACK (NIL T) -7 NIL NIL) (-982 2626747 2626804 2626913 "PTFUNC2" 2627052 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-981 2621247 2625581 2625623 "PTCAT" 2625996 NIL PTCAT (NIL T) -9 NIL 2626158) (-980 2620905 2620940 2621064 "PSQFR" 2621206 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-979 2619492 2619792 2620128 "PSEUDLIN" 2620601 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-978 2606268 2608632 2610953 "PSETPK" 2617255 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-977 2599312 2602026 2602123 "PSETCAT" 2605144 NIL PSETCAT (NIL T T T T) -9 NIL 2605957) (-976 2597148 2597782 2598603 "PSETCAT-" 2598608 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-975 2596497 2596661 2596690 "PSCURVE" 2596958 T PSCURVE (NIL) -9 NIL 2597125) (-974 2592886 2594412 2594478 "PSCAT" 2595322 NIL PSCAT (NIL T T T) -9 NIL 2595562) (-973 2591949 2592165 2592565 "PSCAT-" 2592570 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-972 2590602 2591234 2591448 "PRTITION" 2591755 T PRTITION (NIL) -8 NIL NIL) (-971 2587766 2588415 2588456 "PRSPCAT" 2589970 NIL PRSPCAT (NIL T) -9 NIL 2590538) (-970 2576866 2579072 2581259 "PRS" 2585629 NIL PRS (NIL T T) -7 NIL NIL) (-969 2574764 2576250 2576291 "PRQAGG" 2576474 NIL PRQAGG (NIL T) -9 NIL 2576576) (-968 2574033 2574689 2574746 "PROJSP" 2574751 NIL PROJSP (NIL NIL T) -8 NIL NIL) (-967 2573215 2573956 2574008 "PROJPLPS" 2574013 NIL PROJPLPS (NIL T) -8 NIL NIL) (-966 2572474 2573152 2573197 "PROJPL" 2573202 NIL PROJPL (NIL T) -8 NIL NIL) (-965 2566280 2570672 2571476 "PRODUCT" 2571716 NIL PRODUCT (NIL T T) -8 NIL NIL) (-964 2563555 2565744 2565975 "PR" 2566094 NIL PR (NIL T T) -8 NIL NIL) (-963 2562107 2562264 2562559 "PRJALGPK" 2563395 NIL PRJALGPK (NIL T NIL T T T) -7 NIL NIL) (-962 2561903 2561935 2561994 "PRINT" 2562068 T PRINT (NIL) -7 NIL NIL) (-961 2561243 2561360 2561512 "PRIMES" 2561783 NIL PRIMES (NIL T) -7 NIL NIL) (-960 2559308 2559709 2560175 "PRIMELT" 2560822 NIL PRIMELT (NIL T) -7 NIL NIL) (-959 2559036 2559085 2559114 "PRIMCAT" 2559238 T PRIMCAT (NIL) -9 NIL NIL) (-958 2555203 2558974 2559019 "PRIMARR" 2559024 NIL PRIMARR (NIL T) -8 NIL NIL) (-957 2554210 2554388 2554616 "PRIMARR2" 2555021 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-956 2553853 2553909 2554020 "PREASSOC" 2554148 NIL PREASSOC (NIL T T) -7 NIL NIL) (-955 2553328 2553460 2553489 "PPCURVE" 2553694 T PPCURVE (NIL) -9 NIL 2553830) (-954 2550689 2551088 2551679 "POLYROOT" 2552910 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-953 2544590 2550295 2550454 "POLY" 2550563 NIL POLY (NIL T) -8 NIL NIL) (-952 2543973 2544031 2544265 "POLYLIFT" 2544526 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-951 2540248 2540697 2541326 "POLYCATQ" 2543518 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-950 2527210 2532610 2532676 "POLYCAT" 2536190 NIL POLYCAT (NIL T T T) -9 NIL 2538103) (-949 2520660 2522521 2524905 "POLYCAT-" 2524910 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-948 2520247 2520315 2520435 "POLY2UP" 2520586 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-947 2519879 2519936 2520045 "POLY2" 2520184 NIL POLY2 (NIL T T) -7 NIL NIL) (-946 2518566 2518805 2519080 "POLUTIL" 2519654 NIL POLUTIL (NIL T T) -7 NIL NIL) (-945 2516921 2517198 2517529 "POLTOPOL" 2518288 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-944 2512443 2516857 2516903 "POINT" 2516908 NIL POINT (NIL T) -8 NIL NIL) (-943 2510630 2510987 2511362 "PNTHEORY" 2512088 T PNTHEORY (NIL) -7 NIL NIL) (-942 2509049 2509346 2509758 "PMTOOLS" 2510328 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-941 2508642 2508720 2508837 "PMSYM" 2508965 NIL PMSYM (NIL T) -7 NIL NIL) (-940 2508152 2508221 2508395 "PMQFCAT" 2508567 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-939 2507507 2507617 2507773 "PMPRED" 2508029 NIL PMPRED (NIL T) -7 NIL NIL) (-938 2506903 2506989 2507150 "PMPREDFS" 2507408 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-937 2505548 2505756 2506140 "PMPLCAT" 2506666 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-936 2505080 2505159 2505311 "PMLSAGG" 2505463 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-935 2504555 2504631 2504812 "PMKERNEL" 2504998 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-934 2504172 2504247 2504360 "PMINS" 2504474 NIL PMINS (NIL T) -7 NIL NIL) (-933 2503600 2503669 2503885 "PMFS" 2504097 NIL PMFS (NIL T T T) -7 NIL NIL) (-932 2502828 2502946 2503151 "PMDOWN" 2503477 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-931 2501991 2502150 2502332 "PMASS" 2502666 T PMASS (NIL) -7 NIL NIL) (-930 2501265 2501376 2501539 "PMASSFS" 2501877 NIL PMASSFS (NIL T T) -7 NIL NIL) (-929 2499025 2499278 2499661 "PLPKCRV" 2500989 NIL PLPKCRV (NIL T T T NIL T) -7 NIL NIL) (-928 2498680 2498748 2498842 "PLOTTOOL" 2498951 T PLOTTOOL (NIL) -7 NIL NIL) (-927 2493302 2494491 2495639 "PLOT" 2497552 T PLOT (NIL) -8 NIL NIL) (-926 2489116 2490150 2491071 "PLOT3D" 2492401 T PLOT3D (NIL) -8 NIL NIL) (-925 2488028 2488205 2488440 "PLOT1" 2488920 NIL PLOT1 (NIL T) -7 NIL NIL) (-924 2463423 2468094 2472945 "PLEQN" 2483294 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-923 2462663 2463333 2463400 "PLCS" 2463405 NIL PLCS (NIL T T) -8 NIL NIL) (-922 2461814 2462548 2462619 "PLACESPS" 2462624 NIL PLACESPS (NIL T) -8 NIL NIL) (-921 2461021 2461727 2461784 "PLACES" 2461789 NIL PLACES (NIL T) -8 NIL NIL) (-920 2457745 2458409 2458468 "PLACESC" 2460386 NIL PLACESC (NIL T T) -9 NIL 2460957) (-919 2457063 2457185 2457365 "PINTERP" 2457610 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-918 2456756 2456803 2456906 "PINTERPA" 2457010 NIL PINTERPA (NIL T T) -7 NIL NIL) (-917 2455983 2456550 2456643 "PI" 2456683 T PI (NIL) -8 NIL NIL) (-916 2454370 2455355 2455384 "PID" 2455566 T PID (NIL) -9 NIL 2455700) (-915 2454095 2454132 2454220 "PICOERCE" 2454327 NIL PICOERCE (NIL T) -7 NIL NIL) (-914 2453416 2453554 2453730 "PGROEB" 2453951 NIL PGROEB (NIL T) -7 NIL NIL) (-913 2449003 2449817 2450722 "PGE" 2452531 T PGE (NIL) -7 NIL NIL) (-912 2447127 2447373 2447739 "PGCD" 2448720 NIL PGCD (NIL T T T T) -7 NIL NIL) (-911 2446465 2446568 2446729 "PFRPAC" 2447011 NIL PFRPAC (NIL T) -7 NIL NIL) (-910 2443080 2445013 2445366 "PFR" 2446144 NIL PFR (NIL T) -8 NIL NIL) (-909 2441469 2441713 2442038 "PFOTOOLS" 2442827 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-908 2436334 2436999 2437748 "PFORP" 2440811 NIL PFORP (NIL T T T NIL) -7 NIL NIL) (-907 2434867 2435106 2435457 "PFOQ" 2436091 NIL PFOQ (NIL T T T) -7 NIL NIL) (-906 2433340 2433552 2433915 "PFO" 2434651 NIL PFO (NIL T T T T T) -7 NIL NIL) (-905 2429863 2433229 2433298 "PF" 2433303 NIL PF (NIL NIL) -8 NIL NIL) (-904 2427288 2428569 2428598 "PFECAT" 2429183 T PFECAT (NIL) -9 NIL 2429566) (-903 2426733 2426887 2427101 "PFECAT-" 2427106 NIL PFECAT- (NIL T) -8 NIL NIL) (-902 2425337 2425588 2425889 "PFBRU" 2426482 NIL PFBRU (NIL T T) -7 NIL NIL) (-901 2423204 2423555 2423987 "PFBR" 2424988 NIL PFBR (NIL T T T T) -7 NIL NIL) (-900 2419060 2420584 2421258 "PERM" 2422563 NIL PERM (NIL T) -8 NIL NIL) (-899 2414327 2415267 2416137 "PERMGRP" 2418223 NIL PERMGRP (NIL T) -8 NIL NIL) (-898 2412398 2413391 2413433 "PERMCAT" 2413879 NIL PERMCAT (NIL T) -9 NIL 2414182) (-897 2412051 2412092 2412216 "PERMAN" 2412351 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-896 2409497 2411620 2411751 "PENDTREE" 2411953 NIL PENDTREE (NIL T) -8 NIL NIL) (-895 2407565 2408343 2408385 "PDRING" 2409042 NIL PDRING (NIL T) -9 NIL 2409328) (-894 2406668 2406886 2407248 "PDRING-" 2407253 NIL PDRING- (NIL T T) -8 NIL NIL) (-893 2403810 2404560 2405251 "PDEPROB" 2405997 T PDEPROB (NIL) -8 NIL NIL) (-892 2401357 2401859 2402414 "PDEPACK" 2403275 T PDEPACK (NIL) -7 NIL NIL) (-891 2400269 2400459 2400710 "PDECOMP" 2401156 NIL PDECOMP (NIL T T) -7 NIL NIL) (-890 2397873 2398690 2398719 "PDECAT" 2399506 T PDECAT (NIL) -9 NIL 2400219) (-889 2397624 2397657 2397747 "PCOMP" 2397834 NIL PCOMP (NIL T T) -7 NIL NIL) (-888 2395829 2396425 2396722 "PBWLB" 2397353 NIL PBWLB (NIL T) -8 NIL NIL) (-887 2388334 2389902 2391240 "PATTERN" 2394512 NIL PATTERN (NIL T) -8 NIL NIL) (-886 2387966 2388023 2388132 "PATTERN2" 2388271 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-885 2385723 2386111 2386568 "PATTERN1" 2387555 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-884 2383118 2383672 2384153 "PATRES" 2385288 NIL PATRES (NIL T T) -8 NIL NIL) (-883 2382682 2382749 2382881 "PATRES2" 2383045 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-882 2380565 2380970 2381377 "PATMATCH" 2382349 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-881 2380100 2380283 2380325 "PATMAB" 2380432 NIL PATMAB (NIL T) -9 NIL 2380515) (-880 2378645 2378954 2379212 "PATLRES" 2379905 NIL PATLRES (NIL T T T) -8 NIL NIL) (-879 2378192 2378315 2378357 "PATAB" 2378362 NIL PATAB (NIL T) -9 NIL 2378532) (-878 2375673 2376205 2376778 "PARTPERM" 2377639 T PARTPERM (NIL) -7 NIL NIL) (-877 2375294 2375357 2375459 "PARSURF" 2375604 NIL PARSURF (NIL T) -8 NIL NIL) (-876 2374926 2374983 2375092 "PARSU2" 2375231 NIL PARSU2 (NIL T T) -7 NIL NIL) (-875 2374547 2374610 2374712 "PARSCURV" 2374857 NIL PARSCURV (NIL T) -8 NIL NIL) (-874 2374179 2374236 2374345 "PARSC2" 2374484 NIL PARSC2 (NIL T T) -7 NIL NIL) (-873 2373818 2373876 2373973 "PARPCURV" 2374115 NIL PARPCURV (NIL T) -8 NIL NIL) (-872 2373450 2373507 2373616 "PARPC2" 2373755 NIL PARPC2 (NIL T T) -7 NIL NIL) (-871 2371930 2372048 2372367 "PARAMP" 2373305 NIL PARAMP (NIL T NIL T T T T T) -7 NIL NIL) (-870 2371450 2371536 2371655 "PAN2EXPR" 2371831 T PAN2EXPR (NIL) -7 NIL NIL) (-869 2370256 2370571 2370799 "PALETTE" 2371242 T PALETTE (NIL) -8 NIL NIL) (-868 2357889 2360055 2362171 "PAFF" 2368204 NIL PAFF (NIL T NIL T) -7 NIL NIL) (-867 2344885 2347213 2349424 "PAFFFF" 2355742 NIL PAFFFF (NIL T NIL T) -7 NIL NIL) (-866 2338726 2344144 2344338 "PADICRC" 2344740 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-865 2331925 2338072 2338256 "PADICRAT" 2338574 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-864 2330229 2331862 2331907 "PADIC" 2331912 NIL PADIC (NIL NIL) -8 NIL NIL) (-863 2327429 2329003 2329044 "PADICCT" 2329625 NIL PADICCT (NIL NIL) -9 NIL 2329907) (-862 2326386 2326586 2326854 "PADEPAC" 2327216 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-861 2325598 2325731 2325937 "PADE" 2326248 NIL PADE (NIL T T T) -7 NIL NIL) (-860 2322075 2325216 2325335 "PACRAT" 2325499 T PACRAT (NIL) -8 NIL NIL) (-859 2318136 2321186 2321215 "PACRATC" 2321220 T PACRATC (NIL) -9 NIL 2321300) (-858 2314258 2316223 2316252 "PACPERC" 2317198 T PACPERC (NIL) -9 NIL 2317638) (-857 2310928 2314032 2314123 "PACOFF" 2314199 NIL PACOFF (NIL T) -8 NIL NIL) (-856 2307623 2310283 2310312 "PACFFC" 2310317 T PACFFC (NIL) -9 NIL 2310338) (-855 2303713 2307306 2307407 "PACEXT" 2307554 NIL PACEXT (NIL NIL) -8 NIL NIL) (-854 2299091 2302608 2302637 "PACEXTC" 2302642 T PACEXTC (NIL) -9 NIL 2302686) (-853 2297099 2297931 2298246 "OWP" 2298860 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-852 2296208 2296704 2296876 "OVAR" 2296967 NIL OVAR (NIL NIL) -8 NIL NIL) (-851 2295472 2295593 2295754 "OUT" 2296067 T OUT (NIL) -7 NIL NIL) (-850 2284518 2286697 2288867 "OUTFORM" 2293322 T OUTFORM (NIL) -8 NIL NIL) (-849 2283926 2284247 2284336 "OSI" 2284449 T OSI (NIL) -8 NIL NIL) (-848 2282673 2282900 2283184 "ORTHPOL" 2283674 NIL ORTHPOL (NIL T) -7 NIL NIL) (-847 2280035 2282330 2282470 "OREUP" 2282616 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-846 2277422 2279724 2279852 "ORESUP" 2279977 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-845 2274930 2275436 2276001 "OREPCTO" 2276907 NIL OREPCTO (NIL T T) -7 NIL NIL) (-844 2268800 2271011 2271053 "OREPCAT" 2273401 NIL OREPCAT (NIL T) -9 NIL 2274501) (-843 2265947 2266729 2267787 "OREPCAT-" 2267792 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-842 2265123 2265395 2265424 "ORDSET" 2265733 T ORDSET (NIL) -9 NIL 2265897) (-841 2264642 2264764 2264957 "ORDSET-" 2264962 NIL ORDSET- (NIL T) -8 NIL NIL) (-840 2263251 2264052 2264081 "ORDRING" 2264283 T ORDRING (NIL) -9 NIL 2264408) (-839 2262896 2262990 2263134 "ORDRING-" 2263139 NIL ORDRING- (NIL T) -8 NIL NIL) (-838 2262270 2262751 2262780 "ORDMON" 2262785 T ORDMON (NIL) -9 NIL 2262806) (-837 2261432 2261579 2261774 "ORDFUNS" 2262119 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-836 2260942 2261301 2261330 "ORDFIN" 2261335 T ORDFIN (NIL) -9 NIL 2261356) (-835 2257454 2259534 2259940 "ORDCOMP" 2260569 NIL ORDCOMP (NIL T) -8 NIL NIL) (-834 2256720 2256847 2257033 "ORDCOMP2" 2257314 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-833 2253228 2254110 2254947 "OPTPROB" 2255903 T OPTPROB (NIL) -8 NIL NIL) (-832 2250030 2250669 2251373 "OPTPACK" 2252544 T OPTPACK (NIL) -7 NIL NIL) (-831 2247742 2248482 2248511 "OPTCAT" 2249330 T OPTCAT (NIL) -9 NIL 2249980) (-830 2247510 2247549 2247615 "OPQUERY" 2247696 T OPQUERY (NIL) -7 NIL NIL) (-829 2244636 2245827 2246328 "OP" 2247042 NIL OP (NIL T) -8 NIL NIL) (-828 2241401 2243439 2243805 "ONECOMP" 2244303 NIL ONECOMP (NIL T) -8 NIL NIL) (-827 2240706 2240821 2240995 "ONECOMP2" 2241273 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-826 2240125 2240231 2240361 "OMSERVER" 2240596 T OMSERVER (NIL) -7 NIL NIL) (-825 2237012 2239564 2239605 "OMSAGG" 2239666 NIL OMSAGG (NIL T) -9 NIL 2239730) (-824 2235635 2235898 2236180 "OMPKG" 2236750 T OMPKG (NIL) -7 NIL NIL) (-823 2235064 2235167 2235196 "OM" 2235495 T OM (NIL) -9 NIL NIL) (-822 2233602 2234615 2234783 "OMLO" 2234946 NIL OMLO (NIL T T) -8 NIL NIL) (-821 2232527 2232674 2232901 "OMEXPR" 2233428 NIL OMEXPR (NIL T) -7 NIL NIL) (-820 2231845 2232073 2232209 "OMERR" 2232411 T OMERR (NIL) -8 NIL NIL) (-819 2231023 2231266 2231426 "OMERRK" 2231705 T OMERRK (NIL) -8 NIL NIL) (-818 2230501 2230700 2230808 "OMENC" 2230935 T OMENC (NIL) -8 NIL NIL) (-817 2224396 2225581 2226752 "OMDEV" 2229350 T OMDEV (NIL) -8 NIL NIL) (-816 2223465 2223636 2223830 "OMCONN" 2224222 T OMCONN (NIL) -8 NIL NIL) (-815 2222076 2223062 2223091 "OINTDOM" 2223096 T OINTDOM (NIL) -9 NIL 2223117) (-814 2217727 2218982 2219726 "OFMONOID" 2221364 NIL OFMONOID (NIL T) -8 NIL NIL) (-813 2217165 2217664 2217709 "ODVAR" 2217714 NIL ODVAR (NIL T) -8 NIL NIL) (-812 2214292 2216664 2216848 "ODR" 2217041 NIL ODR (NIL T T NIL) -8 NIL NIL) (-811 2206590 2214068 2214194 "ODPOL" 2214199 NIL ODPOL (NIL T) -8 NIL NIL) (-810 2200384 2206462 2206567 "ODP" 2206572 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-809 2199150 2199365 2199640 "ODETOOLS" 2200158 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-808 2196119 2196775 2197491 "ODESYS" 2198483 NIL ODESYS (NIL T T) -7 NIL NIL) (-807 2191003 2191911 2192935 "ODERTRIC" 2195195 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-806 2190429 2190511 2190705 "ODERED" 2190915 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-805 2187317 2187865 2188542 "ODERAT" 2189852 NIL ODERAT (NIL T T) -7 NIL NIL) (-804 2184277 2184741 2185338 "ODEPRRIC" 2186846 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-803 2182148 2182715 2183224 "ODEPROB" 2183788 T ODEPROB (NIL) -8 NIL NIL) (-802 2178670 2179153 2179800 "ODEPRIM" 2181627 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-801 2177919 2178021 2178281 "ODEPAL" 2178562 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-800 2174081 2174872 2175736 "ODEPACK" 2177075 T ODEPACK (NIL) -7 NIL NIL) (-799 2173114 2173221 2173450 "ODEINT" 2173970 NIL ODEINT (NIL T T) -7 NIL NIL) (-798 2167215 2168640 2170087 "ODEIFTBL" 2171687 T ODEIFTBL (NIL) -8 NIL NIL) (-797 2162550 2163336 2164295 "ODEEF" 2166374 NIL ODEEF (NIL T T) -7 NIL NIL) (-796 2161885 2161974 2162204 "ODECONST" 2162455 NIL ODECONST (NIL T T T) -7 NIL NIL) (-795 2160035 2160670 2160699 "ODECAT" 2161304 T ODECAT (NIL) -9 NIL 2161835) (-794 2156896 2159747 2159866 "OCT" 2159948 NIL OCT (NIL T) -8 NIL NIL) (-793 2156534 2156577 2156704 "OCTCT2" 2156847 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-792 2151358 2153802 2153843 "OC" 2154940 NIL OC (NIL T) -9 NIL 2155790) (-791 2148585 2149333 2150323 "OC-" 2150417 NIL OC- (NIL T T) -8 NIL NIL) (-790 2147962 2148404 2148433 "OCAMON" 2148438 T OCAMON (NIL) -9 NIL 2148459) (-789 2147414 2147821 2147850 "OASGP" 2147855 T OASGP (NIL) -9 NIL 2147875) (-788 2146700 2147163 2147192 "OAMONS" 2147232 T OAMONS (NIL) -9 NIL 2147275) (-787 2146139 2146546 2146575 "OAMON" 2146580 T OAMON (NIL) -9 NIL 2146600) (-786 2145442 2145934 2145963 "OAGROUP" 2145968 T OAGROUP (NIL) -9 NIL 2145988) (-785 2145132 2145182 2145270 "NUMTUBE" 2145386 NIL NUMTUBE (NIL T) -7 NIL NIL) (-784 2138705 2140223 2141759 "NUMQUAD" 2143616 T NUMQUAD (NIL) -7 NIL NIL) (-783 2134461 2135449 2136474 "NUMODE" 2137700 T NUMODE (NIL) -7 NIL NIL) (-782 2131841 2132695 2132724 "NUMINT" 2133647 T NUMINT (NIL) -9 NIL 2134411) (-781 2130789 2130986 2131204 "NUMFMT" 2131643 T NUMFMT (NIL) -7 NIL NIL) (-780 2117167 2120109 2122633 "NUMERIC" 2128304 NIL NUMERIC (NIL T) -7 NIL NIL) (-779 2111570 2116615 2116711 "NTSCAT" 2116716 NIL NTSCAT (NIL T T T T) -9 NIL 2116755) (-778 2110766 2110931 2111123 "NTPOLFN" 2111410 NIL NTPOLFN (NIL T) -7 NIL NIL) (-777 2098562 2107593 2108404 "NSUP" 2109988 NIL NSUP (NIL T) -8 NIL NIL) (-776 2098194 2098251 2098360 "NSUP2" 2098499 NIL NSUP2 (NIL T T) -7 NIL NIL) (-775 2088145 2097968 2098101 "NSMP" 2098106 NIL NSMP (NIL T T) -8 NIL NIL) (-774 2076237 2087727 2087891 "NSDPS" 2088013 NIL NSDPS (NIL T) -8 NIL NIL) (-773 2074669 2074970 2075327 "NREP" 2075925 NIL NREP (NIL T) -7 NIL NIL) (-772 2071758 2072306 2072955 "NPOLYGON" 2074111 NIL NPOLYGON (NIL T T T NIL) -7 NIL NIL) (-771 2070349 2070601 2070959 "NPCOEF" 2071501 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-770 2069631 2070133 2070217 "NOTTING" 2070297 NIL NOTTING (NIL T) -8 NIL NIL) (-769 2068697 2068812 2069028 "NORMRETR" 2069512 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-768 2066738 2067028 2067437 "NORMPK" 2068405 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-767 2066423 2066451 2066575 "NORMMA" 2066704 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-766 2066250 2066380 2066409 "NONE" 2066414 T NONE (NIL) -8 NIL NIL) (-765 2066039 2066068 2066137 "NONE1" 2066214 NIL NONE1 (NIL T) -7 NIL NIL) (-764 2065522 2065584 2065770 "NODE1" 2065971 NIL NODE1 (NIL T T) -7 NIL NIL) (-763 2063816 2064685 2064940 "NNI" 2065287 T NNI (NIL) -8 NIL NIL) (-762 2062236 2062549 2062913 "NLINSOL" 2063484 NIL NLINSOL (NIL T) -7 NIL NIL) (-761 2058404 2059371 2060293 "NIPROB" 2061334 T NIPROB (NIL) -8 NIL NIL) (-760 2057161 2057395 2057697 "NFINTBAS" 2058166 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-759 2056890 2056933 2057014 "NEWTON" 2057112 NIL NEWTON (NIL T) -7 NIL NIL) (-758 2055598 2055829 2056110 "NCODIV" 2056658 NIL NCODIV (NIL T T) -7 NIL NIL) (-757 2055360 2055397 2055472 "NCNTFRAC" 2055555 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-756 2053540 2053904 2054324 "NCEP" 2054985 NIL NCEP (NIL T) -7 NIL NIL) (-755 2052450 2053189 2053218 "NASRING" 2053328 T NASRING (NIL) -9 NIL 2053402) (-754 2052245 2052289 2052383 "NASRING-" 2052388 NIL NASRING- (NIL T) -8 NIL NIL) (-753 2051397 2051896 2051925 "NARNG" 2052042 T NARNG (NIL) -9 NIL 2052133) (-752 2051089 2051156 2051290 "NARNG-" 2051295 NIL NARNG- (NIL T) -8 NIL NIL) (-751 2049968 2050175 2050410 "NAGSP" 2050874 T NAGSP (NIL) -7 NIL NIL) (-750 2041240 2042924 2044597 "NAGS" 2048315 T NAGS (NIL) -7 NIL NIL) (-749 2039788 2040096 2040427 "NAGF07" 2040929 T NAGF07 (NIL) -7 NIL NIL) (-748 2034326 2035617 2036924 "NAGF04" 2038501 T NAGF04 (NIL) -7 NIL NIL) (-747 2027294 2028908 2030541 "NAGF02" 2032713 T NAGF02 (NIL) -7 NIL NIL) (-746 2022518 2023618 2024735 "NAGF01" 2026197 T NAGF01 (NIL) -7 NIL NIL) (-745 2016146 2017712 2019297 "NAGE04" 2020953 T NAGE04 (NIL) -7 NIL NIL) (-744 2007315 2009436 2011566 "NAGE02" 2014036 T NAGE02 (NIL) -7 NIL NIL) (-743 2003268 2004215 2005179 "NAGE01" 2006371 T NAGE01 (NIL) -7 NIL NIL) (-742 2001063 2001597 2002155 "NAGD03" 2002730 T NAGD03 (NIL) -7 NIL NIL) (-741 1992813 1994741 1996695 "NAGD02" 1999129 T NAGD02 (NIL) -7 NIL NIL) (-740 1986624 1988049 1989489 "NAGD01" 1991393 T NAGD01 (NIL) -7 NIL NIL) (-739 1982833 1983655 1984492 "NAGC06" 1985807 T NAGC06 (NIL) -7 NIL NIL) (-738 1981298 1981630 1981986 "NAGC05" 1982497 T NAGC05 (NIL) -7 NIL NIL) (-737 1980674 1980793 1980937 "NAGC02" 1981174 T NAGC02 (NIL) -7 NIL NIL) (-736 1979733 1980290 1980331 "NAALG" 1980410 NIL NAALG (NIL T) -9 NIL 1980471) (-735 1979568 1979597 1979687 "NAALG-" 1979692 NIL NAALG- (NIL T T) -8 NIL NIL) (-734 1970444 1978684 1978959 "MYUP" 1979339 NIL MYUP (NIL NIL T) -8 NIL NIL) (-733 1960807 1968900 1969271 "MYEXPR" 1970139 NIL MYEXPR (NIL NIL T) -8 NIL NIL) (-732 1954757 1955865 1957052 "MULTSQFR" 1959703 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-731 1954076 1954151 1954335 "MULTFACT" 1954669 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-730 1947201 1951110 1951164 "MTSCAT" 1952234 NIL MTSCAT (NIL T T) -9 NIL 1952748) (-729 1946913 1946967 1947059 "MTHING" 1947141 NIL MTHING (NIL T) -7 NIL NIL) (-728 1946705 1946738 1946798 "MSYSCMD" 1946873 T MSYSCMD (NIL) -7 NIL NIL) (-727 1942817 1945460 1945780 "MSET" 1946418 NIL MSET (NIL T) -8 NIL NIL) (-726 1939911 1942377 1942419 "MSETAGG" 1942424 NIL MSETAGG (NIL T) -9 NIL 1942458) (-725 1935760 1937302 1938041 "MRING" 1939217 NIL MRING (NIL T T) -8 NIL NIL) (-724 1935326 1935393 1935524 "MRF2" 1935687 NIL MRF2 (NIL T T T) -7 NIL NIL) (-723 1934944 1934979 1935123 "MRATFAC" 1935285 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-722 1932556 1932851 1933282 "MPRFF" 1934649 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-721 1926570 1932410 1932507 "MPOLY" 1932512 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-720 1926060 1926095 1926303 "MPCPF" 1926529 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-719 1925574 1925617 1925801 "MPC3" 1926011 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-718 1924769 1924850 1925071 "MPC2" 1925489 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-717 1923070 1923407 1923797 "MONOTOOL" 1924429 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-716 1922193 1922528 1922557 "MONOID" 1922834 T MONOID (NIL) -9 NIL 1923006) (-715 1921571 1921734 1921977 "MONOID-" 1921982 NIL MONOID- (NIL T) -8 NIL NIL) (-714 1912497 1918482 1918542 "MONOGEN" 1919216 NIL MONOGEN (NIL T T) -9 NIL 1919669) (-713 1909715 1910450 1911450 "MONOGEN-" 1911569 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-712 1908573 1908993 1909022 "MONADWU" 1909414 T MONADWU (NIL) -9 NIL 1909652) (-711 1907945 1908104 1908352 "MONADWU-" 1908357 NIL MONADWU- (NIL T) -8 NIL NIL) (-710 1907329 1907547 1907576 "MONAD" 1907783 T MONAD (NIL) -9 NIL 1907895) (-709 1907014 1907092 1907224 "MONAD-" 1907229 NIL MONAD- (NIL T) -8 NIL NIL) (-708 1905265 1905927 1906206 "MOEBIUS" 1906767 NIL MOEBIUS (NIL T) -8 NIL NIL) (-707 1904656 1905034 1905075 "MODULE" 1905080 NIL MODULE (NIL T) -9 NIL 1905106) (-706 1904224 1904320 1904510 "MODULE-" 1904515 NIL MODULE- (NIL T T) -8 NIL NIL) (-705 1901893 1902588 1902915 "MODRING" 1904048 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-704 1898839 1900004 1900522 "MODOP" 1901425 NIL MODOP (NIL T T) -8 NIL NIL) (-703 1897026 1897478 1897819 "MODMONOM" 1898638 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-702 1886691 1895222 1895643 "MODMON" 1896656 NIL MODMON (NIL T T) -8 NIL NIL) (-701 1883817 1885535 1885811 "MODFIELD" 1886566 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-700 1882821 1883098 1883288 "MMLFORM" 1883647 T MMLFORM (NIL) -8 NIL NIL) (-699 1882347 1882390 1882569 "MMAP" 1882772 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-698 1880572 1881349 1881391 "MLO" 1881814 NIL MLO (NIL T) -9 NIL 1882055) (-697 1877939 1878454 1879056 "MLIFT" 1880053 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-696 1877330 1877414 1877568 "MKUCFUNC" 1877850 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-695 1876929 1876999 1877122 "MKRECORD" 1877253 NIL MKRECORD (NIL T T) -7 NIL NIL) (-694 1875977 1876138 1876366 "MKFUNC" 1876740 NIL MKFUNC (NIL T) -7 NIL NIL) (-693 1875365 1875469 1875625 "MKFLCFN" 1875860 NIL MKFLCFN (NIL T) -7 NIL NIL) (-692 1874791 1875158 1875247 "MKCHSET" 1875309 NIL MKCHSET (NIL T) -8 NIL NIL) (-691 1874068 1874170 1874355 "MKBCFUNC" 1874684 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-690 1870752 1873622 1873758 "MINT" 1873952 T MINT (NIL) -8 NIL NIL) (-689 1869564 1869807 1870084 "MHROWRED" 1870507 NIL MHROWRED (NIL T) -7 NIL NIL) (-688 1864831 1868005 1868431 "MFLOAT" 1869158 T MFLOAT (NIL) -8 NIL NIL) (-687 1864188 1864264 1864435 "MFINFACT" 1864743 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-686 1860503 1861351 1862235 "MESH" 1863324 T MESH (NIL) -7 NIL NIL) (-685 1858893 1859205 1859558 "MDDFACT" 1860190 NIL MDDFACT (NIL T) -7 NIL NIL) (-684 1855775 1858086 1858128 "MDAGG" 1858383 NIL MDAGG (NIL T) -9 NIL 1858526) (-683 1845463 1855068 1855275 "MCMPLX" 1855588 T MCMPLX (NIL) -8 NIL NIL) (-682 1844604 1844750 1844950 "MCDEN" 1845312 NIL MCDEN (NIL T T) -7 NIL NIL) (-681 1842494 1842764 1843144 "MCALCFN" 1844334 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-680 1840106 1840629 1841191 "MATSTOR" 1841965 NIL MATSTOR (NIL T) -7 NIL NIL) (-679 1836020 1839482 1839728 "MATRIX" 1839893 NIL MATRIX (NIL T) -8 NIL NIL) (-678 1831796 1832499 1833232 "MATLIN" 1835380 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-677 1821561 1824782 1824860 "MATCAT" 1829990 NIL MATCAT (NIL T T T) -9 NIL 1831497) (-676 1817760 1818828 1820239 "MATCAT-" 1820244 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-675 1816354 1816507 1816840 "MATCAT2" 1817595 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-674 1815094 1815360 1815675 "MAPPKG4" 1816085 NIL MAPPKG4 (NIL T T) -7 NIL NIL) (-673 1813206 1813530 1813914 "MAPPKG3" 1814769 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-672 1812187 1812360 1812582 "MAPPKG2" 1813030 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-671 1810686 1810970 1811297 "MAPPKG1" 1811893 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-670 1810297 1810355 1810478 "MAPHACK3" 1810622 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-669 1809889 1809950 1810064 "MAPHACK2" 1810229 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-668 1809327 1809430 1809572 "MAPHACK1" 1809780 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-667 1807433 1808027 1808331 "MAGMA" 1809055 NIL MAGMA (NIL T) -8 NIL NIL) (-666 1803908 1805674 1806134 "M3D" 1807006 NIL M3D (NIL T) -8 NIL NIL) (-665 1798102 1802308 1802350 "LZSTAGG" 1803132 NIL LZSTAGG (NIL T) -9 NIL 1803427) (-664 1794076 1795233 1796690 "LZSTAGG-" 1796695 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-663 1791190 1791967 1792454 "LWORD" 1793621 NIL LWORD (NIL T) -8 NIL NIL) (-662 1784345 1790961 1791095 "LSQM" 1791100 NIL LSQM (NIL NIL T) -8 NIL NIL) (-661 1783569 1783708 1783936 "LSPP" 1784200 NIL LSPP (NIL T T T T) -7 NIL NIL) (-660 1781381 1781682 1782138 "LSMP" 1783258 NIL LSMP (NIL T T T T) -7 NIL NIL) (-659 1778160 1778834 1779564 "LSMP1" 1780683 NIL LSMP1 (NIL T) -7 NIL NIL) (-658 1772117 1777350 1777392 "LSAGG" 1777454 NIL LSAGG (NIL T) -9 NIL 1777532) (-657 1768812 1769736 1770949 "LSAGG-" 1770954 NIL LSAGG- (NIL T T) -8 NIL NIL) (-656 1766438 1767956 1768205 "LPOLY" 1768607 NIL LPOLY (NIL T T) -8 NIL NIL) (-655 1766020 1766105 1766228 "LPEFRAC" 1766347 NIL LPEFRAC (NIL T) -7 NIL NIL) (-654 1763584 1763833 1764265 "LPARSPT" 1765762 NIL LPARSPT (NIL T NIL T T T T T) -7 NIL NIL) (-653 1762059 1762386 1762746 "LOP" 1763256 NIL LOP (NIL T) -7 NIL NIL) (-652 1760408 1761155 1761407 "LO" 1761892 NIL LO (NIL T T T) -8 NIL NIL) (-651 1760059 1760171 1760200 "LOGIC" 1760311 T LOGIC (NIL) -9 NIL 1760392) (-650 1759921 1759944 1760015 "LOGIC-" 1760020 NIL LOGIC- (NIL T) -8 NIL NIL) (-649 1759114 1759254 1759447 "LODOOPS" 1759777 NIL LODOOPS (NIL T T) -7 NIL NIL) (-648 1756526 1759030 1759096 "LODO" 1759101 NIL LODO (NIL T NIL) -8 NIL NIL) (-647 1755066 1755301 1755653 "LODOF" 1756274 NIL LODOF (NIL T T) -7 NIL NIL) (-646 1751465 1753906 1753948 "LODOCAT" 1754386 NIL LODOCAT (NIL T) -9 NIL 1754596) (-645 1751198 1751256 1751383 "LODOCAT-" 1751388 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-644 1748507 1751039 1751157 "LODO2" 1751162 NIL LODO2 (NIL T T) -8 NIL NIL) (-643 1745931 1748444 1748489 "LODO1" 1748494 NIL LODO1 (NIL T) -8 NIL NIL) (-642 1744791 1744956 1745268 "LODEEF" 1745754 NIL LODEEF (NIL T T T) -7 NIL NIL) (-641 1737618 1741783 1741824 "LOCPOWC" 1743286 NIL LOCPOWC (NIL T) -9 NIL 1743863) (-640 1732942 1735780 1735822 "LNAGG" 1736769 NIL LNAGG (NIL T) -9 NIL 1737212) (-639 1732089 1732303 1732645 "LNAGG-" 1732650 NIL LNAGG- (NIL T T) -8 NIL NIL) (-638 1728252 1729014 1729653 "LMOPS" 1731504 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-637 1727646 1728008 1728050 "LMODULE" 1728111 NIL LMODULE (NIL T) -9 NIL 1728153) (-636 1724898 1727291 1727414 "LMDICT" 1727556 NIL LMDICT (NIL T) -8 NIL NIL) (-635 1724055 1724189 1724376 "LISYSER" 1724760 NIL LISYSER (NIL T T) -7 NIL NIL) (-634 1717292 1723005 1723301 "LIST" 1723792 NIL LIST (NIL T) -8 NIL NIL) (-633 1716817 1716891 1717030 "LIST3" 1717212 NIL LIST3 (NIL T T T) -7 NIL NIL) (-632 1715824 1716002 1716230 "LIST2" 1716635 NIL LIST2 (NIL T T) -7 NIL NIL) (-631 1713958 1714270 1714669 "LIST2MAP" 1715471 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-630 1712663 1713343 1713385 "LINEXP" 1713640 NIL LINEXP (NIL T) -9 NIL 1713789) (-629 1711310 1711570 1711867 "LINDEP" 1712415 NIL LINDEP (NIL T T) -7 NIL NIL) (-628 1708077 1708796 1709573 "LIMITRF" 1710565 NIL LIMITRF (NIL T) -7 NIL NIL) (-627 1706354 1706648 1707064 "LIMITPS" 1707772 NIL LIMITPS (NIL T T) -7 NIL NIL) (-626 1700813 1705869 1706095 "LIE" 1706177 NIL LIE (NIL T T) -8 NIL NIL) (-625 1699862 1700305 1700346 "LIECAT" 1700486 NIL LIECAT (NIL T) -9 NIL 1700636) (-624 1699703 1699730 1699818 "LIECAT-" 1699823 NIL LIECAT- (NIL T T) -8 NIL NIL) (-623 1692237 1699082 1699265 "LIB" 1699540 T LIB (NIL) -8 NIL NIL) (-622 1687874 1688755 1689690 "LGROBP" 1691354 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-621 1685729 1686003 1686366 "LF" 1687595 NIL LF (NIL T T) -7 NIL NIL) (-620 1684568 1685260 1685289 "LFCAT" 1685496 T LFCAT (NIL) -9 NIL 1685635) (-619 1681472 1682100 1682788 "LEXTRIPK" 1683932 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-618 1678178 1679042 1679545 "LEXP" 1681052 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-617 1676576 1676889 1677290 "LEADCDET" 1677860 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-616 1675766 1675840 1676069 "LAZM3PK" 1676497 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-615 1670682 1673849 1674384 "LAUPOL" 1675281 NIL LAUPOL (NIL T T) -8 NIL NIL) (-614 1670247 1670291 1670459 "LAPLACE" 1670632 NIL LAPLACE (NIL T T) -7 NIL NIL) (-613 1668177 1669350 1669600 "LA" 1670081 NIL LA (NIL T T T) -8 NIL NIL) (-612 1667233 1667827 1667869 "LALG" 1667931 NIL LALG (NIL T) -9 NIL 1667990) (-611 1666947 1667006 1667142 "LALG-" 1667147 NIL LALG- (NIL T T) -8 NIL NIL) (-610 1665851 1666038 1666337 "KOVACIC" 1666747 NIL KOVACIC (NIL T T) -7 NIL NIL) (-609 1665685 1665709 1665751 "KONVERT" 1665813 NIL KONVERT (NIL T) -9 NIL NIL) (-608 1665519 1665543 1665585 "KOERCE" 1665647 NIL KOERCE (NIL T) -9 NIL NIL) (-607 1663255 1664015 1664407 "KERNEL" 1665159 NIL KERNEL (NIL T) -8 NIL NIL) (-606 1662757 1662838 1662968 "KERNEL2" 1663169 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-605 1656440 1661122 1661177 "KDAGG" 1661554 NIL KDAGG (NIL T T) -9 NIL 1661760) (-604 1655969 1656093 1656298 "KDAGG-" 1656303 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-603 1649118 1655630 1655785 "KAFILE" 1655847 NIL KAFILE (NIL T) -8 NIL NIL) (-602 1643577 1648633 1648859 "JORDAN" 1648941 NIL JORDAN (NIL T T) -8 NIL NIL) (-601 1639920 1641820 1641875 "IXAGG" 1642804 NIL IXAGG (NIL T T) -9 NIL 1643259) (-600 1638839 1639145 1639564 "IXAGG-" 1639569 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-599 1634423 1638761 1638820 "IVECTOR" 1638825 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-598 1633189 1633426 1633692 "ITUPLE" 1634190 NIL ITUPLE (NIL T) -8 NIL NIL) (-597 1631613 1631790 1632098 "ITRIGMNP" 1633011 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-596 1630358 1630562 1630845 "ITFUN3" 1631389 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-595 1629990 1630047 1630156 "ITFUN2" 1630295 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-594 1627783 1628854 1629152 "ITAYLOR" 1629725 NIL ITAYLOR (NIL T) -8 NIL NIL) (-593 1616722 1621922 1623084 "ISUPS" 1626654 NIL ISUPS (NIL T) -8 NIL NIL) (-592 1615826 1615966 1616202 "ISUMP" 1616569 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-591 1611096 1615627 1615706 "ISTRING" 1615779 NIL ISTRING (NIL NIL) -8 NIL NIL) (-590 1610306 1610387 1610603 "IRURPK" 1611010 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-589 1609242 1609443 1609683 "IRSN" 1610086 T IRSN (NIL) -7 NIL NIL) (-588 1607273 1607628 1608063 "IRRF2F" 1608881 NIL IRRF2F (NIL T) -7 NIL NIL) (-587 1607020 1607058 1607134 "IRREDFFX" 1607229 NIL IRREDFFX (NIL T) -7 NIL NIL) (-586 1605635 1605894 1606193 "IROOT" 1606753 NIL IROOT (NIL T) -7 NIL NIL) (-585 1602271 1603323 1604013 "IR" 1604977 NIL IR (NIL T) -8 NIL NIL) (-584 1599884 1600379 1600945 "IR2" 1601749 NIL IR2 (NIL T T) -7 NIL NIL) (-583 1598956 1599069 1599290 "IR2F" 1599767 NIL IR2F (NIL T T) -7 NIL NIL) (-582 1598747 1598781 1598841 "IPRNTPK" 1598916 T IPRNTPK (NIL) -7 NIL NIL) (-581 1595301 1598636 1598705 "IPF" 1598710 NIL IPF (NIL NIL) -8 NIL NIL) (-580 1593618 1595226 1595283 "IPADIC" 1595288 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-579 1593115 1593173 1593363 "INVLAPLA" 1593554 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-578 1582764 1585117 1587503 "INTTR" 1590779 NIL INTTR (NIL T T) -7 NIL NIL) (-577 1579122 1579864 1580721 "INTTOOLS" 1581956 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-576 1578708 1578799 1578916 "INTSLPE" 1579025 T INTSLPE (NIL) -7 NIL NIL) (-575 1576658 1578631 1578690 "INTRVL" 1578695 NIL INTRVL (NIL T) -8 NIL NIL) (-574 1574260 1574772 1575347 "INTRF" 1576143 NIL INTRF (NIL T) -7 NIL NIL) (-573 1573671 1573768 1573910 "INTRET" 1574158 NIL INTRET (NIL T) -7 NIL NIL) (-572 1571668 1572057 1572527 "INTRAT" 1573279 NIL INTRAT (NIL T T) -7 NIL NIL) (-571 1568904 1569487 1570109 "INTPM" 1571157 NIL INTPM (NIL T T) -7 NIL NIL) (-570 1565609 1566208 1566952 "INTPAF" 1568291 NIL INTPAF (NIL T T T) -7 NIL NIL) (-569 1560788 1561750 1562801 "INTPACK" 1564578 T INTPACK (NIL) -7 NIL NIL) (-568 1557642 1560517 1560644 "INT" 1560681 T INT (NIL) -8 NIL NIL) (-567 1556894 1557046 1557254 "INTHERTR" 1557484 NIL INTHERTR (NIL T T) -7 NIL NIL) (-566 1556333 1556413 1556601 "INTHERAL" 1556808 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-565 1554179 1554622 1555079 "INTHEORY" 1555896 T INTHEORY (NIL) -7 NIL NIL) (-564 1545490 1547110 1548888 "INTG0" 1552532 NIL INTG0 (NIL T T T) -7 NIL NIL) (-563 1526063 1530853 1535663 "INTFTBL" 1540700 T INTFTBL (NIL) -8 NIL NIL) (-562 1524100 1524307 1524708 "INTFRSP" 1525853 NIL INTFRSP (NIL T NIL T T T T T T) -7 NIL NIL) (-561 1523349 1523487 1523660 "INTFACT" 1523959 NIL INTFACT (NIL T) -7 NIL NIL) (-560 1522939 1522981 1523132 "INTERGB" 1523301 NIL INTERGB (NIL T NIL T T T) -7 NIL NIL) (-559 1520324 1520770 1521334 "INTEF" 1522493 NIL INTEF (NIL T T) -7 NIL NIL) (-558 1518781 1519530 1519559 "INTDOM" 1519860 T INTDOM (NIL) -9 NIL 1520067) (-557 1518150 1518324 1518566 "INTDOM-" 1518571 NIL INTDOM- (NIL T) -8 NIL NIL) (-556 1516754 1516859 1517249 "INTDIVP" 1518040 NIL INTDIVP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-555 1513240 1515170 1515225 "INTCAT" 1516024 NIL INTCAT (NIL T) -9 NIL 1516345) (-554 1512713 1512815 1512943 "INTBIT" 1513132 T INTBIT (NIL) -7 NIL NIL) (-553 1511384 1511538 1511852 "INTALG" 1512558 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-552 1510841 1510931 1511101 "INTAF" 1511288 NIL INTAF (NIL T T) -7 NIL NIL) (-551 1504307 1510651 1510791 "INTABL" 1510796 NIL INTABL (NIL T T T) -8 NIL NIL) (-550 1499252 1501978 1502007 "INS" 1502975 T INS (NIL) -9 NIL 1503658) (-549 1496492 1497263 1498237 "INS-" 1498310 NIL INS- (NIL T) -8 NIL NIL) (-548 1495267 1495494 1495792 "INPSIGN" 1496245 NIL INPSIGN (NIL T T) -7 NIL NIL) (-547 1494385 1494502 1494699 "INPRODPF" 1495147 NIL INPRODPF (NIL T T) -7 NIL NIL) (-546 1493279 1493396 1493633 "INPRODFF" 1494265 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-545 1492279 1492431 1492691 "INNMFACT" 1493115 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-544 1491476 1491573 1491761 "INMODGCD" 1492178 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-543 1489985 1490229 1490553 "INFSP" 1491221 NIL INFSP (NIL T T T) -7 NIL NIL) (-542 1489169 1489286 1489469 "INFPROD0" 1489865 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-541 1486050 1487234 1487749 "INFORM" 1488662 T INFORM (NIL) -8 NIL NIL) (-540 1485660 1485720 1485818 "INFORM1" 1485985 NIL INFORM1 (NIL T) -7 NIL NIL) (-539 1485183 1485272 1485386 "INFINITY" 1485566 T INFINITY (NIL) -7 NIL NIL) (-538 1482866 1483863 1484206 "INFCLSPT" 1485043 NIL INFCLSPT (NIL T NIL T T T T T T T) -8 NIL NIL) (-537 1480743 1481988 1482282 "INFCLSPS" 1482636 NIL INFCLSPS (NIL T NIL T) -8 NIL NIL) (-536 1473293 1474216 1474437 "INFCLCT" 1479868 NIL INFCLCT (NIL T NIL T T T T T T T) -9 NIL 1480679) (-535 1471911 1472159 1472480 "INEP" 1473041 NIL INEP (NIL T T T) -7 NIL NIL) (-534 1471187 1471808 1471873 "INDE" 1471878 NIL INDE (NIL T) -8 NIL NIL) (-533 1470751 1470819 1470936 "INCRMAPS" 1471114 NIL INCRMAPS (NIL T) -7 NIL NIL) (-532 1466062 1466987 1467931 "INBFF" 1469839 NIL INBFF (NIL T) -7 NIL NIL) (-531 1462457 1465906 1466010 "IMATRIX" 1466015 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-530 1461171 1461294 1461608 "IMATQF" 1462314 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-529 1459393 1459620 1459956 "IMATLIN" 1460928 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-528 1454025 1459317 1459375 "ILIST" 1459380 NIL ILIST (NIL T NIL) -8 NIL NIL) (-527 1451984 1453885 1453998 "IIARRAY2" 1454003 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-526 1447352 1451895 1451959 "IFF" 1451964 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-525 1442401 1446644 1446832 "IFARRAY" 1447209 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-524 1441608 1442305 1442378 "IFAMON" 1442383 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-523 1441191 1441256 1441311 "IEVALAB" 1441518 NIL IEVALAB (NIL T T) -9 NIL NIL) (-522 1440866 1440934 1441094 "IEVALAB-" 1441099 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-521 1440524 1440780 1440843 "IDPO" 1440848 NIL IDPO (NIL T T) -8 NIL NIL) (-520 1439801 1440413 1440488 "IDPOAMS" 1440493 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-519 1439135 1439690 1439765 "IDPOAM" 1439770 NIL IDPOAM (NIL T T) -8 NIL NIL) (-518 1438219 1438469 1438523 "IDPC" 1438936 NIL IDPC (NIL T T) -9 NIL 1439085) (-517 1437715 1438111 1438184 "IDPAM" 1438189 NIL IDPAM (NIL T T) -8 NIL NIL) (-516 1437118 1437607 1437680 "IDPAG" 1437685 NIL IDPAG (NIL T T) -8 NIL NIL) (-515 1433373 1434221 1435116 "IDECOMP" 1436275 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-514 1426249 1427298 1428344 "IDEAL" 1432410 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-513 1424266 1425413 1425686 "ICP" 1426040 NIL ICP (NIL T NIL T) -8 NIL NIL) (-512 1423430 1423542 1423741 "ICDEN" 1424150 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-511 1422529 1422910 1423057 "ICARD" 1423303 T ICARD (NIL) -8 NIL NIL) (-510 1420589 1420902 1421307 "IBPTOOLS" 1422206 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-509 1416203 1420209 1420322 "IBITS" 1420508 NIL IBITS (NIL NIL) -8 NIL NIL) (-508 1412926 1413502 1414197 "IBATOOL" 1415620 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-507 1410706 1411167 1411700 "IBACHIN" 1412461 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-506 1408589 1410552 1410655 "IARRAY2" 1410660 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-505 1404748 1408515 1408572 "IARRAY1" 1408577 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-504 1398678 1403160 1403641 "IAN" 1404287 T IAN (NIL) -8 NIL NIL) (-503 1398189 1398246 1398419 "IALGFACT" 1398615 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-502 1397716 1397829 1397858 "HYPCAT" 1398065 T HYPCAT (NIL) -9 NIL NIL) (-501 1397254 1397371 1397557 "HYPCAT-" 1397562 NIL HYPCAT- (NIL T) -8 NIL NIL) (-500 1396258 1396535 1396725 "HTMLFORM" 1397084 T HTMLFORM (NIL) -8 NIL NIL) (-499 1393047 1394372 1394414 "HOAGG" 1395395 NIL HOAGG (NIL T) -9 NIL 1396004) (-498 1391641 1392040 1392566 "HOAGG-" 1392571 NIL HOAGG- (NIL T T) -8 NIL NIL) (-497 1385459 1391079 1391246 "HEXADEC" 1391494 T HEXADEC (NIL) -8 NIL NIL) (-496 1384207 1384429 1384692 "HEUGCD" 1385236 NIL HEUGCD (NIL T) -7 NIL NIL) (-495 1383310 1384044 1384174 "HELLFDIV" 1384179 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-494 1377027 1378570 1379651 "HEAP" 1382261 NIL HEAP (NIL T) -8 NIL NIL) (-493 1370865 1376942 1377004 "HDP" 1377009 NIL HDP (NIL NIL T) -8 NIL NIL) (-492 1364570 1370500 1370652 "HDMP" 1370766 NIL HDMP (NIL NIL T) -8 NIL NIL) (-491 1363895 1364034 1364198 "HB" 1364426 T HB (NIL) -7 NIL NIL) (-490 1357404 1363741 1363845 "HASHTBL" 1363850 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-489 1355151 1357026 1357208 "HACKPI" 1357242 T HACKPI (NIL) -8 NIL NIL) (-488 1337299 1341168 1345171 "GUESSUP" 1351181 NIL GUESSUP (NIL NIL) -7 NIL NIL) (-487 1308396 1315437 1322133 "GUESSP" 1330623 T GUESSP (NIL) -7 NIL NIL) (-486 1275211 1280482 1285866 "GUESS" 1303340 NIL GUESS (NIL T T T T NIL NIL) -7 NIL NIL) (-485 1248716 1255113 1261249 "GUESSINT" 1269095 T GUESSINT (NIL) -7 NIL NIL) (-484 1224087 1229537 1235104 "GUESSF" 1243201 NIL GUESSF (NIL T) -7 NIL NIL) (-483 1223809 1223846 1223941 "GUESSF1" 1224044 NIL GUESSF1 (NIL T) -7 NIL NIL) (-482 1199970 1205504 1211119 "GUESSAN" 1218214 T GUESSAN (NIL) -7 NIL NIL) (-481 1195665 1199823 1199936 "GTSET" 1199941 NIL GTSET (NIL T T T T) -8 NIL NIL) (-480 1189203 1195543 1195641 "GSTBL" 1195646 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-479 1181433 1188236 1188500 "GSERIES" 1188995 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-478 1180454 1180907 1180936 "GROUP" 1181197 T GROUP (NIL) -9 NIL 1181356) (-477 1179570 1179793 1180137 "GROUP-" 1180142 NIL GROUP- (NIL T) -8 NIL NIL) (-476 1177939 1178258 1178645 "GROEBSOL" 1179247 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-475 1176878 1177140 1177192 "GRMOD" 1177721 NIL GRMOD (NIL T T) -9 NIL 1177889) (-474 1176646 1176682 1176810 "GRMOD-" 1176815 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-473 1171975 1173000 1174000 "GRIMAGE" 1175666 T GRIMAGE (NIL) -8 NIL NIL) (-472 1170442 1170702 1171026 "GRDEF" 1171671 T GRDEF (NIL) -7 NIL NIL) (-471 1169886 1170002 1170143 "GRAY" 1170321 T GRAY (NIL) -7 NIL NIL) (-470 1169116 1169496 1169548 "GRALG" 1169701 NIL GRALG (NIL T T) -9 NIL 1169794) (-469 1168777 1168850 1169013 "GRALG-" 1169018 NIL GRALG- (NIL T T T) -8 NIL NIL) (-468 1165581 1168362 1168540 "GPOLSET" 1168684 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-467 1147784 1149274 1150863 "GPAFF" 1164272 NIL GPAFF (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-466 1147138 1147195 1147453 "GOSPER" 1147721 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-465 1144531 1145125 1145614 "GOPT" 1146669 T GOPT (NIL) -8 NIL NIL) (-464 1141752 1142393 1142930 "GOPT0" 1144014 T GOPT0 (NIL) -8 NIL NIL) (-463 1137511 1138190 1138716 "GMODPOL" 1141451 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-462 1136516 1136700 1136938 "GHENSEL" 1137323 NIL GHENSEL (NIL T T) -7 NIL NIL) (-461 1130567 1131410 1132437 "GENUPS" 1135600 NIL GENUPS (NIL T T) -7 NIL NIL) (-460 1130264 1130315 1130404 "GENUFACT" 1130510 NIL GENUFACT (NIL T) -7 NIL NIL) (-459 1129676 1129753 1129918 "GENPGCD" 1130182 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-458 1129150 1129185 1129398 "GENMFACT" 1129635 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-457 1127718 1127973 1128280 "GENEEZ" 1128893 NIL GENEEZ (NIL T T) -7 NIL NIL) (-456 1126262 1126539 1126863 "GDRAW" 1127414 T GDRAW (NIL) -7 NIL NIL) (-455 1120129 1125873 1126035 "GDMP" 1126185 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-454 1109513 1113902 1115007 "GCNAALG" 1119113 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-453 1107930 1108802 1108831 "GCDDOM" 1109086 T GCDDOM (NIL) -9 NIL 1109243) (-452 1107400 1107527 1107742 "GCDDOM-" 1107747 NIL GCDDOM- (NIL T) -8 NIL NIL) (-451 1106074 1106259 1106562 "GB" 1107180 NIL GB (NIL T T T T) -7 NIL NIL) (-450 1094694 1097020 1099412 "GBINTERN" 1103765 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-449 1092531 1092823 1093244 "GBF" 1094369 NIL GBF (NIL T T T T) -7 NIL NIL) (-448 1091312 1091477 1091744 "GBEUCLID" 1092347 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-447 1090661 1090786 1090935 "GAUSSFAC" 1091183 T GAUSSFAC (NIL) -7 NIL NIL) (-446 1089030 1089332 1089645 "GALUTIL" 1090381 NIL GALUTIL (NIL T) -7 NIL NIL) (-445 1087338 1087612 1087936 "GALPOLYU" 1088757 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-444 1084703 1084993 1085400 "GALFACTU" 1087035 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-443 1076509 1078008 1079616 "GALFACT" 1083135 NIL GALFACT (NIL T) -7 NIL NIL) (-442 1073897 1074554 1074583 "FVFUN" 1075739 T FVFUN (NIL) -9 NIL 1076459) (-441 1073163 1073344 1073373 "FVC" 1073664 T FVC (NIL) -9 NIL 1073847) (-440 1072805 1072960 1073041 "FUNCTION" 1073115 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-439 1070475 1071026 1071515 "FT" 1072336 T FT (NIL) -8 NIL NIL) (-438 1069267 1069776 1069979 "FTEM" 1070292 T FTEM (NIL) -8 NIL NIL) (-437 1067525 1067814 1068217 "FSUPFACT" 1068959 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-436 1065922 1066211 1066543 "FST" 1067213 T FST (NIL) -8 NIL NIL) (-435 1065093 1065199 1065394 "FSRED" 1065804 NIL FSRED (NIL T T) -7 NIL NIL) (-434 1063774 1064029 1064382 "FSPRMELT" 1064809 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-433 1059140 1059845 1060602 "FSPECF" 1063079 NIL FSPECF (NIL T T) -7 NIL NIL) (-432 1041398 1049987 1050028 "FS" 1053876 NIL FS (NIL T) -9 NIL 1056154) (-431 1030048 1033038 1037094 "FS-" 1037391 NIL FS- (NIL T T) -8 NIL NIL) (-430 1029562 1029616 1029793 "FSINT" 1029989 NIL FSINT (NIL T T) -7 NIL NIL) (-429 1027847 1028559 1028860 "FSERIES" 1029343 NIL FSERIES (NIL T T) -8 NIL NIL) (-428 1026861 1026977 1027208 "FSCINT" 1027727 NIL FSCINT (NIL T T) -7 NIL NIL) (-427 1023096 1025806 1025848 "FSAGG" 1026218 NIL FSAGG (NIL T) -9 NIL 1026475) (-426 1020858 1021459 1022255 "FSAGG-" 1022350 NIL FSAGG- (NIL T T) -8 NIL NIL) (-425 1019900 1020043 1020270 "FSAGG2" 1020711 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-424 1017555 1017834 1018388 "FS2UPS" 1019618 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-423 1017137 1017180 1017335 "FS2" 1017506 NIL FS2 (NIL T T T T) -7 NIL NIL) (-422 1015994 1016165 1016474 "FS2EXPXP" 1016962 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-421 1015420 1015535 1015687 "FRUTIL" 1015874 NIL FRUTIL (NIL T) -7 NIL NIL) (-420 1006846 1010931 1012281 "FR" 1014102 NIL FR (NIL T) -8 NIL NIL) (-419 1001926 1004564 1004605 "FRNAALG" 1006001 NIL FRNAALG (NIL T) -9 NIL 1006607) (-418 997605 998675 999950 "FRNAALG-" 1000700 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-417 997243 997286 997413 "FRNAAF2" 997556 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-416 995606 996099 996393 "FRMOD" 997056 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-415 993321 993989 994306 "FRIDEAL" 995397 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-414 992516 992603 992892 "FRIDEAL2" 993228 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-413 991759 992173 992215 "FRETRCT" 992220 NIL FRETRCT (NIL T) -9 NIL 992394) (-412 990871 991102 991453 "FRETRCT-" 991458 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-411 988076 989296 989356 "FRAMALG" 990238 NIL FRAMALG (NIL T T) -9 NIL 990530) (-410 986209 986665 987295 "FRAMALG-" 987518 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-409 980112 985694 985965 "FRAC" 985970 NIL FRAC (NIL T) -8 NIL NIL) (-408 979748 979805 979912 "FRAC2" 980049 NIL FRAC2 (NIL T T) -7 NIL NIL) (-407 979384 979441 979548 "FR2" 979685 NIL FR2 (NIL T T) -7 NIL NIL) (-406 974006 976915 976944 "FPS" 978063 T FPS (NIL) -9 NIL 978617) (-405 973455 973564 973728 "FPS-" 973874 NIL FPS- (NIL T) -8 NIL NIL) (-404 970851 972548 972577 "FPC" 972802 T FPC (NIL) -9 NIL 972944) (-403 970644 970684 970781 "FPC-" 970786 NIL FPC- (NIL T) -8 NIL NIL) (-402 969523 970133 970175 "FPATMAB" 970180 NIL FPATMAB (NIL T) -9 NIL 970330) (-401 967223 967699 968125 "FPARFRAC" 969160 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-400 962618 963115 963797 "FORTRAN" 966655 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-399 960334 960834 961373 "FORT" 962099 T FORT (NIL) -7 NIL NIL) (-398 958010 958571 958600 "FORTFN" 959660 T FORTFN (NIL) -9 NIL 960284) (-397 957773 957823 957852 "FORTCAT" 957911 T FORTCAT (NIL) -9 NIL 957973) (-396 955833 956316 956715 "FORMULA" 957394 T FORMULA (NIL) -8 NIL NIL) (-395 955621 955651 955720 "FORMULA1" 955797 NIL FORMULA1 (NIL T) -7 NIL NIL) (-394 955144 955196 955369 "FORDER" 955563 NIL FORDER (NIL T T T T) -7 NIL NIL) (-393 954240 954404 954597 "FOP" 954971 T FOP (NIL) -7 NIL NIL) (-392 952848 953520 953694 "FNLA" 954122 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-391 951515 951904 951933 "FNCAT" 952505 T FNCAT (NIL) -9 NIL 952798) (-390 951081 951474 951502 "FNAME" 951507 T FNAME (NIL) -8 NIL NIL) (-389 949734 950707 950736 "FMTC" 950741 T FMTC (NIL) -9 NIL 950777) (-388 946052 947259 947887 "FMONOID" 949139 NIL FMONOID (NIL T) -8 NIL NIL) (-387 945273 945796 945944 "FM" 945949 NIL FM (NIL T T) -8 NIL NIL) (-386 942697 943342 943371 "FMFUN" 944515 T FMFUN (NIL) -9 NIL 945223) (-385 941966 942146 942175 "FMC" 942465 T FMC (NIL) -9 NIL 942647) (-384 939178 940012 940067 "FMCAT" 941262 NIL FMCAT (NIL T T) -9 NIL 941756) (-383 938071 938944 939044 "FM1" 939123 NIL FM1 (NIL T T) -8 NIL NIL) (-382 935845 936261 936755 "FLOATRP" 937622 NIL FLOATRP (NIL T) -7 NIL NIL) (-381 929332 933501 934131 "FLOAT" 935235 T FLOAT (NIL) -8 NIL NIL) (-380 926770 927270 927848 "FLOATCP" 928799 NIL FLOATCP (NIL T) -7 NIL NIL) (-379 925555 926403 926445 "FLINEXP" 926450 NIL FLINEXP (NIL T) -9 NIL 926542) (-378 924709 924944 925272 "FLINEXP-" 925277 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-377 923785 923929 924153 "FLASORT" 924561 NIL FLASORT (NIL T T) -7 NIL NIL) (-376 921001 921843 921896 "FLALG" 923123 NIL FLALG (NIL T T) -9 NIL 923590) (-375 914820 918514 918556 "FLAGG" 919818 NIL FLAGG (NIL T) -9 NIL 920466) (-374 913546 913885 914375 "FLAGG-" 914380 NIL FLAGG- (NIL T T) -8 NIL NIL) (-373 912588 912731 912958 "FLAGG2" 913399 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-372 909559 910577 910637 "FINRALG" 911765 NIL FINRALG (NIL T T) -9 NIL 912270) (-371 908719 908948 909287 "FINRALG-" 909292 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-370 908124 908337 908366 "FINITE" 908562 T FINITE (NIL) -9 NIL 908669) (-369 900582 902743 902784 "FINAALG" 906451 NIL FINAALG (NIL T) -9 NIL 907903) (-368 895922 896964 898108 "FINAALG-" 899487 NIL FINAALG- (NIL T T) -8 NIL NIL) (-367 895292 895677 895780 "FILE" 895852 NIL FILE (NIL T) -8 NIL NIL) (-366 893832 894169 894224 "FILECAT" 895002 NIL FILECAT (NIL T T) -9 NIL 895242) (-365 891642 893198 893227 "FIELD" 893267 T FIELD (NIL) -9 NIL 893347) (-364 890262 890647 891158 "FIELD-" 891163 NIL FIELD- (NIL T) -8 NIL NIL) (-363 888075 888897 889244 "FGROUP" 889948 NIL FGROUP (NIL T) -8 NIL NIL) (-362 887165 887329 887549 "FGLMICPK" 887907 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-361 882967 887090 887147 "FFX" 887152 NIL FFX (NIL T NIL) -8 NIL NIL) (-360 882507 882574 882696 "FFSQFR" 882895 NIL FFSQFR (NIL T T) -7 NIL NIL) (-359 882108 882169 882304 "FFSLPE" 882440 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-358 878104 878880 879676 "FFPOLY" 881344 NIL FFPOLY (NIL T) -7 NIL NIL) (-357 877608 877644 877853 "FFPOLY2" 878062 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-356 873430 877527 877590 "FFP" 877595 NIL FFP (NIL T NIL) -8 NIL NIL) (-355 868798 873341 873405 "FF" 873410 NIL FF (NIL NIL NIL) -8 NIL NIL) (-354 863894 868141 868331 "FFNBX" 868652 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-353 858804 863029 863287 "FFNBP" 863748 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-352 853407 858088 858299 "FFNB" 858637 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-351 852239 852437 852752 "FFINTBAS" 853204 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-350 848415 850650 850679 "FFIELDC" 851299 T FFIELDC (NIL) -9 NIL 851675) (-349 847078 847448 847945 "FFIELDC-" 847950 NIL FFIELDC- (NIL T) -8 NIL NIL) (-348 846648 846693 846817 "FFHOM" 847020 NIL FFHOM (NIL T T T) -7 NIL NIL) (-347 844346 844830 845347 "FFF" 846163 NIL FFF (NIL T) -7 NIL NIL) (-346 840042 840807 841651 "FFFG" 843570 NIL FFFG (NIL T T) -7 NIL NIL) (-345 838768 838977 839299 "FFFGF" 839820 NIL FFFGF (NIL T T T) -7 NIL NIL) (-344 837519 837716 837964 "FFFACTSE" 838570 NIL FFFACTSE (NIL T T) -7 NIL NIL) (-343 833107 837261 837362 "FFCGX" 837462 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-342 828709 832839 832946 "FFCGP" 833050 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-341 823862 828436 828544 "FFCG" 828645 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-340 805651 814773 814860 "FFCAT" 820025 NIL FFCAT (NIL T T T) -9 NIL 821510) (-339 800849 801896 803210 "FFCAT-" 804440 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-338 800260 800303 800538 "FFCAT2" 800800 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-337 789430 793236 794454 "FEXPR" 799114 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-336 788432 788867 788909 "FEVALAB" 788993 NIL FEVALAB (NIL T) -9 NIL 789251) (-335 787591 787801 788139 "FEVALAB-" 788144 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-334 786184 786974 787177 "FDIV" 787490 NIL FDIV (NIL T T T T) -8 NIL NIL) (-333 783249 783964 784080 "FDIVCAT" 785648 NIL FDIVCAT (NIL T T T T) -9 NIL 786085) (-332 783011 783038 783208 "FDIVCAT-" 783213 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-331 782231 782318 782595 "FDIV2" 782918 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-330 780917 781176 781465 "FCPAK1" 781962 T FCPAK1 (NIL) -7 NIL NIL) (-329 780045 780417 780558 "FCOMP" 780808 NIL FCOMP (NIL T) -8 NIL NIL) (-328 763673 767088 770651 "FC" 776502 T FC (NIL) -8 NIL NIL) (-327 756217 760260 760301 "FAXF" 762103 NIL FAXF (NIL T) -9 NIL 762794) (-326 753497 754151 754976 "FAXF-" 755441 NIL FAXF- (NIL T T) -8 NIL NIL) (-325 748603 752873 753049 "FARRAY" 753354 NIL FARRAY (NIL T) -8 NIL NIL) (-324 743921 745997 746051 "FAMR" 747074 NIL FAMR (NIL T T) -9 NIL 747531) (-323 742811 743113 743548 "FAMR-" 743553 NIL FAMR- (NIL T T T) -8 NIL NIL) (-322 742399 742442 742593 "FAMR2" 742762 NIL FAMR2 (NIL T T T T T) -7 NIL NIL) (-321 741595 742321 742374 "FAMONOID" 742379 NIL FAMONOID (NIL T) -8 NIL NIL) (-320 739425 740109 740163 "FAMONC" 741104 NIL FAMONC (NIL T T) -9 NIL 741489) (-319 738119 739181 739317 "FAGROUP" 739322 NIL FAGROUP (NIL T) -8 NIL NIL) (-318 735914 736233 736636 "FACUTIL" 737800 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-317 735330 735439 735585 "FACTRN" 735800 NIL FACTRN (NIL T) -7 NIL NIL) (-316 734429 734614 734836 "FACTFUNC" 735140 NIL FACTFUNC (NIL T) -7 NIL NIL) (-315 733845 733954 734100 "FACTEXT" 734315 NIL FACTEXT (NIL T) -7 NIL NIL) (-314 726165 733096 733308 "EXPUPXS" 733701 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-313 723648 724188 724774 "EXPRTUBE" 725599 T EXPRTUBE (NIL) -7 NIL NIL) (-312 722819 722914 723134 "EXPRSOL" 723548 NIL EXPRSOL (NIL T T T T) -7 NIL NIL) (-311 719013 719605 720342 "EXPRODE" 722158 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 704114 717674 718099 "EXPR" 718620 NIL EXPR (NIL T) -8 NIL NIL) (-309 698521 699108 699921 "EXPR2UPS" 703412 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 698157 698214 698321 "EXPR2" 698458 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 689497 697289 697586 "EXPEXPAN" 697994 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 689209 689260 689337 "EXP3D" 689440 T EXP3D (NIL) -7 NIL NIL) (-305 689036 689166 689195 "EXIT" 689200 T EXIT (NIL) -8 NIL NIL) (-304 688663 688725 688838 "EVALCYC" 688968 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 688205 688321 688363 "EVALAB" 688533 NIL EVALAB (NIL T) -9 NIL 688637) (-302 687686 687808 688029 "EVALAB-" 688034 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 685144 686456 686485 "EUCDOM" 687040 T EUCDOM (NIL) -9 NIL 687390) (-300 683549 683991 684581 "EUCDOM-" 684586 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 671089 673847 676597 "ESTOOLS" 680819 T ESTOOLS (NIL) -7 NIL NIL) (-298 670721 670778 670887 "ESTOOLS2" 671026 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 670472 670514 670594 "ESTOOLS1" 670673 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 664398 666126 666155 "ES" 668923 T ES (NIL) -9 NIL 670330) (-295 659346 660632 662449 "ES-" 662613 NIL ES- (NIL T) -8 NIL NIL) (-294 655721 656481 657261 "ESCONT" 658586 T ESCONT (NIL) -7 NIL NIL) (-293 655466 655498 655580 "ESCONT1" 655683 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 655141 655191 655291 "ES2" 655410 NIL ES2 (NIL T T) -7 NIL NIL) (-291 654771 654829 654938 "ES1" 655077 NIL ES1 (NIL T T) -7 NIL NIL) (-290 653987 654116 654292 "ERROR" 654615 T ERROR (NIL) -7 NIL NIL) (-289 647502 653846 653937 "EQTBL" 653942 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 639961 642844 644279 "EQ" 646100 NIL -2993 (NIL T) -8 NIL NIL) (-287 639593 639650 639759 "EQ2" 639898 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 634885 635931 637024 "EP" 638532 NIL EP (NIL T) -7 NIL NIL) (-285 634039 634603 634632 "ENTIRER" 634637 T ENTIRER (NIL) -9 NIL 634683) (-284 630495 631994 632364 "EMR" 633838 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-283 629641 629824 629879 "ELTAGG" 630259 NIL ELTAGG (NIL T T) -9 NIL 630469) (-282 629360 629422 629563 "ELTAGG-" 629568 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-281 629148 629177 629232 "ELTAB" 629316 NIL ELTAB (NIL T T) -9 NIL NIL) (-280 628274 628420 628619 "ELFUTS" 628999 NIL ELFUTS (NIL T T) -7 NIL NIL) (-279 628015 628071 628100 "ELEMFUN" 628205 T ELEMFUN (NIL) -9 NIL NIL) (-278 627885 627906 627974 "ELEMFUN-" 627979 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-277 622815 626018 626060 "ELAGG" 627000 NIL ELAGG (NIL T) -9 NIL 627461) (-276 621100 621534 622197 "ELAGG-" 622202 NIL ELAGG- (NIL T T) -8 NIL NIL) (-275 613970 615769 616595 "EFUPXS" 620377 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-274 607422 609223 610032 "EFULS" 613247 NIL EFULS (NIL T T T) -8 NIL NIL) (-273 604844 605202 605681 "EFSTRUC" 607054 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-272 593856 595421 596982 "EF" 603359 NIL EF (NIL T T) -7 NIL NIL) (-271 592957 593341 593490 "EAB" 593727 T EAB (NIL) -8 NIL NIL) (-270 592166 592916 592944 "E04UCFA" 592949 T E04UCFA (NIL) -8 NIL NIL) (-269 591375 592125 592153 "E04NAFA" 592158 T E04NAFA (NIL) -8 NIL NIL) (-268 590584 591334 591362 "E04MBFA" 591367 T E04MBFA (NIL) -8 NIL NIL) (-267 589793 590543 590571 "E04JAFA" 590576 T E04JAFA (NIL) -8 NIL NIL) (-266 589004 589752 589780 "E04GCFA" 589785 T E04GCFA (NIL) -8 NIL NIL) (-265 588215 588963 588991 "E04FDFA" 588996 T E04FDFA (NIL) -8 NIL NIL) (-264 587424 588174 588202 "E04DGFA" 588207 T E04DGFA (NIL) -8 NIL NIL) (-263 581603 582949 584313 "E04AGNT" 586080 T E04AGNT (NIL) -7 NIL NIL) (-262 580326 580806 580847 "DVARCAT" 581322 NIL DVARCAT (NIL T) -9 NIL 581521) (-261 579530 579742 580056 "DVARCAT-" 580061 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-260 572499 572981 573730 "DTP" 579061 NIL DTP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-259 569948 571921 572078 "DSTREE" 572375 NIL DSTREE (NIL T) -8 NIL NIL) (-258 567417 569262 569304 "DSTRCAT" 569523 NIL DSTRCAT (NIL T) -9 NIL 569657) (-257 560271 567216 567345 "DSMP" 567350 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 555081 556216 557284 "DROPT" 559223 T DROPT (NIL) -8 NIL NIL) (-255 554746 554805 554903 "DROPT1" 555016 NIL DROPT1 (NIL T) -7 NIL NIL) (-254 549861 550987 552124 "DROPT0" 553629 T DROPT0 (NIL) -7 NIL NIL) (-253 548206 548531 548917 "DRAWPT" 549495 T DRAWPT (NIL) -7 NIL NIL) (-252 542793 543716 544795 "DRAW" 547180 NIL DRAW (NIL T) -7 NIL NIL) (-251 542426 542479 542597 "DRAWHACK" 542734 NIL DRAWHACK (NIL T) -7 NIL NIL) (-250 541157 541426 541717 "DRAWCX" 542155 T DRAWCX (NIL) -7 NIL NIL) (-249 540673 540741 540892 "DRAWCURV" 541083 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-248 531145 533103 535218 "DRAWCFUN" 538578 T DRAWCFUN (NIL) -7 NIL NIL) (-247 527998 529874 529916 "DQAGG" 530545 NIL DQAGG (NIL T) -9 NIL 530818) (-246 516426 523167 523251 "DPOLCAT" 525103 NIL DPOLCAT (NIL T T T T) -9 NIL 525647) (-245 511265 512611 514569 "DPOLCAT-" 514574 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 504004 511126 511224 "DPMO" 511229 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 496646 503784 503951 "DPMM" 503956 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 490351 496281 496433 "DMP" 496547 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 489951 490007 490151 "DLP" 490289 NIL DLP (NIL T) -7 NIL NIL) (-240 483601 489052 489279 "DLIST" 489756 NIL DLIST (NIL T) -8 NIL NIL) (-239 480486 482489 482531 "DLAGG" 483081 NIL DLAGG (NIL T) -9 NIL 483310) (-238 479143 479835 479864 "DIVRING" 480014 T DIVRING (NIL) -9 NIL 480122) (-237 478131 478384 478777 "DIVRING-" 478782 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 476559 477724 477860 "DIV" 478028 NIL DIV (NIL T) -8 NIL NIL) (-235 474053 475121 475163 "DIVCAT" 475997 NIL DIVCAT (NIL T) -9 NIL 476328) (-234 472155 472512 472918 "DISPLAY" 473667 T DISPLAY (NIL) -7 NIL NIL) (-233 469648 470861 471243 "DIRRING" 471806 NIL DIRRING (NIL T) -8 NIL NIL) (-232 463508 469562 469625 "DIRPROD" 469630 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 462356 462559 462824 "DIRPROD2" 463301 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 451920 457949 458003 "DIRPCAT" 458261 NIL DIRPCAT (NIL NIL T) -9 NIL 459105) (-229 449246 449888 450769 "DIRPCAT-" 451106 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 448533 448693 448879 "DIOSP" 449080 T DIOSP (NIL) -7 NIL NIL) (-227 445276 447480 447522 "DIOPS" 447956 NIL DIOPS (NIL T) -9 NIL 448184) (-226 444825 444939 445130 "DIOPS-" 445135 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 443692 444330 444359 "DIFRING" 444546 T DIFRING (NIL) -9 NIL 444656) (-224 443338 443415 443567 "DIFRING-" 443572 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 441120 442402 442444 "DIFEXT" 442807 NIL DIFEXT (NIL T) -9 NIL 443099) (-222 439405 439833 440499 "DIFEXT-" 440504 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 436767 438971 439013 "DIAGG" 439018 NIL DIAGG (NIL T) -9 NIL 439038) (-220 436151 436308 436560 "DIAGG-" 436565 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 431521 435110 435387 "DHMATRIX" 435920 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 426732 431335 431409 "DFVEC" 431467 T DFVEC (NIL) -8 NIL NIL) (-217 420616 421905 423286 "DFSFUN" 425371 T DFSFUN (NIL) -7 NIL NIL) (-216 416877 420387 420481 "DFMAT" 420542 T DFMAT (NIL) -8 NIL NIL) (-215 411154 415331 415764 "DFLOAT" 416464 T DFLOAT (NIL) -8 NIL NIL) (-214 409382 409663 410059 "DFINTTLS" 410862 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-213 406401 407403 407803 "DERHAM" 409048 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-212 398014 399931 401366 "DEQUEUE" 404999 NIL DEQUEUE (NIL T) -8 NIL NIL) (-211 397229 397362 397558 "DEGRED" 397876 NIL DEGRED (NIL T T) -7 NIL NIL) (-210 393624 394369 395222 "DEFINTRF" 396457 NIL DEFINTRF (NIL T) -7 NIL NIL) (-209 391151 391620 392219 "DEFINTEF" 393143 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-208 384969 390589 390756 "DECIMAL" 391004 T DECIMAL (NIL) -8 NIL NIL) (-207 382481 382939 383445 "DDFACT" 384513 NIL DDFACT (NIL T T) -7 NIL NIL) (-206 382077 382120 382271 "DBLRESP" 382432 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-205 379787 380121 380490 "DBASE" 381835 NIL DBASE (NIL T) -8 NIL NIL) (-204 378920 379746 379774 "D03FAFA" 379779 T D03FAFA (NIL) -8 NIL NIL) (-203 378054 378879 378907 "D03EEFA" 378912 T D03EEFA (NIL) -8 NIL NIL) (-202 376004 376470 376959 "D03AGNT" 377585 T D03AGNT (NIL) -7 NIL NIL) (-201 375320 375963 375991 "D02EJFA" 375996 T D02EJFA (NIL) -8 NIL NIL) (-200 374636 375279 375307 "D02CJFA" 375312 T D02CJFA (NIL) -8 NIL NIL) (-199 373952 374595 374623 "D02BHFA" 374628 T D02BHFA (NIL) -8 NIL NIL) (-198 373268 373911 373939 "D02BBFA" 373944 T D02BBFA (NIL) -8 NIL NIL) (-197 366467 368054 369660 "D02AGNT" 371682 T D02AGNT (NIL) -7 NIL NIL) (-196 364236 364758 365304 "D01WGTS" 365941 T D01WGTS (NIL) -7 NIL NIL) (-195 363331 364195 364223 "D01TRNS" 364228 T D01TRNS (NIL) -8 NIL NIL) (-194 362426 363290 363318 "D01GBFA" 363323 T D01GBFA (NIL) -8 NIL NIL) (-193 361521 362385 362413 "D01FCFA" 362418 T D01FCFA (NIL) -8 NIL NIL) (-192 360616 361480 361508 "D01ASFA" 361513 T D01ASFA (NIL) -8 NIL NIL) (-191 359711 360575 360603 "D01AQFA" 360608 T D01AQFA (NIL) -8 NIL NIL) (-190 358806 359670 359698 "D01APFA" 359703 T D01APFA (NIL) -8 NIL NIL) (-189 357901 358765 358793 "D01ANFA" 358798 T D01ANFA (NIL) -8 NIL NIL) (-188 356996 357860 357888 "D01AMFA" 357893 T D01AMFA (NIL) -8 NIL NIL) (-187 356091 356955 356983 "D01ALFA" 356988 T D01ALFA (NIL) -8 NIL NIL) (-186 355186 356050 356078 "D01AKFA" 356083 T D01AKFA (NIL) -8 NIL NIL) (-185 354281 355145 355173 "D01AJFA" 355178 T D01AJFA (NIL) -8 NIL NIL) (-184 347578 349129 350690 "D01AGNT" 352740 T D01AGNT (NIL) -7 NIL NIL) (-183 346915 347043 347195 "CYCLOTOM" 347446 T CYCLOTOM (NIL) -7 NIL NIL) (-182 343650 344363 345090 "CYCLES" 346208 T CYCLES (NIL) -7 NIL NIL) (-181 342962 343096 343267 "CVMP" 343511 NIL CVMP (NIL T) -7 NIL NIL) (-180 340734 340991 341367 "CTRIGMNP" 342690 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-179 340108 340207 340360 "CSTTOOLS" 340631 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 335907 336564 337322 "CRFP" 339420 NIL CRFP (NIL T T) -7 NIL NIL) (-177 334954 335139 335367 "CRAPACK" 335711 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 334340 334441 334644 "CPMATCH" 334831 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 334065 334093 334199 "CPIMA" 334306 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 330413 331085 331804 "COORDSYS" 333400 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 326274 328416 328908 "CONTFRAC" 329953 NIL CONTFRAC (NIL T) -8 NIL NIL) (-172 325422 325986 326015 "COMRING" 326020 T COMRING (NIL) -9 NIL 326072) (-171 324503 324780 324964 "COMPPROP" 325258 T COMPPROP (NIL) -8 NIL NIL) (-170 324164 324199 324327 "COMPLPAT" 324462 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-169 314135 323975 324083 "COMPLEX" 324088 NIL COMPLEX (NIL T) -8 NIL NIL) (-168 313771 313828 313935 "COMPLEX2" 314072 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-167 313489 313524 313622 "COMPFACT" 313730 NIL COMPFACT (NIL T T) -7 NIL NIL) (-166 297741 308041 308082 "COMPCAT" 309086 NIL COMPCAT (NIL T) -9 NIL 310467) (-165 287257 290180 293807 "COMPCAT-" 294163 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-164 286986 287014 287117 "COMMUPC" 287223 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-163 286781 286814 286873 "COMMONOP" 286947 T COMMONOP (NIL) -7 NIL NIL) (-162 286364 286532 286619 "COMM" 286714 T COMM (NIL) -8 NIL NIL) (-161 285612 285806 285835 "COMBOPC" 286173 T COMBOPC (NIL) -9 NIL 286348) (-160 284508 284718 284960 "COMBINAT" 285402 NIL COMBINAT (NIL T) -7 NIL NIL) (-159 280706 281279 281919 "COMBF" 283930 NIL COMBF (NIL T T) -7 NIL NIL) (-158 279492 279822 280057 "COLOR" 280491 T COLOR (NIL) -8 NIL NIL) (-157 279132 279179 279304 "CMPLXRT" 279439 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-156 274634 275662 276742 "CLIP" 278072 T CLIP (NIL) -7 NIL NIL) (-155 272970 273740 273979 "CLIF" 274461 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-154 269235 271153 271195 "CLAGG" 272124 NIL CLAGG (NIL T) -9 NIL 272657) (-153 267657 268114 268697 "CLAGG-" 268702 NIL CLAGG- (NIL T T) -8 NIL NIL) (-152 267201 267286 267426 "CINTSLPE" 267566 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-151 264702 265173 265721 "CHVAR" 266729 NIL CHVAR (NIL T T T) -7 NIL NIL) (-150 263920 264484 264513 "CHARZ" 264518 T CHARZ (NIL) -9 NIL 264533) (-149 263674 263714 263792 "CHARPOL" 263874 NIL CHARPOL (NIL T) -7 NIL NIL) (-148 262776 263373 263402 "CHARNZ" 263449 T CHARNZ (NIL) -9 NIL 263505) (-147 260799 261466 261801 "CHAR" 262461 T CHAR (NIL) -8 NIL NIL) (-146 260524 260585 260614 "CFCAT" 260725 T CFCAT (NIL) -9 NIL NIL) (-145 254657 260181 260299 "CDFVEC" 260426 T CDFVEC (NIL) -8 NIL NIL) (-144 250372 254414 254515 "CDFMAT" 254576 T CDFMAT (NIL) -8 NIL NIL) (-143 249617 249728 249910 "CDEN" 250256 NIL CDEN (NIL T T T) -7 NIL NIL) (-142 245609 248770 249050 "CCLASS" 249357 T CCLASS (NIL) -8 NIL NIL) (-141 240662 241638 242391 "CARTEN" 244912 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-140 239770 239918 240139 "CARTEN2" 240509 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-139 238065 238920 239177 "CARD" 239533 T CARD (NIL) -8 NIL NIL) (-138 237436 237764 237793 "CACHSET" 237925 T CACHSET (NIL) -9 NIL 238002) (-137 236931 237227 237256 "CABMON" 237306 T CABMON (NIL) -9 NIL 237362) (-136 234494 236623 236730 "BTREE" 236857 NIL BTREE (NIL T) -8 NIL NIL) (-135 231998 234142 234264 "BTOURN" 234404 NIL BTOURN (NIL T) -8 NIL NIL) (-134 229455 231502 231544 "BTCAT" 231612 NIL BTCAT (NIL T) -9 NIL 231689) (-133 229122 229202 229351 "BTCAT-" 229356 NIL BTCAT- (NIL T T) -8 NIL NIL) (-132 224312 228182 228211 "BTAGG" 228467 T BTAGG (NIL) -9 NIL 228646) (-131 223735 223879 224109 "BTAGG-" 224114 NIL BTAGG- (NIL T) -8 NIL NIL) (-130 220785 223013 223228 "BSTREE" 223552 NIL BSTREE (NIL T) -8 NIL NIL) (-129 219923 220049 220233 "BRILL" 220641 NIL BRILL (NIL T) -7 NIL NIL) (-128 216663 218684 218726 "BRAGG" 219375 NIL BRAGG (NIL T) -9 NIL 219632) (-127 215192 215598 216153 "BRAGG-" 216158 NIL BRAGG- (NIL T T) -8 NIL NIL) (-126 208391 214538 214722 "BPADICRT" 215040 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-125 206695 208328 208373 "BPADIC" 208378 NIL BPADIC (NIL NIL) -8 NIL NIL) (-124 206393 206423 206537 "BOUNDZRO" 206659 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-123 201908 202999 203866 "BOP" 205546 T BOP (NIL) -8 NIL NIL) (-122 199531 199975 200494 "BOP1" 201422 NIL BOP1 (NIL T) -7 NIL NIL) (-121 197884 198574 198868 "BOOLEAN" 199257 T BOOLEAN (NIL) -8 NIL NIL) (-120 197245 197623 197678 "BMODULE" 197683 NIL BMODULE (NIL T T) -9 NIL 197748) (-119 193588 194258 195044 "BLUPPACK" 196577 NIL BLUPPACK (NIL T NIL T T T) -7 NIL NIL) (-118 192980 193465 193534 "BLQT" 193539 T BLQT (NIL) -8 NIL NIL) (-117 191409 191884 191913 "BLMETCT" 192558 T BLMETCT (NIL) -9 NIL 192930) (-116 190808 191290 191357 "BLHN" 191362 T BLHN (NIL) -8 NIL NIL) (-115 189626 189885 190168 "BLAS1" 190545 T BLAS1 (NIL) -7 NIL NIL) (-114 185436 189424 189497 "BITS" 189573 T BITS (NIL) -8 NIL NIL) (-113 184507 184968 185120 "BINFILE" 185304 T BINFILE (NIL) -8 NIL NIL) (-112 178329 183948 184114 "BINARY" 184361 T BINARY (NIL) -8 NIL NIL) (-111 176196 177618 177660 "BGAGG" 177920 NIL BGAGG (NIL T) -9 NIL 178057) (-110 176027 176059 176150 "BGAGG-" 176155 NIL BGAGG- (NIL T T) -8 NIL NIL) (-109 175125 175411 175616 "BFUNCT" 175842 T BFUNCT (NIL) -8 NIL NIL) (-108 173817 173995 174282 "BEZOUT" 174950 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-107 172780 173002 173261 "BEZIER" 173591 NIL BEZIER (NIL T) -7 NIL NIL) (-106 169303 171632 171962 "BBTREE" 172483 NIL BBTREE (NIL T) -8 NIL NIL) (-105 169036 169089 169118 "BASTYPE" 169237 T BASTYPE (NIL) -9 NIL NIL) (-104 168889 168917 168990 "BASTYPE-" 168995 NIL BASTYPE- (NIL T) -8 NIL NIL) (-103 168323 168399 168551 "BALFACT" 168800 NIL BALFACT (NIL T T) -7 NIL NIL) (-102 167687 167810 167958 "AXSERV" 168195 T AXSERV (NIL) -7 NIL NIL) (-101 166500 167097 167285 "AUTOMOR" 167532 NIL AUTOMOR (NIL T) -8 NIL NIL) (-100 166212 166217 166246 "ATTREG" 166251 T ATTREG (NIL) -9 NIL NIL) (-99 164491 164909 165261 "ATTRBUT" 165878 T ATTRBUT (NIL) -8 NIL NIL) (-98 164026 164139 164166 "ATRIG" 164367 T ATRIG (NIL) -9 NIL NIL) (-97 163835 163876 163963 "ATRIG-" 163968 NIL ATRIG- (NIL T) -8 NIL NIL) (-96 157395 158964 160075 "ASTACK" 162755 NIL ASTACK (NIL T) -8 NIL NIL) (-95 155902 156199 156563 "ASSOCEQ" 157078 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-94 154934 155561 155685 "ASP9" 155809 NIL ASP9 (NIL NIL) -8 NIL NIL) (-93 154698 154882 154921 "ASP8" 154926 NIL ASP8 (NIL NIL) -8 NIL NIL) (-92 153568 154303 154445 "ASP80" 154587 NIL ASP80 (NIL NIL) -8 NIL NIL) (-91 152467 153203 153335 "ASP7" 153467 NIL ASP7 (NIL NIL) -8 NIL NIL) (-90 151423 152144 152262 "ASP78" 152380 NIL ASP78 (NIL NIL) -8 NIL NIL) (-89 150394 151103 151220 "ASP77" 151337 NIL ASP77 (NIL NIL) -8 NIL NIL) (-88 149309 150032 150163 "ASP74" 150294 NIL ASP74 (NIL NIL) -8 NIL NIL) (-87 148210 148944 149076 "ASP73" 149208 NIL ASP73 (NIL NIL) -8 NIL NIL) (-86 147165 147887 148005 "ASP6" 148123 NIL ASP6 (NIL NIL) -8 NIL NIL) (-85 146114 146842 146960 "ASP55" 147078 NIL ASP55 (NIL NIL) -8 NIL NIL) (-84 145064 145788 145907 "ASP50" 146026 NIL ASP50 (NIL NIL) -8 NIL NIL) (-83 144152 144765 144875 "ASP4" 144985 NIL ASP4 (NIL NIL) -8 NIL NIL) (-82 143240 143853 143963 "ASP49" 144073 NIL ASP49 (NIL NIL) -8 NIL NIL) (-81 142025 142779 142947 "ASP42" 143129 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-80 140803 141558 141728 "ASP41" 141912 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-79 139755 140480 140598 "ASP35" 140716 NIL ASP35 (NIL NIL) -8 NIL NIL) (-78 139520 139703 139742 "ASP34" 139747 NIL ASP34 (NIL NIL) -8 NIL NIL) (-77 139257 139324 139400 "ASP33" 139475 NIL ASP33 (NIL NIL) -8 NIL NIL) (-76 138153 138892 139024 "ASP31" 139156 NIL ASP31 (NIL NIL) -8 NIL NIL) (-75 137918 138101 138140 "ASP30" 138145 NIL ASP30 (NIL NIL) -8 NIL NIL) (-74 137653 137722 137798 "ASP29" 137873 NIL ASP29 (NIL NIL) -8 NIL NIL) (-73 137418 137601 137640 "ASP28" 137645 NIL ASP28 (NIL NIL) -8 NIL NIL) (-72 137183 137366 137405 "ASP27" 137410 NIL ASP27 (NIL NIL) -8 NIL NIL) (-71 136267 136881 136992 "ASP24" 137103 NIL ASP24 (NIL NIL) -8 NIL NIL) (-70 135184 135908 136038 "ASP20" 136168 NIL ASP20 (NIL NIL) -8 NIL NIL) (-69 134272 134885 134995 "ASP1" 135105 NIL ASP1 (NIL NIL) -8 NIL NIL) (-68 133216 133946 134065 "ASP19" 134184 NIL ASP19 (NIL NIL) -8 NIL NIL) (-67 132953 133020 133096 "ASP12" 133171 NIL ASP12 (NIL NIL) -8 NIL NIL) (-66 131806 132552 132696 "ASP10" 132840 NIL ASP10 (NIL NIL) -8 NIL NIL) (-65 129711 131650 131741 "ARRAY2" 131746 NIL ARRAY2 (NIL T) -8 NIL NIL) (-64 125533 129359 129473 "ARRAY1" 129628 NIL ARRAY1 (NIL T) -8 NIL NIL) (-63 124565 124738 124959 "ARRAY12" 125356 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-62 118964 120829 120905 "ARR2CAT" 123535 NIL ARR2CAT (NIL T T T) -9 NIL 124293) (-61 116398 117142 118096 "ARR2CAT-" 118101 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-60 115146 115298 115604 "APPRULE" 116234 NIL APPRULE (NIL T T T) -7 NIL NIL) (-59 114797 114845 114964 "APPLYORE" 115092 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-58 114321 114409 114519 "API" 114705 T API (NIL) -7 NIL NIL) (-57 113295 113586 113781 "ANY" 114144 T ANY (NIL) -8 NIL NIL) (-56 112573 112696 112853 "ANY1" 113169 NIL ANY1 (NIL T) -7 NIL NIL) (-55 110092 111010 111337 "ANTISYM" 112297 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-54 109919 110051 110078 "ANON" 110083 T ANON (NIL) -8 NIL NIL) (-53 103986 108458 108912 "AN" 109483 T AN (NIL) -8 NIL NIL) (-52 100281 101679 101731 "AMR" 102479 NIL AMR (NIL T T) -9 NIL 103073) (-51 99393 99614 99977 "AMR-" 99982 NIL AMR- (NIL T T T) -8 NIL NIL) (-50 83955 99310 99371 "ALIST" 99376 NIL ALIST (NIL T T) -8 NIL NIL) (-49 80792 83549 83718 "ALGSC" 83873 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-48 77350 77904 78510 "ALGPKG" 80233 NIL ALGPKG (NIL T T) -7 NIL NIL) (-47 76627 76728 76912 "ALGMFACT" 77236 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-46 72375 73059 73710 "ALGMANIP" 76154 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-45 63689 72001 72151 "ALGFF" 72308 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-44 62885 63016 63195 "ALGFACT" 63547 NIL ALGFACT (NIL T) -7 NIL NIL) (-43 61870 62480 62519 "ALGEBRA" 62579 NIL ALGEBRA (NIL T) -9 NIL 62638) (-42 61588 61647 61779 "ALGEBRA-" 61784 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-41 43395 59120 59173 "ALAGG" 59309 NIL ALAGG (NIL T T) -9 NIL 59470) (-40 42930 43043 43070 "AHYP" 43271 T AHYP (NIL) -9 NIL NIL) (-39 41861 42109 42136 "AGG" 42635 T AGG (NIL) -9 NIL 42913) (-38 41295 41457 41671 "AGG-" 41676 NIL AGG- (NIL T) -8 NIL NIL) (-37 38844 39425 39464 "AFSPCAT" 40736 NIL AFSPCAT (NIL T) -9 NIL 41231) (-36 36523 36945 37362 "AF" 38487 NIL AF (NIL T T) -7 NIL NIL) (-35 35863 36452 36506 "AFFSP" 36511 NIL AFFSP (NIL NIL T) -8 NIL NIL) (-34 35120 35790 35839 "AFFPLPS" 35844 NIL AFFPLPS (NIL T) -8 NIL NIL) (-33 34454 35061 35103 "AFFPL" 35108 NIL AFFPL (NIL T) -8 NIL NIL) (-32 31167 31654 32282 "AFALGRES" 33959 NIL AFALGRES (NIL T NIL T T T) -7 NIL NIL) (-31 29813 29990 30304 "AFALGGRO" 30986 NIL AFALGGRO (NIL T NIL T T T) -7 NIL NIL) (-30 29082 29340 29496 "ACPLOT" 29675 T ACPLOT (NIL) -8 NIL NIL) (-29 18442 26425 26477 "ACFS" 27188 NIL ACFS (NIL T) -9 NIL 27427) (-28 16456 16946 17721 "ACFS-" 17726 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12669 14625 14652 "ACF" 15531 T ACF (NIL) -9 NIL 15944) (-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 +((-1275 3579603 3579608 3579613 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3579588 3579593 3579598 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3579573 3579578 3579583 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3579558 3579563 3579568 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3579543 3579548 3579553 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1270 3578673 3579418 3579495 "ZMOD" 3579500 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1269 3577783 3577947 3578156 "ZLINDEP" 3578505 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1268 3567087 3568851 3570823 "ZDSOLVE" 3575913 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1267 3566333 3566474 3566663 "YSTREAM" 3566933 NIL YSTREAM (NIL T) -7 NIL NIL) (-1266 3564098 3565634 3565838 "XRPOLY" 3566176 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1265 3560552 3561881 3562461 "XPR" 3563565 NIL XPR (NIL T T) -8 NIL NIL) (-1264 3558262 3559883 3560087 "XPOLY" 3560383 NIL XPOLY (NIL T) -8 NIL NIL) (-1263 3556066 3557444 3557500 "XPOLYC" 3557788 NIL XPOLYC (NIL T T) -9 NIL 3557901) (-1262 3552440 3554585 3554972 "XPBWPOLY" 3555725 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1261 3548318 3550628 3550671 "XF" 3551292 NIL XF (NIL T) -9 NIL 3551689) (-1260 3547939 3548027 3548196 "XF-" 3548201 NIL XF- (NIL T T) -8 NIL NIL) (-1259 3543288 3544587 3544643 "XFALG" 3546815 NIL XFALG (NIL T T) -9 NIL 3547602) (-1258 3542421 3542525 3542730 "XEXPPKG" 3543180 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1257 3540518 3542271 3542367 "XDPOLY" 3542372 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1256 3539390 3540000 3540044 "XALG" 3540107 NIL XALG (NIL T) -9 NIL 3540226) (-1255 3532859 3537367 3537861 "WUTSET" 3538982 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1254 3530668 3531475 3531826 "WP" 3532642 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1253 3529554 3529752 3530047 "WFFINTBS" 3530465 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1252 3527458 3527885 3528347 "WEIER" 3529126 NIL WEIER (NIL T) -7 NIL NIL) (-1251 3526604 3527028 3527071 "VSPACE" 3527207 NIL VSPACE (NIL T) -9 NIL 3527281) (-1250 3526442 3526469 3526560 "VSPACE-" 3526565 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1249 3526188 3526231 3526302 "VOID" 3526393 T VOID (NIL) -8 NIL NIL) (-1248 3524324 3524683 3525089 "VIEW" 3525804 T VIEW (NIL) -7 NIL NIL) (-1247 3520749 3521387 3522124 "VIEWDEF" 3523609 T VIEWDEF (NIL) -7 NIL NIL) (-1246 3510088 3512297 3514470 "VIEW3D" 3518598 T VIEW3D (NIL) -8 NIL NIL) (-1245 3502370 3503999 3505578 "VIEW2D" 3508531 T VIEW2D (NIL) -8 NIL NIL) (-1244 3497778 3502140 3502232 "VECTOR" 3502313 NIL VECTOR (NIL T) -8 NIL NIL) (-1243 3496355 3496614 3496932 "VECTOR2" 3497508 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1242 3489920 3494166 3494210 "VECTCAT" 3495205 NIL VECTCAT (NIL T) -9 NIL 3495785) (-1241 3488934 3489188 3489578 "VECTCAT-" 3489583 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1240 3488415 3488585 3488705 "VARIABLE" 3488849 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1239 3480457 3486248 3486726 "UTSZ" 3487985 NIL UTSZ (NIL T NIL) -8 NIL NIL) (-1238 3480063 3480113 3480247 "UTSSOL" 3480401 NIL UTSSOL (NIL T T T) -7 NIL NIL) (-1237 3478895 3479049 3479310 "UTSODETL" 3479890 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1236 3476335 3476795 3477319 "UTSODE" 3478436 NIL UTSODE (NIL T T) -7 NIL NIL) (-1235 3468168 3473963 3474451 "UTS" 3475905 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1234 3459454 3464814 3464858 "UTSCAT" 3465970 NIL UTSCAT (NIL T) -9 NIL 3466721) (-1233 3456809 3457524 3458513 "UTSCAT-" 3458518 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1232 3456436 3456479 3456612 "UTS2" 3456760 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1231 3450750 3453309 3453353 "URAGG" 3455423 NIL URAGG (NIL T) -9 NIL 3456145) (-1230 3447689 3448552 3449675 "URAGG-" 3449680 NIL URAGG- (NIL T T) -8 NIL NIL) (-1229 3443367 3446303 3446775 "UPXSSING" 3447353 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1228 3435254 3442484 3442765 "UPXS" 3443144 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1227 3428282 3435158 3435230 "UPXSCONS" 3435235 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1226 3418494 3425319 3425382 "UPXSCCA" 3426038 NIL UPXSCCA (NIL T T) -9 NIL 3426280) (-1225 3418132 3418217 3418391 "UPXSCCA-" 3418396 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1224 3408276 3414874 3414918 "UPXSCAT" 3415566 NIL UPXSCAT (NIL T) -9 NIL 3416168) (-1223 3407706 3407785 3407964 "UPXS2" 3408191 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1222 3406360 3406613 3406964 "UPSQFREE" 3407449 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1221 3400195 3403245 3403301 "UPSCAT" 3404462 NIL UPSCAT (NIL T T) -9 NIL 3405230) (-1220 3399399 3399606 3399933 "UPSCAT-" 3399938 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1219 3385388 3393428 3393472 "UPOLYC" 3395573 NIL UPOLYC (NIL T) -9 NIL 3396788) (-1218 3376717 3379142 3382289 "UPOLYC-" 3382294 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1217 3376344 3376387 3376520 "UPOLYC2" 3376668 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1216 3367755 3375910 3376048 "UP" 3376254 NIL UP (NIL NIL T) -8 NIL NIL) (-1215 3367094 3367201 3367365 "UPMP" 3367644 NIL UPMP (NIL T T) -7 NIL NIL) (-1214 3366647 3366728 3366867 "UPDIVP" 3367007 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1213 3365215 3365464 3365780 "UPDECOMP" 3366396 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1212 3364450 3364562 3364747 "UPCDEN" 3365099 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1211 3363969 3364038 3364187 "UP2" 3364375 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1210 3362490 3363177 3363452 "UNISEG" 3363729 NIL UNISEG (NIL T) -8 NIL NIL) (-1209 3361707 3361834 3362038 "UNISEG2" 3362334 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1208 3360767 3360947 3361173 "UNIFACT" 3361523 NIL UNIFACT (NIL T) -7 NIL NIL) (-1207 3344651 3359946 3360196 "ULS" 3360575 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1206 3332606 3344555 3344627 "ULSCONS" 3344632 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1205 3315273 3327290 3327353 "ULSCCAT" 3328073 NIL ULSCCAT (NIL T T) -9 NIL 3328369) (-1204 3314323 3314568 3314956 "ULSCCAT-" 3314961 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1203 3304259 3310771 3310815 "ULSCAT" 3311678 NIL ULSCAT (NIL T) -9 NIL 3312401) (-1202 3303689 3303768 3303947 "ULS2" 3304174 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1201 3295827 3301680 3302180 "UFPS" 3303224 NIL UFPS (NIL T) -8 NIL NIL) (-1200 3295524 3295581 3295679 "UFPS1" 3295764 NIL UFPS1 (NIL T) -7 NIL NIL) (-1199 3293917 3294884 3294915 "UFD" 3295127 T UFD (NIL) -9 NIL 3295241) (-1198 3293711 3293757 3293852 "UFD-" 3293857 NIL UFD- (NIL T) -8 NIL NIL) (-1197 3292793 3292976 3293192 "UDVO" 3293517 T UDVO (NIL) -7 NIL NIL) (-1196 3290611 3291020 3291490 "UDPO" 3292358 NIL UDPO (NIL T) -7 NIL NIL) (-1195 3290543 3290548 3290579 "TYPE" 3290584 T TYPE (NIL) -9 NIL NIL) (-1194 3289514 3289716 3289956 "TWOFACT" 3290337 NIL TWOFACT (NIL T) -7 NIL NIL) (-1193 3288586 3288917 3289116 "TUPLE" 3289350 NIL TUPLE (NIL T) -8 NIL NIL) (-1192 3286277 3286796 3287335 "TUBETOOL" 3288069 T TUBETOOL (NIL) -7 NIL NIL) (-1191 3285126 3285331 3285572 "TUBE" 3286070 NIL TUBE (NIL T) -8 NIL NIL) (-1190 3279846 3284100 3284382 "TS" 3284879 NIL TS (NIL T) -8 NIL NIL) (-1189 3268520 3272605 3272703 "TSETCAT" 3277972 NIL TSETCAT (NIL T T T T) -9 NIL 3279502) (-1188 3263255 3264852 3266743 "TSETCAT-" 3266748 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1187 3257526 3258372 3259310 "TRMANIP" 3262395 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1186 3256967 3257030 3257193 "TRIMAT" 3257458 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1185 3254763 3255000 3255364 "TRIGMNIP" 3256716 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1184 3254282 3254395 3254426 "TRIGCAT" 3254639 T TRIGCAT (NIL) -9 NIL NIL) (-1183 3253951 3254030 3254171 "TRIGCAT-" 3254176 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1182 3250854 3252809 3253090 "TREE" 3253705 NIL TREE (NIL T) -8 NIL NIL) (-1181 3250127 3250655 3250686 "TRANFUN" 3250721 T TRANFUN (NIL) -9 NIL 3250787) (-1180 3249406 3249597 3249877 "TRANFUN-" 3249882 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1179 3249210 3249242 3249303 "TOPSP" 3249367 T TOPSP (NIL) -7 NIL NIL) (-1178 3248558 3248673 3248827 "TOOLSIGN" 3249091 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1177 3247193 3247735 3247974 "TEXTFILE" 3248341 T TEXTFILE (NIL) -8 NIL NIL) (-1176 3245058 3245572 3246010 "TEX" 3246777 T TEX (NIL) -8 NIL NIL) (-1175 3244839 3244870 3244942 "TEX1" 3245021 NIL TEX1 (NIL T) -7 NIL NIL) (-1174 3244487 3244550 3244640 "TEMUTL" 3244771 T TEMUTL (NIL) -7 NIL NIL) (-1173 3242641 3242921 3243246 "TBCMPPK" 3244210 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1172 3234386 3240646 3240703 "TBAGG" 3241103 NIL TBAGG (NIL T T) -9 NIL 3241314) (-1171 3229456 3230944 3232698 "TBAGG-" 3232703 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1170 3228840 3228947 3229092 "TANEXP" 3229345 NIL TANEXP (NIL T) -7 NIL NIL) (-1169 3222353 3228697 3228790 "TABLE" 3228795 NIL TABLE (NIL T T) -8 NIL NIL) (-1168 3221766 3221864 3222002 "TABLEAU" 3222250 NIL TABLEAU (NIL T) -8 NIL NIL) (-1167 3216374 3217594 3218842 "TABLBUMP" 3220552 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1166 3212837 3213532 3214315 "SYSSOLP" 3215625 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1165 3209971 3210579 3211217 "SYMTAB" 3212221 T SYMTAB (NIL) -8 NIL NIL) (-1164 3205220 3206122 3207105 "SYMS" 3209010 T SYMS (NIL) -8 NIL NIL) (-1163 3202452 3204684 3204911 "SYMPOLY" 3205028 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1162 3201969 3202044 3202167 "SYMFUNC" 3202364 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1161 3197947 3199206 3200028 "SYMBOL" 3201169 T SYMBOL (NIL) -8 NIL NIL) (-1160 3191486 3193175 3194895 "SWITCH" 3196249 T SWITCH (NIL) -8 NIL NIL) (-1159 3184712 3190309 3190611 "SUTS" 3191242 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1158 3176598 3183829 3184110 "SUPXS" 3184489 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1157 3168083 3176216 3176342 "SUP" 3176507 NIL SUP (NIL T) -8 NIL NIL) (-1156 3167242 3167369 3167586 "SUPFRACF" 3167951 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1155 3157814 3167044 3167158 "SUPEXPR" 3167163 NIL SUPEXPR (NIL T) -8 NIL NIL) (-1154 3157435 3157494 3157607 "SUP2" 3157749 NIL SUP2 (NIL T T) -7 NIL NIL) (-1153 3155848 3156122 3156485 "SUMRF" 3157134 NIL SUMRF (NIL T) -7 NIL NIL) (-1152 3155162 3155228 3155427 "SUMFS" 3155769 NIL SUMFS (NIL T T) -7 NIL NIL) (-1151 3139086 3154341 3154591 "SULS" 3154970 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1150 3138408 3138611 3138751 "SUCH" 3138994 NIL SUCH (NIL T T) -8 NIL NIL) (-1149 3132302 3133314 3134273 "SUBSPACE" 3137496 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1148 3131734 3131824 3131987 "SUBRESP" 3132191 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1147 3125103 3126399 3127710 "STTF" 3130470 NIL STTF (NIL T) -7 NIL NIL) (-1146 3119276 3120396 3121543 "STTFNC" 3124003 NIL STTFNC (NIL T) -7 NIL NIL) (-1145 3110595 3112462 3114254 "STTAYLOR" 3117519 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1144 3103851 3110459 3110542 "STRTBL" 3110547 NIL STRTBL (NIL T) -8 NIL NIL) (-1143 3099242 3103806 3103837 "STRING" 3103842 T STRING (NIL) -8 NIL NIL) (-1142 3094106 3098584 3098615 "STRICAT" 3098674 T STRICAT (NIL) -9 NIL 3098736) (-1141 3086833 3091633 3092251 "STREAM" 3093523 NIL STREAM (NIL T) -8 NIL NIL) (-1140 3086343 3086420 3086564 "STREAM3" 3086750 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1139 3085325 3085508 3085743 "STREAM2" 3086156 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1138 3085013 3085065 3085158 "STREAM1" 3085267 NIL STREAM1 (NIL T) -7 NIL NIL) (-1137 3084029 3084210 3084441 "STINPROD" 3084829 NIL STINPROD (NIL T) -7 NIL NIL) (-1136 3083606 3083790 3083821 "STEP" 3083901 T STEP (NIL) -9 NIL 3083979) (-1135 3077161 3083505 3083582 "STBL" 3083587 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1134 3072375 3076413 3076457 "STAGG" 3076610 NIL STAGG (NIL T) -9 NIL 3076699) (-1133 3070077 3070679 3071551 "STAGG-" 3071556 NIL STAGG- (NIL T T) -8 NIL NIL) (-1132 3063569 3065138 3066253 "STACK" 3068997 NIL STACK (NIL T) -8 NIL NIL) (-1131 3056294 3061710 3062166 "SREGSET" 3063199 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1130 3048720 3050088 3051601 "SRDCMPK" 3054900 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1129 3041698 3046158 3046189 "SRAGG" 3047492 T SRAGG (NIL) -9 NIL 3048100) (-1128 3040715 3040970 3041349 "SRAGG-" 3041354 NIL SRAGG- (NIL T) -8 NIL NIL) (-1127 3035163 3039638 3040062 "SQMATRIX" 3040338 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1126 3028919 3031881 3032608 "SPLTREE" 3034508 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1125 3024909 3025575 3026221 "SPLNODE" 3028345 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1124 3023955 3024188 3024219 "SPFCAT" 3024663 T SPFCAT (NIL) -9 NIL NIL) (-1123 3022692 3022902 3023166 "SPECOUT" 3023713 T SPECOUT (NIL) -7 NIL NIL) (-1122 3014662 3016409 3016453 "SPACEC" 3020826 NIL SPACEC (NIL T) -9 NIL 3022642) (-1121 3012833 3014594 3014643 "SPACE3" 3014648 NIL SPACE3 (NIL T) -8 NIL NIL) (-1120 3011587 3011758 3012048 "SORTPAK" 3012639 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1119 3009637 3009940 3010359 "SOLVETRA" 3011251 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1118 3008648 3008870 3009144 "SOLVESER" 3009410 NIL SOLVESER (NIL T) -7 NIL NIL) (-1117 3003868 3004749 3005751 "SOLVERAD" 3007700 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1116 2999683 3000292 3001021 "SOLVEFOR" 3003235 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1115 2993986 2999031 2999129 "SNTSCAT" 2999134 NIL SNTSCAT (NIL T T T T) -9 NIL 2999204) (-1114 2988084 2992311 2992701 "SMTS" 2993677 NIL SMTS (NIL T T T) -8 NIL NIL) (-1113 2982488 2987972 2988049 "SMP" 2988054 NIL SMP (NIL T T) -8 NIL NIL) (-1112 2980647 2980948 2981346 "SMITH" 2982185 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1111 2973589 2977787 2977891 "SMATCAT" 2979242 NIL SMATCAT (NIL NIL T T T) -9 NIL 2979789) (-1110 2970529 2971352 2972530 "SMATCAT-" 2972535 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1109 2968282 2969799 2969843 "SKAGG" 2970104 NIL SKAGG (NIL T) -9 NIL 2970239) (-1108 2964340 2967386 2967664 "SINT" 2968026 T SINT (NIL) -8 NIL NIL) (-1107 2964112 2964150 2964216 "SIMPAN" 2964296 T SIMPAN (NIL) -7 NIL NIL) (-1106 2962950 2963171 2963446 "SIGNRF" 2963871 NIL SIGNRF (NIL T) -7 NIL NIL) (-1105 2961755 2961906 2962197 "SIGNEF" 2962779 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1104 2959447 2959901 2960406 "SHP" 2961297 NIL SHP (NIL T NIL) -7 NIL NIL) (-1103 2953271 2959348 2959424 "SHDP" 2959429 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1102 2952759 2952951 2952982 "SGROUP" 2953134 T SGROUP (NIL) -9 NIL 2953221) (-1101 2952529 2952581 2952685 "SGROUP-" 2952690 NIL SGROUP- (NIL T) -8 NIL NIL) (-1100 2949365 2950062 2950785 "SGCF" 2951828 T SGCF (NIL) -7 NIL NIL) (-1099 2943766 2948811 2948909 "SFRTCAT" 2948914 NIL SFRTCAT (NIL T T T T) -9 NIL 2948953) (-1098 2937190 2938205 2939341 "SFRGCD" 2942749 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1097 2930318 2931389 2932575 "SFQCMPK" 2936123 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1096 2929940 2930029 2930139 "SFORT" 2930259 NIL SFORT (NIL T T) -8 NIL NIL) (-1095 2929085 2929780 2929901 "SEXOF" 2929906 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1094 2928219 2928966 2929034 "SEX" 2929039 T SEX (NIL) -8 NIL NIL) (-1093 2922994 2923683 2923779 "SEXCAT" 2927550 NIL SEXCAT (NIL T T T T T) -9 NIL 2928169) (-1092 2920174 2922928 2922976 "SET" 2922981 NIL SET (NIL T) -8 NIL NIL) (-1091 2918425 2918887 2919192 "SETMN" 2919915 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1090 2918030 2918156 2918187 "SETCAT" 2918304 T SETCAT (NIL) -9 NIL 2918389) (-1089 2917810 2917862 2917961 "SETCAT-" 2917966 NIL SETCAT- (NIL T) -8 NIL NIL) (-1088 2917473 2917623 2917654 "SETCATD" 2917713 T SETCATD (NIL) -9 NIL 2917760) (-1087 2913859 2915933 2915977 "SETAGG" 2916847 NIL SETAGG (NIL T) -9 NIL 2917187) (-1086 2913317 2913433 2913670 "SETAGG-" 2913675 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1085 2912520 2912813 2912875 "SEGXCAT" 2913161 NIL SEGXCAT (NIL T T) -9 NIL 2913281) (-1084 2911580 2912190 2912370 "SEG" 2912375 NIL SEG (NIL T) -8 NIL NIL) (-1083 2910486 2910699 2910743 "SEGCAT" 2911325 NIL SEGCAT (NIL T) -9 NIL 2911563) (-1082 2909537 2909867 2910066 "SEGBIND" 2910322 NIL SEGBIND (NIL T) -8 NIL NIL) (-1081 2909158 2909217 2909330 "SEGBIND2" 2909472 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1080 2908379 2908505 2908708 "SEG2" 2909003 NIL SEG2 (NIL T T) -7 NIL NIL) (-1079 2907816 2908314 2908361 "SDVAR" 2908366 NIL SDVAR (NIL T) -8 NIL NIL) (-1078 2900060 2907586 2907716 "SDPOL" 2907721 NIL SDPOL (NIL T) -8 NIL NIL) (-1077 2898653 2898919 2899238 "SCPKG" 2899775 NIL SCPKG (NIL T) -7 NIL NIL) (-1076 2897874 2898007 2898186 "SCACHE" 2898508 NIL SCACHE (NIL T) -7 NIL NIL) (-1075 2897313 2897634 2897719 "SAOS" 2897811 T SAOS (NIL) -8 NIL NIL) (-1074 2896878 2896913 2897086 "SAERFFC" 2897272 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1073 2890767 2896775 2896855 "SAE" 2896860 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1072 2890360 2890395 2890554 "SAEFACT" 2890726 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1071 2888681 2888995 2889396 "RURPK" 2890026 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1070 2887317 2887596 2887908 "RULESET" 2888515 NIL RULESET (NIL T T T) -8 NIL NIL) (-1069 2884504 2885007 2885472 "RULE" 2886998 NIL RULE (NIL T T T) -8 NIL NIL) (-1068 2884143 2884298 2884381 "RULECOLD" 2884456 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1067 2878992 2879786 2880706 "RSETGCD" 2883342 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1066 2868255 2873300 2873398 "RSETCAT" 2877517 NIL RSETCAT (NIL T T T T) -9 NIL 2878614) (-1065 2866182 2866721 2867545 "RSETCAT-" 2867550 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1064 2858569 2859944 2861464 "RSDCMPK" 2864781 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1063 2856573 2857014 2857089 "RRCC" 2858175 NIL RRCC (NIL T T) -9 NIL 2858519) (-1062 2855924 2856098 2856377 "RRCC-" 2856382 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1061 2830071 2839700 2839768 "RPOLCAT" 2850432 NIL RPOLCAT (NIL T T T) -9 NIL 2853580) (-1060 2821571 2823909 2827031 "RPOLCAT-" 2827036 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1059 2812630 2819782 2820264 "ROUTINE" 2821111 T ROUTINE (NIL) -8 NIL NIL) (-1058 2809330 2812181 2812330 "ROMAN" 2812503 T ROMAN (NIL) -8 NIL NIL) (-1057 2807605 2808190 2808450 "ROIRC" 2809135 NIL ROIRC (NIL T T) -8 NIL NIL) (-1056 2803943 2806243 2806274 "RNS" 2806578 T RNS (NIL) -9 NIL 2806852) (-1055 2802452 2802835 2803369 "RNS-" 2803444 NIL RNS- (NIL T) -8 NIL NIL) (-1054 2801874 2802282 2802313 "RNG" 2802318 T RNG (NIL) -9 NIL 2802339) (-1053 2801265 2801627 2801671 "RMODULE" 2801733 NIL RMODULE (NIL T) -9 NIL 2801775) (-1052 2800101 2800195 2800531 "RMCAT2" 2801166 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1051 2796810 2799279 2799602 "RMATRIX" 2799837 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1050 2789756 2791990 2792106 "RMATCAT" 2795465 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2796442) (-1049 2789131 2789278 2789585 "RMATCAT-" 2789590 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1048 2788698 2788773 2788901 "RINTERP" 2789050 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1047 2787741 2788305 2788336 "RING" 2788448 T RING (NIL) -9 NIL 2788543) (-1046 2787533 2787577 2787674 "RING-" 2787679 NIL RING- (NIL T) -8 NIL NIL) (-1045 2786374 2786611 2786869 "RIDIST" 2787297 T RIDIST (NIL) -7 NIL NIL) (-1044 2777690 2785842 2786048 "RGCHAIN" 2786222 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1043 2776490 2776731 2777010 "RFP" 2777445 NIL RFP (NIL T) -7 NIL NIL) (-1042 2773484 2774098 2774768 "RF" 2775854 NIL RF (NIL T) -7 NIL NIL) (-1041 2773130 2773193 2773296 "RFFACTOR" 2773415 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1040 2772855 2772890 2772987 "RFFACT" 2773089 NIL RFFACT (NIL T) -7 NIL NIL) (-1039 2770972 2771336 2771718 "RFDIST" 2772495 T RFDIST (NIL) -7 NIL NIL) (-1038 2770425 2770517 2770680 "RETSOL" 2770874 NIL RETSOL (NIL T T) -7 NIL NIL) (-1037 2770012 2770092 2770136 "RETRACT" 2770329 NIL RETRACT (NIL T) -9 NIL NIL) (-1036 2769861 2769886 2769973 "RETRACT-" 2769978 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1035 2762727 2769514 2769641 "RESULT" 2769756 T RESULT (NIL) -8 NIL NIL) (-1034 2761307 2761996 2762195 "RESRING" 2762630 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1033 2760943 2760992 2761090 "RESLATC" 2761244 NIL RESLATC (NIL T) -7 NIL NIL) (-1032 2760649 2760683 2760790 "REPSQ" 2760902 NIL REPSQ (NIL T) -7 NIL NIL) (-1031 2758071 2758651 2759253 "REP" 2760069 T REP (NIL) -7 NIL NIL) (-1030 2757769 2757803 2757914 "REPDB" 2758030 NIL REPDB (NIL T) -7 NIL NIL) (-1029 2751687 2753066 2754285 "REP2" 2756585 NIL REP2 (NIL T) -7 NIL NIL) (-1028 2748068 2748749 2749555 "REP1" 2750916 NIL REP1 (NIL T) -7 NIL NIL) (-1027 2740794 2746209 2746665 "REGSET" 2747698 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1026 2739609 2739944 2740193 "REF" 2740580 NIL REF (NIL T) -8 NIL NIL) (-1025 2738986 2739089 2739256 "REDORDER" 2739493 NIL REDORDER (NIL T T) -7 NIL NIL) (-1024 2735848 2736314 2736923 "RECOP" 2738520 NIL RECOP (NIL T T) -7 NIL NIL) (-1023 2731788 2735061 2735288 "RECLOS" 2735676 NIL RECLOS (NIL T) -8 NIL NIL) (-1022 2730840 2731021 2731236 "REALSOLV" 2731595 T REALSOLV (NIL) -7 NIL NIL) (-1021 2730685 2730726 2730757 "REAL" 2730762 T REAL (NIL) -9 NIL 2730797) (-1020 2727168 2727970 2728854 "REAL0Q" 2729850 NIL REAL0Q (NIL T) -7 NIL NIL) (-1019 2722769 2723757 2724818 "REAL0" 2726149 NIL REAL0 (NIL T) -7 NIL NIL) (-1018 2722174 2722246 2722453 "RDIV" 2722691 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1017 2721242 2721416 2721629 "RDIST" 2721996 NIL RDIST (NIL T) -7 NIL NIL) (-1016 2719839 2720126 2720498 "RDETRS" 2720950 NIL RDETRS (NIL T T) -7 NIL NIL) (-1015 2717651 2718105 2718643 "RDETR" 2719381 NIL RDETR (NIL T T) -7 NIL NIL) (-1014 2716262 2716540 2716944 "RDEEFS" 2717367 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1013 2714757 2715063 2715495 "RDEEF" 2715950 NIL RDEEF (NIL T T) -7 NIL NIL) (-1012 2708948 2711883 2711914 "RCFIELD" 2713209 T RCFIELD (NIL) -9 NIL 2713940) (-1011 2707012 2707516 2708212 "RCFIELD-" 2708287 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1010 2703370 2705149 2705193 "RCAGG" 2706277 NIL RCAGG (NIL T) -9 NIL 2706740) (-1009 2702998 2703092 2703255 "RCAGG-" 2703260 NIL RCAGG- (NIL T T) -8 NIL NIL) (-1008 2702334 2702445 2702610 "RATRET" 2702882 NIL RATRET (NIL T) -7 NIL NIL) (-1007 2701887 2701954 2702075 "RATFACT" 2702262 NIL RATFACT (NIL T) -7 NIL NIL) (-1006 2701195 2701315 2701467 "RANDSRC" 2701757 T RANDSRC (NIL) -7 NIL NIL) (-1005 2700929 2700973 2701046 "RADUTIL" 2701144 T RADUTIL (NIL) -7 NIL NIL) (-1004 2693917 2699662 2699981 "RADIX" 2700644 NIL RADIX (NIL NIL) -8 NIL NIL) (-1003 2685480 2693759 2693889 "RADFF" 2693894 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-1002 2685126 2685201 2685232 "RADCAT" 2685392 T RADCAT (NIL) -9 NIL NIL) (-1001 2684908 2684956 2685056 "RADCAT-" 2685061 NIL RADCAT- (NIL T) -8 NIL NIL) (-1000 2678155 2679773 2680926 "QUEUE" 2683790 NIL QUEUE (NIL T) -8 NIL NIL) (-999 2674646 2678092 2678137 "QUAT" 2678142 NIL QUAT (NIL T) -8 NIL NIL) (-998 2674284 2674327 2674454 "QUATCT2" 2674597 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-997 2668021 2671405 2671446 "QUATCAT" 2672226 NIL QUATCAT (NIL T) -9 NIL 2672984) (-996 2664165 2665202 2666589 "QUATCAT-" 2666683 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-995 2661725 2663283 2663325 "QUAGG" 2663700 NIL QUAGG (NIL T) -9 NIL 2663875) (-994 2660650 2661123 2661295 "QFORM" 2661597 NIL QFORM (NIL NIL T) -8 NIL NIL) (-993 2651877 2657144 2657185 "QFCAT" 2657843 NIL QFCAT (NIL T) -9 NIL 2658832) (-992 2647449 2648650 2650241 "QFCAT-" 2650335 NIL QFCAT- (NIL T T) -8 NIL NIL) (-991 2647087 2647130 2647257 "QFCAT2" 2647400 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-990 2646547 2646657 2646787 "QEQUAT" 2646977 T QEQUAT (NIL) -8 NIL NIL) (-989 2639695 2640766 2641950 "QCMPACK" 2645480 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-988 2637275 2637696 2638122 "QALGSET" 2639352 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-987 2636520 2636694 2636926 "QALGSET2" 2637095 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-986 2635211 2635434 2635751 "PWFFINTB" 2636293 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-985 2633393 2633561 2633915 "PUSHVAR" 2635025 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-984 2629310 2630364 2630406 "PTRANFN" 2632290 NIL PTRANFN (NIL T) -9 NIL NIL) (-983 2627712 2628003 2628325 "PTPACK" 2629021 NIL PTPACK (NIL T) -7 NIL NIL) (-982 2627344 2627401 2627510 "PTFUNC2" 2627649 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-981 2621844 2626178 2626220 "PTCAT" 2626593 NIL PTCAT (NIL T) -9 NIL 2626755) (-980 2621502 2621537 2621661 "PSQFR" 2621803 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-979 2620089 2620389 2620725 "PSEUDLIN" 2621198 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-978 2606865 2609229 2611550 "PSETPK" 2617852 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-977 2599909 2602623 2602720 "PSETCAT" 2605741 NIL PSETCAT (NIL T T T T) -9 NIL 2606554) (-976 2597745 2598379 2599200 "PSETCAT-" 2599205 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-975 2597094 2597258 2597287 "PSCURVE" 2597555 T PSCURVE (NIL) -9 NIL 2597722) (-974 2593483 2595009 2595075 "PSCAT" 2595919 NIL PSCAT (NIL T T T) -9 NIL 2596159) (-973 2592546 2592762 2593162 "PSCAT-" 2593167 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-972 2591199 2591831 2592045 "PRTITION" 2592352 T PRTITION (NIL) -8 NIL NIL) (-971 2588363 2589012 2589053 "PRSPCAT" 2590567 NIL PRSPCAT (NIL T) -9 NIL 2591135) (-970 2577463 2579669 2581856 "PRS" 2586226 NIL PRS (NIL T T) -7 NIL NIL) (-969 2575361 2576847 2576888 "PRQAGG" 2577071 NIL PRQAGG (NIL T) -9 NIL 2577173) (-968 2574630 2575286 2575343 "PROJSP" 2575348 NIL PROJSP (NIL NIL T) -8 NIL NIL) (-967 2573812 2574553 2574605 "PROJPLPS" 2574610 NIL PROJPLPS (NIL T) -8 NIL NIL) (-966 2573071 2573749 2573794 "PROJPL" 2573799 NIL PROJPL (NIL T) -8 NIL NIL) (-965 2566877 2571269 2572073 "PRODUCT" 2572313 NIL PRODUCT (NIL T T) -8 NIL NIL) (-964 2564152 2566341 2566572 "PR" 2566691 NIL PR (NIL T T) -8 NIL NIL) (-963 2562704 2562861 2563156 "PRJALGPK" 2563992 NIL PRJALGPK (NIL T NIL T T T) -7 NIL NIL) (-962 2562500 2562532 2562591 "PRINT" 2562665 T PRINT (NIL) -7 NIL NIL) (-961 2561840 2561957 2562109 "PRIMES" 2562380 NIL PRIMES (NIL T) -7 NIL NIL) (-960 2559905 2560306 2560772 "PRIMELT" 2561419 NIL PRIMELT (NIL T) -7 NIL NIL) (-959 2559633 2559682 2559711 "PRIMCAT" 2559835 T PRIMCAT (NIL) -9 NIL NIL) (-958 2555800 2559571 2559616 "PRIMARR" 2559621 NIL PRIMARR (NIL T) -8 NIL NIL) (-957 2554807 2554985 2555213 "PRIMARR2" 2555618 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-956 2554450 2554506 2554617 "PREASSOC" 2554745 NIL PREASSOC (NIL T T) -7 NIL NIL) (-955 2553925 2554057 2554086 "PPCURVE" 2554291 T PPCURVE (NIL) -9 NIL 2554427) (-954 2551286 2551685 2552276 "POLYROOT" 2553507 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-953 2545187 2550892 2551051 "POLY" 2551160 NIL POLY (NIL T) -8 NIL NIL) (-952 2544570 2544628 2544862 "POLYLIFT" 2545123 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-951 2540845 2541294 2541923 "POLYCATQ" 2544115 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-950 2527807 2533207 2533273 "POLYCAT" 2536787 NIL POLYCAT (NIL T T T) -9 NIL 2538700) (-949 2521257 2523118 2525502 "POLYCAT-" 2525507 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-948 2520844 2520912 2521032 "POLY2UP" 2521183 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-947 2520476 2520533 2520642 "POLY2" 2520781 NIL POLY2 (NIL T T) -7 NIL NIL) (-946 2519163 2519402 2519677 "POLUTIL" 2520251 NIL POLUTIL (NIL T T) -7 NIL NIL) (-945 2517518 2517795 2518126 "POLTOPOL" 2518885 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-944 2513040 2517454 2517500 "POINT" 2517505 NIL POINT (NIL T) -8 NIL NIL) (-943 2511227 2511584 2511959 "PNTHEORY" 2512685 T PNTHEORY (NIL) -7 NIL NIL) (-942 2509646 2509943 2510355 "PMTOOLS" 2510925 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-941 2509239 2509317 2509434 "PMSYM" 2509562 NIL PMSYM (NIL T) -7 NIL NIL) (-940 2508749 2508818 2508992 "PMQFCAT" 2509164 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-939 2508104 2508214 2508370 "PMPRED" 2508626 NIL PMPRED (NIL T) -7 NIL NIL) (-938 2507500 2507586 2507747 "PMPREDFS" 2508005 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-937 2506145 2506353 2506737 "PMPLCAT" 2507263 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-936 2505677 2505756 2505908 "PMLSAGG" 2506060 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-935 2505152 2505228 2505409 "PMKERNEL" 2505595 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-934 2504769 2504844 2504957 "PMINS" 2505071 NIL PMINS (NIL T) -7 NIL NIL) (-933 2504197 2504266 2504482 "PMFS" 2504694 NIL PMFS (NIL T T T) -7 NIL NIL) (-932 2503425 2503543 2503748 "PMDOWN" 2504074 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-931 2502588 2502747 2502929 "PMASS" 2503263 T PMASS (NIL) -7 NIL NIL) (-930 2501862 2501973 2502136 "PMASSFS" 2502474 NIL PMASSFS (NIL T T) -7 NIL NIL) (-929 2499622 2499875 2500258 "PLPKCRV" 2501586 NIL PLPKCRV (NIL T T T NIL T) -7 NIL NIL) (-928 2499277 2499345 2499439 "PLOTTOOL" 2499548 T PLOTTOOL (NIL) -7 NIL NIL) (-927 2493899 2495088 2496236 "PLOT" 2498149 T PLOT (NIL) -8 NIL NIL) (-926 2489713 2490747 2491668 "PLOT3D" 2492998 T PLOT3D (NIL) -8 NIL NIL) (-925 2488625 2488802 2489037 "PLOT1" 2489517 NIL PLOT1 (NIL T) -7 NIL NIL) (-924 2464020 2468691 2473542 "PLEQN" 2483891 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-923 2463260 2463930 2463997 "PLCS" 2464002 NIL PLCS (NIL T T) -8 NIL NIL) (-922 2462411 2463145 2463216 "PLACESPS" 2463221 NIL PLACESPS (NIL T) -8 NIL NIL) (-921 2461618 2462324 2462381 "PLACES" 2462386 NIL PLACES (NIL T) -8 NIL NIL) (-920 2458342 2459006 2459065 "PLACESC" 2460983 NIL PLACESC (NIL T T) -9 NIL 2461554) (-919 2457660 2457782 2457962 "PINTERP" 2458207 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-918 2457353 2457400 2457503 "PINTERPA" 2457607 NIL PINTERPA (NIL T T) -7 NIL NIL) (-917 2456580 2457147 2457240 "PI" 2457280 T PI (NIL) -8 NIL NIL) (-916 2454967 2455952 2455981 "PID" 2456163 T PID (NIL) -9 NIL 2456297) (-915 2454692 2454729 2454817 "PICOERCE" 2454924 NIL PICOERCE (NIL T) -7 NIL NIL) (-914 2454013 2454151 2454327 "PGROEB" 2454548 NIL PGROEB (NIL T) -7 NIL NIL) (-913 2449600 2450414 2451319 "PGE" 2453128 T PGE (NIL) -7 NIL NIL) (-912 2447724 2447970 2448336 "PGCD" 2449317 NIL PGCD (NIL T T T T) -7 NIL NIL) (-911 2447062 2447165 2447326 "PFRPAC" 2447608 NIL PFRPAC (NIL T) -7 NIL NIL) (-910 2443677 2445610 2445963 "PFR" 2446741 NIL PFR (NIL T) -8 NIL NIL) (-909 2442066 2442310 2442635 "PFOTOOLS" 2443424 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-908 2436931 2437596 2438345 "PFORP" 2441408 NIL PFORP (NIL T T T NIL) -7 NIL NIL) (-907 2435464 2435703 2436054 "PFOQ" 2436688 NIL PFOQ (NIL T T T) -7 NIL NIL) (-906 2433937 2434149 2434512 "PFO" 2435248 NIL PFO (NIL T T T T T) -7 NIL NIL) (-905 2430460 2433826 2433895 "PF" 2433900 NIL PF (NIL NIL) -8 NIL NIL) (-904 2427885 2429166 2429195 "PFECAT" 2429780 T PFECAT (NIL) -9 NIL 2430163) (-903 2427330 2427484 2427698 "PFECAT-" 2427703 NIL PFECAT- (NIL T) -8 NIL NIL) (-902 2425934 2426185 2426486 "PFBRU" 2427079 NIL PFBRU (NIL T T) -7 NIL NIL) (-901 2423801 2424152 2424584 "PFBR" 2425585 NIL PFBR (NIL T T T T) -7 NIL NIL) (-900 2419657 2421181 2421855 "PERM" 2423160 NIL PERM (NIL T) -8 NIL NIL) (-899 2414924 2415864 2416734 "PERMGRP" 2418820 NIL PERMGRP (NIL T) -8 NIL NIL) (-898 2412995 2413988 2414030 "PERMCAT" 2414476 NIL PERMCAT (NIL T) -9 NIL 2414779) (-897 2412648 2412689 2412813 "PERMAN" 2412948 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-896 2410094 2412217 2412348 "PENDTREE" 2412550 NIL PENDTREE (NIL T) -8 NIL NIL) (-895 2408162 2408940 2408982 "PDRING" 2409639 NIL PDRING (NIL T) -9 NIL 2409925) (-894 2407265 2407483 2407845 "PDRING-" 2407850 NIL PDRING- (NIL T T) -8 NIL NIL) (-893 2404407 2405157 2405848 "PDEPROB" 2406594 T PDEPROB (NIL) -8 NIL NIL) (-892 2401954 2402456 2403011 "PDEPACK" 2403872 T PDEPACK (NIL) -7 NIL NIL) (-891 2400866 2401056 2401307 "PDECOMP" 2401753 NIL PDECOMP (NIL T T) -7 NIL NIL) (-890 2398470 2399287 2399316 "PDECAT" 2400103 T PDECAT (NIL) -9 NIL 2400816) (-889 2398221 2398254 2398344 "PCOMP" 2398431 NIL PCOMP (NIL T T) -7 NIL NIL) (-888 2396426 2397022 2397319 "PBWLB" 2397950 NIL PBWLB (NIL T) -8 NIL NIL) (-887 2388931 2390499 2391837 "PATTERN" 2395109 NIL PATTERN (NIL T) -8 NIL NIL) (-886 2388563 2388620 2388729 "PATTERN2" 2388868 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-885 2386320 2386708 2387165 "PATTERN1" 2388152 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-884 2383715 2384269 2384750 "PATRES" 2385885 NIL PATRES (NIL T T) -8 NIL NIL) (-883 2383279 2383346 2383478 "PATRES2" 2383642 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-882 2381162 2381567 2381974 "PATMATCH" 2382946 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-881 2380697 2380880 2380922 "PATMAB" 2381029 NIL PATMAB (NIL T) -9 NIL 2381112) (-880 2379242 2379551 2379809 "PATLRES" 2380502 NIL PATLRES (NIL T T T) -8 NIL NIL) (-879 2378789 2378912 2378954 "PATAB" 2378959 NIL PATAB (NIL T) -9 NIL 2379129) (-878 2376270 2376802 2377375 "PARTPERM" 2378236 T PARTPERM (NIL) -7 NIL NIL) (-877 2375891 2375954 2376056 "PARSURF" 2376201 NIL PARSURF (NIL T) -8 NIL NIL) (-876 2375523 2375580 2375689 "PARSU2" 2375828 NIL PARSU2 (NIL T T) -7 NIL NIL) (-875 2375144 2375207 2375309 "PARSCURV" 2375454 NIL PARSCURV (NIL T) -8 NIL NIL) (-874 2374776 2374833 2374942 "PARSC2" 2375081 NIL PARSC2 (NIL T T) -7 NIL NIL) (-873 2374415 2374473 2374570 "PARPCURV" 2374712 NIL PARPCURV (NIL T) -8 NIL NIL) (-872 2374047 2374104 2374213 "PARPC2" 2374352 NIL PARPC2 (NIL T T) -7 NIL NIL) (-871 2372527 2372645 2372964 "PARAMP" 2373902 NIL PARAMP (NIL T NIL T T T T T) -7 NIL NIL) (-870 2372047 2372133 2372252 "PAN2EXPR" 2372428 T PAN2EXPR (NIL) -7 NIL NIL) (-869 2370853 2371168 2371396 "PALETTE" 2371839 T PALETTE (NIL) -8 NIL NIL) (-868 2358486 2360652 2362768 "PAFF" 2368801 NIL PAFF (NIL T NIL T) -7 NIL NIL) (-867 2345482 2347810 2350021 "PAFFFF" 2356339 NIL PAFFFF (NIL T NIL T) -7 NIL NIL) (-866 2339323 2344741 2344935 "PADICRC" 2345337 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-865 2332522 2338669 2338853 "PADICRAT" 2339171 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-864 2330826 2332459 2332504 "PADIC" 2332509 NIL PADIC (NIL NIL) -8 NIL NIL) (-863 2328026 2329600 2329641 "PADICCT" 2330222 NIL PADICCT (NIL NIL) -9 NIL 2330504) (-862 2326983 2327183 2327451 "PADEPAC" 2327813 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-861 2326195 2326328 2326534 "PADE" 2326845 NIL PADE (NIL T T T) -7 NIL NIL) (-860 2322672 2325813 2325932 "PACRAT" 2326096 T PACRAT (NIL) -8 NIL NIL) (-859 2318733 2321783 2321812 "PACRATC" 2321817 T PACRATC (NIL) -9 NIL 2321897) (-858 2314855 2316820 2316849 "PACPERC" 2317795 T PACPERC (NIL) -9 NIL 2318235) (-857 2311525 2314629 2314720 "PACOFF" 2314796 NIL PACOFF (NIL T) -8 NIL NIL) (-856 2308220 2310880 2310909 "PACFFC" 2310914 T PACFFC (NIL) -9 NIL 2310935) (-855 2304310 2307903 2308004 "PACEXT" 2308151 NIL PACEXT (NIL NIL) -8 NIL NIL) (-854 2299688 2303205 2303234 "PACEXTC" 2303239 T PACEXTC (NIL) -9 NIL 2303283) (-853 2297696 2298528 2298843 "OWP" 2299457 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-852 2296805 2297301 2297473 "OVAR" 2297564 NIL OVAR (NIL NIL) -8 NIL NIL) (-851 2296069 2296190 2296351 "OUT" 2296664 T OUT (NIL) -7 NIL NIL) (-850 2285115 2287294 2289464 "OUTFORM" 2293919 T OUTFORM (NIL) -8 NIL NIL) (-849 2284523 2284844 2284933 "OSI" 2285046 T OSI (NIL) -8 NIL NIL) (-848 2283270 2283497 2283781 "ORTHPOL" 2284271 NIL ORTHPOL (NIL T) -7 NIL NIL) (-847 2280632 2282927 2283067 "OREUP" 2283213 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-846 2278019 2280321 2280449 "ORESUP" 2280574 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-845 2275527 2276033 2276598 "OREPCTO" 2277504 NIL OREPCTO (NIL T T) -7 NIL NIL) (-844 2269397 2271608 2271650 "OREPCAT" 2273998 NIL OREPCAT (NIL T) -9 NIL 2275098) (-843 2266544 2267326 2268384 "OREPCAT-" 2268389 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-842 2265720 2265992 2266021 "ORDSET" 2266330 T ORDSET (NIL) -9 NIL 2266494) (-841 2265239 2265361 2265554 "ORDSET-" 2265559 NIL ORDSET- (NIL T) -8 NIL NIL) (-840 2263848 2264649 2264678 "ORDRING" 2264880 T ORDRING (NIL) -9 NIL 2265005) (-839 2263493 2263587 2263731 "ORDRING-" 2263736 NIL ORDRING- (NIL T) -8 NIL NIL) (-838 2262867 2263348 2263377 "ORDMON" 2263382 T ORDMON (NIL) -9 NIL 2263403) (-837 2262029 2262176 2262371 "ORDFUNS" 2262716 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-836 2261539 2261898 2261927 "ORDFIN" 2261932 T ORDFIN (NIL) -9 NIL 2261953) (-835 2258051 2260131 2260537 "ORDCOMP" 2261166 NIL ORDCOMP (NIL T) -8 NIL NIL) (-834 2257317 2257444 2257630 "ORDCOMP2" 2257911 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-833 2253825 2254707 2255544 "OPTPROB" 2256500 T OPTPROB (NIL) -8 NIL NIL) (-832 2250627 2251266 2251970 "OPTPACK" 2253141 T OPTPACK (NIL) -7 NIL NIL) (-831 2248339 2249079 2249108 "OPTCAT" 2249927 T OPTCAT (NIL) -9 NIL 2250577) (-830 2248107 2248146 2248212 "OPQUERY" 2248293 T OPQUERY (NIL) -7 NIL NIL) (-829 2245233 2246424 2246925 "OP" 2247639 NIL OP (NIL T) -8 NIL NIL) (-828 2241998 2244036 2244402 "ONECOMP" 2244900 NIL ONECOMP (NIL T) -8 NIL NIL) (-827 2241303 2241418 2241592 "ONECOMP2" 2241870 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-826 2240722 2240828 2240958 "OMSERVER" 2241193 T OMSERVER (NIL) -7 NIL NIL) (-825 2237609 2240161 2240202 "OMSAGG" 2240263 NIL OMSAGG (NIL T) -9 NIL 2240327) (-824 2236232 2236495 2236777 "OMPKG" 2237347 T OMPKG (NIL) -7 NIL NIL) (-823 2235661 2235764 2235793 "OM" 2236092 T OM (NIL) -9 NIL NIL) (-822 2234199 2235212 2235380 "OMLO" 2235543 NIL OMLO (NIL T T) -8 NIL NIL) (-821 2233124 2233271 2233498 "OMEXPR" 2234025 NIL OMEXPR (NIL T) -7 NIL NIL) (-820 2232442 2232670 2232806 "OMERR" 2233008 T OMERR (NIL) -8 NIL NIL) (-819 2231620 2231863 2232023 "OMERRK" 2232302 T OMERRK (NIL) -8 NIL NIL) (-818 2231098 2231297 2231405 "OMENC" 2231532 T OMENC (NIL) -8 NIL NIL) (-817 2224993 2226178 2227349 "OMDEV" 2229947 T OMDEV (NIL) -8 NIL NIL) (-816 2224062 2224233 2224427 "OMCONN" 2224819 T OMCONN (NIL) -8 NIL NIL) (-815 2222673 2223659 2223688 "OINTDOM" 2223693 T OINTDOM (NIL) -9 NIL 2223714) (-814 2218324 2219579 2220323 "OFMONOID" 2221961 NIL OFMONOID (NIL T) -8 NIL NIL) (-813 2217762 2218261 2218306 "ODVAR" 2218311 NIL ODVAR (NIL T) -8 NIL NIL) (-812 2214889 2217261 2217445 "ODR" 2217638 NIL ODR (NIL T T NIL) -8 NIL NIL) (-811 2207187 2214665 2214791 "ODPOL" 2214796 NIL ODPOL (NIL T) -8 NIL NIL) (-810 2200981 2207059 2207164 "ODP" 2207169 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-809 2199747 2199962 2200237 "ODETOOLS" 2200755 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-808 2196716 2197372 2198088 "ODESYS" 2199080 NIL ODESYS (NIL T T) -7 NIL NIL) (-807 2191600 2192508 2193532 "ODERTRIC" 2195792 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-806 2191026 2191108 2191302 "ODERED" 2191512 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-805 2187914 2188462 2189139 "ODERAT" 2190449 NIL ODERAT (NIL T T) -7 NIL NIL) (-804 2184874 2185338 2185935 "ODEPRRIC" 2187443 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-803 2182745 2183312 2183821 "ODEPROB" 2184385 T ODEPROB (NIL) -8 NIL NIL) (-802 2179267 2179750 2180397 "ODEPRIM" 2182224 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-801 2178516 2178618 2178878 "ODEPAL" 2179159 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-800 2174678 2175469 2176333 "ODEPACK" 2177672 T ODEPACK (NIL) -7 NIL NIL) (-799 2173711 2173818 2174047 "ODEINT" 2174567 NIL ODEINT (NIL T T) -7 NIL NIL) (-798 2167812 2169237 2170684 "ODEIFTBL" 2172284 T ODEIFTBL (NIL) -8 NIL NIL) (-797 2163147 2163933 2164892 "ODEEF" 2166971 NIL ODEEF (NIL T T) -7 NIL NIL) (-796 2162482 2162571 2162801 "ODECONST" 2163052 NIL ODECONST (NIL T T T) -7 NIL NIL) (-795 2160632 2161267 2161296 "ODECAT" 2161901 T ODECAT (NIL) -9 NIL 2162432) (-794 2157493 2160344 2160463 "OCT" 2160545 NIL OCT (NIL T) -8 NIL NIL) (-793 2157131 2157174 2157301 "OCTCT2" 2157444 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-792 2151955 2154399 2154440 "OC" 2155537 NIL OC (NIL T) -9 NIL 2156387) (-791 2149182 2149930 2150920 "OC-" 2151014 NIL OC- (NIL T T) -8 NIL NIL) (-790 2148559 2149001 2149030 "OCAMON" 2149035 T OCAMON (NIL) -9 NIL 2149056) (-789 2148011 2148418 2148447 "OASGP" 2148452 T OASGP (NIL) -9 NIL 2148472) (-788 2147297 2147760 2147789 "OAMONS" 2147829 T OAMONS (NIL) -9 NIL 2147872) (-787 2146736 2147143 2147172 "OAMON" 2147177 T OAMON (NIL) -9 NIL 2147197) (-786 2146039 2146531 2146560 "OAGROUP" 2146565 T OAGROUP (NIL) -9 NIL 2146585) (-785 2145729 2145779 2145867 "NUMTUBE" 2145983 NIL NUMTUBE (NIL T) -7 NIL NIL) (-784 2139302 2140820 2142356 "NUMQUAD" 2144213 T NUMQUAD (NIL) -7 NIL NIL) (-783 2135058 2136046 2137071 "NUMODE" 2138297 T NUMODE (NIL) -7 NIL NIL) (-782 2132438 2133292 2133321 "NUMINT" 2134244 T NUMINT (NIL) -9 NIL 2135008) (-781 2131386 2131583 2131801 "NUMFMT" 2132240 T NUMFMT (NIL) -7 NIL NIL) (-780 2117764 2120706 2123230 "NUMERIC" 2128901 NIL NUMERIC (NIL T) -7 NIL NIL) (-779 2112167 2117212 2117308 "NTSCAT" 2117313 NIL NTSCAT (NIL T T T T) -9 NIL 2117352) (-778 2111363 2111528 2111720 "NTPOLFN" 2112007 NIL NTPOLFN (NIL T) -7 NIL NIL) (-777 2099159 2108190 2109001 "NSUP" 2110585 NIL NSUP (NIL T) -8 NIL NIL) (-776 2098791 2098848 2098957 "NSUP2" 2099096 NIL NSUP2 (NIL T T) -7 NIL NIL) (-775 2088742 2098565 2098698 "NSMP" 2098703 NIL NSMP (NIL T T) -8 NIL NIL) (-774 2076834 2088324 2088488 "NSDPS" 2088610 NIL NSDPS (NIL T) -8 NIL NIL) (-773 2075266 2075567 2075924 "NREP" 2076522 NIL NREP (NIL T) -7 NIL NIL) (-772 2072355 2072903 2073552 "NPOLYGON" 2074708 NIL NPOLYGON (NIL T T T NIL) -7 NIL NIL) (-771 2070946 2071198 2071556 "NPCOEF" 2072098 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-770 2070228 2070730 2070814 "NOTTING" 2070894 NIL NOTTING (NIL T) -8 NIL NIL) (-769 2069294 2069409 2069625 "NORMRETR" 2070109 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-768 2067335 2067625 2068034 "NORMPK" 2069002 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-767 2067020 2067048 2067172 "NORMMA" 2067301 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-766 2066847 2066977 2067006 "NONE" 2067011 T NONE (NIL) -8 NIL NIL) (-765 2066636 2066665 2066734 "NONE1" 2066811 NIL NONE1 (NIL T) -7 NIL NIL) (-764 2066119 2066181 2066367 "NODE1" 2066568 NIL NODE1 (NIL T T) -7 NIL NIL) (-763 2064413 2065282 2065537 "NNI" 2065884 T NNI (NIL) -8 NIL NIL) (-762 2062833 2063146 2063510 "NLINSOL" 2064081 NIL NLINSOL (NIL T) -7 NIL NIL) (-761 2059001 2059968 2060890 "NIPROB" 2061931 T NIPROB (NIL) -8 NIL NIL) (-760 2057758 2057992 2058294 "NFINTBAS" 2058763 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-759 2057487 2057530 2057611 "NEWTON" 2057709 NIL NEWTON (NIL T) -7 NIL NIL) (-758 2056195 2056426 2056707 "NCODIV" 2057255 NIL NCODIV (NIL T T) -7 NIL NIL) (-757 2055957 2055994 2056069 "NCNTFRAC" 2056152 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-756 2054137 2054501 2054921 "NCEP" 2055582 NIL NCEP (NIL T) -7 NIL NIL) (-755 2053047 2053786 2053815 "NASRING" 2053925 T NASRING (NIL) -9 NIL 2053999) (-754 2052842 2052886 2052980 "NASRING-" 2052985 NIL NASRING- (NIL T) -8 NIL NIL) (-753 2051994 2052493 2052522 "NARNG" 2052639 T NARNG (NIL) -9 NIL 2052730) (-752 2051686 2051753 2051887 "NARNG-" 2051892 NIL NARNG- (NIL T) -8 NIL NIL) (-751 2050565 2050772 2051007 "NAGSP" 2051471 T NAGSP (NIL) -7 NIL NIL) (-750 2041837 2043521 2045194 "NAGS" 2048912 T NAGS (NIL) -7 NIL NIL) (-749 2040385 2040693 2041024 "NAGF07" 2041526 T NAGF07 (NIL) -7 NIL NIL) (-748 2034923 2036214 2037521 "NAGF04" 2039098 T NAGF04 (NIL) -7 NIL NIL) (-747 2027891 2029505 2031138 "NAGF02" 2033310 T NAGF02 (NIL) -7 NIL NIL) (-746 2023115 2024215 2025332 "NAGF01" 2026794 T NAGF01 (NIL) -7 NIL NIL) (-745 2016743 2018309 2019894 "NAGE04" 2021550 T NAGE04 (NIL) -7 NIL NIL) (-744 2007912 2010033 2012163 "NAGE02" 2014633 T NAGE02 (NIL) -7 NIL NIL) (-743 2003865 2004812 2005776 "NAGE01" 2006968 T NAGE01 (NIL) -7 NIL NIL) (-742 2001660 2002194 2002752 "NAGD03" 2003327 T NAGD03 (NIL) -7 NIL NIL) (-741 1993410 1995338 1997292 "NAGD02" 1999726 T NAGD02 (NIL) -7 NIL NIL) (-740 1987221 1988646 1990086 "NAGD01" 1991990 T NAGD01 (NIL) -7 NIL NIL) (-739 1983430 1984252 1985089 "NAGC06" 1986404 T NAGC06 (NIL) -7 NIL NIL) (-738 1981895 1982227 1982583 "NAGC05" 1983094 T NAGC05 (NIL) -7 NIL NIL) (-737 1981271 1981390 1981534 "NAGC02" 1981771 T NAGC02 (NIL) -7 NIL NIL) (-736 1980330 1980887 1980928 "NAALG" 1981007 NIL NAALG (NIL T) -9 NIL 1981068) (-735 1980165 1980194 1980284 "NAALG-" 1980289 NIL NAALG- (NIL T T) -8 NIL NIL) (-734 1971041 1979281 1979556 "MYUP" 1979936 NIL MYUP (NIL NIL T) -8 NIL NIL) (-733 1961404 1969497 1969868 "MYEXPR" 1970736 NIL MYEXPR (NIL NIL T) -8 NIL NIL) (-732 1955354 1956462 1957649 "MULTSQFR" 1960300 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-731 1954673 1954748 1954932 "MULTFACT" 1955266 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-730 1947798 1951707 1951761 "MTSCAT" 1952831 NIL MTSCAT (NIL T T) -9 NIL 1953345) (-729 1947510 1947564 1947656 "MTHING" 1947738 NIL MTHING (NIL T) -7 NIL NIL) (-728 1947302 1947335 1947395 "MSYSCMD" 1947470 T MSYSCMD (NIL) -7 NIL NIL) (-727 1943414 1946057 1946377 "MSET" 1947015 NIL MSET (NIL T) -8 NIL NIL) (-726 1940508 1942974 1943016 "MSETAGG" 1943021 NIL MSETAGG (NIL T) -9 NIL 1943055) (-725 1936357 1937899 1938638 "MRING" 1939814 NIL MRING (NIL T T) -8 NIL NIL) (-724 1935923 1935990 1936121 "MRF2" 1936284 NIL MRF2 (NIL T T T) -7 NIL NIL) (-723 1935541 1935576 1935720 "MRATFAC" 1935882 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-722 1933153 1933448 1933879 "MPRFF" 1935246 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-721 1927167 1933007 1933104 "MPOLY" 1933109 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-720 1926657 1926692 1926900 "MPCPF" 1927126 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-719 1926171 1926214 1926398 "MPC3" 1926608 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-718 1925366 1925447 1925668 "MPC2" 1926086 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-717 1923667 1924004 1924394 "MONOTOOL" 1925026 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-716 1922790 1923125 1923154 "MONOID" 1923431 T MONOID (NIL) -9 NIL 1923603) (-715 1922168 1922331 1922574 "MONOID-" 1922579 NIL MONOID- (NIL T) -8 NIL NIL) (-714 1913094 1919079 1919139 "MONOGEN" 1919813 NIL MONOGEN (NIL T T) -9 NIL 1920266) (-713 1910312 1911047 1912047 "MONOGEN-" 1912166 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-712 1909170 1909590 1909619 "MONADWU" 1910011 T MONADWU (NIL) -9 NIL 1910249) (-711 1908542 1908701 1908949 "MONADWU-" 1908954 NIL MONADWU- (NIL T) -8 NIL NIL) (-710 1907926 1908144 1908173 "MONAD" 1908380 T MONAD (NIL) -9 NIL 1908492) (-709 1907611 1907689 1907821 "MONAD-" 1907826 NIL MONAD- (NIL T) -8 NIL NIL) (-708 1905862 1906524 1906803 "MOEBIUS" 1907364 NIL MOEBIUS (NIL T) -8 NIL NIL) (-707 1905253 1905631 1905672 "MODULE" 1905677 NIL MODULE (NIL T) -9 NIL 1905703) (-706 1904821 1904917 1905107 "MODULE-" 1905112 NIL MODULE- (NIL T T) -8 NIL NIL) (-705 1902490 1903185 1903512 "MODRING" 1904645 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-704 1899436 1900601 1901119 "MODOP" 1902022 NIL MODOP (NIL T T) -8 NIL NIL) (-703 1897623 1898075 1898416 "MODMONOM" 1899235 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-702 1887288 1895819 1896240 "MODMON" 1897253 NIL MODMON (NIL T T) -8 NIL NIL) (-701 1884414 1886132 1886408 "MODFIELD" 1887163 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-700 1883418 1883695 1883885 "MMLFORM" 1884244 T MMLFORM (NIL) -8 NIL NIL) (-699 1882944 1882987 1883166 "MMAP" 1883369 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-698 1881169 1881946 1881988 "MLO" 1882411 NIL MLO (NIL T) -9 NIL 1882652) (-697 1878536 1879051 1879653 "MLIFT" 1880650 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-696 1877927 1878011 1878165 "MKUCFUNC" 1878447 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-695 1877526 1877596 1877719 "MKRECORD" 1877850 NIL MKRECORD (NIL T T) -7 NIL NIL) (-694 1876574 1876735 1876963 "MKFUNC" 1877337 NIL MKFUNC (NIL T) -7 NIL NIL) (-693 1875962 1876066 1876222 "MKFLCFN" 1876457 NIL MKFLCFN (NIL T) -7 NIL NIL) (-692 1875388 1875755 1875844 "MKCHSET" 1875906 NIL MKCHSET (NIL T) -8 NIL NIL) (-691 1874665 1874767 1874952 "MKBCFUNC" 1875281 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-690 1871349 1874219 1874355 "MINT" 1874549 T MINT (NIL) -8 NIL NIL) (-689 1870161 1870404 1870681 "MHROWRED" 1871104 NIL MHROWRED (NIL T) -7 NIL NIL) (-688 1865428 1868602 1869028 "MFLOAT" 1869755 T MFLOAT (NIL) -8 NIL NIL) (-687 1864785 1864861 1865032 "MFINFACT" 1865340 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-686 1861100 1861948 1862832 "MESH" 1863921 T MESH (NIL) -7 NIL NIL) (-685 1859490 1859802 1860155 "MDDFACT" 1860787 NIL MDDFACT (NIL T) -7 NIL NIL) (-684 1856372 1858683 1858725 "MDAGG" 1858980 NIL MDAGG (NIL T) -9 NIL 1859123) (-683 1846060 1855665 1855872 "MCMPLX" 1856185 T MCMPLX (NIL) -8 NIL NIL) (-682 1845201 1845347 1845547 "MCDEN" 1845909 NIL MCDEN (NIL T T) -7 NIL NIL) (-681 1843091 1843361 1843741 "MCALCFN" 1844931 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-680 1840703 1841226 1841788 "MATSTOR" 1842562 NIL MATSTOR (NIL T) -7 NIL NIL) (-679 1836617 1840079 1840325 "MATRIX" 1840490 NIL MATRIX (NIL T) -8 NIL NIL) (-678 1832393 1833096 1833829 "MATLIN" 1835977 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-677 1822158 1825379 1825457 "MATCAT" 1830587 NIL MATCAT (NIL T T T) -9 NIL 1832094) (-676 1818357 1819425 1820836 "MATCAT-" 1820841 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-675 1816951 1817104 1817437 "MATCAT2" 1818192 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-674 1815691 1815957 1816272 "MAPPKG4" 1816682 NIL MAPPKG4 (NIL T T) -7 NIL NIL) (-673 1813803 1814127 1814511 "MAPPKG3" 1815366 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-672 1812784 1812957 1813179 "MAPPKG2" 1813627 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-671 1811283 1811567 1811894 "MAPPKG1" 1812490 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-670 1810894 1810952 1811075 "MAPHACK3" 1811219 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-669 1810486 1810547 1810661 "MAPHACK2" 1810826 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-668 1809924 1810027 1810169 "MAPHACK1" 1810377 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-667 1808030 1808624 1808928 "MAGMA" 1809652 NIL MAGMA (NIL T) -8 NIL NIL) (-666 1804505 1806271 1806731 "M3D" 1807603 NIL M3D (NIL T) -8 NIL NIL) (-665 1798699 1802905 1802947 "LZSTAGG" 1803729 NIL LZSTAGG (NIL T) -9 NIL 1804024) (-664 1794673 1795830 1797287 "LZSTAGG-" 1797292 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-663 1791787 1792564 1793051 "LWORD" 1794218 NIL LWORD (NIL T) -8 NIL NIL) (-662 1784942 1791558 1791692 "LSQM" 1791697 NIL LSQM (NIL NIL T) -8 NIL NIL) (-661 1784166 1784305 1784533 "LSPP" 1784797 NIL LSPP (NIL T T T T) -7 NIL NIL) (-660 1781978 1782279 1782735 "LSMP" 1783855 NIL LSMP (NIL T T T T) -7 NIL NIL) (-659 1778757 1779431 1780161 "LSMP1" 1781280 NIL LSMP1 (NIL T) -7 NIL NIL) (-658 1772714 1777947 1777989 "LSAGG" 1778051 NIL LSAGG (NIL T) -9 NIL 1778129) (-657 1769409 1770333 1771546 "LSAGG-" 1771551 NIL LSAGG- (NIL T T) -8 NIL NIL) (-656 1767035 1768553 1768802 "LPOLY" 1769204 NIL LPOLY (NIL T T) -8 NIL NIL) (-655 1766617 1766702 1766825 "LPEFRAC" 1766944 NIL LPEFRAC (NIL T) -7 NIL NIL) (-654 1764181 1764430 1764862 "LPARSPT" 1766359 NIL LPARSPT (NIL T NIL T T T T T) -7 NIL NIL) (-653 1762656 1762983 1763343 "LOP" 1763853 NIL LOP (NIL T) -7 NIL NIL) (-652 1761005 1761752 1762004 "LO" 1762489 NIL LO (NIL T T T) -8 NIL NIL) (-651 1760656 1760768 1760797 "LOGIC" 1760908 T LOGIC (NIL) -9 NIL 1760989) (-650 1760518 1760541 1760612 "LOGIC-" 1760617 NIL LOGIC- (NIL T) -8 NIL NIL) (-649 1759711 1759851 1760044 "LODOOPS" 1760374 NIL LODOOPS (NIL T T) -7 NIL NIL) (-648 1757123 1759627 1759693 "LODO" 1759698 NIL LODO (NIL T NIL) -8 NIL NIL) (-647 1755663 1755898 1756250 "LODOF" 1756871 NIL LODOF (NIL T T) -7 NIL NIL) (-646 1752062 1754503 1754545 "LODOCAT" 1754983 NIL LODOCAT (NIL T) -9 NIL 1755193) (-645 1751795 1751853 1751980 "LODOCAT-" 1751985 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-644 1749104 1751636 1751754 "LODO2" 1751759 NIL LODO2 (NIL T T) -8 NIL NIL) (-643 1746528 1749041 1749086 "LODO1" 1749091 NIL LODO1 (NIL T) -8 NIL NIL) (-642 1745388 1745553 1745865 "LODEEF" 1746351 NIL LODEEF (NIL T T T) -7 NIL NIL) (-641 1738215 1742380 1742421 "LOCPOWC" 1743883 NIL LOCPOWC (NIL T) -9 NIL 1744460) (-640 1733539 1736377 1736419 "LNAGG" 1737366 NIL LNAGG (NIL T) -9 NIL 1737809) (-639 1732686 1732900 1733242 "LNAGG-" 1733247 NIL LNAGG- (NIL T T) -8 NIL NIL) (-638 1728849 1729611 1730250 "LMOPS" 1732101 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-637 1728243 1728605 1728647 "LMODULE" 1728708 NIL LMODULE (NIL T) -9 NIL 1728750) (-636 1725495 1727888 1728011 "LMDICT" 1728153 NIL LMDICT (NIL T) -8 NIL NIL) (-635 1724652 1724786 1724973 "LISYSER" 1725357 NIL LISYSER (NIL T T) -7 NIL NIL) (-634 1717889 1723602 1723898 "LIST" 1724389 NIL LIST (NIL T) -8 NIL NIL) (-633 1717414 1717488 1717627 "LIST3" 1717809 NIL LIST3 (NIL T T T) -7 NIL NIL) (-632 1716421 1716599 1716827 "LIST2" 1717232 NIL LIST2 (NIL T T) -7 NIL NIL) (-631 1714555 1714867 1715266 "LIST2MAP" 1716068 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-630 1713260 1713940 1713982 "LINEXP" 1714237 NIL LINEXP (NIL T) -9 NIL 1714386) (-629 1711907 1712167 1712464 "LINDEP" 1713012 NIL LINDEP (NIL T T) -7 NIL NIL) (-628 1708674 1709393 1710170 "LIMITRF" 1711162 NIL LIMITRF (NIL T) -7 NIL NIL) (-627 1706950 1707245 1707661 "LIMITPS" 1708369 NIL LIMITPS (NIL T T) -7 NIL NIL) (-626 1701409 1706465 1706691 "LIE" 1706773 NIL LIE (NIL T T) -8 NIL NIL) (-625 1700458 1700901 1700942 "LIECAT" 1701082 NIL LIECAT (NIL T) -9 NIL 1701232) (-624 1700299 1700326 1700414 "LIECAT-" 1700419 NIL LIECAT- (NIL T T) -8 NIL NIL) (-623 1692833 1699678 1699861 "LIB" 1700136 T LIB (NIL) -8 NIL NIL) (-622 1688470 1689351 1690286 "LGROBP" 1691950 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-621 1685951 1686275 1686686 "LF" 1688143 NIL LF (NIL T T) -7 NIL NIL) (-620 1684648 1685378 1685407 "LFCAT" 1685682 T LFCAT (NIL) -9 NIL 1685857) (-619 1681552 1682180 1682868 "LEXTRIPK" 1684012 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-618 1678258 1679122 1679625 "LEXP" 1681132 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-617 1676656 1676969 1677370 "LEADCDET" 1677940 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-616 1675846 1675920 1676149 "LAZM3PK" 1676577 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-615 1670762 1673929 1674464 "LAUPOL" 1675361 NIL LAUPOL (NIL T T) -8 NIL NIL) (-614 1670327 1670371 1670539 "LAPLACE" 1670712 NIL LAPLACE (NIL T T) -7 NIL NIL) (-613 1668257 1669430 1669680 "LA" 1670161 NIL LA (NIL T T T) -8 NIL NIL) (-612 1667313 1667907 1667949 "LALG" 1668011 NIL LALG (NIL T) -9 NIL 1668070) (-611 1667027 1667086 1667222 "LALG-" 1667227 NIL LALG- (NIL T T) -8 NIL NIL) (-610 1665931 1666118 1666417 "KOVACIC" 1666827 NIL KOVACIC (NIL T T) -7 NIL NIL) (-609 1665765 1665789 1665831 "KONVERT" 1665893 NIL KONVERT (NIL T) -9 NIL NIL) (-608 1665599 1665623 1665665 "KOERCE" 1665727 NIL KOERCE (NIL T) -9 NIL NIL) (-607 1663335 1664095 1664487 "KERNEL" 1665239 NIL KERNEL (NIL T) -8 NIL NIL) (-606 1662837 1662918 1663048 "KERNEL2" 1663249 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-605 1656520 1661202 1661257 "KDAGG" 1661634 NIL KDAGG (NIL T T) -9 NIL 1661840) (-604 1656049 1656173 1656378 "KDAGG-" 1656383 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-603 1649198 1655710 1655865 "KAFILE" 1655927 NIL KAFILE (NIL T) -8 NIL NIL) (-602 1643657 1648713 1648939 "JORDAN" 1649021 NIL JORDAN (NIL T T) -8 NIL NIL) (-601 1640000 1641900 1641955 "IXAGG" 1642884 NIL IXAGG (NIL T T) -9 NIL 1643339) (-600 1638919 1639225 1639644 "IXAGG-" 1639649 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-599 1634503 1638841 1638900 "IVECTOR" 1638905 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-598 1633269 1633506 1633772 "ITUPLE" 1634270 NIL ITUPLE (NIL T) -8 NIL NIL) (-597 1631693 1631870 1632178 "ITRIGMNP" 1633091 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-596 1630438 1630642 1630925 "ITFUN3" 1631469 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-595 1630070 1630127 1630236 "ITFUN2" 1630375 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-594 1627863 1628934 1629232 "ITAYLOR" 1629805 NIL ITAYLOR (NIL T) -8 NIL NIL) (-593 1616802 1622002 1623164 "ISUPS" 1626734 NIL ISUPS (NIL T) -8 NIL NIL) (-592 1615906 1616046 1616282 "ISUMP" 1616649 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-591 1611176 1615707 1615786 "ISTRING" 1615859 NIL ISTRING (NIL NIL) -8 NIL NIL) (-590 1610386 1610467 1610683 "IRURPK" 1611090 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-589 1609322 1609523 1609763 "IRSN" 1610166 T IRSN (NIL) -7 NIL NIL) (-588 1607353 1607708 1608143 "IRRF2F" 1608961 NIL IRRF2F (NIL T) -7 NIL NIL) (-587 1607100 1607138 1607214 "IRREDFFX" 1607309 NIL IRREDFFX (NIL T) -7 NIL NIL) (-586 1605715 1605974 1606273 "IROOT" 1606833 NIL IROOT (NIL T) -7 NIL NIL) (-585 1602351 1603403 1604093 "IR" 1605057 NIL IR (NIL T) -8 NIL NIL) (-584 1599964 1600459 1601025 "IR2" 1601829 NIL IR2 (NIL T T) -7 NIL NIL) (-583 1599036 1599149 1599370 "IR2F" 1599847 NIL IR2F (NIL T T) -7 NIL NIL) (-582 1598827 1598861 1598921 "IPRNTPK" 1598996 T IPRNTPK (NIL) -7 NIL NIL) (-581 1595381 1598716 1598785 "IPF" 1598790 NIL IPF (NIL NIL) -8 NIL NIL) (-580 1593698 1595306 1595363 "IPADIC" 1595368 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-579 1593195 1593253 1593443 "INVLAPLA" 1593634 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-578 1582844 1585197 1587583 "INTTR" 1590859 NIL INTTR (NIL T T) -7 NIL NIL) (-577 1579202 1579944 1580801 "INTTOOLS" 1582036 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-576 1578788 1578879 1578996 "INTSLPE" 1579105 T INTSLPE (NIL) -7 NIL NIL) (-575 1576738 1578711 1578770 "INTRVL" 1578775 NIL INTRVL (NIL T) -8 NIL NIL) (-574 1574340 1574852 1575427 "INTRF" 1576223 NIL INTRF (NIL T) -7 NIL NIL) (-573 1573751 1573848 1573990 "INTRET" 1574238 NIL INTRET (NIL T) -7 NIL NIL) (-572 1571748 1572137 1572607 "INTRAT" 1573359 NIL INTRAT (NIL T T) -7 NIL NIL) (-571 1568984 1569567 1570189 "INTPM" 1571237 NIL INTPM (NIL T T) -7 NIL NIL) (-570 1565689 1566288 1567032 "INTPAF" 1568371 NIL INTPAF (NIL T T T) -7 NIL NIL) (-569 1560868 1561830 1562881 "INTPACK" 1564658 T INTPACK (NIL) -7 NIL NIL) (-568 1557722 1560597 1560724 "INT" 1560761 T INT (NIL) -8 NIL NIL) (-567 1556974 1557126 1557334 "INTHERTR" 1557564 NIL INTHERTR (NIL T T) -7 NIL NIL) (-566 1556413 1556493 1556681 "INTHERAL" 1556888 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-565 1554259 1554702 1555159 "INTHEORY" 1555976 T INTHEORY (NIL) -7 NIL NIL) (-564 1545570 1547190 1548968 "INTG0" 1552612 NIL INTG0 (NIL T T T) -7 NIL NIL) (-563 1526143 1530933 1535743 "INTFTBL" 1540780 T INTFTBL (NIL) -8 NIL NIL) (-562 1524180 1524387 1524788 "INTFRSP" 1525933 NIL INTFRSP (NIL T NIL T T T T T T) -7 NIL NIL) (-561 1523429 1523567 1523740 "INTFACT" 1524039 NIL INTFACT (NIL T) -7 NIL NIL) (-560 1523019 1523061 1523212 "INTERGB" 1523381 NIL INTERGB (NIL T NIL T T T) -7 NIL NIL) (-559 1520404 1520850 1521414 "INTEF" 1522573 NIL INTEF (NIL T T) -7 NIL NIL) (-558 1518861 1519610 1519639 "INTDOM" 1519940 T INTDOM (NIL) -9 NIL 1520147) (-557 1518230 1518404 1518646 "INTDOM-" 1518651 NIL INTDOM- (NIL T) -8 NIL NIL) (-556 1516834 1516939 1517329 "INTDIVP" 1518120 NIL INTDIVP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-555 1513320 1515250 1515305 "INTCAT" 1516104 NIL INTCAT (NIL T) -9 NIL 1516425) (-554 1512793 1512895 1513023 "INTBIT" 1513212 T INTBIT (NIL) -7 NIL NIL) (-553 1511464 1511618 1511932 "INTALG" 1512638 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-552 1510921 1511011 1511181 "INTAF" 1511368 NIL INTAF (NIL T T) -7 NIL NIL) (-551 1504387 1510731 1510871 "INTABL" 1510876 NIL INTABL (NIL T T T) -8 NIL NIL) (-550 1499332 1502058 1502087 "INS" 1503055 T INS (NIL) -9 NIL 1503738) (-549 1496572 1497343 1498317 "INS-" 1498390 NIL INS- (NIL T) -8 NIL NIL) (-548 1495347 1495574 1495872 "INPSIGN" 1496325 NIL INPSIGN (NIL T T) -7 NIL NIL) (-547 1494465 1494582 1494779 "INPRODPF" 1495227 NIL INPRODPF (NIL T T) -7 NIL NIL) (-546 1493359 1493476 1493713 "INPRODFF" 1494345 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-545 1492359 1492511 1492771 "INNMFACT" 1493195 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-544 1491556 1491653 1491841 "INMODGCD" 1492258 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-543 1490065 1490309 1490633 "INFSP" 1491301 NIL INFSP (NIL T T T) -7 NIL NIL) (-542 1489249 1489366 1489549 "INFPROD0" 1489945 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-541 1486130 1487314 1487829 "INFORM" 1488742 T INFORM (NIL) -8 NIL NIL) (-540 1485740 1485800 1485898 "INFORM1" 1486065 NIL INFORM1 (NIL T) -7 NIL NIL) (-539 1485263 1485352 1485466 "INFINITY" 1485646 T INFINITY (NIL) -7 NIL NIL) (-538 1482946 1483943 1484286 "INFCLSPT" 1485123 NIL INFCLSPT (NIL T NIL T T T T T T T) -8 NIL NIL) (-537 1480823 1482068 1482362 "INFCLSPS" 1482716 NIL INFCLSPS (NIL T NIL T) -8 NIL NIL) (-536 1473373 1474296 1474517 "INFCLCT" 1479948 NIL INFCLCT (NIL T NIL T T T T T T T) -9 NIL 1480759) (-535 1471991 1472239 1472560 "INEP" 1473121 NIL INEP (NIL T T T) -7 NIL NIL) (-534 1471267 1471888 1471953 "INDE" 1471958 NIL INDE (NIL T) -8 NIL NIL) (-533 1470831 1470899 1471016 "INCRMAPS" 1471194 NIL INCRMAPS (NIL T) -7 NIL NIL) (-532 1466142 1467067 1468011 "INBFF" 1469919 NIL INBFF (NIL T) -7 NIL NIL) (-531 1462537 1465986 1466090 "IMATRIX" 1466095 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-530 1461251 1461374 1461688 "IMATQF" 1462394 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-529 1459473 1459700 1460036 "IMATLIN" 1461008 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-528 1454105 1459397 1459455 "ILIST" 1459460 NIL ILIST (NIL T NIL) -8 NIL NIL) (-527 1452064 1453965 1454078 "IIARRAY2" 1454083 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-526 1447432 1451975 1452039 "IFF" 1452044 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-525 1442481 1446724 1446912 "IFARRAY" 1447289 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-524 1441688 1442385 1442458 "IFAMON" 1442463 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-523 1441271 1441336 1441391 "IEVALAB" 1441598 NIL IEVALAB (NIL T T) -9 NIL NIL) (-522 1440946 1441014 1441174 "IEVALAB-" 1441179 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-521 1440604 1440860 1440923 "IDPO" 1440928 NIL IDPO (NIL T T) -8 NIL NIL) (-520 1439881 1440493 1440568 "IDPOAMS" 1440573 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-519 1439215 1439770 1439845 "IDPOAM" 1439850 NIL IDPOAM (NIL T T) -8 NIL NIL) (-518 1438299 1438549 1438603 "IDPC" 1439016 NIL IDPC (NIL T T) -9 NIL 1439165) (-517 1437795 1438191 1438264 "IDPAM" 1438269 NIL IDPAM (NIL T T) -8 NIL NIL) (-516 1437198 1437687 1437760 "IDPAG" 1437765 NIL IDPAG (NIL T T) -8 NIL NIL) (-515 1433453 1434301 1435196 "IDECOMP" 1436355 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-514 1426329 1427378 1428424 "IDEAL" 1432490 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-513 1424346 1425493 1425766 "ICP" 1426120 NIL ICP (NIL T NIL T) -8 NIL NIL) (-512 1423510 1423622 1423821 "ICDEN" 1424230 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-511 1422609 1422990 1423137 "ICARD" 1423383 T ICARD (NIL) -8 NIL NIL) (-510 1420669 1420982 1421387 "IBPTOOLS" 1422286 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-509 1416283 1420289 1420402 "IBITS" 1420588 NIL IBITS (NIL NIL) -8 NIL NIL) (-508 1413006 1413582 1414277 "IBATOOL" 1415700 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-507 1410786 1411247 1411780 "IBACHIN" 1412541 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-506 1408669 1410632 1410735 "IARRAY2" 1410740 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-505 1404828 1408595 1408652 "IARRAY1" 1408657 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-504 1398758 1403240 1403721 "IAN" 1404367 T IAN (NIL) -8 NIL NIL) (-503 1398269 1398326 1398499 "IALGFACT" 1398695 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-502 1397796 1397909 1397938 "HYPCAT" 1398145 T HYPCAT (NIL) -9 NIL NIL) (-501 1397334 1397451 1397637 "HYPCAT-" 1397642 NIL HYPCAT- (NIL T) -8 NIL NIL) (-500 1396338 1396615 1396805 "HTMLFORM" 1397164 T HTMLFORM (NIL) -8 NIL NIL) (-499 1393127 1394452 1394494 "HOAGG" 1395475 NIL HOAGG (NIL T) -9 NIL 1396084) (-498 1391721 1392120 1392646 "HOAGG-" 1392651 NIL HOAGG- (NIL T T) -8 NIL NIL) (-497 1385539 1391159 1391326 "HEXADEC" 1391574 T HEXADEC (NIL) -8 NIL NIL) (-496 1384287 1384509 1384772 "HEUGCD" 1385316 NIL HEUGCD (NIL T) -7 NIL NIL) (-495 1383390 1384124 1384254 "HELLFDIV" 1384259 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-494 1377107 1378650 1379731 "HEAP" 1382341 NIL HEAP (NIL T) -8 NIL NIL) (-493 1370945 1377022 1377084 "HDP" 1377089 NIL HDP (NIL NIL T) -8 NIL NIL) (-492 1364650 1370580 1370732 "HDMP" 1370846 NIL HDMP (NIL NIL T) -8 NIL NIL) (-491 1363975 1364114 1364278 "HB" 1364506 T HB (NIL) -7 NIL NIL) (-490 1357484 1363821 1363925 "HASHTBL" 1363930 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-489 1355231 1357106 1357288 "HACKPI" 1357322 T HACKPI (NIL) -8 NIL NIL) (-488 1337379 1341248 1345251 "GUESSUP" 1351261 NIL GUESSUP (NIL NIL) -7 NIL NIL) (-487 1308476 1315517 1322213 "GUESSP" 1330703 T GUESSP (NIL) -7 NIL NIL) (-486 1275291 1280562 1285946 "GUESS" 1303420 NIL GUESS (NIL T T T T NIL NIL) -7 NIL NIL) (-485 1248796 1255193 1261329 "GUESSINT" 1269175 T GUESSINT (NIL) -7 NIL NIL) (-484 1224167 1229617 1235184 "GUESSF" 1243281 NIL GUESSF (NIL T) -7 NIL NIL) (-483 1223889 1223926 1224021 "GUESSF1" 1224124 NIL GUESSF1 (NIL T) -7 NIL NIL) (-482 1200050 1205584 1211199 "GUESSAN" 1218294 T GUESSAN (NIL) -7 NIL NIL) (-481 1195745 1199903 1200016 "GTSET" 1200021 NIL GTSET (NIL T T T T) -8 NIL NIL) (-480 1189283 1195623 1195721 "GSTBL" 1195726 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-479 1181513 1188316 1188580 "GSERIES" 1189075 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-478 1180534 1180987 1181016 "GROUP" 1181277 T GROUP (NIL) -9 NIL 1181436) (-477 1179650 1179873 1180217 "GROUP-" 1180222 NIL GROUP- (NIL T) -8 NIL NIL) (-476 1178019 1178338 1178725 "GROEBSOL" 1179327 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-475 1176958 1177220 1177272 "GRMOD" 1177801 NIL GRMOD (NIL T T) -9 NIL 1177969) (-474 1176726 1176762 1176890 "GRMOD-" 1176895 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-473 1172055 1173080 1174080 "GRIMAGE" 1175746 T GRIMAGE (NIL) -8 NIL NIL) (-472 1170522 1170782 1171106 "GRDEF" 1171751 T GRDEF (NIL) -7 NIL NIL) (-471 1169966 1170082 1170223 "GRAY" 1170401 T GRAY (NIL) -7 NIL NIL) (-470 1169196 1169576 1169628 "GRALG" 1169781 NIL GRALG (NIL T T) -9 NIL 1169874) (-469 1168857 1168930 1169093 "GRALG-" 1169098 NIL GRALG- (NIL T T T) -8 NIL NIL) (-468 1165661 1168442 1168620 "GPOLSET" 1168764 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-467 1147864 1149354 1150943 "GPAFF" 1164352 NIL GPAFF (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-466 1147218 1147275 1147533 "GOSPER" 1147801 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-465 1144611 1145205 1145694 "GOPT" 1146749 T GOPT (NIL) -8 NIL NIL) (-464 1141832 1142473 1143010 "GOPT0" 1144094 T GOPT0 (NIL) -8 NIL NIL) (-463 1137591 1138270 1138796 "GMODPOL" 1141531 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-462 1136596 1136780 1137018 "GHENSEL" 1137403 NIL GHENSEL (NIL T T) -7 NIL NIL) (-461 1130647 1131490 1132517 "GENUPS" 1135680 NIL GENUPS (NIL T T) -7 NIL NIL) (-460 1130344 1130395 1130484 "GENUFACT" 1130590 NIL GENUFACT (NIL T) -7 NIL NIL) (-459 1129756 1129833 1129998 "GENPGCD" 1130262 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-458 1129230 1129265 1129478 "GENMFACT" 1129715 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-457 1127798 1128053 1128360 "GENEEZ" 1128973 NIL GENEEZ (NIL T T) -7 NIL NIL) (-456 1126342 1126619 1126943 "GDRAW" 1127494 T GDRAW (NIL) -7 NIL NIL) (-455 1120209 1125953 1126115 "GDMP" 1126265 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-454 1109593 1113982 1115087 "GCNAALG" 1119193 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-453 1108010 1108882 1108911 "GCDDOM" 1109166 T GCDDOM (NIL) -9 NIL 1109323) (-452 1107480 1107607 1107822 "GCDDOM-" 1107827 NIL GCDDOM- (NIL T) -8 NIL NIL) (-451 1106154 1106339 1106642 "GB" 1107260 NIL GB (NIL T T T T) -7 NIL NIL) (-450 1094774 1097100 1099492 "GBINTERN" 1103845 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-449 1092611 1092903 1093324 "GBF" 1094449 NIL GBF (NIL T T T T) -7 NIL NIL) (-448 1091392 1091557 1091824 "GBEUCLID" 1092427 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-447 1090741 1090866 1091015 "GAUSSFAC" 1091263 T GAUSSFAC (NIL) -7 NIL NIL) (-446 1089110 1089412 1089725 "GALUTIL" 1090461 NIL GALUTIL (NIL T) -7 NIL NIL) (-445 1087418 1087692 1088016 "GALPOLYU" 1088837 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-444 1084783 1085073 1085480 "GALFACTU" 1087115 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-443 1076589 1078088 1079696 "GALFACT" 1083215 NIL GALFACT (NIL T) -7 NIL NIL) (-442 1073977 1074634 1074663 "FVFUN" 1075819 T FVFUN (NIL) -9 NIL 1076539) (-441 1073243 1073424 1073453 "FVC" 1073744 T FVC (NIL) -9 NIL 1073927) (-440 1072885 1073040 1073121 "FUNCTION" 1073195 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-439 1070555 1071106 1071595 "FT" 1072416 T FT (NIL) -8 NIL NIL) (-438 1069347 1069856 1070059 "FTEM" 1070372 T FTEM (NIL) -8 NIL NIL) (-437 1067605 1067894 1068297 "FSUPFACT" 1069039 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-436 1066002 1066291 1066623 "FST" 1067293 T FST (NIL) -8 NIL NIL) (-435 1065173 1065279 1065474 "FSRED" 1065884 NIL FSRED (NIL T T) -7 NIL NIL) (-434 1063854 1064109 1064462 "FSPRMELT" 1064889 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-433 1059220 1059925 1060682 "FSPECF" 1063159 NIL FSPECF (NIL T T) -7 NIL NIL) (-432 1041478 1050067 1050108 "FS" 1053956 NIL FS (NIL T) -9 NIL 1056234) (-431 1030128 1033118 1037174 "FS-" 1037471 NIL FS- (NIL T T) -8 NIL NIL) (-430 1029642 1029696 1029873 "FSINT" 1030069 NIL FSINT (NIL T T) -7 NIL NIL) (-429 1027927 1028639 1028940 "FSERIES" 1029423 NIL FSERIES (NIL T T) -8 NIL NIL) (-428 1026941 1027057 1027288 "FSCINT" 1027807 NIL FSCINT (NIL T T) -7 NIL NIL) (-427 1023176 1025886 1025928 "FSAGG" 1026298 NIL FSAGG (NIL T) -9 NIL 1026555) (-426 1020938 1021539 1022335 "FSAGG-" 1022430 NIL FSAGG- (NIL T T) -8 NIL NIL) (-425 1019980 1020123 1020350 "FSAGG2" 1020791 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-424 1017635 1017914 1018468 "FS2UPS" 1019698 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-423 1017217 1017260 1017415 "FS2" 1017586 NIL FS2 (NIL T T T T) -7 NIL NIL) (-422 1016074 1016245 1016554 "FS2EXPXP" 1017042 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-421 1015500 1015615 1015767 "FRUTIL" 1015954 NIL FRUTIL (NIL T) -7 NIL NIL) (-420 1006926 1011011 1012361 "FR" 1014182 NIL FR (NIL T) -8 NIL NIL) (-419 1002006 1004644 1004685 "FRNAALG" 1006081 NIL FRNAALG (NIL T) -9 NIL 1006687) (-418 997685 998755 1000030 "FRNAALG-" 1000780 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-417 997323 997366 997493 "FRNAAF2" 997636 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-416 995686 996179 996473 "FRMOD" 997136 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-415 993401 994069 994386 "FRIDEAL" 995477 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-414 992596 992683 992972 "FRIDEAL2" 993308 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-413 991839 992253 992295 "FRETRCT" 992300 NIL FRETRCT (NIL T) -9 NIL 992474) (-412 990951 991182 991533 "FRETRCT-" 991538 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-411 988156 989376 989436 "FRAMALG" 990318 NIL FRAMALG (NIL T T) -9 NIL 990610) (-410 986289 986745 987375 "FRAMALG-" 987598 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-409 980192 985774 986045 "FRAC" 986050 NIL FRAC (NIL T) -8 NIL NIL) (-408 979828 979885 979992 "FRAC2" 980129 NIL FRAC2 (NIL T T) -7 NIL NIL) (-407 979464 979521 979628 "FR2" 979765 NIL FR2 (NIL T T) -7 NIL NIL) (-406 974086 976995 977024 "FPS" 978143 T FPS (NIL) -9 NIL 978697) (-405 973535 973644 973808 "FPS-" 973954 NIL FPS- (NIL T) -8 NIL NIL) (-404 970931 972628 972657 "FPC" 972882 T FPC (NIL) -9 NIL 973024) (-403 970724 970764 970861 "FPC-" 970866 NIL FPC- (NIL T) -8 NIL NIL) (-402 969603 970213 970255 "FPATMAB" 970260 NIL FPATMAB (NIL T) -9 NIL 970410) (-401 967303 967779 968205 "FPARFRAC" 969240 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-400 962698 963195 963877 "FORTRAN" 966735 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-399 960414 960914 961453 "FORT" 962179 T FORT (NIL) -7 NIL NIL) (-398 958090 958651 958680 "FORTFN" 959740 T FORTFN (NIL) -9 NIL 960364) (-397 957853 957903 957932 "FORTCAT" 957991 T FORTCAT (NIL) -9 NIL 958053) (-396 955913 956396 956795 "FORMULA" 957474 T FORMULA (NIL) -8 NIL NIL) (-395 955701 955731 955800 "FORMULA1" 955877 NIL FORMULA1 (NIL T) -7 NIL NIL) (-394 955224 955276 955449 "FORDER" 955643 NIL FORDER (NIL T T T T) -7 NIL NIL) (-393 954320 954484 954677 "FOP" 955051 T FOP (NIL) -7 NIL NIL) (-392 952928 953600 953774 "FNLA" 954202 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-391 951595 951984 952013 "FNCAT" 952585 T FNCAT (NIL) -9 NIL 952878) (-390 951161 951554 951582 "FNAME" 951587 T FNAME (NIL) -8 NIL NIL) (-389 949814 950787 950816 "FMTC" 950821 T FMTC (NIL) -9 NIL 950857) (-388 946132 947339 947967 "FMONOID" 949219 NIL FMONOID (NIL T) -8 NIL NIL) (-387 945353 945876 946024 "FM" 946029 NIL FM (NIL T T) -8 NIL NIL) (-386 942777 943422 943451 "FMFUN" 944595 T FMFUN (NIL) -9 NIL 945303) (-385 942046 942226 942255 "FMC" 942545 T FMC (NIL) -9 NIL 942727) (-384 939258 940092 940147 "FMCAT" 941342 NIL FMCAT (NIL T T) -9 NIL 941836) (-383 938151 939024 939124 "FM1" 939203 NIL FM1 (NIL T T) -8 NIL NIL) (-382 935925 936341 936835 "FLOATRP" 937702 NIL FLOATRP (NIL T) -7 NIL NIL) (-381 929412 933581 934211 "FLOAT" 935315 T FLOAT (NIL) -8 NIL NIL) (-380 926850 927350 927928 "FLOATCP" 928879 NIL FLOATCP (NIL T) -7 NIL NIL) (-379 925635 926483 926525 "FLINEXP" 926530 NIL FLINEXP (NIL T) -9 NIL 926622) (-378 924789 925024 925352 "FLINEXP-" 925357 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-377 923865 924009 924233 "FLASORT" 924641 NIL FLASORT (NIL T T) -7 NIL NIL) (-376 921081 921923 921976 "FLALG" 923203 NIL FLALG (NIL T T) -9 NIL 923670) (-375 914900 918594 918636 "FLAGG" 919898 NIL FLAGG (NIL T) -9 NIL 920546) (-374 913626 913965 914455 "FLAGG-" 914460 NIL FLAGG- (NIL T T) -8 NIL NIL) (-373 912668 912811 913038 "FLAGG2" 913479 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-372 909639 910657 910717 "FINRALG" 911845 NIL FINRALG (NIL T T) -9 NIL 912350) (-371 908799 909028 909367 "FINRALG-" 909372 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-370 908204 908417 908446 "FINITE" 908642 T FINITE (NIL) -9 NIL 908749) (-369 900662 902823 902864 "FINAALG" 906531 NIL FINAALG (NIL T) -9 NIL 907983) (-368 896002 897044 898188 "FINAALG-" 899567 NIL FINAALG- (NIL T T) -8 NIL NIL) (-367 895372 895757 895860 "FILE" 895932 NIL FILE (NIL T) -8 NIL NIL) (-366 893912 894249 894304 "FILECAT" 895082 NIL FILECAT (NIL T T) -9 NIL 895322) (-365 891722 893278 893307 "FIELD" 893347 T FIELD (NIL) -9 NIL 893427) (-364 890342 890727 891238 "FIELD-" 891243 NIL FIELD- (NIL T) -8 NIL NIL) (-363 888155 888977 889324 "FGROUP" 890028 NIL FGROUP (NIL T) -8 NIL NIL) (-362 887245 887409 887629 "FGLMICPK" 887987 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-361 883047 887170 887227 "FFX" 887232 NIL FFX (NIL T NIL) -8 NIL NIL) (-360 882587 882654 882776 "FFSQFR" 882975 NIL FFSQFR (NIL T T) -7 NIL NIL) (-359 882188 882249 882384 "FFSLPE" 882520 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-358 878184 878960 879756 "FFPOLY" 881424 NIL FFPOLY (NIL T) -7 NIL NIL) (-357 877688 877724 877933 "FFPOLY2" 878142 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-356 873510 877607 877670 "FFP" 877675 NIL FFP (NIL T NIL) -8 NIL NIL) (-355 868878 873421 873485 "FF" 873490 NIL FF (NIL NIL NIL) -8 NIL NIL) (-354 863974 868221 868411 "FFNBX" 868732 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-353 858884 863109 863367 "FFNBP" 863828 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-352 853487 858168 858379 "FFNB" 858717 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-351 852319 852517 852832 "FFINTBAS" 853284 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-350 848495 850730 850759 "FFIELDC" 851379 T FFIELDC (NIL) -9 NIL 851755) (-349 847158 847528 848025 "FFIELDC-" 848030 NIL FFIELDC- (NIL T) -8 NIL NIL) (-348 846728 846773 846897 "FFHOM" 847100 NIL FFHOM (NIL T T T) -7 NIL NIL) (-347 844426 844910 845427 "FFF" 846243 NIL FFF (NIL T) -7 NIL NIL) (-346 840122 840887 841731 "FFFG" 843650 NIL FFFG (NIL T T) -7 NIL NIL) (-345 838848 839057 839379 "FFFGF" 839900 NIL FFFGF (NIL T T T) -7 NIL NIL) (-344 837599 837796 838044 "FFFACTSE" 838650 NIL FFFACTSE (NIL T T) -7 NIL NIL) (-343 833187 837341 837442 "FFCGX" 837542 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-342 828789 832919 833026 "FFCGP" 833130 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-341 823942 828516 828624 "FFCG" 828725 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-340 805731 814853 814940 "FFCAT" 820105 NIL FFCAT (NIL T T T) -9 NIL 821590) (-339 800929 801976 803290 "FFCAT-" 804520 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-338 800340 800383 800618 "FFCAT2" 800880 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-337 789510 793316 794534 "FEXPR" 799194 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-336 788512 788947 788989 "FEVALAB" 789073 NIL FEVALAB (NIL T) -9 NIL 789331) (-335 787671 787881 788219 "FEVALAB-" 788224 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-334 786264 787054 787257 "FDIV" 787570 NIL FDIV (NIL T T T T) -8 NIL NIL) (-333 783329 784044 784160 "FDIVCAT" 785728 NIL FDIVCAT (NIL T T T T) -9 NIL 786165) (-332 783091 783118 783288 "FDIVCAT-" 783293 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-331 782311 782398 782675 "FDIV2" 782998 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-330 780997 781256 781545 "FCPAK1" 782042 T FCPAK1 (NIL) -7 NIL NIL) (-329 780125 780497 780638 "FCOMP" 780888 NIL FCOMP (NIL T) -8 NIL NIL) (-328 763753 767168 770731 "FC" 776582 T FC (NIL) -8 NIL NIL) (-327 756297 760340 760381 "FAXF" 762183 NIL FAXF (NIL T) -9 NIL 762874) (-326 753577 754231 755056 "FAXF-" 755521 NIL FAXF- (NIL T T) -8 NIL NIL) (-325 748683 752953 753129 "FARRAY" 753434 NIL FARRAY (NIL T) -8 NIL NIL) (-324 744001 746077 746131 "FAMR" 747154 NIL FAMR (NIL T T) -9 NIL 747611) (-323 742891 743193 743628 "FAMR-" 743633 NIL FAMR- (NIL T T T) -8 NIL NIL) (-322 742479 742522 742673 "FAMR2" 742842 NIL FAMR2 (NIL T T T T T) -7 NIL NIL) (-321 741675 742401 742454 "FAMONOID" 742459 NIL FAMONOID (NIL T) -8 NIL NIL) (-320 739505 740189 740243 "FAMONC" 741184 NIL FAMONC (NIL T T) -9 NIL 741569) (-319 738199 739261 739397 "FAGROUP" 739402 NIL FAGROUP (NIL T) -8 NIL NIL) (-318 735994 736313 736716 "FACUTIL" 737880 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-317 735410 735519 735665 "FACTRN" 735880 NIL FACTRN (NIL T) -7 NIL NIL) (-316 734509 734694 734916 "FACTFUNC" 735220 NIL FACTFUNC (NIL T) -7 NIL NIL) (-315 733925 734034 734180 "FACTEXT" 734395 NIL FACTEXT (NIL T) -7 NIL NIL) (-314 726245 733176 733388 "EXPUPXS" 733781 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-313 723728 724268 724854 "EXPRTUBE" 725679 T EXPRTUBE (NIL) -7 NIL NIL) (-312 722899 722994 723214 "EXPRSOL" 723628 NIL EXPRSOL (NIL T T T T) -7 NIL NIL) (-311 719093 719685 720422 "EXPRODE" 722238 NIL EXPRODE (NIL T T) -7 NIL NIL) (-310 704114 717754 718179 "EXPR" 718700 NIL EXPR (NIL T) -8 NIL NIL) (-309 698521 699108 699921 "EXPR2UPS" 703412 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-308 698157 698214 698321 "EXPR2" 698458 NIL EXPR2 (NIL T T) -7 NIL NIL) (-307 689497 697289 697586 "EXPEXPAN" 697994 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-306 689209 689260 689337 "EXP3D" 689440 T EXP3D (NIL) -7 NIL NIL) (-305 689036 689166 689195 "EXIT" 689200 T EXIT (NIL) -8 NIL NIL) (-304 688663 688725 688838 "EVALCYC" 688968 NIL EVALCYC (NIL T) -7 NIL NIL) (-303 688205 688321 688363 "EVALAB" 688533 NIL EVALAB (NIL T) -9 NIL 688637) (-302 687686 687808 688029 "EVALAB-" 688034 NIL EVALAB- (NIL T T) -8 NIL NIL) (-301 685144 686456 686485 "EUCDOM" 687040 T EUCDOM (NIL) -9 NIL 687390) (-300 683549 683991 684581 "EUCDOM-" 684586 NIL EUCDOM- (NIL T) -8 NIL NIL) (-299 671089 673847 676597 "ESTOOLS" 680819 T ESTOOLS (NIL) -7 NIL NIL) (-298 670721 670778 670887 "ESTOOLS2" 671026 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-297 670472 670514 670594 "ESTOOLS1" 670673 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-296 664398 666126 666155 "ES" 668923 T ES (NIL) -9 NIL 670330) (-295 659346 660632 662449 "ES-" 662613 NIL ES- (NIL T) -8 NIL NIL) (-294 655721 656481 657261 "ESCONT" 658586 T ESCONT (NIL) -7 NIL NIL) (-293 655466 655498 655580 "ESCONT1" 655683 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-292 655141 655191 655291 "ES2" 655410 NIL ES2 (NIL T T) -7 NIL NIL) (-291 654771 654829 654938 "ES1" 655077 NIL ES1 (NIL T T) -7 NIL NIL) (-290 653987 654116 654292 "ERROR" 654615 T ERROR (NIL) -7 NIL NIL) (-289 647502 653846 653937 "EQTBL" 653942 NIL EQTBL (NIL T T) -8 NIL NIL) (-288 639961 642844 644279 "EQ" 646100 NIL -2995 (NIL T) -8 NIL NIL) (-287 639593 639650 639759 "EQ2" 639898 NIL EQ2 (NIL T T) -7 NIL NIL) (-286 634885 635931 637024 "EP" 638532 NIL EP (NIL T) -7 NIL NIL) (-285 634039 634603 634632 "ENTIRER" 634637 T ENTIRER (NIL) -9 NIL 634683) (-284 630495 631994 632364 "EMR" 633838 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-283 629641 629824 629879 "ELTAGG" 630259 NIL ELTAGG (NIL T T) -9 NIL 630469) (-282 629360 629422 629563 "ELTAGG-" 629568 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-281 629148 629177 629232 "ELTAB" 629316 NIL ELTAB (NIL T T) -9 NIL NIL) (-280 628274 628420 628619 "ELFUTS" 628999 NIL ELFUTS (NIL T T) -7 NIL NIL) (-279 628015 628071 628100 "ELEMFUN" 628205 T ELEMFUN (NIL) -9 NIL NIL) (-278 627885 627906 627974 "ELEMFUN-" 627979 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-277 622815 626018 626060 "ELAGG" 627000 NIL ELAGG (NIL T) -9 NIL 627461) (-276 621100 621534 622197 "ELAGG-" 622202 NIL ELAGG- (NIL T T) -8 NIL NIL) (-275 613970 615769 616595 "EFUPXS" 620377 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-274 607422 609223 610032 "EFULS" 613247 NIL EFULS (NIL T T T) -8 NIL NIL) (-273 604844 605202 605681 "EFSTRUC" 607054 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-272 593856 595421 596982 "EF" 603359 NIL EF (NIL T T) -7 NIL NIL) (-271 592957 593341 593490 "EAB" 593727 T EAB (NIL) -8 NIL NIL) (-270 592166 592916 592944 "E04UCFA" 592949 T E04UCFA (NIL) -8 NIL NIL) (-269 591375 592125 592153 "E04NAFA" 592158 T E04NAFA (NIL) -8 NIL NIL) (-268 590584 591334 591362 "E04MBFA" 591367 T E04MBFA (NIL) -8 NIL NIL) (-267 589793 590543 590571 "E04JAFA" 590576 T E04JAFA (NIL) -8 NIL NIL) (-266 589004 589752 589780 "E04GCFA" 589785 T E04GCFA (NIL) -8 NIL NIL) (-265 588215 588963 588991 "E04FDFA" 588996 T E04FDFA (NIL) -8 NIL NIL) (-264 587424 588174 588202 "E04DGFA" 588207 T E04DGFA (NIL) -8 NIL NIL) (-263 581603 582949 584313 "E04AGNT" 586080 T E04AGNT (NIL) -7 NIL NIL) (-262 580326 580806 580847 "DVARCAT" 581322 NIL DVARCAT (NIL T) -9 NIL 581521) (-261 579530 579742 580056 "DVARCAT-" 580061 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-260 572499 572981 573730 "DTP" 579061 NIL DTP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-259 569948 571921 572078 "DSTREE" 572375 NIL DSTREE (NIL T) -8 NIL NIL) (-258 567417 569262 569304 "DSTRCAT" 569523 NIL DSTRCAT (NIL T) -9 NIL 569657) (-257 560271 567216 567345 "DSMP" 567350 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 555081 556216 557284 "DROPT" 559223 T DROPT (NIL) -8 NIL NIL) (-255 554746 554805 554903 "DROPT1" 555016 NIL DROPT1 (NIL T) -7 NIL NIL) (-254 549861 550987 552124 "DROPT0" 553629 T DROPT0 (NIL) -7 NIL NIL) (-253 548206 548531 548917 "DRAWPT" 549495 T DRAWPT (NIL) -7 NIL NIL) (-252 542793 543716 544795 "DRAW" 547180 NIL DRAW (NIL T) -7 NIL NIL) (-251 542426 542479 542597 "DRAWHACK" 542734 NIL DRAWHACK (NIL T) -7 NIL NIL) (-250 541157 541426 541717 "DRAWCX" 542155 T DRAWCX (NIL) -7 NIL NIL) (-249 540673 540741 540892 "DRAWCURV" 541083 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-248 531145 533103 535218 "DRAWCFUN" 538578 T DRAWCFUN (NIL) -7 NIL NIL) (-247 527998 529874 529916 "DQAGG" 530545 NIL DQAGG (NIL T) -9 NIL 530818) (-246 516426 523167 523251 "DPOLCAT" 525103 NIL DPOLCAT (NIL T T T T) -9 NIL 525647) (-245 511265 512611 514569 "DPOLCAT-" 514574 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 504004 511126 511224 "DPMO" 511229 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 496646 503784 503951 "DPMM" 503956 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 490351 496281 496433 "DMP" 496547 NIL DMP (NIL NIL T) -8 NIL NIL) (-241 489951 490007 490151 "DLP" 490289 NIL DLP (NIL T) -7 NIL NIL) (-240 483601 489052 489279 "DLIST" 489756 NIL DLIST (NIL T) -8 NIL NIL) (-239 480486 482489 482531 "DLAGG" 483081 NIL DLAGG (NIL T) -9 NIL 483310) (-238 479143 479835 479864 "DIVRING" 480014 T DIVRING (NIL) -9 NIL 480122) (-237 478131 478384 478777 "DIVRING-" 478782 NIL DIVRING- (NIL T) -8 NIL NIL) (-236 476559 477724 477860 "DIV" 478028 NIL DIV (NIL T) -8 NIL NIL) (-235 474053 475121 475163 "DIVCAT" 475997 NIL DIVCAT (NIL T) -9 NIL 476328) (-234 472155 472512 472918 "DISPLAY" 473667 T DISPLAY (NIL) -7 NIL NIL) (-233 469648 470861 471243 "DIRRING" 471806 NIL DIRRING (NIL T) -8 NIL NIL) (-232 463508 469562 469625 "DIRPROD" 469630 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 462356 462559 462824 "DIRPROD2" 463301 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 451920 457949 458003 "DIRPCAT" 458261 NIL DIRPCAT (NIL NIL T) -9 NIL 459105) (-229 449246 449888 450769 "DIRPCAT-" 451106 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 448533 448693 448879 "DIOSP" 449080 T DIOSP (NIL) -7 NIL NIL) (-227 445276 447480 447522 "DIOPS" 447956 NIL DIOPS (NIL T) -9 NIL 448184) (-226 444825 444939 445130 "DIOPS-" 445135 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 443692 444330 444359 "DIFRING" 444546 T DIFRING (NIL) -9 NIL 444656) (-224 443338 443415 443567 "DIFRING-" 443572 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 441120 442402 442444 "DIFEXT" 442807 NIL DIFEXT (NIL T) -9 NIL 443099) (-222 439405 439833 440499 "DIFEXT-" 440504 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 436767 438971 439013 "DIAGG" 439018 NIL DIAGG (NIL T) -9 NIL 439038) (-220 436151 436308 436560 "DIAGG-" 436565 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 431521 435110 435387 "DHMATRIX" 435920 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 426732 431335 431409 "DFVEC" 431467 T DFVEC (NIL) -8 NIL NIL) (-217 420616 421905 423286 "DFSFUN" 425371 T DFSFUN (NIL) -7 NIL NIL) (-216 416877 420387 420481 "DFMAT" 420542 T DFMAT (NIL) -8 NIL NIL) (-215 411154 415331 415764 "DFLOAT" 416464 T DFLOAT (NIL) -8 NIL NIL) (-214 409382 409663 410059 "DFINTTLS" 410862 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-213 406401 407403 407803 "DERHAM" 409048 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-212 398014 399931 401366 "DEQUEUE" 404999 NIL DEQUEUE (NIL T) -8 NIL NIL) (-211 397229 397362 397558 "DEGRED" 397876 NIL DEGRED (NIL T T) -7 NIL NIL) (-210 393624 394369 395222 "DEFINTRF" 396457 NIL DEFINTRF (NIL T) -7 NIL NIL) (-209 391151 391620 392219 "DEFINTEF" 393143 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-208 384969 390589 390756 "DECIMAL" 391004 T DECIMAL (NIL) -8 NIL NIL) (-207 382481 382939 383445 "DDFACT" 384513 NIL DDFACT (NIL T T) -7 NIL NIL) (-206 382077 382120 382271 "DBLRESP" 382432 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-205 379787 380121 380490 "DBASE" 381835 NIL DBASE (NIL T) -8 NIL NIL) (-204 378920 379746 379774 "D03FAFA" 379779 T D03FAFA (NIL) -8 NIL NIL) (-203 378054 378879 378907 "D03EEFA" 378912 T D03EEFA (NIL) -8 NIL NIL) (-202 376004 376470 376959 "D03AGNT" 377585 T D03AGNT (NIL) -7 NIL NIL) (-201 375320 375963 375991 "D02EJFA" 375996 T D02EJFA (NIL) -8 NIL NIL) (-200 374636 375279 375307 "D02CJFA" 375312 T D02CJFA (NIL) -8 NIL NIL) (-199 373952 374595 374623 "D02BHFA" 374628 T D02BHFA (NIL) -8 NIL NIL) (-198 373268 373911 373939 "D02BBFA" 373944 T D02BBFA (NIL) -8 NIL NIL) (-197 366467 368054 369660 "D02AGNT" 371682 T D02AGNT (NIL) -7 NIL NIL) (-196 364236 364758 365304 "D01WGTS" 365941 T D01WGTS (NIL) -7 NIL NIL) (-195 363331 364195 364223 "D01TRNS" 364228 T D01TRNS (NIL) -8 NIL NIL) (-194 362426 363290 363318 "D01GBFA" 363323 T D01GBFA (NIL) -8 NIL NIL) (-193 361521 362385 362413 "D01FCFA" 362418 T D01FCFA (NIL) -8 NIL NIL) (-192 360616 361480 361508 "D01ASFA" 361513 T D01ASFA (NIL) -8 NIL NIL) (-191 359711 360575 360603 "D01AQFA" 360608 T D01AQFA (NIL) -8 NIL NIL) (-190 358806 359670 359698 "D01APFA" 359703 T D01APFA (NIL) -8 NIL NIL) (-189 357901 358765 358793 "D01ANFA" 358798 T D01ANFA (NIL) -8 NIL NIL) (-188 356996 357860 357888 "D01AMFA" 357893 T D01AMFA (NIL) -8 NIL NIL) (-187 356091 356955 356983 "D01ALFA" 356988 T D01ALFA (NIL) -8 NIL NIL) (-186 355186 356050 356078 "D01AKFA" 356083 T D01AKFA (NIL) -8 NIL NIL) (-185 354281 355145 355173 "D01AJFA" 355178 T D01AJFA (NIL) -8 NIL NIL) (-184 347578 349129 350690 "D01AGNT" 352740 T D01AGNT (NIL) -7 NIL NIL) (-183 346915 347043 347195 "CYCLOTOM" 347446 T CYCLOTOM (NIL) -7 NIL NIL) (-182 343650 344363 345090 "CYCLES" 346208 T CYCLES (NIL) -7 NIL NIL) (-181 342962 343096 343267 "CVMP" 343511 NIL CVMP (NIL T) -7 NIL NIL) (-180 340734 340991 341367 "CTRIGMNP" 342690 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-179 340108 340207 340360 "CSTTOOLS" 340631 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-178 335907 336564 337322 "CRFP" 339420 NIL CRFP (NIL T T) -7 NIL NIL) (-177 334954 335139 335367 "CRAPACK" 335711 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 334340 334441 334644 "CPMATCH" 334831 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 334065 334093 334199 "CPIMA" 334306 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 330413 331085 331804 "COORDSYS" 333400 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 326274 328416 328908 "CONTFRAC" 329953 NIL CONTFRAC (NIL T) -8 NIL NIL) (-172 325422 325986 326015 "COMRING" 326020 T COMRING (NIL) -9 NIL 326072) (-171 324503 324780 324964 "COMPPROP" 325258 T COMPPROP (NIL) -8 NIL NIL) (-170 324164 324199 324327 "COMPLPAT" 324462 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-169 314135 323975 324083 "COMPLEX" 324088 NIL COMPLEX (NIL T) -8 NIL NIL) (-168 313771 313828 313935 "COMPLEX2" 314072 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-167 313489 313524 313622 "COMPFACT" 313730 NIL COMPFACT (NIL T T) -7 NIL NIL) (-166 297741 308041 308082 "COMPCAT" 309086 NIL COMPCAT (NIL T) -9 NIL 310467) (-165 287257 290180 293807 "COMPCAT-" 294163 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-164 286986 287014 287117 "COMMUPC" 287223 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-163 286781 286814 286873 "COMMONOP" 286947 T COMMONOP (NIL) -7 NIL NIL) (-162 286364 286532 286619 "COMM" 286714 T COMM (NIL) -8 NIL NIL) (-161 285612 285806 285835 "COMBOPC" 286173 T COMBOPC (NIL) -9 NIL 286348) (-160 284508 284718 284960 "COMBINAT" 285402 NIL COMBINAT (NIL T) -7 NIL NIL) (-159 280706 281279 281919 "COMBF" 283930 NIL COMBF (NIL T T) -7 NIL NIL) (-158 279492 279822 280057 "COLOR" 280491 T COLOR (NIL) -8 NIL NIL) (-157 279132 279179 279304 "CMPLXRT" 279439 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-156 274634 275662 276742 "CLIP" 278072 T CLIP (NIL) -7 NIL NIL) (-155 272970 273740 273979 "CLIF" 274461 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-154 269235 271153 271195 "CLAGG" 272124 NIL CLAGG (NIL T) -9 NIL 272657) (-153 267657 268114 268697 "CLAGG-" 268702 NIL CLAGG- (NIL T T) -8 NIL NIL) (-152 267201 267286 267426 "CINTSLPE" 267566 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-151 264702 265173 265721 "CHVAR" 266729 NIL CHVAR (NIL T T T) -7 NIL NIL) (-150 263920 264484 264513 "CHARZ" 264518 T CHARZ (NIL) -9 NIL 264533) (-149 263674 263714 263792 "CHARPOL" 263874 NIL CHARPOL (NIL T) -7 NIL NIL) (-148 262776 263373 263402 "CHARNZ" 263449 T CHARNZ (NIL) -9 NIL 263505) (-147 260799 261466 261801 "CHAR" 262461 T CHAR (NIL) -8 NIL NIL) (-146 260524 260585 260614 "CFCAT" 260725 T CFCAT (NIL) -9 NIL NIL) (-145 254657 260181 260299 "CDFVEC" 260426 T CDFVEC (NIL) -8 NIL NIL) (-144 250372 254414 254515 "CDFMAT" 254576 T CDFMAT (NIL) -8 NIL NIL) (-143 249617 249728 249910 "CDEN" 250256 NIL CDEN (NIL T T T) -7 NIL NIL) (-142 245609 248770 249050 "CCLASS" 249357 T CCLASS (NIL) -8 NIL NIL) (-141 240662 241638 242391 "CARTEN" 244912 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-140 239770 239918 240139 "CARTEN2" 240509 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-139 238065 238920 239177 "CARD" 239533 T CARD (NIL) -8 NIL NIL) (-138 237436 237764 237793 "CACHSET" 237925 T CACHSET (NIL) -9 NIL 238002) (-137 236931 237227 237256 "CABMON" 237306 T CABMON (NIL) -9 NIL 237362) (-136 234494 236623 236730 "BTREE" 236857 NIL BTREE (NIL T) -8 NIL NIL) (-135 231998 234142 234264 "BTOURN" 234404 NIL BTOURN (NIL T) -8 NIL NIL) (-134 229455 231502 231544 "BTCAT" 231612 NIL BTCAT (NIL T) -9 NIL 231689) (-133 229122 229202 229351 "BTCAT-" 229356 NIL BTCAT- (NIL T T) -8 NIL NIL) (-132 224312 228182 228211 "BTAGG" 228467 T BTAGG (NIL) -9 NIL 228646) (-131 223735 223879 224109 "BTAGG-" 224114 NIL BTAGG- (NIL T) -8 NIL NIL) (-130 220785 223013 223228 "BSTREE" 223552 NIL BSTREE (NIL T) -8 NIL NIL) (-129 219923 220049 220233 "BRILL" 220641 NIL BRILL (NIL T) -7 NIL NIL) (-128 216663 218684 218726 "BRAGG" 219375 NIL BRAGG (NIL T) -9 NIL 219632) (-127 215192 215598 216153 "BRAGG-" 216158 NIL BRAGG- (NIL T T) -8 NIL NIL) (-126 208391 214538 214722 "BPADICRT" 215040 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-125 206695 208328 208373 "BPADIC" 208378 NIL BPADIC (NIL NIL) -8 NIL NIL) (-124 206393 206423 206537 "BOUNDZRO" 206659 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-123 201908 202999 203866 "BOP" 205546 T BOP (NIL) -8 NIL NIL) (-122 199531 199975 200494 "BOP1" 201422 NIL BOP1 (NIL T) -7 NIL NIL) (-121 197884 198574 198868 "BOOLEAN" 199257 T BOOLEAN (NIL) -8 NIL NIL) (-120 197245 197623 197678 "BMODULE" 197683 NIL BMODULE (NIL T T) -9 NIL 197748) (-119 193588 194258 195044 "BLUPPACK" 196577 NIL BLUPPACK (NIL T NIL T T T) -7 NIL NIL) (-118 192980 193465 193534 "BLQT" 193539 T BLQT (NIL) -8 NIL NIL) (-117 191409 191884 191913 "BLMETCT" 192558 T BLMETCT (NIL) -9 NIL 192930) (-116 190808 191290 191357 "BLHN" 191362 T BLHN (NIL) -8 NIL NIL) (-115 189626 189885 190168 "BLAS1" 190545 T BLAS1 (NIL) -7 NIL NIL) (-114 185436 189424 189497 "BITS" 189573 T BITS (NIL) -8 NIL NIL) (-113 184507 184968 185120 "BINFILE" 185304 T BINFILE (NIL) -8 NIL NIL) (-112 178329 183948 184114 "BINARY" 184361 T BINARY (NIL) -8 NIL NIL) (-111 176196 177618 177660 "BGAGG" 177920 NIL BGAGG (NIL T) -9 NIL 178057) (-110 176027 176059 176150 "BGAGG-" 176155 NIL BGAGG- (NIL T T) -8 NIL NIL) (-109 175125 175411 175616 "BFUNCT" 175842 T BFUNCT (NIL) -8 NIL NIL) (-108 173817 173995 174282 "BEZOUT" 174950 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-107 172780 173002 173261 "BEZIER" 173591 NIL BEZIER (NIL T) -7 NIL NIL) (-106 169303 171632 171962 "BBTREE" 172483 NIL BBTREE (NIL T) -8 NIL NIL) (-105 169036 169089 169118 "BASTYPE" 169237 T BASTYPE (NIL) -9 NIL NIL) (-104 168889 168917 168990 "BASTYPE-" 168995 NIL BASTYPE- (NIL T) -8 NIL NIL) (-103 168323 168399 168551 "BALFACT" 168800 NIL BALFACT (NIL T T) -7 NIL NIL) (-102 167687 167810 167958 "AXSERV" 168195 T AXSERV (NIL) -7 NIL NIL) (-101 166500 167097 167285 "AUTOMOR" 167532 NIL AUTOMOR (NIL T) -8 NIL NIL) (-100 166212 166217 166246 "ATTREG" 166251 T ATTREG (NIL) -9 NIL NIL) (-99 164491 164909 165261 "ATTRBUT" 165878 T ATTRBUT (NIL) -8 NIL NIL) (-98 164026 164139 164166 "ATRIG" 164367 T ATRIG (NIL) -9 NIL NIL) (-97 163835 163876 163963 "ATRIG-" 163968 NIL ATRIG- (NIL T) -8 NIL NIL) (-96 157395 158964 160075 "ASTACK" 162755 NIL ASTACK (NIL T) -8 NIL NIL) (-95 155902 156199 156563 "ASSOCEQ" 157078 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-94 154934 155561 155685 "ASP9" 155809 NIL ASP9 (NIL NIL) -8 NIL NIL) (-93 154698 154882 154921 "ASP8" 154926 NIL ASP8 (NIL NIL) -8 NIL NIL) (-92 153568 154303 154445 "ASP80" 154587 NIL ASP80 (NIL NIL) -8 NIL NIL) (-91 152467 153203 153335 "ASP7" 153467 NIL ASP7 (NIL NIL) -8 NIL NIL) (-90 151423 152144 152262 "ASP78" 152380 NIL ASP78 (NIL NIL) -8 NIL NIL) (-89 150394 151103 151220 "ASP77" 151337 NIL ASP77 (NIL NIL) -8 NIL NIL) (-88 149309 150032 150163 "ASP74" 150294 NIL ASP74 (NIL NIL) -8 NIL NIL) (-87 148210 148944 149076 "ASP73" 149208 NIL ASP73 (NIL NIL) -8 NIL NIL) (-86 147165 147887 148005 "ASP6" 148123 NIL ASP6 (NIL NIL) -8 NIL NIL) (-85 146114 146842 146960 "ASP55" 147078 NIL ASP55 (NIL NIL) -8 NIL NIL) (-84 145064 145788 145907 "ASP50" 146026 NIL ASP50 (NIL NIL) -8 NIL NIL) (-83 144152 144765 144875 "ASP4" 144985 NIL ASP4 (NIL NIL) -8 NIL NIL) (-82 143240 143853 143963 "ASP49" 144073 NIL ASP49 (NIL NIL) -8 NIL NIL) (-81 142025 142779 142947 "ASP42" 143129 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-80 140803 141558 141728 "ASP41" 141912 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-79 139755 140480 140598 "ASP35" 140716 NIL ASP35 (NIL NIL) -8 NIL NIL) (-78 139520 139703 139742 "ASP34" 139747 NIL ASP34 (NIL NIL) -8 NIL NIL) (-77 139257 139324 139400 "ASP33" 139475 NIL ASP33 (NIL NIL) -8 NIL NIL) (-76 138153 138892 139024 "ASP31" 139156 NIL ASP31 (NIL NIL) -8 NIL NIL) (-75 137918 138101 138140 "ASP30" 138145 NIL ASP30 (NIL NIL) -8 NIL NIL) (-74 137653 137722 137798 "ASP29" 137873 NIL ASP29 (NIL NIL) -8 NIL NIL) (-73 137418 137601 137640 "ASP28" 137645 NIL ASP28 (NIL NIL) -8 NIL NIL) (-72 137183 137366 137405 "ASP27" 137410 NIL ASP27 (NIL NIL) -8 NIL NIL) (-71 136267 136881 136992 "ASP24" 137103 NIL ASP24 (NIL NIL) -8 NIL NIL) (-70 135184 135908 136038 "ASP20" 136168 NIL ASP20 (NIL NIL) -8 NIL NIL) (-69 134272 134885 134995 "ASP1" 135105 NIL ASP1 (NIL NIL) -8 NIL NIL) (-68 133216 133946 134065 "ASP19" 134184 NIL ASP19 (NIL NIL) -8 NIL NIL) (-67 132953 133020 133096 "ASP12" 133171 NIL ASP12 (NIL NIL) -8 NIL NIL) (-66 131806 132552 132696 "ASP10" 132840 NIL ASP10 (NIL NIL) -8 NIL NIL) (-65 129711 131650 131741 "ARRAY2" 131746 NIL ARRAY2 (NIL T) -8 NIL NIL) (-64 125533 129359 129473 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99310 99371 "ALIST" 99376 NIL ALIST (NIL T T) -8 NIL NIL) (-49 80792 83549 83718 "ALGSC" 83873 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-48 77350 77904 78510 "ALGPKG" 80233 NIL ALGPKG (NIL T T) -7 NIL NIL) (-47 76627 76728 76912 "ALGMFACT" 77236 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-46 72375 73059 73710 "ALGMANIP" 76154 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-45 63689 72001 72151 "ALGFF" 72308 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-44 62885 63016 63195 "ALGFACT" 63547 NIL ALGFACT (NIL T) -7 NIL NIL) (-43 61870 62480 62519 "ALGEBRA" 62579 NIL ALGEBRA (NIL T) -9 NIL 62638) (-42 61588 61647 61779 "ALGEBRA-" 61784 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-41 43395 59120 59173 "ALAGG" 59309 NIL ALAGG (NIL T T) -9 NIL 59470) (-40 42930 43043 43070 "AHYP" 43271 T AHYP (NIL) -9 NIL NIL) (-39 41861 42109 42136 "AGG" 42635 T AGG (NIL) -9 NIL 42913) (-38 41295 41457 41671 "AGG-" 41676 NIL AGG- (NIL T) -8 NIL NIL) (-37 38844 39425 39464 "AFSPCAT" 40736 NIL AFSPCAT (NIL T) -9 NIL 41231) (-36 36523 36945 37362 "AF" 38487 NIL AF (NIL T T) -7 NIL NIL) (-35 35863 36452 36506 "AFFSP" 36511 NIL AFFSP (NIL NIL T) -8 NIL NIL) (-34 35120 35790 35839 "AFFPLPS" 35844 NIL AFFPLPS (NIL T) -8 NIL NIL) (-33 34454 35061 35103 "AFFPL" 35108 NIL AFFPL (NIL T) -8 NIL NIL) (-32 31167 31654 32282 "AFALGRES" 33959 NIL AFALGRES (NIL T NIL T T T) -7 NIL NIL) (-31 29813 29990 30304 "AFALGGRO" 30986 NIL AFALGGRO (NIL T NIL T T T) -7 NIL NIL) (-30 29082 29340 29496 "ACPLOT" 29675 T ACPLOT (NIL) -8 NIL NIL) (-29 18442 26425 26477 "ACFS" 27188 NIL ACFS (NIL T) -9 NIL 27427) (-28 16456 16946 17721 "ACFS-" 17726 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12669 14625 14652 "ACF" 15531 T ACF (NIL) -9 NIL 15944) (-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/operation.daase b/src/share/algebra/operation.daase index e804043..6f152f0 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,3227 +1,3229 @@ -(830305 . 3487447481) -(((*1 *1 *2) (-12 (-5 *2 (-634 *1)) (-4 *1 (-296)))) ((*1 *1 *1) (-4 *1 (-296))) ((*1 *1 *2) (-12 (-5 *2 (-634 (-850))) (-5 *1 (-850)))) ((*1 *1 *1) (-5 *1 (-850)))) -(((*1 *2 *3) (-12 (-5 *3 (-944 *2)) (-5 *1 (-983 *2)) (-4 *2 (-1047))))) -(((*1 *2 *1 *1 *1) (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1))) (-4 *1 (-301)))) ((*1 *2 *1 *1) (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2704 *1))) (-4 *1 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a/src/share/algebra/users.daase/index.kaf b/src/share/algebra/users.daase/index.kaf index 6efa0b5..2daa077 100755 --- a/src/share/algebra/users.daase/index.kaf +++ b/src/share/algebra/users.daase/index.kaf @@ -1,15 +1,19 @@ -209919 (|FunctionSpaceUnivariatePolynomialFactor| |GenUFactorize| |LinearOrdinaryDifferentialOperatorFactorizer|) +234547 (|ProjectiveAlgebraicSetPackage|) +(|ProjectiveAlgebraicSetPackage|) +(|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |BlowUpPackage| |DesingTreePackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) +(|AffinePlane|) +(|FunctionSpaceUnivariatePolynomialFactor| |GenUFactorize| |LinearOrdinaryDifferentialOperatorFactorizer|) (|GenericNonAssociativeAlgebra|) (|Expression|) (|AlgebraicIntegrate|) (|ElementaryIntegration|) (|ConstantLODE| |ElementaryFunctionStructurePackage| |Expression| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |GenusZeroIntegration| |InnerAlgebraicNumber| |IntegrationResultToFunction| |TransSolvePackage| |TranscendentalManipulations|) -(|AlgFactor| |Expression| |FunctionSpaceUnivariatePolynomialFactor| |PolynomialAN2Expression| |SimplifyAlgebraicNumberConvertPackage| |ToolsForSign|) +(|AlgFactor| |Expression| |FunctionSpaceUnivariatePolynomialFactor| |GuessAlgebraicNumber| |PolynomialAN2Expression| |SimplifyAlgebraicNumberConvertPackage| |ToolsForSign|) (|d01TransformFunctionType|) (|d03AgentsPackage|) (|DeRhamComplex|) -(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnyFunctions1| |DrawOption| |DrawOptionFunctions1| |ExpertSystemToolsPackage| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |FortranTemplate| |FunctionSpaceAttachPredicates| |GenUFactorize| |GenerateUnivariatePowerSeries| |InputForm| |InputFormFunctions1| |Library| |MakeFloatCompiledFunction| |MakeFunction| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |OpenMathPackage| |OpenMathServerPackage| |OutputPackage| |PartialFractionPackage| |Pattern| |PatternFunctions1| |PatternMatchPushDown| |RadixUtilities| |Result| |RoutinesTable| |TemplateUtilities| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |d01TransformFunctionType| |d01alfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType|) -(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |DrawOption| |DrawOptionFunctions1| |ExpertSystemToolsPackage| |FunctionSpaceAttachPredicates| |GenUFactorize| |InputFormFunctions1| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |OpenMathServerPackage| |OutputPackage| |Pattern| |PatternFunctions1| |PatternMatchPushDown| |RoutinesTable| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |d01TransformFunctionType| |d01alfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnyFunctions1| |DrawOption| |DrawOptionFunctions1| |ExpertSystemToolsPackage| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |FortranTemplate| |FunctionSpaceAttachPredicates| |GenUFactorize| |GenerateUnivariatePowerSeries| |GuessOption| |GuessOptionFunctions0| |InputForm| |InputFormFunctions1| |Library| |MakeFloatCompiledFunction| |MakeFunction| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |OpenMathPackage| |OpenMathServerPackage| |OutputPackage| |PartialFractionPackage| |Pattern| |PatternFunctions1| |PatternMatchPushDown| |RadixUtilities| |Result| |RoutinesTable| |TemplateUtilities| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |d01TransformFunctionType| |d01alfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |DrawOption| |DrawOptionFunctions1| |ExpertSystemToolsPackage| |FunctionSpaceAttachPredicates| |GenUFactorize| |GuessOption| |GuessOptionFunctions0| |InputFormFunctions1| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |OpenMathServerPackage| |OutputPackage| |Pattern| |PatternFunctions1| |PatternMatchPushDown| |RoutinesTable| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |d01TransformFunctionType| |d01alfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType|) (|RewriteRule| |Ruleset| |TranscendentalManipulations|) (|LinearOrdinaryDifferentialOperator2|) (|NagIntegrationPackage| |NagRootFindingPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType|) @@ -48,28 +52,30 @@ (|PrimitiveRatDE| |PrimitiveRatRicDE|) (|BalancedPAdicRational|) (|ExpertSystemContinuityPackage|) -(|AlgebraicFunction| |AlgebraicManipulations| |AlgebraicNumber| |ApplyRules| |Asp8| |BasicOperatorFunctions1| |CombinatorialFunction| |CommonOperators| |ComplexTrigonometricManipulations| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |FortranExpression| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationTools| |Kernel| |KernelFunctions2| |LaplaceTransform| |LiouvillianFunction| |ModuleOperator| |NonLinearFirstOrderODESolver| |Operator| |Pattern| |PatternFunctions2| |PatternMatchKernel| |PatternMatchPushDown| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |Switch| |TranscendentalManipulations| |TrigonometricManipulations| |d01WeightsPackage| |d01anfAnnaType| |d01asfAnnaType|) -(|AlgebraicFunction| |CombinatorialFunction| |ElementaryFunction| |ExpressionSpace&| |FunctionSpace&| |FunctionalSpecialFunction| |KernelFunctions2| |LiouvillianFunction|) +(|AlgebraicFunction| |AlgebraicManipulations| |AlgebraicNumber| |ApplyRules| |Asp8| |BasicOperatorFunctions1| |CombinatorialFunction| |CommonOperators| |ComplexTrigonometricManipulations| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |FortranExpression| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |Guess| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationTools| |Kernel| |KernelFunctions2| |LaplaceTransform| |LiouvillianFunction| |ModuleOperator| |MyExpression| |NonLinearFirstOrderODESolver| |Operator| |Pattern| |PatternFunctions2| |PatternMatchKernel| |PatternMatchPushDown| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |RecurrenceOperator| |Switch| |TranscendentalManipulations| |TrigonometricManipulations| |d01WeightsPackage| |d01anfAnnaType| |d01asfAnnaType|) +(|AlgebraicFunction| |CombinatorialFunction| |ElementaryFunction| |ExpressionSpace&| |FunctionSpace&| |FunctionalSpecialFunction| |KernelFunctions2| |LiouvillianFunction| |RecurrenceOperator|) (|BalancedBinaryTree| |BinarySearchTree| |BinaryTournament|) (|SetOfMIntegersInOneToN|) -(|AbelianMonoid&| |AbelianMonoidRing&| |Aggregate&| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnonymousFunction| |AntiSymm| |Any| |AnyFunctions1| |ApplyRules| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BasicType&| |BezoutMatrix| |BinaryExpansion| |BinaryFile| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&| |BitAggregate&| |Bits| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Collection&| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |CommuteUnivariatePolynomialCategory| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPattern| |ComplexPatternMatch| |ComplexRootFindingPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclicStreamTools| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |Dictionary&| |DifferentialPolynomialCategory&| 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|ExpertSystemToolsPackage| |ExpertSystemToolsPackage1| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtAlgBasis| |ExtensibleLinearAggregate&| |ExtensionField&| |FGLMIfCanPackage| |Factored| |FactoredFunctions| |FactoringUtilities| |Field&| |File| |FileName| |FindOrderFinite| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteDivisorCategory&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteLinearAggregate&| |FiniteLinearAggregateFunctions2| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranExpression| |FortranOutputStackPackage| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionalIdeal| |FramedModule| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionCalled| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaussianFactorizationPackage| |GcdDomain&| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GraphImage| |GraphicsDefaults| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |HallBasis| |HashTable| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexCard| |IndexedAggregate&| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySign| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |Integer| |IntegerBits| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerLinearDependence| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRetractions| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegralBasisTools| |IntegralDomain&| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |IrrRepSymNatPackage| |IrredPolyOverFiniteField| |Kernel| |KeyedAccessFile| |KeyedDictionary&| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LazyStreamAggregate&| |LeadingCoefDetermination| |LexTriangularPackage| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearPolynomialEquationByFractions| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LiouvillianFunction| |List| |ListAggregate&| |ListMonoidOps| |ListMultiDictionary| 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|RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealZeroPackage| |RectangularMatrix| |RectangularMatrixCategory&| |RecursiveAggregate&| |RecursivePolynomialCategory&| |ReductionOfOrder| |Reference| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentBinding| |SegmentFunctions2| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SingletonAsOrderedSet| |SmithNormalForm| |SortPackage| |SparseMultivariatePolynomial| 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|UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UniversalSegmentFunctions2| |UserDefinedPartialOrdering| |Variable| |Vector| |VectorFunctions2| |ViewDefaultsPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |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|) +(|DesingTreePackage|) +(|AbelianMonoid&| |AbelianMonoidRing&| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |Aggregate&| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnonymousFunction| |AntiSymm| |Any| |AnyFunctions1| |ApplyRules| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |AxiomServer| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BasicType&| |BezoutMatrix| |BinaryExpansion| |BinaryFile| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&| |BitAggregate&| |Bits| |BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Collection&| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |CommuteUnivariatePolynomialCategory| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPattern| |ComplexPatternMatch| |ComplexRootFindingPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclicStreamTools| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DesingTreePackage| |Dictionary&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| 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|ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtAlgBasis| |ExtensibleLinearAggregate&| |ExtensionField&| |FGLMIfCanPackage| |Factored| |FactoredFunctions| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |Field&| |File| |FileName| |FindOrderFinite| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRingFunctions2| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteDivisorCategory&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| 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|InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |Integer| |IntegerBits| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerLinearDependence| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRetractions| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegralBasisTools| |IntegralDomain&| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |IntersectionDivisorPackage| |Interval| |InverseLaplaceTransform| |IrrRepSymNatPackage| |IrredPolyOverFiniteField| |Kernel| |KeyedAccessFile| |KeyedDictionary&| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LazyStreamAggregate&| |LeadingCoefDetermination| |LexTriangularPackage| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearPolynomialEquationByFractions| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |LiouvillianFunction| |List| |ListAggregate&| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |LocalParametrizationOfSimplePointPackage| |Localize| |LyndonWord| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |MakeFloatCompiledFunction| |MathMLFormat| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |MergeThing| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonadWithUnit&| |Monoid&| |MonoidRing| |MonomialExtensionTools| |MultFiniteFactorize| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NPCoef| |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagPolynomialRootsPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewtonPolygon| |NonCommutativeOperatorDivision| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |None| |NormInMonogenicAlgebra| |NormRetractPackage| |NormalizationPackage| |NottinghamGroup| |NumberFieldIntegralBasis| |NumberFormats| |NumberTheoreticPolynomialFunctions| |NumericContinuedFraction| |NumericTubePlot| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalOrdinaryDifferentialEquations| |NumericalPDEProblem| |NumericalQuadrature| |ODEIntegration| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |OpenMathConnection| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OpenMathPackage| |OpenMathServerPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedRing&| |OrderedSet&| |OrderedVariableList| |OrderingFunctions| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |PadeApproximantPackage| |PadeApproximants| |Palette| |ParametricLinearEquations| |ParametrizationPackage| |PartialFraction| |Partition| |Pattern| |PatternFunctions1| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchListResult| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResult| |PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |PendantTree| |Permanent| |Permutation| |PermutationGroup| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |Plot| |Plot3D| |PlotTools| |PoincareBirkhoffWittLyndonBasis| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PolToPol| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialComposition| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialNumberTheoryFunctions| |PolynomialPackageForCurve| |PolynomialRing| |PolynomialRoots| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PositiveInteger| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |PushVariables| |QuadraticForm| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |Queue| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions| |RationalFactorize| |RationalFunctionDefiniteIntegration| |RationalFunctionLimitPackage| |RationalInterpolation| |RationalLODE| |RationalRetractions| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealZeroPackage| |RectangularMatrix| |RectangularMatrixCategory&| |RecurrenceOperator| |RecursiveAggregate&| |RecursivePolynomialCategory&| |ReductionOfOrder| |Reference| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RootsFindingPackage| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentBinding| |SegmentFunctions2| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SingletonAsOrderedSet| |SmithNormalForm| |SortPackage| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stack| |StorageEfficientMatrixOperations| |Stream| |StreamAggregate&| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |String| |StringAggregate&| |StringTable| |StructuralConstantsPackage| |SturmHabichtPackage| |SubResultantPackage| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |SupFractionFactorizer| |Switch| |Symbol| |SymbolTable| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Table| |TableAggregate&| |TableauxBumpers| |TabulatedComputationPackage| |TaylorSeries| |TaylorSolve| |TexFormat| |TextFile| |TheSymbolTable| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |ToolsForSign| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TransSolvePackage| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalManipulations| |TranscendentalRischDE| |TranscendentalRischDESystem| |Tree| |TriangularSetCategory&| |TrigonometricManipulations| |TubePlot| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UnaryRecursiveAggregate&| |UniqueFactorizationDomain&| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesConstructorCategory&| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UniversalSegmentFunctions2| |UserDefinedPartialOrdering| |Variable| |Vector| |VectorFunctions2| |ViewDefaultsPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |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|) (|PrimitiveRatDE| |RationalLODE|) (|GaloisGroupFactorizer|) -(|CliffordAlgebra| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |Equation| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |HomogeneousDirectProduct| |InnerFiniteField| |InnerPrimeField| |OrderedDirectProduct| |PrimeField| |RectangularMatrix| |SplitHomogeneousDirectProduct|) +(|CliffordAlgebra| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |Equation| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |HomogeneousDirectProduct| |InnerFiniteField| |InnerPrimeField| |OrderedDirectProduct| |PrimeField| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |RectangularMatrix| |SplitHomogeneousDirectProduct|) (|CartesianTensorFunctions2|) (|AlgebraicFunctionField| |AlgebraicIntegration| |PureAlgebraicIntegration| |RadicalFunctionField|) -(|Character| |CharacterClass| |Float| |FortranTemplate| |IndexedBits| |IndexedString| |LieExponentials| |NumberFormats| |OutputForm| |RadixExpansion| |RecursivePolynomialCategory&| |ScriptFormulaFormat| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |Tree|) -(|Character| |IndexedString| |String| |StringAggregate&|) +(|AxiomServer| |Character| |CharacterClass| |Float| |FortranTemplate| |HTMLFormat| |IndexedBits| |IndexedString| |LieExponentials| |MathMLFormat| |NumberFormats| |OutputForm| |RadixExpansion| |RecursivePolynomialCategory&| |ScriptFormulaFormat| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |Tree|) +(|Character| |IndexedString| |MathMLFormat| |String| |StringAggregate&|) (|MonogenicAlgebra&|) (|PAdicWildFunctionFieldIntegralBasis|) (|FramedNonAssociativeAlgebra&| |GenericNonAssociativeAlgebra|) (|GraphImage| |Palette| |ThreeDimensionalViewport| |TwoDimensionalViewport| |ViewDefaultsPackage|) (|Expression|) -(|FractionalIdeal| |PAdicWildFunctionFieldIntegralBasis| |UnivariatePolynomialCommonDenominator|) +(|FractionFreeFastGaussianFractions| |FractionalIdeal| |PAdicWildFunctionFieldIntegralBasis| |UnivariatePolynomialCommonDenominator|) (|AlgebraicFunction| |CombinatorialFunction| |ElementaryFunction| |ExpressionSpace&| |FunctionSpace&| |FunctionalSpecialFunction| |LiouvillianFunction|) (|FreeNilpotentLie|) (|DoubleResultantPackage| |InnerAlgFactor| |InnerAlgebraicNumber| |PolynomialFactorizationByRecursion| |TranscendentalIntegration| |TwoFactorize|) -(|AlgebraicNumber| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexFunctions2| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |DoubleFloatSpecialFunctions| |DrawComplex| |FloatingComplexPackage| |GaussianFactorizationPackage| |InnerAlgebraicNumber| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerTrigonometricManipulations| |MachineComplex| |NagSpecialFunctionsPackage| |Numeric| |TransSolvePackage| |TrigonometricManipulations| |d02AgentsPackage|) +(|AlgebraicNumber| |BlasLevelOne| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexFactorization| |ComplexFunctions2| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |DoubleFloatSpecialFunctions| |DrawComplex| |FloatingComplexPackage| |GaussianFactorizationPackage| |InnerAlgebraicNumber| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerTrigonometricManipulations| |MachineComplex| |NagSpecialFunctionsPackage| |Numeric| |TransSolvePackage| |TrigonometricManipulations| |d02AgentsPackage|) +(|ComplexDoubleFloatMatrix|) (|ComplexRootPackage| |GenUFactorize| |NumericComplexEigenPackage|) (|Numeric| |TransSolvePackage|) (|ComplexCategory&|) @@ -85,17 +91,21 @@ (|OperationsQuery|) (|ElementaryFunctionDefiniteIntegration| |RationalFunctionDefiniteIntegration|) (|RadicalSolvePackage|) +(|PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) +(|GeneralPackageForAlgebraicFunctionField| |IntersectionDivisorPackage|) (|LinearOrdinaryDifferentialOperatorsOps| |OrderlyDifferentialPolynomial| |SequentialDifferentialPolynomial|) -(|AlgebraGivenByStructuralConstants| |CartesianTensor| |CliffordAlgebra| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |HomogeneousDirectProduct| |IdealDecompositionPackage| |LieSquareMatrix| |LinGroebnerPackage| |OrderedDirectProduct| |Permanent| |PolToPol| |QuadraticForm| |RectangularMatrix| |SplitHomogeneousDirectProduct| |SquareMatrix|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AlgebraGivenByStructuralConstants| |BlowUpPackage| |CartesianTensor| |CliffordAlgebra| |DesingTreePackage| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |HomogeneousDirectProduct| |IdealDecompositionPackage| |InfinitlyClosePoint| |LieSquareMatrix| |LinGroebnerPackage| |OrderedDirectProduct| |PackageForAlgebraicFunctionFieldOverFiniteField| |Permanent| |PolToPol| |QuadraticForm| |RectangularMatrix| |SplitHomogeneousDirectProduct| |SquareMatrix|) (|FiniteFieldCategory&|) (|TopLevelDrawFunctions|) (|ChineseRemainderToolsForIntegralBases| |FiniteFieldCategory&| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |GenUFactorize| |IrredPolyOverFiniteField| |MultFiniteFactorize| |PAdicWildFunctionFieldIntegralBasis| |SparseUnivariatePolynomial| |TwoFactorize| |WildFunctionFieldIntegralBasis|) -(|FGLMIfCanPackage| |GroebnerSolve| |IdealDecompositionPackage| |LinGroebnerPackage| |PolToPol| |QuasiAlgebraicSet2|) -(|AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |BalancedPAdicRational| |BasicFunctions| |BinaryExpansion| |Color| |CommonOperators| |ComplexCategory&| |DecimalExpansion| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |ExpertSystemContinuityPackage| |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExpressionTubePlot| |Factored| |Float| |FortranCode| |Fraction| |GraphImage| |HexadecimalExpansion| |InnerAlgebraicNumber| |InputForm| |Integer| |IntegerNumberSystem&| |MachineFloat| |MachineInteger| |MeshCreationRoutinesForThreeDimensions| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagRootFindingPackage| |NagSpecialFunctionsPackage| |NumericTubePlot| |OpenMathDevice| |OpenMathServerPackage| |OutputForm| |PAdicRational| |PAdicRationalConstructor| |Pi| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RomanNumeral| |SExpression| |SingleInteger| |SparseUnivariateLaurentSeries| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TubePlotTools| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |ViewDefaultsPackage| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |BlowUpPackage| |DesingTreePackage| |FGLMIfCanPackage| |GroebnerSolve| |IdealDecompositionPackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InterfaceGroebnerPackage| |LinGroebnerPackage| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PolToPol| |QuasiAlgebraicSet2|) +(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |Plcs|) +(|AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |BalancedPAdicRational| |BasicFunctions| |BinaryExpansion| |BlasLevelOne| |Color| |ComplexCategory&| |DecimalExpansion| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatSpecialFunctions| |DoubleFloatVector| |DrawComplex| |ExpertSystemContinuityPackage| |ExpertSystemContinuityPackage1| |ExpertSystemToolsPackage| |ExponentialExpansion| |Export3D| |ExpressionTubePlot| |Factored| |Float| |FortranCode| |Fraction| |GnuDraw| |GraphImage| |HexadecimalExpansion| |InnerAlgebraicNumber| |InputForm| |Integer| |IntegerNumberSystem&| |MachineFloat| |MachineInteger| |MeshCreationRoutinesForThreeDimensions| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagRootFindingPackage| |NagSpecialFunctionsPackage| |NumericTubePlot| |OpenMathDevice| |OpenMathServerPackage| |OutputForm| |PAdicRational| |PAdicRationalConstructor| |Pi| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RomanNumeral| |SExpression| |SingleInteger| |SparseUnivariateLaurentSeries| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TubePlotTools| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |ViewDefaultsPackage| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|DoubleFloat|) +(|DoubleFloatMatrix|) (|AlgebraicIntegrate|) -(|DrawOptionFunctions1| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) -(|GraphImage| |MeshCreationRoutinesForThreeDimensions| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TwoDimensionalViewport|) +(|DrawOptionFunctions1| |GnuDraw| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) +(|GnuDraw| |GraphImage| |MeshCreationRoutinesForThreeDimensions| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TwoDimensionalViewport|) (|DrawOptionFunctions0|) (|RadicalEigenPackage|) (|Expression|) @@ -104,11 +114,12 @@ (|ComplexTrigonometricManipulations| |ElementaryRischDE| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GenusZeroIntegration| |ODEIntegration| |PowerSeriesLimitPackage| |TransSolvePackage| |TrigonometricManipulations|) (|SparseUnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor|) (|FunctionSpaceToExponentialExpansion|) -(|FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |LaplaceTransform|) +(|FunctionSpaceComplexIntegration| |FunctionSpaceIntegration|) (|ElementaryIntegration|) (|ElementaryIntegration|) -(|AlgebraicNumber| |ApplyRules| |ArrayStack| |AssociationList| |BalancedBinaryTree| |BalancedPAdicRational| |BinaryExpansion| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |CharacterClass| |Complex| |ComplexRootFindingPackage| |DataList| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |EigenPackage| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |EqTable| |Equation| |EquationFunctions2| |Evalable&| |ExpertSystemContinuityPackage| |ExponentialExpansion| |Expression| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |Factored| |FlexibleArray| |FloatingComplexPackage| |FloatingRealPackage| |FortranExpression| |FortranProgram| |Fraction| |FullyEvalableOver&| |FunctionSpace&| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InnerAlgebraicNumber| |InnerIndexedTwoDimensionalArray| |InnerNumericFloatSolvePackage| |InnerTable| |KeyedAccessFile| |LaplaceTransform| |Library| |LieExponentials| |LieSquareMatrix| |List| |ListMultiDictionary| |MachineComplex| |Matrix| |ModMonic| |Multiset| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearSolvePackage| |Octonion| |OneDimensionalArray| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternMatch| |PendantTree| |Point| |Polynomial| |PolynomialCategory&| |PolynomialIdeals| |PowerSeriesLimitPackage| |PrimitiveArray| |Quaternion| |Queue| |RadicalSolvePackage| |RadixExpansion| |RationalFunction| |RationalFunctionLimitPackage| |RationalRicDE| |RectangularMatrix| |RegularChain| |RegularTriangularSet| |Result| |RetractSolvePackage| |RewriteRule| |RoutinesTable| |SequentialDifferentialPolynomial| |Set| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SplitHomogeneousDirectProduct| |SplittingTree| |SquareFreeRegularTriangularSet| |SquareMatrix| |Stack| |Stream| |String| |StringTable| |SystemSolvePackage| |Table| |TaylorSeries| |ThreeDimensionalMatrix| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |Tree| |TwoDimensionalArray| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |Vector| |WuWenTsunTriangularSet| |d01AgentsPackage| |d01TransformFunctionType| |d02AgentsPackage| |d03AgentsPackage|) +(|AlgebraicNumber| |ApplyRules| |ArrayStack| |AssociationList| |BalancedBinaryTree| |BalancedPAdicRational| |BinaryExpansion| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |CharacterClass| |Complex| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexRootFindingPackage| |DataList| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |DoubleFloatMatrix| |DoubleFloatVector| |EigenPackage| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |EqTable| |Equation| |EquationFunctions2| |Evalable&| |ExpertSystemContinuityPackage| |ExponentialExpansion| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |Factored| |FlexibleArray| |FloatingComplexPackage| |FloatingRealPackage| |FortranExpression| |FortranProgram| |Fraction| |FullyEvalableOver&| |FunctionSpace&| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InnerAlgebraicNumber| |InnerIndexedTwoDimensionalArray| |InnerNumericFloatSolvePackage| |InnerTable| |KeyedAccessFile| |LaplaceTransform| |Library| |LieExponentials| |LieSquareMatrix| |List| |ListMultiDictionary| |MachineComplex| |Matrix| |ModMonic| |Multiset| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearSolvePackage| |Octonion| |OneDimensionalArray| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternMatch| |PendantTree| |Point| |Polynomial| |PolynomialCategory&| |PolynomialIdeals| |PowerSeriesLimitPackage| |PrimitiveArray| |Quaternion| |Queue| |RadicalSolvePackage| |RadixExpansion| |RationalFunction| |RationalFunctionLimitPackage| |RationalRicDE| |RectangularMatrix| |RecurrenceOperator| |RegularChain| |RegularTriangularSet| |Result| |RetractSolvePackage| |RewriteRule| |RoutinesTable| |SequentialDifferentialPolynomial| |Set| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SplitHomogeneousDirectProduct| |SplittingTree| |SquareFreeRegularTriangularSet| |SquareMatrix| |Stack| |Stream| |String| |StringTable| |SystemSolvePackage| |Table| |TaylorSeries| |ThreeDimensionalMatrix| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |Tree| |TwoDimensionalArray| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |Vector| |WuWenTsunTriangularSet| |d01AgentsPackage| |d01TransformFunctionType| |d02AgentsPackage| |d03AgentsPackage|) (|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AttributeButtons| |RoutinesTable| |d01AgentsPackage|) +(|ParametricLinearEquations|) (|InnerModularGcd|) (|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AttributeButtons| |ErrorFunctions| |OpenMathPackage| |ResolveLatticeCompletion| |RoutinesTable| |d01AgentsPackage|) (|d01AgentsPackage| |e04gcfAnnaType|) @@ -117,29 +128,35 @@ (|d02AgentsPackage| |e04nafAnnaType|) (|FunctionSpaceToExponentialExpansion|) (|ExponentialExpansion| |FunctionSpaceToExponentialExpansion| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AttachPredicates| |ComplexTrigonometricManipulations| |DeRhamComplex| |DegreeReductionPackage| |DrawNumericHack| |ElementaryFunctionSign| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExpressionFunctions2| |ExpressionToOpenMath| |ExpressionTubePlot| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranProgram| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |InnerAlgebraicNumber| |IntegrationResultRFToFunction| |MachineInteger| |MeshCreationRoutinesForThreeDimensions| |Numeric| |PatternMatchAssertions| |PiCoercions| |PolynomialAN2Expression| |RadicalEigenPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SimplifyAlgebraicNumberConvertPackage| |Switch| |ToolsForSign| |TransSolvePackage| |TransSolvePackageService| |TrigonometricManipulations| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AttachPredicates| |ComplexTrigonometricManipulations| |DeRhamComplex| |DegreeReductionPackage| |DrawNumericHack| |ElementaryFunctionSign| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExpressionFunctions2| |ExpressionToOpenMath| |ExpressionTubePlot| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranProgram| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GnuDraw| |GuessAlgebraicNumber| |GuessFinite| |GuessFiniteFunctions| |GuessInteger| |GuessPolynomial| |InnerAlgebraicNumber| |IntegrationResultRFToFunction| |MachineInteger| |MappingPackage4| |MeshCreationRoutinesForThreeDimensions| |MyExpression| |Numeric| |PatternMatchAssertions| |PiCoercions| |PolynomialAN2Expression| |RadicalEigenPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SimplifyAlgebraicNumberConvertPackage| |Switch| |ToolsForSign| |TransSolvePackage| |TransSolvePackageService| |TrigonometricManipulations| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|AnnaOrdinaryDifferentialEquationPackage| |ExpertSystemToolsPackage| |FortranExpression| |InnerAlgebraicNumber| |MachineInteger| |Numeric| |TransSolvePackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |e04AgentsPackage|) +(|RecurrenceOperator|) (|Expression| |ExpressionFunctions2| |FunctionSpaceFunctions2| |InnerTrigonometricManipulations|) (|AntiSymm| |DeRhamComplex|) -(|AlgFactor| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicMultFact| |AlgebraicNumber| |BalancedFactorisation| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |ChangeOfVariable| |ChineseRemainderToolsForIntegralBases| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclotomicPolynomialPackage| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DoubleFloat| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionSign| |Equation| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |Field&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |Float| |Fraction| |FullPartialFractionExpansion| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaussianFactorizationPackage| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralUnivariatePowerSeries| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerSolve| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerMultFact| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegerFactorizationPackage| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LinearOrdinaryDifferentialOperatorFactorizer| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |ModularField| |MonomialExtensionTools| |MultFiniteFactorize| |MultivariateFactorize| |MultivariatePolynomial| |MultivariateSquareFree| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |ParametricLinearEquations| |PartialFraction| |PartialFractionPackage| |Pi| |PlaneAlgebraicCurvePlot| |PointsOfFiniteOrder| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |QuasiAlgebraicSet| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFactorize| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunctionSign| |RationalRicDE| |RealClosure| |RealZeroPackage| |RomanNumeral| |SAERationalFunctionAlgFactor| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SturmHabichtPackage| |SupFractionFactorizer| |SystemSolvePackage| |TransSolvePackage| |TranscendentalIntegration| |TranscendentalManipulations| |TwoFactorize| |UniqueFactorizationDomain&| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |WildFunctionFieldIntegralBasis|) +(|AlgFactor| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicMultFact| |AlgebraicNumber| |BalancedFactorisation| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |ChangeOfVariable| |ChineseRemainderToolsForIntegralBases| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexRootFindingPackage| |ComplexRootPackage| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclotomicPolynomialPackage| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DirichletRing| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DoubleFloat| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionSign| |Equation| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |Field&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldSquareFreeDecomposition| |Float| |Fraction| |FullPartialFractionExpansion| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaussianFactorizationPackage| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralUnivariatePowerSeries| |GeneralizedMultivariateFactorize| |GosperSummationMethod| |GroebnerFactorizationPackage| |GroebnerSolve| |Guess| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerMultFact| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegerFactorizationPackage| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegrationResultToFunction| |InverseLaplaceTransform| |Kovacic| |LinearOrdinaryDifferentialOperatorFactorizer| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |ModularField| |MonomialExtensionTools| |MultFiniteFactorize| |MultivariateFactorize| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |ParametricLinearEquations| |PartialFraction| |PartialFractionPackage| |Pi| |PlaneAlgebraicCurvePlot| |PointsOfFiniteOrder| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |QuasiAlgebraicSet| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFactorize| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunctionSign| |RationalRicDE| |RealClosure| |RealZeroPackage| |RomanNumeral| |RootsFindingPackage| |SAERationalFunctionAlgFactor| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SturmHabichtPackage| |SupFractionFactorizer| |SystemSolvePackage| |TransSolvePackage| |TranscendentalIntegration| |TranscendentalManipulations| |TwoFactorize| |UniqueFactorizationDomain&| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |WildFunctionFieldIntegralBasis|) (|ComplexCategory&| |Integer| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate|) (|ChangeOfVariable| |PolynomialRoots| |TranscendentalManipulations|) (|FunctionSpaceUnivariatePolynomialFactor| |Integer| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |RationalFunctionFactor| |UnivariatePolynomialCategory&|) (|InnerMultFact| |MultFiniteFactorize| |MultivariateSquareFree| |PolynomialGcdPackage|) +(|PseudoAlgebraicClosureOfAlgExtOfRationalNumber|) +(|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfRationalNumber|) (|BinaryFile| |ParametricLinearEquations| |TextFile|) -(|BinaryFile| |File| |FortranOutputStackPackage| |FortranPackage| |FortranTemplate| |KeyedAccessFile| |Library| |NagEigenPackage| |NagIntegrationPackage| |NagLinearEquationSolvingPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagRootFindingPackage| |ParametricLinearEquations| |TextFile|) +(|BinaryFile| |Export3D| |File| |FortranOutputStackPackage| |FortranPackage| |FortranTemplate| |GnuDraw| |KeyedAccessFile| |Library| |NagEigenPackage| |NagIntegrationPackage| |NagLinearEquationSolvingPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagRootFindingPackage| |ParametricLinearEquations| |TextFile|) +(|FractionFreeFastGaussianFractions|) (|AlgebraicIntegrate| |FindOrderFinite| |FiniteDivisorFunctions2| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |ReducedDivisor|) (|FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension|) (|InnerFiniteField|) (|FiniteField| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension|) +(|PseudoAlgebraicClosureOfFiniteField| |RootsFindingPackage|) (|FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial|) (|FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension|) (|FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldExtension| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldPolynomialPackage2| |MultFiniteFactorize|) (|SparseUnivariatePolynomial|) +(|FiniteFieldFactorizationWithSizeParseBySideEffect|) (|DirectProductFunctions2| |InnerCommonDenominator| |ListFunctions2| |MatrixLinearAlgebraFunctions| |OneDimensionalArrayFunctions2| |PrimitiveArrayFunctions2| |VectorFunctions2|) (|OneDimensionalArrayAggregate&|) (|GaloisGroupUtilities|) -(|AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |Asp19| |AttributeButtons| |BalancedPAdicRational| |BinaryExpansion| |BrillhartTests| |ComplexCategory&| |DecimalExpansion| |DoubleFloat| |DrawComplex| |DrawNumericHack| |DrawOption| |DrawOptionFunctions0| |ElementaryFunctionSign| |ExpertSystemToolsPackage| |ExponentialExpansion| |Factored| |Float| |FortranExpression| |Fraction| |GraphImage| |HexadecimalExpansion| |InnerAlgebraicNumber| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |Integer| |IntegerNumberSystem&| |MachineComplex| |MachineFloat| |MachineInteger| |NumberFormats| |Numeric| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |OpenMathServerPackage| |PAdicRational| |PAdicRationalConstructor| |Pi| |PlaneAlgebraicCurvePlot| |QuotientFieldCategory&| |RadixExpansion| |RandomFloatDistributions| |RealNumberSystem&| |RealSolvePackage| |RomanNumeral| |RoutinesTable| |SingleInteger| |SparseUnivariateLaurentSeries| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TwoDimensionalViewport| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |ViewDefaultsPackage| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |d03fafAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |Asp19| |AttributeButtons| |BalancedPAdicRational| |BinaryExpansion| |BrillhartTests| |ComplexCategory&| |DecimalExpansion| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |DrawNumericHack| |DrawOption| |DrawOptionFunctions0| |ElementaryFunctionSign| |ExpertSystemToolsPackage| |ExponentialExpansion| |Factored| |Float| |FortranExpression| |Fraction| |GraphImage| |HexadecimalExpansion| |InnerAlgebraicNumber| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |Integer| |IntegerNumberSystem&| |Interval| |MachineComplex| |MachineFloat| |MachineInteger| |NumberFormats| |Numeric| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |OpenMathServerPackage| |PAdicRational| |PAdicRationalConstructor| |Pi| |PlaneAlgebraicCurvePlot| |QuotientFieldCategory&| |RadixExpansion| |RandomFloatDistributions| |RealNumberSystem&| |RealSolvePackage| |RomanNumeral| |RoutinesTable| |SingleInteger| |SparseUnivariateLaurentSeries| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TwoDimensionalViewport| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |ViewDefaultsPackage| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |d03fafAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|RealSolvePackage|) (|Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |FortranCodePackage1| |FortranProgram|) (|Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp31| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp80| |Asp9|) @@ -148,7 +165,9 @@ (|Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |FortranPackage| |FortranType| |SimpleFortranProgram| |SymbolTable|) (|Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |FortranCode| |FortranPackage| |SymbolTable| |TheSymbolTable|) (|FourierSeries|) -(|AbelianMonoidRing&| |AlgFactor| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedFunctionSpace&| |Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp31| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp80| |Asp9| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |ChangeOfVariable| |CoerceVectorMatrixPackage| |CombinatorialFunction| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexRootFindingPackage| |ContinuedFraction| |CycleIndicators| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |DoubleFloat| |DoubleResultantPackage| |EigenPackage| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EvaluateCycleIndicators| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |Factored| |FiniteDivisor| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranExpression| |FourierSeries| |Fraction| |FractionFunctions2| |FractionalIdeal| |FullPartialFractionExpansion| |FullyRetractableTo&| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |InfiniteProductFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerModularGcd| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |Integer| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LieSquareMatrix| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |LinearSystemPolynomialPackage| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |ModularField| |MonogenicAlgebra&| |MonomialExtensionTools| |MultipleMap| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearSolvePackage| |NormalizationPackage| |NumberTheoreticPolynomialFunctions| |Numeric| |ODEIntegration| |Octonion| |OctonionCategory&| |OnePointCompletion| |OrderedCompletion| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrthogonalPolynomialFunctions| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PadeApproximantPackage| |PadeApproximants| |ParametricLinearEquations| |PartialFraction| |PartialFractionPackage| |PatternMatchIntegration| |Pi| |PiCoercions| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialAN2Expression| |PolynomialCategory&| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursionUnivariate| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialRoots| |PolynomialSolveByFormulas| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |QuasiAlgebraicSet2| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadicalCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RadixUtilities| |RandomIntegerDistributions| |RationalFactorize| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunctionIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalIntegration| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RecursivePolynomialCategory&| |ReducedDivisor| |RetractSolvePackage| |RightOpenIntervalRootCharacterization| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StructuralConstantsPackage| |SturmHabichtPackage| |SupFractionFactorizer| |SymmetricPolynomial| |SystemSolvePackage| |TangentExpansions| |TaylorSeries| |ToolsForSign| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TransSolvePackageService| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |TwoDimensionalPlotClipping| |UTSodetools| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |XExponentialPackage| |XPBWPolynomial| |ZeroDimensionalSolvePackage| |d01TransformFunctionType| |d01WeightsPackage| |d01aqfAnnaType| |d02AgentsPackage| |e04AgentsPackage| |e04ucfAnnaType|) +(|AbelianMonoidRing&| |AlgFactor| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedFunctionSpace&| |Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp31| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp80| |Asp9| |BalancedPAdicRational| |BinaryExpansion| |BoundIntegerRoots| |ChangeOfVariable| |CoerceVectorMatrixPackage| |CombinatorialFunction| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexRootFindingPackage| |ContinuedFraction| |CycleIndicators| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |DoubleFloat| |DoubleFloatSpecialFunctions| |DoubleResultantPackage| |EigenPackage| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EvaluateCycleIndicators| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |Factored| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FiniteDivisor| |FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranExpression| |FourierSeries| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionFunctions2| |FractionalIdeal| |FullPartialFractionExpansion| |FullyRetractableTo&| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GeneralDistributedMultivariatePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |Guess| |GuessInteger| |GuessPolynomial| |GuessUnivariatePolynomial| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |InfiniteProductFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerModularGcd| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |Integer| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |Interval| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LieSquareMatrix| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |LinearSystemPolynomialPackage| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |ModularField| |MonogenicAlgebra&| |MonomialExtensionTools| |MultipleMap| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearSolvePackage| |NormalizationPackage| |NumberTheoreticPolynomialFunctions| |Numeric| |ODEIntegration| |Octonion| |OctonionCategory&| |OnePointCompletion| |OrderedCompletion| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrthogonalPolynomialFunctions| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PadeApproximantPackage| |PadeApproximants| |ParametricLinearEquations| |PartialFraction| |PartialFractionPackage| |PatternMatchIntegration| |Pi| |PiCoercions| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialAN2Expression| |PolynomialCategory&| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursionUnivariate| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialRoots| |PolynomialSolveByFormulas| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveRatDE| |PrimitiveRatRicDE| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PureAlgebraicIntegration| |PureAlgebraicLODE| |QuasiAlgebraicSet2| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadicalCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RadixUtilities| |RationalFactorize| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunctionIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalIntegration| |RationalInterpolation| |RationalLODE| |RationalRetractions| |RationalRicDE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RecurrenceOperator| |RecursivePolynomialCategory&| |ReducedDivisor| |RetractSolvePackage| |RightOpenIntervalRootCharacterization| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StructuralConstantsPackage| |SturmHabichtPackage| |SupFractionFactorizer| |SymmetricPolynomial| |SystemSolvePackage| |TangentExpansions| |TaylorSeries| |TaylorSolve| |ToolsForSign| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |TransSolvePackageService| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem| |TwoDimensionalPlotClipping| |UTSodetools| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesFunctions2| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |XExponentialPackage| |XPBWPolynomial| |ZeroDimensionalSolvePackage| |d01TransformFunctionType| |d01WeightsPackage| |d01aqfAnnaType| |d02AgentsPackage| |e04AgentsPackage| |e04ucfAnnaType|) +(|FractionFreeFastGaussianFractions| |Guess|) +(|Guess|) (|FiniteDivisor| |FiniteDivisorFunctions2| |FractionalIdealFunctions2| |FramedModule| |HyperellipticFiniteDivisor| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational|) (|FiniteDivisorFunctions2|) (|FiniteDivisor|) @@ -162,7 +181,7 @@ (|AttachPredicates| |PatternMatchIntegration|) (|FunctionSpaceIntegration|) (|ElementaryFunctionSign| |ExpressionFunctions2| |InnerTrigonometricManipulations|) -(|ElementaryFunctionDefiniteIntegration| |GeneralUnivariatePowerSeries| |LaplaceTransform| |ODEIntegration| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeries|) +(|ElementaryFunctionDefiniteIntegration| |GeneralUnivariatePowerSeries| |LaplaceTransform| |ODEIntegration| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) (|ElementaryFunctionLODESolver| |ElementaryIntegration| |ElementaryRischDE|) (|FunctionSpaceToExponentialExpansion|) (|AlgebraicIntegrate| |ConstantLODE| |ElementaryFunctionLODESolver| |IntegrationResultToFunction|) @@ -175,18 +194,23 @@ (|MultivariateFactorize| |NumericRealEigenPackage|) (|DistributedMultivariatePolynomial| |HomogeneousDistributedMultivariatePolynomial|) (|GaloisGroupFactorizer| |PAdicWildFunctionFieldIntegralBasis| |UnivariateFactorize|) +(|PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) (|PolynomialCategory&|) (|LexTriangularPackage| |PolynomialSetUtilitiesPackage| |QuasiComponentPackage| |RegularSetDecompositionPackage| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage|) (|SparseTable|) (|PolynomialSetUtilitiesPackage| |WuWenTsunTriangularSet|) -(|GroebnerSolve| |MPolyCatPolyFactorizer| |SystemSolvePackage|) +(|GroebnerSolve| |Guess| |MPolyCatPolyFactorizer| |SystemSolvePackage|) (|PureAlgebraicIntegration|) (|FunctionSpaceSum| |RationalFunctionSum|) -(|TopLevelDrawFunctionsForPoints| |TwoDimensionalViewport| |ViewportPackage|) +(|GnuDraw| |TopLevelDrawFunctionsForPoints| |TwoDimensionalViewport| |ViewportPackage|) (|PlotTools| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) (|Permanent|) -(|GroebnerFactorizationPackage| |GroebnerPackage| |GroebnerSolve| |LinGroebnerPackage| |ParametricLinearEquations| |PolynomialIdeals| |QuasiAlgebraicSet|) -(|FGLMIfCanPackage| |GroebnerSolve| |IdealDecompositionPackage| |LinGroebnerPackage| |ParametricLinearEquations| |PolynomialIdeals| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |ResidueRing|) +(|GroebnerFactorizationPackage| |GroebnerPackage| |GroebnerSolve| |LinGroebnerPackage| |PolynomialIdeals| |QuasiAlgebraicSet|) +(|FGLMIfCanPackage| |GeneralPackageForAlgebraicFunctionField| |GroebnerSolve| |IdealDecompositionPackage| |InterfaceGroebnerPackage| |LinGroebnerPackage| |PolynomialIdeals| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |ResidueRing|) +(|GuessAlgebraicNumber| |GuessFinite| |GuessInteger| |GuessPolynomial| |GuessUnivariatePolynomial|) +(|GuessFinite|) +(|Guess| |GuessOptionFunctions0|) +(|Guess|) (|FreeNilpotentLie|) (|EqTable| |StringTable| |TabulatedComputationPackage|) (|Integer|) @@ -205,10 +229,13 @@ (|IndexedTwoDimensionalArray| |IndexedVector| |OneDimensionalArray|) (|String|) (|IndexedMatrix| |Vector|) +(|PackageForAlgebraicFunctionField|) (|InfiniteTupleFunctions2| |InfiniteTupleFunctions3|) +(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) +(|PackageForAlgebraicFunctionFieldOverFiniteField|) (|SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor|) (|AlgebraicNumber|) -(|AlgebraicFunctionField| |AlgebraicIntegrate| |ElementaryFunctionStructurePackage| |FractionalIdeal| |FunctionFieldCategory&| |InnerMatrixQuotientFieldFunctions| |PrimitiveRatDE| |RadicalFunctionField| |RationalLODE|) +(|AlgebraicFunctionField| |AlgebraicIntegrate| |ElementaryFunctionStructurePackage| |FractionFreeFastGaussian| |FractionalIdeal| |FunctionFieldCategory&| |InnerMatrixQuotientFieldFunctions| |PrimitiveRatDE| |RadicalFunctionField| |RationalLODE|) (|FreeAbelianGroup| |FreeAbelianMonoid|) (|IndexedMatrix| |IndexedTwoDimensionalArray| |Matrix| |TwoDimensionalArray|) (|InnerMatrixQuotientFieldFunctions| |MatrixLinearAlgebraFunctions|) @@ -223,17 +250,17 @@ (|InnerFiniteField| |PrimeField|) (|SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries|) (|Table|) -(|SparseMultivariateTaylorSeries| |UnivariateTaylorSeries|) +(|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| |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| |SquareFreeRegularTriangularSet| |SquareMatrix| |Stream| |String| |StringTable| |Symbol| |SymbolTable| |Table| |TemplateUtilities| |TopLevelDrawFunctions| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |WuWenTsunTriangularSet|) +(|AssociationList| |BalancedPAdicRational| |BasicOperatorFunctions1| |BinaryExpansion| |Bits| |Boolean| |CharacterClass| |CommonOperators| |Complex| |ComplexCategory&| |ComplexDoubleFloatVector| |DataList| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |DoubleFloatVector| |EqTable| |ExponentialExpansion| |Export3D| |Expression| |Factored| |FlexibleArray| |Float| |FortranPackage| |FortranProgram| |Fraction| |FunctionSpace&| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GnuDraw| |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&| |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| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BezoutMatrix| |BinaryExpansion| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexRootFindingPackage| |ComplexRootPackage| |ContinuedFraction| |CoordinateSystems| |CycleIndicators| |CyclotomicPolynomialPackage| |DataList| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |DivisionRing&| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |EigenPackage| |ElementaryFunction| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EllipticFunctionsUnivariateTaylorSeries| |Equation| |EuclideanDomain&| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtensibleLinearAggregate&| |Factored| |FactoredFunctions| |FactoredFunctions2| |FactoringUtilities| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteLinearAggregate&| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FloatingPointSystem&| |FortranCode| |FortranExpression| |FortranProgram| |FortranTemplate| |FourierSeries| |Fraction| |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| |GeneralPolynomialGcdPackage| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |GraphImage| |GraphicsDefaults| |GrayCode| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Group&| |HallBasis| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperbolicFunctionCategory&| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |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| |InverseLaplaceTransform| |IrrRepSymNatPackage| |KeyedAccessFile| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LazyStreamAggregate&| |LeadingCoefDetermination| |LeftAlgebra&| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| |LiouvillianFunction| |List| |ListAggregate&| |ListMonoidOps| |ListToMap| |LocalAlgebra| |Localize| |LyndonWord| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |MakeFloatCompiledFunction| |MappingPackage1| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |MonogenicAlgebra&| |MonoidRing| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NPCoef| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonAssociativeRing&| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NumberFieldIntegralBasis| |NumberFormats| |NumberTheoreticPolynomialFunctions| |NumericContinuedFraction| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODEIntegration| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |OpenMathDevice| |OpenMathError| |OpenMathServerPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedRing&| |OrderedVariableList| |OrderingFunctions| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |ParadoxicalCombinatorsForStreams| |ParametricLinearEquations| |PartialFraction| |Partition| |PartitionsAndPermutations| |Pattern| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchPolynomialCategory| |PendantTree| |Permanent| |Permutation| |PermutationGroup| |PermutationGroupExamples| |Pi| |PiCoercions| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |PointFunctions2| |PointPackage| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialCategory&| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialRoots| |PolynomialSolveByFormulas| |PowerSeriesCategory&| |PowerSeriesLimitPackage| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |QuadraticForm| |Quaternion| |QuaternionCategory&| |QuotientFieldCategory&| |RadicalCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RadixUtilities| |RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions| |RandomNumberSource| |RationalFactorize| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalLODE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RectangularMatrix| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecursivePolynomialCategory&| |ReduceLODE| |ReductionOfOrder| |RegularTriangularSet| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RightOpenIntervalRootCharacterization| |Ring&| |RomanNumeral| |RoutinesTable| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentFunctions2| |SequentialDifferentialPolynomial| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SortPackage| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |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| |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| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |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|) +(|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&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |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| |DirichletRing| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |DivisionRing&| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatSpecialFunctions| |DoubleFloatVector| |DrawComplex| |EigenPackage| |ElementaryFunction| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EllipticFunctionsUnivariateTaylorSeries| |Equation| |EuclideanDomain&| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Export3D| |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| |GnuDraw| |GosperSummationMethod| |GraphImage| |GraphicsDefaults| |GrayCode| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Group&| |Guess| |GuessFinite| |GuessFiniteFunctions| |GuessOption| |GuessOptionFunctions0| |HTMLFormat| |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| |IntegerNumberSystem&| |IrrRepSymNatPackage| |MultivariateLifting| |RepresentationPackage1| |SetOfMIntegersInOneToN| |SymmetricGroupCombinatoricFunctions|) +(|ComplexRootFindingPackage| |GaloisGroupUtilities| |Guess| |IntegerNumberSystem&| |IrrRepSymNatPackage| |MultivariateLifting| |RepresentationPackage1| |SetOfMIntegersInOneToN| |SymmetricGroupCombinatoricFunctions|) (|CyclotomicPolynomialPackage| |Factored| |GaussianFactorizationPackage| |IntegerNumberSystem&| |NumberFieldIntegralBasis|) (|ElementaryFunctionStructurePackage|) (|InnerPrimeField|) -(|CycleIndicators| |FiniteFieldPolynomialPackage| |PolynomialNumberTheoryFunctions|) +(|CycleIndicators| |DirichletRing| |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|) @@ -241,16 +268,19 @@ (|PAdicWildFunctionFieldIntegralBasis|) (|FunctionFieldIntegralBasis| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |WildFunctionFieldIntegralBasis|) (|AnnaNumericalIntegrationPackage| |d01AgentsPackage|) -(|AlgebraicIntegrate| |AlgebraicIntegration| |ElementaryIntegration| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenusZeroIntegration| |IntegrationResultFunctions2| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |LaplaceTransform| |PureAlgebraicIntegration| |RationalFunctionIntegration| |RationalIntegration| |TranscendentalIntegration|) +(|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| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |FortranExpression| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceFunctions2| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GenusZeroIntegration| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |KernelFunctions2| |LaplaceTransform| |LiouvillianFunction| |NonLinearFirstOrderODESolver| |ODEIntegration| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |RadicalEigenPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RewriteRule| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TrigonometricManipulations| |d01AgentsPackage| |d01WeightsPackage|) +(|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| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |KernelFunctions2| |LaplaceTransform| |LiouvillianFunction| |MyExpression| |NonLinearFirstOrderODESolver| |ODEIntegration| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PatternMatchKernel| |PointsOfFiniteOrder| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |RadicalEigenPackage| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RecurrenceOperator| |RewriteRule| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TrigonometricManipulations| |d01AgentsPackage| |d01WeightsPackage|) (|Expression|) (|Library|) (|ElementaryFunctionLODESolver|) @@ -266,18 +296,21 @@ (|ElementaryFunctionLODESolver|) (|LinearOrdinaryDifferentialOperator|) (|PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&|) +(|InterpolateFormsPackage|) (|AlgebraGivenByStructuralConstants| |AlgebraicHermiteIntegration| |CliffordAlgebra| |ElementaryFunctionLODESolver| |FramedNonAssociativeAlgebra&| |GosperSummationMethod| |LinearDependence| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |ODETools| |RationalLODE| |StructuralConstantsPackage| |TransSolvePackageService|) (|SystemSolvePackage|) +(|InterpolateFormsPackage| |LinearSystemFromPowerSeriesPackage|) (|Expression| |PowerSeriesLimitPackage|) -(|AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |Any| |ApplyRules| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttachPredicates| |AttributeButtons| |BagAggregate&| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BoundIntegerRoots| |CRApackage| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| |Character| |CharacterClass| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Collection&| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclotomicPolynomialPackage| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |Dictionary&| |DictionaryOperations&| |DifferentialExtension&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DisplayPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DoubleFloat| |DrawComplex| |DrawOption| |DrawOptionFunctions0| |DrawOptionFunctions1| |EigenPackage| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |EllipticFunctionsUnivariateTaylorSeries| |EqTable| |Equation| |ErrorFunctions| |EuclideanDomain&| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |Evalable&| |EvaluateCycleIndicators| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtAlgBasis| |ExtensibleLinearAggregate&| |FGLMIfCanPackage| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |FactoringUtilities| |Field&| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteLinearAggregateFunctions2| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FiniteSetAggregateFunctions2| |FlexibleArray| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranOutputStackPackage| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |Fraction| |FractionalIdeal| |FramedAlgebra&| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FullyEvalableOver&| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaussianFactorizationPackage| |GcdDomain&| |GenExEuclid| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |HallBasis| |HashTable| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedAggregate&| |IndexedBits| |IndexedDirectProductObject| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerEvalable&| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegrationFunctionsTable| |IntegrationResult| |IntegrationResultFunctions2| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |IrrRepSymNatPackage| |Kernel| |KernelFunctions2| |KeyedAccessFile| |KeyedDictionary&| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LazyStreamAggregate&| |LeadingCoefDetermination| |LexTriangularPackage| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearPolynomialEquationByFractions| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LiouvillianFunction| |List| |ListFunctions2| |ListFunctions3| |ListMonoidOps| |ListMultiDictionary| |ListToMap| |LyndonWord| |MPolyCatFunctions2| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |MappingPackage1| |Matrix| |MatrixCategory&| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |MergeThing| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModuleOperator| |MoebiusTransform| |MonogenicAlgebra&| |MonoidRing| |MonoidRingFunctions2| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NAGLinkSupportPackage| |NPCoef| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |NonLinearSolvePackage| |NormRetractPackage| |NormalizationPackage| |NumberFieldIntegralBasis| |NumberFormats| |NumericComplexEigenPackage| |NumericRealEigenPackage| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODEIntegration| |ODEIntensityFunctionsTable| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OpenMathError| |OpenMathPackage| |OppositeMonogenicLinearOperator| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PadeApproximants| |Palette| |ParadoxicalCombinatorsForStreams| |ParametricLinearEquations| |PartialDifferentialRing&| |PartialFraction| |PartialFractionPackage| |Partition| |PartitionsAndPermutations| |Pattern| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchResult| |PatternMatchResultFunctions2| |PatternMatchTools| |PendantTree| |Permutation| |PermutationGroup| |PermutationGroupExamples| |Pi| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |PoincareBirkhoffWittLyndonBasis| |Point| |PointFunctions2| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PolyGroebner| |Polynomial| |PolynomialCategory&| |PolynomialCategoryQuotientFunctions| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| |PolynomialRing| |PolynomialRoots| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PowerSeriesLimitPackage| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |Queue| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomDistributions| |RationalFactorize| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalFunctionSign| |RationalIntegration| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RectangularMatrix| |RecursiveAggregate&| |RecursivePolynomialCategory&| |ReductionOfOrder| |Reference| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentFunctions2| |SequentialDifferentialPolynomial| |Set| |SetAggregate&| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingleInteger| |SmithNormalForm| |SortedCache| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stack| |Stream| |StreamAggregate&| |StreamFunctions2| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |String| |StringTable| |StructuralConstantsPackage| |SturmHabichtPackage| |SubResultantPackage| |SubSpace| |SubSpaceComponentProperty| |SupFractionFactorizer| |Switch| |Symbol| |SymbolTable| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Table| |TableAggregate&| |Tableau| |TableauxBumpers| |TangentExpansions| |TaylorSeries| |TexFormat| |TheSymbolTable| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TransSolvePackage| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalManipulations| |TranscendentalRischDESystem| |Tree| |TriangularSetCategory&| |TrigonometricManipulations| |TubePlot| |TubePlotTools| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UnaryRecursiveAggregate&| |UniqueFactorizationDomain&| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialSquareFree| |UnivariatePowerSeriesCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |Vector| |VectorCategory&| |VectorFunctions2| |ViewDefaultsPackage| |ViewportPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) -(|AlgebraPackage| |Asp19| |Asp55| |ElementaryFunctionSign| |FiniteSetAggregateFunctions2| |FramedNonAssociativeAlgebra&| |GaloisGroupFactorizer| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |MatrixCommonDenominator| |PAdicWildFunctionFieldIntegralBasis| |PermutationGroupExamples| |RealSolvePackage| |ThreeSpace| |TwoDimensionalPlotClipping| |UnivariateTaylorSeriesODESolver|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |Any| |ApplicationProgramInterface| |ApplyRules| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttachPredicates| |AttributeButtons| |AxiomServer| |BagAggregate&| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |Bezier| |BinaryExpansion| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |BoundIntegerRoots| 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|ComplexDoubleFloatVector| |CycleIndicators| |DecimalExpansion| |DenavitHartenbergMatrix| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |DoubleFloatVector| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ExpertSystemToolsPackage| |ExpertSystemToolsPackage2| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |Guess| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |IndexedVector| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegralBasisPolynomialTools| |IntegralBasisTools| |InterpolateFormsPackage| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |MachineComplex| |MachineInteger| |Matrix| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |ParametricLinearEquations| |Point| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationExplicit&| |PrecomputedAssociatedEquations| |PrimeField| |PseudoAlgebraicClosureOfFiniteField| |PseudoLinearNormalForm| |PureAlgebraicLODE| |Quaternion| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadixExpansion| |RationalInterpolation| |RationalLODE| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |ReduceLODE| |RepresentationPackage1| |RepresentationPackage2| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StorageEfficientMatrixOperations| |StructuralConstantsPackage| |SymmetricGroupCombinatoricFunctions| |SystemODESolver| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalRischDESystem| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |VectorCategory&| |WildFunctionFieldIntegralBasis| |d01alfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|AlgebraicHermiteIntegration| |Asp19| |Asp20| |Asp31| |Asp35| |Asp41| |Asp42| |Asp74| |Asp77| |Asp80| |CoerceVectorMatrixPackage| |ComplexCategory&| |FractionalIdeal| |FramedAlgebra&| |FunctionFieldCategory&| |InnerMatrixQuotientFieldFunctions| |LinearDependence| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |ReduceLODE| |SimpleAlgebraicExtension| |SmithNormalForm|) (|AlgebraicFunctionField| |FractionalIdeal| |FramedModule| |FunctionFieldCategory&| |QuotientFieldCategory&|) (|IndexedMatrix| |Matrix|) @@ -307,7 +341,7 @@ (|ContinuedFraction|) (|MonoidRingFunctions2|) (|TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalRischDE| |TranscendentalRischDESystem|) -(|FortranOutputStackPackage| |FortranPackage| |NAGLinkSupportPackage|) +(|FortranOutputStackPackage| |FortranPackage| |Guess| |NAGLinkSupportPackage|) (|GeneralizedMultivariateFactorize| |MPolyCatRationalFunctionFactorizer|) (|Asp19| |Asp31| |Asp35| |Asp41| |Asp42| |Asp49| |Asp55| |d02AgentsPackage| |e04nafAnnaType|) (|FunctionFieldCategoryFunctions2| |PointsOfFiniteOrder| |ReducedDivisor|) @@ -315,6 +349,8 @@ (|Equation| |GeneralizedMultivariateFactorize| |GroebnerFactorizationPackage| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |ParametricLinearEquations| |PartialFractionPackage| |PolynomialSetUtilitiesPackage| |QuasiAlgebraicSet| |RadicalSolvePackage| |RationalFunctionFactor| |SupFractionFactorizer| |TransSolvePackage|) (|InnerMultFact| |MultFiniteFactorize| |MultivariateSquareFree| |PolynomialGcdPackage|) (|InnerMultFact| |PolynomialCategory&| |SupFractionFactorizer|) +(|GuessUnivariatePolynomial|) +(|MyExpression|) (|Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |NagEigenPackage| |NagIntegrationPackage| |NagLinearEquationSolvingPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagRootFindingPackage|) (|MultivariateLifting|) (|d02AgentsPackage|) @@ -322,13 +358,16 @@ (|AnnaNumericalOptimizationPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) (|d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType|) (|d03eefAnnaType|) +(|PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) (|LexTriangularPackage| |RationalUnivariateRepresentationPackage| |RegularChain| |ZeroDimensionalSolvePackage|) (|NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2|) (|NewSparseMultivariatePolynomial|) +(|Guess|) +(|BlowUpPackage|) (|ElementaryFunctionODESolver|) (|RationalRicDE|) -(|AbelianGroup&| |AbelianMonoid&| |AbelianMonoidRing&| |Aggregate&| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |ApplyUnivariateSkewPolynomial| |ArrayStack| |Asp19| |Asp20| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp41| |Asp42| |Asp55| |Asp74| |Asp77| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |Automorphism| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicOperator| |BasicOperatorFunctions1| |BezoutMatrix| |BinaryExpansion| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&| |Bits| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CRApackage| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |CharacteristicPolynomialInMonogenicalAlgebra| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Collection&| |CommonOperators| |CommuteUnivariatePolynomialCategory| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPatternMatch| |ComplexRootFindingPackage| |ConstantLODE| |ContinuedFraction| |CoordinateSystems| |CyclicStreamTools| |CyclotomicPolynomialPackage| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |Dictionary&| |DifferentialExtension&| |DifferentialPolynomialCategory&| |DifferentialRing&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |DoubleFloat| |DoubleFloatSpecialFunctions| |DoubleResultantPackage| |DrawComplex| |EigenPackage| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |EqTable| |Equation| |EuclideanDomain&| |EuclideanModularRing| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |ExtAlgBasis| |ExtensibleLinearAggregate&| |ExtensionField&| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoringUtilities| |Field&| |FieldOfPrimeCharacteristic&| |FindOrderFinite| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FortranExpression| |FourierSeries| |Fraction| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GcdDomain&| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GraphImage| |GrayCode| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerSolve| |Group&| |HallBasis| |HashTable| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteProductFiniteField| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySign| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegralBasisTools| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |IrrRepSymNatPackage| |IrredPolyOverFiniteField| |Kernel| |KernelFunctions2| |KeyedAccessFile| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LazyStreamAggregate&| |LeadingCoefDetermination| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearPolynomialEquationByFractions| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |List| |ListAggregate&| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MachineFloat| |MachineInteger| |MakeCachableSet| |MappingPackage1| |MappingPackageInternalHacks1| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |MonadWithUnit&| |MonogenicAlgebra&| |Monoid&| |MonoidRing| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NAGLinkSupportPackage| |NPCoef| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonCommutativeOperatorDivision| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NormInMonogenicAlgebra| |NormRetractPackage| |NormalizationPackage| |NumberFieldIntegralBasis| |NumberFormats| |NumberTheoreticPolynomialFunctions| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |Operator| |OppositeMonogenicLinearOperator| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PadeApproximantPackage| |PadeApproximants| |ParametricLinearEquations| |ParametricPlaneCurve| |ParametricPlaneCurveFunctions2| |ParametricSpaceCurve| |ParametricSpaceCurveFunctions2| |ParametricSurface| |ParametricSurfaceFunctions2| |PartialDifferentialRing&| |PartialFraction| |Partition| |Pattern| |PatternFunctions2| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchPushDown| |PatternMatchTools| |PendantTree| |Permanent| |Permutation| |PermutationGroup| |Pi| |PlaneAlgebraicCurvePlot| |PoincareBirkhoffWittLyndonBasis| |Point| |PointPackage| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialComposition| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolationAlgorithms| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PositiveInteger| |PowerSeriesCategory&| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |PushVariables| |QuadraticForm| |QuasiAlgebraicSet| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |Queue| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalLODE| |RationalRicDE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealZeroPackage| |RectangularMatrix| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecursivePolynomialCategory&| |ReduceLODE| |ReducedDivisor| |ReductionOfOrder| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |SExpressionOf| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SortPackage| |SortedCache| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stack| |StorageEfficientMatrixOperations| |Stream| |StreamAggregate&| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |String| |StringAggregate&| |StringTable| |StructuralConstantsPackage| |SturmHabichtPackage| |SubResultantPackage| |SubSpace| |Symbol| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Table| |TableAggregate&| |Tableau| |TabulatedComputationPackage| |TangentExpansions| |TaylorSeries| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalManipulations| |TranscendentalRischDE| |TranscendentalRischDESystem| |Tree| |TriangularMatrixOperations| |TriangularSetCategory&| |TubePlotTools| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UTSodetools| |UnaryRecursiveAggregate&| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |Vector| |VectorCategory&| |ViewDefaultsPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01aqfAnnaType| |d01fcfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) -(|AlgebraicFunction| |Any| |AnyFunctions1| |BasicOperator| |BasicOperatorFunctions1| |CombinatorialFunction| |CommonOperators| |FunctionSpace&| |FunctionSpaceAttachPredicates| |LaplaceTransform| |LiouvillianFunction| |ModuleOperator| |NoneFunctions1|) +(|AbelianGroup&| |AbelianMonoid&| |AbelianMonoidRing&| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |Aggregate&| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |ApplyUnivariateSkewPolynomial| |ArrayStack| |Asp19| |Asp20| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp41| |Asp42| |Asp55| |Asp74| |Asp77| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |Automorphism| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicOperator| |BasicOperatorFunctions1| |BezoutMatrix| |BinaryExpansion| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&| |Bits| |BlowUpPackage| |Boolean| |BoundIntegerRoots| |BrillhartTests| |CRApackage| |CardinalNumber| |CartesianTensor| |ChangeOfVariable| |Character| |CharacterClass| |CharacteristicPolynomialInMonogenicalAlgebra| |CharacteristicPolynomialPackage| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |Collection&| |CommonOperators| |CommuteUnivariatePolynomialCategory| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPatternMatch| |ComplexRootFindingPackage| |ConstantLODE| |ContinuedFraction| |CoordinateSystems| |CyclicStreamTools| |CyclotomicPolynomialPackage| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DesingTreePackage| |Dictionary&| |DifferentialExtension&| |DifferentialPolynomialCategory&| |DifferentialRing&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DiscreteLogarithmPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatSpecialFunctions| |DoubleFloatVector| |DoubleResultantPackage| |DrawComplex| |EigenPackage| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |EqTable| |Equation| |EuclideanDomain&| |EuclideanModularRing| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Export3D| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToUnivariatePowerSeries| |ExtAlgBasis| |ExtensibleLinearAggregate&| |ExtensionField&| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |Field&| |FieldOfPrimeCharacteristic&| |FindOrderFinite| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FortranExpression| |FourierSeries| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GcdDomain&| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GraphImage| |GrayCode| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerSolve| |Group&| |Guess| |GuessOption| |GuessOptionFunctions0| |HallBasis| |HashTable| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfClsPt| |InfiniteProductFiniteField| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySign| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegralBasisTools| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InterfaceGroebnerPackage| |InternalRationalUnivariateRepresentationPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |Interval| |InverseLaplaceTransform| |IrrRepSymNatPackage| |IrredPolyOverFiniteField| |Kernel| |KernelFunctions2| |KeyedAccessFile| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LazyStreamAggregate&| |LeadingCoefDetermination| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinGroebnerPackage| |LinearAggregate&| |LinearDependence| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperatorsOps| |LinearPolynomialEquationByFractions| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |List| |ListAggregate&| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |LocalParametrizationOfSimplePointPackage| |Localize| |LyndonWord| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MachineFloat| |MachineInteger| |MakeCachableSet| |MappingPackage1| |MappingPackageInternalHacks1| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |MonadWithUnit&| |MonogenicAlgebra&| |Monoid&| |MonoidRing| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NPCoef| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewtonInterpolation| |NewtonPolygon| |NonCommutativeOperatorDivision| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NormInMonogenicAlgebra| |NormRetractPackage| |NormalizationPackage| |NottinghamGroup| |NumberFieldIntegralBasis| |NumberFormats| |NumberTheoreticPolynomialFunctions| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODETools| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |Operator| |OppositeMonogenicLinearOperator| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |PadeApproximantPackage| |PadeApproximants| |ParametricLinearEquations| |ParametricPlaneCurve| |ParametricPlaneCurveFunctions2| |ParametricSpaceCurve| |ParametricSpaceCurveFunctions2| |ParametricSurface| |ParametricSurfaceFunctions2| |ParametrizationPackage| |PartialDifferentialRing&| |PartialFraction| |Partition| |Pattern| |PatternFunctions2| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchPushDown| |PatternMatchTools| |PendantTree| |Permanent| |Permutation| |PermutationGroup| |Pi| |PlaneAlgebraicCurvePlot| |PoincareBirkhoffWittLyndonBasis| |Point| |PointPackage| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialComposition| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolationAlgorithms| |PolynomialNumberTheoryFunctions| |PolynomialPackageForCurve| |PolynomialRing| |PolynomialRoots| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PositiveInteger| |PowerSeriesCategory&| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |PushVariables| |QuadraticForm| |QuasiAlgebraicSet| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |Queue| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalInterpolation| |RationalLODE| |RationalRicDE| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealZeroPackage| |RectangularMatrix| |RectangularMatrixCategory&| |RectangularMatrixCategoryFunctions2| |RecurrenceOperator| |RecursivePolynomialCategory&| |ReduceLODE| |ReducedDivisor| |ReductionOfOrder| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RootsFindingPackage| |RoutinesTable| |SExpressionOf| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SmithNormalForm| |SortPackage| |SortedCache| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stack| |StorageEfficientMatrixOperations| |Stream| |StreamAggregate&| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |String| |StringAggregate&| |StringTable| |StructuralConstantsPackage| |SturmHabichtPackage| |SubResultantPackage| |SubSpace| |Symbol| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Table| |TableAggregate&| |Tableau| |TabulatedComputationPackage| |TangentExpansions| |TaylorSeries| |TaylorSolve| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalHermiteIntegration| |TranscendentalIntegration| |TranscendentalManipulations| |TranscendentalRischDE| |TranscendentalRischDESystem| |Tree| |TriangularMatrixOperations| |TriangularSetCategory&| |TubePlotTools| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UTSodetools| |UnaryRecursiveAggregate&| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialCategoryFunctions2| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialMultiplicationPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |Vector| |VectorCategory&| |ViewDefaultsPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |WuWenTsunTriangularSet| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ZeroDimensionalSolvePackage| |d01AgentsPackage| |d01aqfAnnaType| |d01fcfAnnaType| |d02AgentsPackage| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) +(|AlgebraicFunction| |Any| |AnyFunctions1| |BasicOperator| |BasicOperatorFunctions1| |CombinatorialFunction| |CommonOperators| |FunctionSpace&| |FunctionSpaceAttachPredicates| |FunctionalSpecialFunction| |LaplaceTransform| |LiouvillianFunction| |ModuleOperator| |NoneFunctions1| |RecurrenceOperator|) (|AnyFunctions1| |ModuleOperator|) (|InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |LexTriangularPackage| |RationalUnivariateRepresentationPackage| |ZeroDimensionalSolvePackage|) (|OutputForm| |RomanNumeral|) @@ -344,7 +383,7 @@ (|AnnaOrdinaryDifferentialEquationPackage| |d02AgentsPackage|) (|ConstantLODE| |ElementaryFunctionLODESolver|) (|LyndonWord| |OneDimensionalArrayFunctions2| |TwoDimensionalArray|) -(|AlgebraicFunctionField| |Complex| |ExtensionField&| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |Infinity| |InnerFiniteField| |InnerPrimeField| |MachineComplex| |MoebiusTransform| |OnePointCompletionFunctions2| |PowerSeriesLimitPackage| |PrimeField| |RadicalFunctionField| |RationalFunctionLimitPackage| |SimpleAlgebraicExtension|) +(|AlgebraicFunctionField| |Complex| |DoubleFloatSpecialFunctions| |ExtensionField&| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |Infinity| |InnerFiniteField| |InnerPrimeField| |MachineComplex| |MoebiusTransform| |OnePointCompletionFunctions2| |PowerSeriesLimitPackage| |PrimeField| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |RadicalFunctionField| |RationalFunctionLimitPackage| |SimpleAlgebraicExtension|) (|RationalFunctionLimitPackage|) (|OpenMathServerPackage|) (|Complex| |DoubleFloat| |ExpressionToOpenMath| |Float| |Fraction| |Integer| |List| |OpenMathConnection| |OpenMathPackage| |OpenMathServerPackage| |SingleInteger| |String| |Symbol|) @@ -355,21 +394,23 @@ (|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionSign| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |Infinity| |InnerSparseUnivariatePowerSeries| |LaplaceTransform| |OrderedCompletionFunctions2| |PatternMatchIntegration| |PowerSeriesLimitPackage| |RationalFunctionDefiniteIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariatePuiseuxSeriesWithExponentialSingularity| |d01AgentsPackage| |d01TransformFunctionType| |d03AgentsPackage| |e04AgentsPackage| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04ucfAnnaType|) (|RationalFunctionDefiniteIntegration| |RationalFunctionLimitPackage|) (|LiePolynomial| |LyndonWord| |Magma| |PoincareBirkhoffWittLyndonBasis| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XRecursivePolynomial|) -(|DistributedMultivariatePolynomial| |FGLMIfCanPackage| |GeneralDistributedMultivariatePolynomial| |GroebnerSolve| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |LexTriangularPackage| |LinGroebnerPackage| |MultivariatePolynomial| |PolToPol| |QuasiAlgebraicSet2| |RationalUnivariateRepresentationPackage| |RegularChain| |ZeroDimensionalSolvePackage|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |DesingTreePackage| |DistributedMultivariatePolynomial| |FGLMIfCanPackage| |GeneralDistributedMultivariatePolynomial| |GroebnerSolve| |Guess| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InterpolateFormsPackage| |LexTriangularPackage| |LinGroebnerPackage| |LocalParametrizationOfSimplePointPackage| |MultivariatePolynomial| |PolToPol| |ProjectiveAlgebraicSetPackage| |QuasiAlgebraicSet2| |RationalUnivariateRepresentationPackage| |RegularChain| |ZeroDimensionalSolvePackage|) (|FullPartialFractionExpansion|) (|FullPartialFractionExpansion| |LinearOrdinaryDifferentialOperatorsOps| |OrderlyDifferentialPolynomial|) -(|Algebra&| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |BinaryFile| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |Boolean| |CRApackage| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexRootFindingPackage| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DenavitHartenbergMatrix| |Dequeue| |DictionaryOperations&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |DoubleFloat| |DrawOption| |ElementaryFunctionODESolver| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EqTable| |Equation| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |Exit| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionToOpenMath| |ExtAlgBasis| |Factored| |File| |FileName| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FortranCode| |FortranExpression| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionCalled| |FunctionSpace&| |GaloisGroupFactorizationUtilities| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfiniteTuple| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InputForm| |Integer| |IntegerMod| |IntegrationResult| |InternalRationalUnivariateRepresentationPackage| |Kernel| |KeyedAccessFile| |LaurentPolynomial| |LeftAlgebra&| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LiouvillianFunction| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |Matrix| |MatrixCategory&| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |Multiset| |MultivariatePolynomial| |NAGLinkSupportPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonAssociativeRing&| |NonNegativeInteger| |None| |NormalizationPackage| |NumberFormats| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalOrdinaryDifferentialEquations| |NumericalPDEProblem| |NumericalQuadrature| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |OnePointCompletion| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OpenMathPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |PartialFraction| |Partition| |Pattern| |PatternMatchListResult| |PatternMatchResult| |PendantTree| |Permutation| |PermutationGroup| |Pi| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |Polynomial| |PolynomialIdeals| |PolynomialRing| |PositiveInteger| |PrimeField| |PrimitiveArray| |PrintPackage| |Product| |QuadraticForm| |QuasiAlgebraicSet| |Quaternion| |QuaternionCategory&| |QueryEquation| |Queue| |QuotientFieldCategory&| |RadicalFunctionField| |RadixExpansion| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealZeroPackage| |RectangularMatrix| |RecursivePolynomialCategory&| |Reference| |RegularChain| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RewriteRule| |RightOpenIntervalRootCharacterization| |Ring&| |RomanNumeral| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |ScriptFormulaFormat1| |Segment| |SegmentBinding| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingleInteger| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |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| |TexFormat| |TexFormat1| |TextFile| |TheSymbolTable| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctionsForCompiledFunctions| |Tree| |TriangularSetCategory&| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory&| |TwoDimensionalViewport| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |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| |IndexCard| |InternalRationalUnivariateRepresentationPackage| |NormalizationPackage| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |RationalUnivariateRepresentationPackage| |TabulatedComputationPackage| |ZeroDimensionalSolvePackage|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |Algebra&| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |BinaryFile| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |CRApackage| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexRootFindingPackage| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DesingTreePackage| |DictionaryOperations&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatVector| |DrawOption| |ElementaryFunctionODESolver| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EqTable| |Equation| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |Exit| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionToOpenMath| |ExtAlgBasis| |Factored| |File| |FileName| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FortranCode| |FortranExpression| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebra&| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FullPartialFractionExpansion| |FunctionCalled| |FunctionSpace&| |GaloisGroupFactorizationUtilities| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |Guess| |GuessOption| |GuessOptionFunctions0| |HTMLFormat| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfClsPt| |InfiniteTuple| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InputForm| |Integer| |IntegerMod| |IntegrationResult| |InternalRationalUnivariateRepresentationPackage| |IntersectionDivisorPackage| |Interval| |Kernel| |KeyedAccessFile| |LaurentPolynomial| |LeftAlgebra&| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |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| |OpenMathErrorKind| |OpenMathPackage| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |PartialFraction| |Partition| |Pattern| |PatternMatchListResult| |PatternMatchResult| |PendantTree| |Permutation| |PermutationGroup| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |Polynomial| |PolynomialIdeals| |PolynomialRing| |PositiveInteger| |PrimeField| |PrimitiveArray| |PrintPackage| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |QuadraticForm| |QuasiAlgebraicSet| |Quaternion| |QuaternionCategory&| |QueryEquation| |Queue| |QuotientFieldCategory&| |RadicalFunctionField| |RadixExpansion| |RationalInterpolation| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealNumberSystem&| |RealZeroPackage| |RectangularMatrix| |RecurrenceOperator| |RecursivePolynomialCategory&| |Reference| |RegularChain| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RewriteRule| |RightOpenIntervalRootCharacterization| |Ring&| |RomanNumeral| |RoutinesTable| |RuleCalled| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |ScriptFormulaFormat1| |Segment| |SegmentBinding| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingleInteger| |SingletonAsOrderedSet| |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|) +(|DirichletRing| |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| |TopLevelDrawFunctionsForCompiledFunctions| |TwoDimensionalViewport| |ViewDefaultsPackage| |ViewportPackage|) (|EllipticFunctionsUnivariateTaylorSeries| |InnerSparseUnivariatePowerSeries| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |UnivariateTaylorSeriesODESolver| |WeierstrassPreparation|) (|ParametricPlaneCurveFunctions2| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions|) (|ParametricSpaceCurveFunctions2| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions|) (|ParametricSurfaceFunctions2| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions|) -(|CycleIndicators| |EvaluateCycleIndicators| |Permutation| |PermutationGroupExamples| |SymmetricPolynomial|) -(|CycleIndicators| |IrrRepSymNatPackage| |Partition| |SymmetricGroupCombinatoricFunctions|) -(|ApplyRules| |BalancedPAdicRational| |BinaryExpansion| |Complex| |ComplexCategory&| |ComplexPattern| |ComplexPatternMatch| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |ExponentialExpansion| |Expression| |Float| |Fraction| |FunctionSpace&| |GeneralDistributedMultivariatePolynomial| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |Integer| |IntegerNumberSystem&| |Kernel| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |OrderedVariableList| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResult| |PatternMatchSymbol| |PatternMatchTools| |Polynomial| |PolynomialCategory&| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RecursivePolynomialCategory&| |RewriteRule| |RomanNumeral| |SequentialDifferentialPolynomial| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |Symbol| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial|) +(|DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InterpolateFormsPackage| |IntersectionDivisorPackage|) +(|CycleIndicators| |EvaluateCycleIndicators| |Guess| |Permutation| |PermutationGroupExamples| |SymmetricPolynomial|) +(|CycleIndicators| |Guess| |IrrRepSymNatPackage| |Partition| |SymmetricGroupCombinatoricFunctions|) +(|ApplyRules| |BalancedPAdicRational| |BinaryExpansion| |Complex| |ComplexCategory&| |ComplexPattern| |ComplexPatternMatch| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |ExponentialExpansion| |Expression| |Float| |Fraction| |FunctionSpace&| |GeneralDistributedMultivariatePolynomial| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |Integer| |IntegerNumberSystem&| |Kernel| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |OrderedVariableList| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |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&|) @@ -380,7 +421,7 @@ (|Expression| |PolynomialCategory&|) (|ComplexPatternMatch| |PatternMatchFunctionSpace| |PatternMatchPolynomialCategory| |PatternMatchQuotientFieldCategory|) (|QuotientFieldCategory&|) -(|ApplyRules| |BalancedPAdicRational| |BinaryExpansion| |Complex| |ComplexCategory&| |ComplexPatternMatch| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |ExponentialExpansion| |Expression| |Float| |Fraction| |GeneralDistributedMultivariatePolynomial| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |Integer| |IntegerNumberSystem&| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchListResult| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |Polynomial| |PolynomialCategory&| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RomanNumeral| |SequentialDifferentialPolynomial| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |Symbol| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial|) +(|ApplyRules| |BalancedPAdicRational| |BinaryExpansion| |Complex| |ComplexCategory&| |ComplexPatternMatch| |DecimalExpansion| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |ExponentialExpansion| |Expression| |Float| |Fraction| |GeneralDistributedMultivariatePolynomial| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |Integer| |IntegerNumberSystem&| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchListResult| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchQuotientFieldCategory| |PatternMatchResultFunctions2| |PatternMatchSymbol| |PatternMatchTools| |Polynomial| |PolynomialCategory&| |QuotientFieldCategory&| |RadixExpansion| |RealNumberSystem&| |RomanNumeral| |SequentialDifferentialPolynomial| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |Symbol| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial|) (|ComplexPatternMatch| |PatternMatchPushDown|) (|Symbol|) (|PatternMatchFunctionSpace| |PatternMatchPolynomialCategory|) @@ -388,19 +429,22 @@ (|PermutationGroupExamples|) (|FortranExpression| |PiCoercions|) (|FortranExpression|) +(|PackageForAlgebraicFunctionField|) +(|PackageForAlgebraicFunctionFieldOverFiniteField|) (|TopLevelDrawFunctionsForAlgebraicCurves|) +(|Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField|) (|GraphicsDefaults| |PlaneAlgebraicCurvePlot| |PlotFunctions1| |TopLevelDrawFunctionsForCompiledFunctions| |TwoDimensionalPlotClipping|) (|ExpressionTubePlot| |TopLevelDrawFunctionsForCompiledFunctions|) (|GraphImage|) (|LieExponentials| |XPBWPolynomial|) -(|CoordinateSystems| |DenavitHartenbergMatrix| |DrawComplex| |ExpressionTubePlot| |GraphImage| |MeshCreationRoutinesForThreeDimensions| |NumericTubePlot| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |PointFunctions2| |PointPackage| |SubSpace| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TubePlotTools| |TwoDimensionalPlotClipping|) +(|CoordinateSystems| |DenavitHartenbergMatrix| |DrawComplex| |Export3D| |ExpressionTubePlot| |GnuDraw| |GraphImage| |MeshCreationRoutinesForThreeDimensions| |NumericTubePlot| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |PointFunctions2| |PointPackage| |SubSpace| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TubePlotTools| |TwoDimensionalPlotClipping|) (|GraphImage| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PlotTools| |ThreeDimensionalViewport| |TubePlotTools| |TwoDimensionalPlotClipping|) (|AlgebraicIntegrate|) (|PointsOfFiniteOrder| |PointsOfFiniteOrderRational|) (|FGLMIfCanPackage| |GroebnerSolve|) (|FunctionFieldCategory&| |PrimitiveElement|) -(|AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp30| |Asp31| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |CoerceVectorMatrixPackage| |ComplexPatternMatch| |ComplexRootPackage| |DefiniteIntegrationTools| |DiophantineSolutionPackage| |EigenPackage| |Equation| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |FGLMIfCanPackage| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranPackage| |FortranType| |FramedNonAssociativeAlgebra&| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpacePrimitiveElement| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GenericNonAssociativeAlgebra| |IdealDecompositionPackage| |InnerAlgebraicNumber| |InnerNumericFloatSolvePackage| |LexTriangularPackage| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |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| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealSolvePackage| |RecursivePolynomialCategory&| |RepresentationPackage1| |RetractSolvePackage| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariateTaylorSeries| |StructuralConstantsPackage| |SymbolTable| |SystemSolvePackage| |TaylorSeries| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackage| |UnivariateLaurentSeriesConstructor| |UnivariateTaylorSeries| |WeierstrassPreparation| |ZeroDimensionalSolvePackage| |e04AgentsPackage| |e04mbfAnnaType| |e04nafAnnaType|) -(|CombinatorialFunction| |DifferentialSparseMultivariatePolynomial| |ElementaryFunctionStructurePackage| |Expression| |ExpressionSpaceODESolver| |FunctionSpace&| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GosperSummationMethod| |InnerTrigonometricManipulations| |MRationalFactorize| |ParametricLinearEquations| |PolynomialAN2Expression| |PolynomialCategory&| |PolynomialFunctions2| |QuasiAlgebraicSet2| |RationalFunction| |RealSolvePackage| |TransSolvePackage| |TranscendentalManipulations|) +(|AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |Asp1| |Asp10| |Asp19| |Asp20| |Asp24| |Asp30| |Asp31| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |CoerceVectorMatrixPackage| |ComplexPatternMatch| |ComplexRootPackage| |DefiniteIntegrationTools| |DiophantineSolutionPackage| |EigenPackage| |Equation| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |FGLMIfCanPackage| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranPackage| |FortranType| |FramedNonAssociativeAlgebra&| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpacePrimitiveElement| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GenericNonAssociativeAlgebra| |IdealDecompositionPackage| |InnerAlgebraicNumber| |InnerNumericFloatSolvePackage| |LexTriangularPackage| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |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| |TranscendentalManipulations|) (|AlgFactor| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |ElementaryFunctionLODESolver| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |Expression| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |GenusZeroIntegration| |RationalFunction| |RationalFunctionIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign|) (|AlgebraicallyClosedField&|) (|PolynomialCategory&|) @@ -410,21 +454,28 @@ (|IdealDecompositionPackage| |QuasiAlgebraicSet2|) (|PolynomialInterpolation|) (|InnerPolySum| |NumberTheoreticPolynomialFunctions|) +(|DesingTreePackage| |LocalParametrizationOfSimplePointPackage| |ProjectiveAlgebraicSetPackage|) (|GeneralDistributedMultivariatePolynomial| |QuasiAlgebraicSet| |SparseUnivariatePolynomial| |SymmetricPolynomial| |UnivariatePuiseuxSeriesWithExponentialSingularity|) (|AlgebraicFunction| |AlgebraicManipulations| |IntegrationResultToFunction| |PatternMatchIntegration|) (|InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |QuasiComponentPackage| |RationalUnivariateRepresentationPackage| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |WuWenTsunTriangularSet| |ZeroDimensionalSolvePackage|) (|RadicalSolvePackage|) (|PolynomialCategory&|) -(|AbelianGroup&| |AbelianMonoid&| |AbelianMonoidRing&| |AbelianSemiGroup&| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |Asp19| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AttributeButtons| |Automorphism| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BinaryExpansion| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |CommonOperators| |Complex| |ComplexCategory&| |ComplexRootFindingPackage| |ConstantLODE| |ContinuedFraction| |CoordinateSystems| |CycleIndicators| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |DrawOption| |DrawOptionFunctions0| |ElementaryFunction| |ElementaryFunctionLODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |EllipticFunctionsUnivariateTaylorSeries| |Equation| |EuclideanModularRing| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionTubePlot| |Factored| |FactoringUtilities| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |Float| |FloatingPointSystem&| |FortranExpression| |FourierSeries| |Fraction| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GraphImage| |GrayCode| |Group&| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InnerTrigonometricManipulations| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegralBasisTools| |IntegrationResult| |IntegrationResultToFunction| |InverseLaplaceTransform| |IrredPolyOverFiniteField| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorFactorizer| |LiouvillianFunction| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularField| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |Monad&| |MonadWithUnit&| |MonogenicAlgebra&| |Monoid&| |MonoidRing| |MultFiniteFactorize| |MultivariatePolynomial| |MultivariateSquareFree| |NagEigenPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonAssociativeAlgebra&| |NonLinearFirstOrderODESolver| |NonNegativeInteger| |NumberFieldIntegralBasis| |NumberFormats| |Numeric| |NumericTubePlot| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |Octonion| |OctonionCategory&| |OnePointCompletion| |Operator| |OppositeMonogenicLinearOperator| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OrthogonalPolynomialFunctions| |OutputForm| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |ParametricLinearEquations| |PartialFraction| |Partition| |PatternMatchIntegration| |Permanent| |Permutation| |PermutationGroupExamples| |Pi| |PlaneAlgebraicCurvePlot| |Plot| |Plot3D| |PoincareBirkhoffWittLyndonBasis| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |Polynomial| |PolynomialFactorizationByRecursion| |PolynomialGcdPackage| |PolynomialNumberTheoryFunctions| |PolynomialRing| |PolynomialSolveByFormulas| |PositiveInteger| |PowerSeriesCategory&| |PrecomputedAssociatedEquations| |PrimeField| |Product| |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| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StreamTranscendentalFunctions| |SturmHabichtPackage| |SubSpace| |SymmetricFunctions| |SymmetricPolynomial| |TangentExpansions| |TaylorSeries| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TranscendentalFunctionCategory&| |TranscendentalIntegration| |TranscendentalManipulations| |TubePlotTools| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialMultiplicationPackage| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |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|) +(|AbelianGroup&| |AbelianMonoid&| |AbelianMonoidRing&| |AbelianSemiGroup&| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |Asp19| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AttributeButtons| |Automorphism| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |Bezier| |BinaryExpansion| |BlowUpPackage| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |Complex| |ComplexCategory&| |ComplexRootFindingPackage| |ConstantLODE| |ContinuedFraction| |CoordinateSystems| |CycleIndicators| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DesingTreePackage| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DiscreteLogarithmPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |DivisionRing&| |Divisor| |DoubleFloat| |DoubleFloatSpecialFunctions| |DrawComplex| |DrawOption| |DrawOptionFunctions0| |ElementaryFunction| |ElementaryFunctionLODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |EllipticFunctionsUnivariateTaylorSeries| |Equation| |EuclideanModularRing| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionTubePlot| |Factored| |FactoringUtilities| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteLinearAggregateSort| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |Float| |FloatingPointSystem&| |FortranExpression| |FourierSeries| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeAbelianGroup| |FreeAbelianMonoid| |FreeGroup| |FreeModule| |FreeModule1| |FreeMonoid| |FreeNilpotentLie| |FunctionFieldCategory&| |FunctionFieldIntegralBasis| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionalSpecialFunction| |GaloisGroupFactorizationUtilities| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GeneralHenselPackage| |GeneralModulePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GnuDraw| |GraphImage| |GrayCode| |Group&| |Guess| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InnerTrigonometricManipulations| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberSystem&| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegralBasisTools| |IntegrationResult| |IntegrationResultToFunction| |InterfaceGroebnerPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |Interval| |InverseLaplaceTransform| |IrredPolyOverFiniteField| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorFactorizer| |LiouvillianFunction| |LocalAlgebra| |LocalParametrizationOfSimplePointPackage| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularField| |ModularRing| |Module&| |ModuleOperator| |MoebiusTransform| |Monad&| |MonadWithUnit&| |MonogenicAlgebra&| |Monoid&| |MonoidRing| |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|) -(|Character| |DistinctDegreeFactorize| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |IndexedFlexibleArray| |InnerIndexedTwoDimensionalArray| |InnerNumericFloatSolvePackage| |LinearSystemMatrixPackage| |MatrixLinearAlgebraFunctions| |ModMonic| |NumberFormats| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |RadicalFunctionField| |ReductionOfOrder| |StorageEfficientMatrixOperations| |SubResultantPackage| |Symbol| |ThreeDimensionalMatrix| |TranscendentalIntegration| |Tuple|) +(|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| |PackageForAlgebraicFunctionFieldOverFiniteField|) +(|ProjectivePlane|) +(|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField|) +(|FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber|) (|SystemODESolver|) (|NewSparseUnivariatePolynomial| |SparseUnivariatePolynomial| |SubResultantPackage|) (|ElementaryFunctionLODESolver| |ElementaryIntegration| |ElementaryRischDE|) @@ -439,7 +490,7 @@ (|TransSolvePackage|) (|BinaryExpansion| |DecimalExpansion| |HexadecimalExpansion|) (|RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions|) -(|AlgFactor| |BoundIntegerRoots| |FunctionSpaceUnivariatePolynomialFactor| |GenUFactorize| |PointsOfFiniteOrder| |SimpleAlgebraicExtensionAlgFactor|) +(|AlgFactor| |BoundIntegerRoots| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FunctionSpaceUnivariatePolynomialFactor| |GenUFactorize| |PointsOfFiniteOrder| |RootsFindingPackage| |SimpleAlgebraicExtensionAlgFactor|) (|NonLinearSolvePackage| |RationalFunctionSum|) (|SAERationalFunctionAlgFactor|) (|IntegrationResultRFToFunction|) @@ -451,6 +502,7 @@ (|RightOpenIntervalRootCharacterization|) (|PlaneAlgebraicCurvePlot|) (|DefiniteIntegrationTools| |InnerNumericFloatSolvePackage| |RealZeroPackageQ|) +(|Guess|) (|PureAlgebraicLODE|) (|ElementaryFunctionLODESolver|) (|AlgebraicFunctionField| |Any| |CardinalNumber| |CommonOperators| |Float| |FramedModule| |InnerSparseUnivariatePowerSeries| |RadicalFunctionField| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Symbol| |ThreeDimensionalViewport| |UserDefinedPartialOrdering| |ViewDefaultsPackage|) @@ -458,32 +510,34 @@ (|RegularTriangularSet|) (|RegularChain|) (|RegularSetDecompositionPackage| |RegularTriangularSet|) -(|AbelianGroup&| |AbelianMonoid&| |AbelianSemiGroup&|) -(|DivisionRing&| |Group&| |InnerTaylorSeries| |ModuleOperator| |Monad&| |MonadWithUnit&| |Monoid&| |PAdicRationalConstructor| |SemiGroup&| |SparseUnivariatePolynomial|) +(|AbelianGroup&| |AbelianMonoid&| |AbelianSemiGroup&| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber|) +(|DivisionRing&| |Group&| |InnerTaylorSeries| |ModuleOperator| |Monad&| |MonadWithUnit&| |Monoid&| |NeitherSparseOrDensePowerSeries| |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| |FortranCode| |FortranPackage| |FortranProgram| |FortranScalarType| |InputForm| |NAGLinkSupportPackage| |NumberFormats| |OpenMathPackage| |Result| |SymbolTable|) +(|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| |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| |LiouvillianFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SegmentBindingFunctions2| |TopLevelDrawFunctions|) +(|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| |GnuDraw| |Guess| |LiouvillianFunction| |MyExpression| |RationalFunctionDefiniteIntegration| |RationalFunctionSum| |SegmentBindingFunctions2| |TopLevelDrawFunctions|) (|DrawNumericHack| |RationalFunctionSum|) (|SegmentBindingFunctions2| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) (|SequentialDifferentialPolynomial|) -(|BasicOperator| |ExpressionSpace&| |Factored| |GaloisGroupFactorizer| |GeneralPolynomialSet| |IntegerPrimesPackage| |ModularHermitianRowReduction| |MonoidRing| |ParametricLinearEquations| |Pattern| |Permutation| |PermutationGroup| |PolynomialSetCategory&| |QuasiAlgebraicSet| |RandomDistributions| |SymmetricGroupCombinatoricFunctions| |ThreeDimensionalViewport| |ThreeSpace|) +(|ApplicationProgramInterface| |BasicOperator| |ExpressionSpace&| |Factored| |GaloisGroupFactorizer| |GeneralPolynomialSet| |IntegerPrimesPackage| |ModularHermitianRowReduction| |MonoidRing| |ParametricLinearEquations| |Pattern| |Permutation| |PermutationGroup| |PolynomialSetCategory&| |QuasiAlgebraicSet| |RandomDistributions| |SymmetricGroupCombinatoricFunctions| |ThreeDimensionalViewport| |ThreeSpace|) (|AlgebraicFunctionField| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtensionByPolynomial| |RadicalFunctionField|) -(|AlgebraGivenByStructuralConstants| |AlgebraicFunctionField| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BinaryExpansion| |BinaryFile| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |Commutator| |Complex| |ComplexRootFindingPackage| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |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| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerNormalBasisFieldFunctions| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InputForm| |Integer| |IntegerMod| |IntegrationResult| |Kernel| |KeyedAccessFile| |LaurentPolynomial| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |Matrix| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |Multiset| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonNegativeInteger| |None| |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| |PoincareBirkhoffWittLyndonBasis| |Point| |Polynomial| |PolynomialIdeals| |PolynomialRing| |PositiveInteger| |PowerSeriesLimitPackage| |PrimeField| |PrimitiveArray| |Product| |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| |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| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |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|) -(|ExponentialOfUnivariatePuiseuxSeries| |GeneralUnivariatePowerSeries| |InnerSparseUnivariatePowerSeries| |ModMonic| |MultivariateSquareFree| |NewSparseUnivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePowerSeriesCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeries|) +(|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| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexRootFindingPackage| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatVector| |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| |HTMLFormat| |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|) +(|ExponentialOfUnivariatePuiseuxSeries| |GeneralUnivariatePowerSeries| |InnerSparseUnivariatePowerSeries| |ModMonic| |MultivariateSquareFree| |MyUnivariatePolynomial| |NeitherSparseOrDensePowerSeries| |NewSparseUnivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePowerSeriesCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) (|TranscendentalRischDESystem|) (|Kernel| |MakeCachableSet|) -(|AlgebraicFunction| |AlgebraicManipulations| |AlgebraicNumber| |CombinatorialFunction| |ComplexTrigonometricManipulations| |DifferentialSparseMultivariatePolynomial| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |Expression| |ExpressionSpaceODESolver| |FunctionSpace&| |FunctionSpaceFunctions2| |FunctionSpacePrimitiveElement| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GosperSummationMethod| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |LaplaceTransform| |MRationalFactorize| |MultFiniteFactorize| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |NonLinearFirstOrderODESolver| |ODEIntegration| |OrderlyDifferentialPolynomial| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PointsOfFiniteOrder| |Polynomial| |PureAlgebraicIntegration| |SequentialDifferentialPolynomial| |TransSolvePackage| |TranscendentalManipulations|) +(|AlgebraicFunction| |AlgebraicManipulations| |AlgebraicNumber| |CombinatorialFunction| |ComplexTrigonometricManipulations| |DifferentialSparseMultivariatePolynomial| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |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|) -(|AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryExpansion| |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| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteRankNonAssociativeAlgebra&| |Float| |FloatingComplexPackage| |FortranExpression| |Fraction| |FractionalIdeal| |FramedNonAssociativeAlgebra&| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GcdDomain&| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralPolynomialGcdPackage| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GroebnerSolve| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |InfiniteProductFiniteField| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySum| |InnerPrimeField| |InnerTrigonometricManipulations| |Integer| |IntegerCombinatoricFunctions| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegrationResult| |IntegrationResultFunctions2| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |IrredPolyOverFiniteField| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LeadingCoefDetermination| |LieSquareMatrix| |LinGroebnerPackage| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |LinearSystemPolynomialPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MachineFloat| |MachineInteger| |ModMonic| |ModularField| |MultFiniteFactorize| |MultivariateFactorize| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |NPCoef| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |NonLinearSolvePackage| |NormInMonogenicAlgebra| |NormRetractPackage| |NumberTheoreticPolynomialFunctions| |NumericComplexEigenPackage| |NumericRealEigenPackage| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PartialFraction| |PartialFractionPackage| |PatternMatchIntegration| |Pi| |PiCoercions| |PlaneAlgebraicCurvePlot| |PointsOfFiniteOrder| |Polynomial| |PolynomialCategory&| |PolynomialCategoryLifting| |PolynomialCategoryQuotientFunctions| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialNumberTheoryFunctions| |PolynomialSquareFree| |PolynomialToUnivariatePolynomial| |PrimeField| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PushVariables| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFactorize| |RationalFunctionFactor| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealZeroPackageQ| |RecursivePolynomialCategory&| |ReducedDivisor| |RetractSolvePackage| |RomanNumeral| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SupFractionFactorizer| |SymmetricFunctions| |SystemSolvePackage| |TangentExpansions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalManipulations| |TwoFactorize| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |WeierstrassPreparation| |WeightedPolynomials| |ZeroDimensionalSolvePackage|) -(|AlgebraicIntegration| |DefiniteIntegrationTools| |ElementaryFunctionLODESolver| |FiniteFieldPolynomialPackage2| |FunctionSpace&| |FunctionSpaceReduce| |GenusZeroIntegration| |InnerAlgebraicNumber| |InnerPolySum| |InnerTrigonometricManipulations| |IntegrationResultFunctions2| |MultivariateLifting| |Pi| |PiCoercions| |PointsOfFiniteOrder| |PolynomialCategoryQuotientFunctions| |PureAlgebraicIntegration| |RadicalSolvePackage| |RealClosedField&| |TranscendentalIntegration| |TranscendentalManipulations|) +(|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| |InfiniteProductFiniteField| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySum| |InnerPrimeField| |InnerTrigonometricManipulations| |Integer| |IntegerCombinatoricFunctions| |IntegerSolveLinearPolynomialEquation| |IntegralBasisPolynomialTools| |IntegrationResult| |IntegrationResultFunctions2| |IntegrationResultToFunction| |IntegrationTools| |Interval| |InverseLaplaceTransform| |IrredPolyOverFiniteField| |Kovacic| |LaplaceTransform| |LaurentPolynomial| |LeadingCoefDetermination| |LieSquareMatrix| |LinGroebnerPackage| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |LinearSystemPolynomialPackage| |LocalParametrizationOfSimplePointPackage| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MachineFloat| |MachineInteger| |MatrixCategory&| |ModMonic| |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| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialNumberTheoryFunctions| |PolynomialSquareFree| |PolynomialToUnivariatePolynomial| |PrimeField| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |ProjectiveAlgebraicSetPackage| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PureAlgebraicIntegration| |PushVariables| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFactorize| |RationalFunctionFactor| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealZeroPackageQ| |RecurrenceOperator| |RecursivePolynomialCategory&| |ReducedDivisor| |RetractSolvePackage| |RomanNumeral| |RootsFindingPackage| |SequentialDifferentialPolynomial| |SimpleAlgebraicExtension| |SingleInteger| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePolynomialFunctions2| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SupFractionFactorizer| |SymmetricFunctions| |SystemSolvePackage| |TangentExpansions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalIntegration| |TranscendentalManipulations| |TwoFactorize| |UnivariateFactorize| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |WeierstrassPreparation| |WeightedPolynomials| |ZeroDimensionalSolvePackage|) +(|ExpressionSolve| |TaylorSolve|) +(|AlgebraicIntegration| |DefiniteIntegrationTools| |ElementaryFunctionLODESolver| |FiniteFieldPolynomialPackage2| |FunctionSpace&| |FunctionSpaceReduce| |GenusZeroIntegration| |Guess| |InnerAlgebraicNumber| |InnerPolySum| |InnerTrigonometricManipulations| |IntegrationResultFunctions2| |MultivariateLifting| |Pi| |PiCoercions| |PointsOfFiniteOrder| |PolynomialCategoryQuotientFunctions| |PureAlgebraicIntegration| |RadicalSolvePackage| |RealClosedField&| |TranscendentalIntegration| |TranscendentalManipulations|) (|LinearOrdinaryDifferentialOperator| |UnivariateSkewPolynomial|) (|SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries|) (|SplittingTree| |WuWenTsunTriangularSet|) @@ -495,41 +549,43 @@ (|AlgebraGivenByStructuralConstants| |CartesianTensor| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |Permanent| |QuadraticForm|) (|FortranOutputStackPackage| |Queue|) (|Matrix|) -(|BalancedPAdicInteger| |BasicFunctions| |ContinuedFraction| |CycleIndicators| |ElementaryFunctionsUnivariateLaurentSeries| |EllipticFunctionsUnivariateTaylorSeries| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialOfUnivariatePuiseuxSeries| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfiniteTuple| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerPAdicInteger| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |NumericContinuedFraction| |PAdicInteger| |PAdicRationalConstructor| |PadeApproximants| |ParadoxicalCombinatorsForStreams| |PartitionsAndPermutations| |RadixExpansion| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Stream| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |TableauxBumpers| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UniversalSegmentFunctions2| |WeierstrassPreparation| |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01aqfAnnaType| |e04gcfAnnaType|) -(|PartitionsAndPermutations|) -(|ContinuedFraction| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfiniteTupleFunctions2| |PartitionsAndPermutations| |SparseMultivariateTaylorSeries| |Stream| |StreamFunctions3| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |TableauxBumpers| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeriesFunctions2| |UniversalSegmentFunctions2| |WeierstrassPreparation|) -(|InfiniteTupleFunctions3| |PartitionsAndPermutations| |SparseMultivariateTaylorSeries| |Stream| |StreamTaylorSeriesOperations| |WeierstrassPreparation|) +(|BalancedPAdicInteger| |BasicFunctions| |ContinuedFraction| |CycleIndicators| |DirichletRing| |ElementaryFunctionsUnivariateLaurentSeries| |EllipticFunctionsUnivariateTaylorSeries| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialOfUnivariatePuiseuxSeries| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |Guess| |InfiniteProductCharacteristicZero| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfiniteTuple| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerPAdicInteger| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |LinearSystemFromPowerSeriesPackage| |NeitherSparseOrDensePowerSeries| |NumericContinuedFraction| |PAdicInteger| |PAdicRationalConstructor| |PadeApproximants| |ParadoxicalCombinatorsForStreams| |PartitionsAndPermutations| |RadixExpansion| |SparseMultivariateTaylorSeries| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Stream| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |TableauxBumpers| |TaylorSolve| |UnivariateFormalPowerSeries| |UnivariateFormalPowerSeriesFunctions| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesFunctions2| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |UniversalSegmentFunctions2| |WeierstrassPreparation| |d01AgentsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01aqfAnnaType| |e04gcfAnnaType|) +(|Guess| |PartitionsAndPermutations|) +(|ContinuedFraction| |DirichletRing| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |FractionFreeFastGaussian| |Guess| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InfiniteTupleFunctions2| |PartitionsAndPermutations| |SparseMultivariateTaylorSeries| |Stream| |StreamFunctions3| |StreamInfiniteProduct| |StreamTaylorSeriesOperations| |TableauxBumpers| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeriesFunctions2| |UniversalSegmentFunctions2| |WeierstrassPreparation|) +(|InfiniteTupleFunctions3| |PartitionsAndPermutations| |SparseMultivariateTaylorSeries| |Stream| |StreamTaylorSeriesOperations| |UnivariateFormalPowerSeriesFunctions| |WeierstrassPreparation|) (|InfiniteProductCharacteristicZero| |InfiniteProductPrimeField|) -(|EllipticFunctionsUnivariateTaylorSeries| |InfiniteProductFiniteField| |InnerTaylorSeries| |SparseMultivariateTaylorSeries| |StreamInfiniteProduct| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateLaurentSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |WeierstrassPreparation|) +(|DirichletRing| |EllipticFunctionsUnivariateTaylorSeries| |InfiniteProductFiniteField| |InnerTaylorSeries| |SparseMultivariateTaylorSeries| |StreamInfiniteProduct| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateLaurentSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |WeierstrassPreparation|) (|ElementaryFunctionsUnivariateLaurentSeries| |InfiniteProductFiniteField| |SparseMultivariateTaylorSeries| |StreamInfiniteProduct| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesCategory&|) (|UnivariateTaylorSeriesCategory&|) -(|AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |BinaryFile| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexPattern| |ComplexPatternMatch| |ComplexRootFindingPackage| |ComplexTrigonometricManipulations| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DictionaryOperations&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |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| |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| |HashTable| |Heap| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IndexCard| |IndexedBits| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerPAdicInteger| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTaylorSeries| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |Integer| |IntegerMod| |IntegrationResult| |IntegrationResultToFunction| |IntegrationTools| |InternalPrintPackage| |InternalRationalUnivariateRepresentationPackage| |Kernel| |KeyedAccessFile| |LaplaceTransform| |LaurentPolynomial| |Library| |LieExponentials| |LiePolynomial| |LieSquareMatrix| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LiouvillianFunction| |List| |ListMonoidOps| |ListMultiDictionary| |LocalAlgebra| |Localize| |LyndonWord| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeCachableSet| |MakeFloatCompiledFunction| |Matrix| |ModMonic| |ModularField| |ModularRing| |ModuleMonomial| |ModuleOperator| |MoebiusTransform| |MonoidRing| |MoreSystemCommands| |Multiset| |MultivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NonNegativeInteger| |None| |NormalizationPackage| |NumberFormats| |NumericalIntegrationProblem| |NumericalODEProblem| |NumericalOptimizationProblem| |NumericalOrdinaryDifferentialEquations| |NumericalPDEProblem| |NumericalQuadrature| |ODEIntegration| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OnePointCompletion| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OpenMathPackage| |OpenMathServerPackage| |OperationsQuery| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |ParametricLinearEquations| |PartialFraction| |Partition| |Pattern| |PatternMatchAssertions| |PatternMatchIntegration| |PatternMatchKernel| 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|SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentBinding| |SequentialDifferentialPolynomial| |SequentialDifferentialVariable| |Set| |SetCategory&| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SingletonAsOrderedSet| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |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| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |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|) +(|AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |AxiomServer| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |BinaryFile| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |CardinalNumber| |CartesianTensor| |Character| |CharacterClass| |CliffordAlgebra| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexPattern| |ComplexPatternMatch| |ComplexRootFindingPackage| |ComplexTrigonometricManipulations| |ContinuedFraction| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DictionaryOperations&| |DifferentialSparseMultivariatePolynomial| |DirectProduct| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DiscreteLogarithmPackage| |DisplayPackage| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatVector| |DrawComplex| |DrawOption| |DrawOptionFunctions0| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ElementaryIntegration| |ElementaryRischDE| |EqTable| |Equation| |ErrorFunctions| |EuclideanGroebnerBasisPackage| |EuclideanModularRing| |Exit| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Export3D| |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| |GnuDraw| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |Guess| |GuessOption| |GuessOptionFunctions0| |HTMLFormat| |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| |NumericalOrdinaryDifferentialEquations| |NumericalPDEProblem| |NumericalQuadrature| |ODEIntegration| |Octonion| |OctonionCategory&| |OneDimensionalArray| |OnePointCompletion| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| |OpenMathError| |OpenMathErrorKind| |OpenMathPackage| |OpenMathServerPackage| |OperationsQuery| |Operator| |OppositeMonogenicLinearOperator| |OrdSetInts| |OrderedCompletion| |OrderedDirectProduct| |OrderedFreeMonoid| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OrderlyDifferentialVariable| |OrdinaryDifferentialRing| |OrdinaryWeightedPolynomials| |OutputForm| |OutputPackage| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |ParametricLinearEquations| |PartialFraction| |Partition| |Pattern| |PatternMatchAssertions| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchListResult| |PatternMatchResult| |PendantTree| |Permutation| |PermutationGroup| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |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|) +(|Export3D| |ThreeSpace|) (|MeshCreationRoutinesForThreeDimensions| |SubSpace| |ThreeDimensionalViewport| |ThreeSpace|) (|EigenPackage| |PolynomialIdeals| |RadicalEigenPackage| |RadicalSolvePackage|) (|Expression|) (|Asp12| |Asp30| |Asp35| |Asp55| |Asp74| |Asp8| |FortranCode|) -(|AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |Any| |ApplyRules| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AttachPredicates| |AttributeButtons| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |Boolean| |CombinatorialFunction| |CommonOperators| |Complex| |ComplexCategory&| |ComplexPattern| |ComplexPatternMatch| |ComplexRootPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |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| |ExpressionSpace&| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |FGLMIfCanPackage| |Factored| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasisExtensionByPolynomial| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranType| |Fraction| |FramedNonAssociativeAlgebra&| |FullPartialFractionExpansion| |FullyEvalableOver&| |FunctionCalled| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |HexadecimalExpansion| |HomogeneousDirectProduct| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexCard| |InnerAlgebraicNumber| |InnerNumericFloatSolvePackage| |InnerSparseUnivariatePowerSeries| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InternalPrintPackage| |InverseLaplaceTransform| |Kernel| |KeyedAccessFile| |LaplaceTransform| |LaurentPolynomial| |LexTriangularPackage| |Library| |LieSquareMatrix| |LinGroebnerPackage| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorsOps| |LiouvillianFunction| |List| |ListMultiDictionary| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |Matrix| |ModMonic| |MonogenicAlgebra&| |Multiset| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |NonLinearSolvePackage| |NumberFormats| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODEIntegration| |Octonion| |OctonionCategory&| |OpenMathDevice| |OpenMathError| |OpenMathErrorKind| |OrdSetInts| |OrderedDirectProduct| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OutputForm| |PAdicRational| |PAdicRationalConstructor| |ParametricLinearEquations| |PartialFractionPackage| |Pattern| |PatternFunctions2| |PatternMatch| |PatternMatchAssertions| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPushDown| |PatternMatchResult| |PatternMatchSymbol| |PermutationGroup| |Pi| |PlaneAlgebraicCurvePlot| |PlotFunctions1| |PolToPol| |Polynomial| |PolynomialAN2Expression| |PolynomialFunctions2| |PolynomialIdeals| |PolynomialToUnivariatePolynomial| |PowerSeriesLimitPackage| |PrimitiveElement| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet2| |Quaternion| |QuaternionCategory&| |QueryEquation| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosure| |RealSolvePackage| |RectangularMatrix| |RecursivePolynomialCategory&| |RepresentationPackage1| |Result| |RetractSolvePackage| |RewriteRule| |RomanNumeral| |RoutinesTable| |RuleCalled| |SExpression| |SegmentBinding| |SegmentBindingFunctions2| |SequentialDifferentialPolynomial| |Set| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingletonAsOrderedSet| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StructuralConstantsPackage| |Switch| |Symbol| |SymbolTable| |SystemSolvePackage| |TaylorSeries| |TheSymbolTable| |ThreeDimensionalMatrix| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCategory&| |Variable| |Vector| |WeierstrassPreparation| |XPolynomial| |ZeroDimensionalSolvePackage| |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|) +(|AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |Any| |ApplicationProgramInterface| |ApplyRules| |Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |AttachPredicates| |AttributeButtons| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicOperatorFunctions1| |BinaryExpansion| |Boolean| |CombinatorialFunction| |CommonOperators| |Complex| |ComplexCategory&| |ComplexPattern| |ComplexPatternMatch| |ComplexRootPackage| |ComplexTrigonometricManipulations| |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| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasisExtensionByPolynomial| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranType| |Fraction| |FramedNonAssociativeAlgebra&| |FullPartialFractionExpansion| |FullyEvalableOver&| |FunctionCalled| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |Guess| |GuessAlgebraicNumber| |GuessFinite| |GuessInteger| |GuessOption| |GuessOptionFunctions0| |GuessPolynomial| |GuessUnivariatePolynomial| |HexadecimalExpansion| |HomogeneousDirectProduct| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexCard| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerNumericFloatSolvePackage| |InnerSparseUnivariatePowerSeries| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |IntegrationResult| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InternalPrintPackage| |InverseLaplaceTransform| |Kernel| |KeyedAccessFile| |LaplaceTransform| |LaurentPolynomial| |LexTriangularPackage| |Library| |LieSquareMatrix| |LinGroebnerPackage| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorsOps| |LiouvillianFunction| |List| |ListMultiDictionary| |MPolyCatRationalFunctionFactorizer| |MachineComplex| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |Matrix| |ModMonic| |MonogenicAlgebra&| |Multiset| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NeitherSparseOrDensePowerSeries| |NewSparseUnivariatePolynomial| |NonLinearFirstOrderODESolver| |NonLinearSolvePackage| |NumberFormats| |NumericComplexEigenPackage| |NumericRealEigenPackage| |ODEIntegration| |Octonion| |OctonionCategory&| |OpenMathDevice| |OpenMathError| |OpenMathErrorKind| |OrdSetInts| |OrderedDirectProduct| |OrderedVariableList| |OrderlyDifferentialPolynomial| |OutputForm| |PAdicRational| |PAdicRationalConstructor| |ParametricLinearEquations| |PartialFractionPackage| |Pattern| |PatternFunctions2| |PatternMatch| |PatternMatchAssertions| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPushDown| |PatternMatchResult| |PatternMatchSymbol| |PermutationGroup| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |PlotFunctions1| |PolToPol| |Polynomial| |PolynomialAN2Expression| |PolynomialFunctions2| |PolynomialIdeals| |PolynomialToUnivariatePolynomial| |PowerSeriesLimitPackage| |PrimitiveElement| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet2| |Quaternion| |QuaternionCategory&| |QueryEquation| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionFactor| |RationalFunctionIntegration| |RationalFunctionLimitPackage| |RationalFunctionSign| |RationalFunctionSum| |RationalInterpolation| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosure| |RealSolvePackage| |RectangularMatrix| |RecurrenceOperator| |RecursivePolynomialCategory&| |RepresentationPackage1| |Result| |RetractSolvePackage| |RewriteRule| |RomanNumeral| |RoutinesTable| |RuleCalled| |SExpression| |SegmentBinding| |SegmentBindingFunctions2| |SequentialDifferentialPolynomial| |Set| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingletonAsOrderedSet| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StructuralConstantsPackage| |Switch| |Symbol| |SymbolTable| |SystemSolvePackage| |TaylorSeries| |TheSymbolTable| |ThreeDimensionalMatrix| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TransSolvePackageService| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |Variable| |Vector| |WeierstrassPreparation| |XPolynomial| |ZeroDimensionalSolvePackage| |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|) (|Asp1| |Asp10| |Asp12| |Asp19| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp4| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp74| |Asp77| |Asp78| |Asp8| |Asp80| |Asp9| |FortranPackage| |FortranProgram| |TheSymbolTable|) (|TangentExpansions|) (|IrrRepSymNatPackage| |RepresentationPackage1|) (|CycleIndicators| |EvaluateCycleIndicators|) (|PureAlgebraicLODE|) (|EigenPackage| |NonLinearSolvePackage| |RadicalSolvePackage| |RetractSolvePackage| |TransSolvePackage|) -(|AlgebraicFunctionField| |Complex| |DiscreteLogarithmPackage| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |InnerFiniteField| |InnerPrimeField| |MachineComplex| |Multiset| |PrimeField| |RadicalFunctionField| |RandomDistributions| |Result| |SimpleAlgebraicExtension| |SymbolTable| |TransSolvePackage|) +(|AlgebraicFunctionField| |Complex| |DiscreteLogarithmPackage| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |InnerFiniteField| |InnerPrimeField| |MachineComplex| |Multiset| |PrimeField| |PseudoAlgebraicClosureOfFiniteField| |RadicalFunctionField| |RandomDistributions| |Result| |SimpleAlgebraicExtension| |SymbolTable| |TransSolvePackage|) (|TableauxBumpers|) (|QuasiComponentPackage| |RegularTriangularSetGcdPackage| |SquareFreeQuasiComponentPackage| |SquareFreeRegularTriangularSetGcdPackage|) (|ElementaryFunctionStructurePackage|) (|WeierstrassPreparation|) +(|ExpressionSolve|) (|FortranTemplate|) (|TexFormat1|) -(|FortranTemplate|) +(|Export3D| |FortranTemplate| |GnuDraw|) (|FortranCode| |FortranPackage| |FortranProgram|) (|NagPartialDifferentialEquationsPackage|) -(|DrawComplex| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints|) -(|DrawComplex| |DrawOption| |DrawOptionFunctions0| |MeshCreationRoutinesForThreeDimensions| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TopLevelThreeSpace|) +(|DrawComplex| |GnuDraw| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints|) +(|DrawComplex| |DrawOption| |DrawOptionFunctions0| |GnuDraw| |MeshCreationRoutinesForThreeDimensions| |ThreeDimensionalViewport| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |TopLevelThreeSpace|) (|ElementaryFunctionSign| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |RationalFunctionSign|) +(|GnuDraw|) (|TopLevelDrawFunctions|) (|TransSolvePackage|) (|TranscendentalIntegration|) @@ -537,21 +593,23 @@ (|FunctionSpaceIntegration| |SimplifyAlgebraicNumberConvertPackage| |TransSolvePackage| |d01TransformFunctionType|) (|ElementaryRischDE| |RationalIntegration|) (|ElementaryRischDESystem|) -(|BinaryTree| |PendantTree|) +(|BinaryTree| |HTMLFormat| |PendantTree|) (|ChineseRemainderToolsForIntegralBases| |FunctionFieldIntegralBasis| |IntegralBasisTools| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |WildFunctionFieldIntegralBasis|) (|ElementaryFunctionSign| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultRFToFunction| |LaplaceTransform| |PatternMatchIntegration| |TransSolvePackage|) (|ExpressionTubePlot| |NumericTubePlot| |TopLevelDrawFunctionsForCompiledFunctions|) (|ExpressionTubePlot| |NumericTubePlot|) (|DrawComplex|) (|TopLevelDrawFunctionsForCompiledFunctions|) -(|TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |ViewportPackage|) +(|GnuDraw| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| |ViewportPackage|) (|MultFiniteFactorize| |SparseUnivariatePolynomial|) +(|Guess| |NottinghamGroup| |RecurrenceOperator| |UnivariateFormalPowerSeriesFunctions|) +(|Guess|) (|UnivariateLaurentSeriesFunctions2| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesFunctions2|) (|UnivariateLaurentSeries|) (|UnivariatePuiseuxSeriesFunctions2|) -(|PadeApproximantPackage| |PolynomialInterpolation| |PolynomialToUnivariatePolynomial| |SparseUnivariateTaylorSeries| |SturmHabichtPackage| |UnivariatePolynomialFunctions2| |UnivariateTaylorSeries|) -(|AlgFactor| |AlgebraicFunctionField| |AlgebraicIntegrate| |BoundIntegerRoots| |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexCategory&| |DoubleResultantPackage| |FiniteDivisorFunctions2| |Fraction| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupPolynomialUtilities| |GeneralPolynomialGcdPackage| |InnerAlgFactor| |InnerMultFact| |InnerNumericEigenPackage| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |MultFiniteFactorize| |MultipleMap| |MultivariateSquareFree| |NewSparseUnivariatePolynomialFunctions2| |NormInMonogenicAlgebra| |PartialFractionPackage| |PointsOfFiniteOrder| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialToUnivariatePolynomial| |PrimitiveRatDE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalRicDE| |RealZeroPackageQ| |ReducedDivisor| |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| |TranscendentalIntegration| |TwoFactorize| |UnivariatePolynomialFunctions2|) -(|ChangeOfVariable| |DefiniteIntegrationTools| |DoubleResultantPackage| |FiniteDivisor| |FunctionFieldCategory&| |InnerPolySum| |PointsOfFiniteOrder| |PointsOfFiniteOrderTools| |PureAlgebraicIntegration|) +(|GeneralPackageForAlgebraicFunctionField| |Guess| |PadeApproximantPackage| |PolynomialInterpolation| |PolynomialToUnivariatePolynomial| |SparseUnivariateTaylorSeries| |SturmHabichtPackage| |UnivariateFormalPowerSeries| |UnivariatePolynomialFunctions2| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) +(|AlgFactor| |AlgebraicFunctionField| |AlgebraicIntegrate| |BoundIntegerRoots| |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexCategory&| |DoubleResultantPackage| |FiniteDivisorFunctions2| |Fraction| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupPolynomialUtilities| |GeneralPolynomialGcdPackage| |InnerAlgFactor| |InnerMultFact| |InnerNumericEigenPackage| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearPolynomialEquationByFractions| |MultFiniteFactorize| |MultipleMap| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |NormInMonogenicAlgebra| |PartialFractionPackage| |PointsOfFiniteOrder| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialToUnivariatePolynomial| |PrimitiveRatDE| |RadicalFunctionField| |RationalFactorize| |RationalFunctionFactor| |RationalRicDE| |RealZeroPackageQ| |ReducedDivisor| |SparseUnivariatePolynomialFunctions2| |SupFractionFactorizer| |TranscendentalIntegration| |TwoFactorize| |UnivariatePolynomialFunctions2|) +(|ChangeOfVariable| |DefiniteIntegrationTools| |DoubleResultantPackage| |FiniteDivisor| |FunctionFieldCategory&| |Guess| |InnerPolySum| |PointsOfFiniteOrder| |PointsOfFiniteOrderTools| |PureAlgebraicIntegration|) (|GaloisGroupFactorizer|) (|UnivariatePolynomialDecompositionPackage|) (|FiniteFieldCategory&| |Integer| |PolynomialSquareFree| |SparseUnivariatePolynomial| |UnivariatePolynomialCategory&|) @@ -559,17 +617,18 @@ (|SparseUnivariatePuiseuxSeries| |UnivariatePuiseuxSeries|) (|ExponentialExpansion| |FunctionSpaceToExponentialExpansion|) (|SparseUnivariateSkewPolynomial|) -(|PadeApproximantPackage| |RationalRicDE| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| |UnivariatePuiseuxSeries|) +(|PadeApproximantPackage| |RationalRicDE| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesFunctions2| |UnivariatePuiseuxSeries|) +(|GeneralPackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) (|UnivariateLaurentSeriesFunctions2|) -(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AssociationList| |Bits| |DataList| |DisplayPackage| |ExtensibleLinearAggregate&| |FlexibleArray| |Float| |GaloisGroupUtilities| |GenerateUnivariatePowerSeries| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedOneDimensionalArray| |IndexedString| |IndexedVector| |InnerNormalBasisFieldFunctions| |LazyStreamAggregate&| |List| |ListAggregate&| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |Point| |PrimitiveArray| |Stream| |StreamAggregate&| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |UniversalSegmentFunctions2| |Vector|) +(|AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AssociationList| |AxiomServer| |Bits| |ComplexDoubleFloatVector| |DataList| |DisplayPackage| |DoubleFloatVector| |ExtensibleLinearAggregate&| |FlexibleArray| |Float| |GaloisGroupUtilities| |GenerateUnivariatePowerSeries| |IndexedBits| |IndexedFlexibleArray| |IndexedList| |IndexedOneDimensionalArray| |IndexedString| |IndexedVector| |InnerNormalBasisFieldFunctions| |LazyStreamAggregate&| |List| |ListAggregate&| |MathMLFormat| |NeitherSparseOrDensePowerSeries| |OneDimensionalArray| |OneDimensionalArrayAggregate&| |Point| |PrimitiveArray| |Stream| |StreamAggregate&| |String| |StringAggregate&| |Symbol| |TemplateUtilities| |TexFormat| |UniversalSegmentFunctions2| |Vector|) (|GenerateUnivariatePowerSeries|) (|FunctionSpace&| |Polynomial| |UserDefinedVariableOrdering|) -(|GeneralUnivariatePowerSeries| |PolynomialToUnivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariateLaurentSeries| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariateSkewPolynomial| |UnivariateTaylorSeries|) -(|AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |AnnaOrdinaryDifferentialEquationPackage| |Asp10| |Asp19| |Asp20| |Asp28| |Asp31| |Asp35| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp78| |Asp8| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |CartesianTensor| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexIntegerSolveLinearPolynomialEquation| |DecimalExpansion| |DenavitHartenbergMatrix| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeNilpotentLie| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |GaloisGroupPolynomialUtilities| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |GrayCode| |HallBasis| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegerLinearDependence| |IntegerPrimesPackage| |IntegerSolveLinearPolynomialEquation| |IntegralBasisTools| |IntegrationResultToFunction| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |MachineComplex| |MachineInteger| |Matrix| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariateLifting| |MultivariatePolynomial| |NPCoef| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODETools| |OrderedDirectProduct| |OrderingFunctions| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |ParametricLinearEquations| |Permanent| |Permutation| |PermutationGroup| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PolToPol| |Polynomial| |PolynomialCategory&| |PolynomialFactorizationExplicit&| |PolynomialIdeals| |PrimeField| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicLODE| |Quaternion| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadixExpansion| |RandomDistributions| |RationalLODE| |RealZeroPackage| |RectangularMatrix| |ReduceLODE| |RepresentationPackage1| |RepresentationPackage2| |RomanNumeral| |SequentialDifferentialPolynomial| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SingleInteger| |SparseMultivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SplitHomogeneousDirectProduct| |SquareMatrix| |SquareMatrixCategory&| |StructuralConstantsPackage| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SystemODESolver| |SystemSolvePackage| |TangentExpansions| |ThreeDimensionalMatrix| |TransSolvePackageService| |TranscendentalRischDESystem| |TwoDimensionalViewport| |UTSodetools| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |VectorFunctions2| |WildFunctionFieldIntegralBasis| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03eefAnnaType| |e04AgentsPackage| |e04fdfAnnaType| |e04gcfAnnaType| |e04ucfAnnaType|) +(|GeneralUnivariatePowerSeries| |MyUnivariatePolynomial| |PolynomialToUnivariatePolynomial| |SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariatePolynomial| |UnivariatePuiseuxSeries| |UnivariateSkewPolynomial| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) +(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicNumber| |AnnaOrdinaryDifferentialEquationPackage| |Asp10| |Asp19| |Asp20| |Asp28| |Asp31| |Asp35| |Asp41| |Asp42| |Asp49| |Asp50| |Asp55| |Asp6| |Asp7| |Asp73| |Asp78| |Asp8| |Asp80| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicRational| |BinaryExpansion| |BlowUpPackage| |CartesianTensor| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Complex| |ComplexCategory&| |ComplexIntegerSolveLinearPolynomialEquation| |DecimalExpansion| |DenavitHartenbergMatrix| |DesingTreePackage| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductFunctions2| |DirectProductMatrixModule| |DirectProductModule| |DistributedMultivariatePolynomial| |EigenPackage| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExponentialExpansion| |Expression| |FiniteAlgebraicExtensionField&| |FiniteDivisor| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FortranCode| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FractionalIdealFunctions2| |FramedAlgebra&| |FramedModule| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebraFunctions2| |FreeNilpotentLie| |FullyLinearlyExplicitRingOver&| |FunctionFieldCategory&| |GaloisGroupPolynomialUtilities| |GenExEuclid| |GeneralDistributedMultivariatePolynomial| |GenericNonAssociativeAlgebra| |GosperSummationMethod| |GrayCode| |Guess| |HallBasis| |HexadecimalExpansion| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |InfinitlyClosePoint| |InnerAlgebraicNumber| |InnerFiniteField| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerPrimeField| |Integer| |IntegerLinearDependence| |IntegerPrimesPackage| |IntegerSolveLinearPolynomialEquation| |IntegralBasisTools| |IntegrationResultToFunction| |InterpolateFormsPackage| |IrrRepSymNatPackage| |LieSquareMatrix| |LinGroebnerPackage| |LinearDependence| |LinearOrdinaryDifferentialOperatorsOps| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |MachineComplex| |MachineInteger| |Matrix| |MatrixLinearAlgebraFunctions| |ModMonic| |ModularHermitianRowReduction| |MonogenicAlgebra&| |MultiVariableCalculusFunctions| |MultivariateLifting| |MultivariatePolynomial| |MyExpression| |MyUnivariatePolynomial| |NPCoef| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NumberFieldIntegralBasis| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |ODETools| |OrderedDirectProduct| |OrderingFunctions| |OrderlyDifferentialPolynomial| |PAdicRational| |PAdicRationalConstructor| |PAdicWildFunctionFieldIntegralBasis| |PackageForPoly| |ParametricLinearEquations| |Permanent| |Permutation| |PermutationGroup| |Point| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PolToPol| |Polynomial| |PolynomialCategory&| 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