diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index bd431b0..a276c8b 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -350,6 +350,210 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{AdditiveValuationAttribute}{ATADDVA} +\pagepic{ps/v102additivevaluationattribute.eps}{ATADDVA}{1.00} +\begin{chunk}{AdditiveValuationAttribute.input} +\end{chunk} +\begin{chunk}{AdditiveValuationAttribute.help} +==================================================================== +AdditiveValuationAttribute +==================================================================== + +The class of all euclidean domains such that +euclideanSize(a*b) = euclideanSize(a)*euclideanSize(b) + +See Also: +o )show AdditiveValuationAttribute + +\end{chunk} + +\begin{chunk}{category ATADDVA AdditiveValuationAttribute} +)abbrev category ATADDVA AdditiveValuationAttribute +++ Description: +++ The class of all euclidean domains such that +++ \spad{euclideanSize(a*b) = euclideanSize(a)+euclideanSize(b)} + +AdditiveValuationAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATADDVA.dotabb} +"ATADDVA" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATADDVA"]; +"ATADDVA" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATADDVA.dotfull} +"AdditiveValuationAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATADDVA"]; +"AdditiveValuationAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATADDVA.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"AdditiveValuationAttribute()" [color=lightblue]; +"AdditiveValuationAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{ApproximateAttribute}{ATAPPRO} +\pagepic{ps/v102approximateattribute.eps}{ATAPPRO}{1.00} +\begin{chunk}{ApproximateAttribute.input} +\end{chunk} +\begin{chunk}{ApproximateAttribute.help} +==================================================================== +ApproximateAttribute +==================================================================== + +An approximation to the real numbers. + +See Also: +o )show ApproximateAttribute + +\end{chunk} + +\begin{chunk}{category ATAPPRO ApproximateAttribute} +)abbrev category ATAPPRO ApproximateAttribute +++ Description: +++ An approximation to the real numbers. + +ApproximateAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATAPPRO.dotabb} +"ATAPPRO" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATAPPRO"]; +"ATAPPRO" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATAPPRO.dotfull} +"ApproximateAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATAPPRO"]; +"ApproximateAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATAPPRO.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"ApproximateAttribute()" [color=lightblue]; +"ApproximateAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{ArbitraryExponentAttribute}{ATARBEX} +\pagepic{ps/v102arbitraryexponentattribute.eps}{ATARBEX}{1.00} +\begin{chunk}{ArbitraryExponentAttribute.input} +\end{chunk} +\begin{chunk}{ArbitraryExponentAttribute.help} +==================================================================== +ArbitraryExponentAttribute +==================================================================== + +Approximate numbers with arbitrarily large exponents + +See Also: +o )show ArbitraryExponentAttribute + +\end{chunk} + +\begin{chunk}{category ATARBEX ArbitraryExponentAttribute} +)abbrev category ATARBEX ArbitraryExponentAttribute +++ Description: +++ Approximate numbers with arbitrarily large exponents + +ArbitraryExponentAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATARBEX.dotabb} +"ATARBEX" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBEX"]; +"ATARBEX" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATARBEX.dotfull} +"ArbitraryExponentAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBEX"]; +"ArbitraryExponentAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATARBEX.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"ArbitraryExponentAttribute()" [color=lightblue]; +"ArbitraryExponentAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{ArbitraryPrecisionAttribute}{ATARBPR} +\pagepic{ps/v102arbitraryprecisionattribute.eps}{ATARBPR}{1.00} +\begin{chunk}{ArbitraryPrecisionAttribute.input} +\end{chunk} +\begin{chunk}{ArbitraryPrecisionAttribute.help} +==================================================================== +ArbitraryPrecisionAttribute +==================================================================== + +Approximate numbers for which the user can set the precision +for subsequent calculations. + +See Also: +o )show ArbitraryPrecisionAttribute + +\end{chunk} + +\begin{chunk}{category ATARBPR ArbitraryPrecisionAttribute} +)abbrev category ATARBPR ArbitraryPrecisionAttribute +++ Description: +++ Approximate numbers for which the user can set the precision +++ for subsequent calculations. + +ArbitraryPrecisionAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATARBPR.dotabb} +"ATARBPR" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBPR"]; +"ATARBPR" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATARBPR.dotfull} +"ArbitraryPrecisionAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBPR"]; +"ArbitraryPrecisionAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATARBPR.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"ArbitraryPrecisionAttribute()" [color=lightblue]; +"ArbitraryPrecisionAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{ArcHyperbolicFunctionCategory}{AHYP} \pagepic{ps/v102archyperbolicfunctioncategory.ps}{AHYP}{1.00} \begin{chunk}{ArcHyperbolicFunctionCategory.input} @@ -874,6 +1078,222 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{CanonicalAttribute}{ATCANON} +\pagepic{ps/v102canonicalattribute.eps}{ATCANON}{1.00} +\begin{chunk}{CanonicalAttribute.input} +\end{chunk} +\begin{chunk}{CanonicalAttribute.help} +==================================================================== +CanonicalAttribute +==================================================================== + +The class of all domains which have canonical represenntation, +that is, mathematically equal elements ahve the same data structure. + +See Also: +o )show CanonicalAttribute + +\end{chunk} + +\begin{chunk}{category ATCANON CanonicalAttribute} +)abbrev category ATCANON CanonicalAttribute +++ Description: +++ The class of all domains which have canonical represenntation, +++ that is, mathematically equal elements ahve the same data structure. + +CanonicalAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATCANON.dotabb} +"ATCANON" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANON"]; +"ATCANON" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATCANON.dotfull} +"CanonicalAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANON"]; +"CanonicalAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATCANON.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"CanonicalAttribute()" [color=lightblue]; +"CanonicalAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{CanonicalClosedAttribute}{ATCANCL} +\pagepic{ps/v102canonicalclosedattribute.eps}{ATCANCL}{1.00} +\begin{chunk}{CanonicalClosedAttribute.input} +\end{chunk} +\begin{chunk}{CanonicalClosedAttribute.help} +==================================================================== +CanonicalClosedAttribute +==================================================================== + +The class of all integral domains such that +unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b) + +See Also: +o )show CanonicalClosedAttribute + +\end{chunk} + +\begin{chunk}{category ATCANCL CanonicalClosedAttribute} +)abbrev category ATCANCL CanonicalClosedAttribute +++ Description: +++ The class of all integral domains such that +++ \spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)} + +CanonicalClosedAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATCANCL.dotabb} +"ATCANCL" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANCL"]; +"ATCANCL" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATCANCL.dotfull} +"CanonicalClosedAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANCL"]; +"CanonicalClosedAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATCANCL.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"CanonicalClosedAttribute()" [color=lightblue]; +"CanonicalClosedAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{CanonicalUnitNormalAttribute}{ATCUNOR} +\pagepic{ps/v102canonicalunitnormalattribute.eps}{ATCUNOR}{1.00} +\begin{chunk}{CanonicalUnitNormalAttribute.input} +\end{chunk} +\begin{chunk}{CanonicalUnitNormalAttribute.help} +==================================================================== +CanonicalUnitNormalAttribute +==================================================================== + +The class of all integral domains such that we can choose a canonical +representative for each class of associate elements. That is, +associates?(a,b) returns true if and only if +unitCanonical(a) = unitCanonical(b) + +See Also: +o )show CanonicalUnitNormalAttribute + +\end{chunk} + +\begin{chunk}{category ATCUNOR CanonicalUnitNormalAttribute} +)abbrev category ATCUNOR CanonicalUnitNormalAttribute +++ Description: +++ The class of all integral domains such that we can choose a canonical +++ representative for each class of associate elements. That is, +++ \spad{associates?(a,b)} returns true if and only if +++ \spad{unitCanonical(a)} = \spad{unitCanonical(b)} + +CanonicalUnitNormalAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATCUNOR.dotabb} +"ATCUNOR" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCUNOR"]; +"ATCUNOR" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATCUNOR.dotfull} +"CanonicalUnitNormalAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCUNOR"]; +"CanonicalUnitNormalAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATCUNOR.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"CanonicalUnitNormalAttribute()" [color=lightblue]; +"CanonicalUnitNormalAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{CentralAttribute}{ATCENRL} +\pagepic{ps/v102centralattribute.eps}{ATCENRL}{1.00} +\begin{chunk}{CentralAttribute.input} +\end{chunk} +\begin{chunk}{CentralAttribute.help} +==================================================================== +CentralAttribute +==================================================================== + +Central is true if, given an algebra over a ring R, the image of R +is the center of the algebra. For example, the set of members of the +algebra which commute with all others is precisely the image of R +in the algebra. + +See Also: +o )show CentralAttribute + +\end{chunk} + +\begin{chunk}{category ATCENRL CentralAttribute} +)abbrev category ATCENRL CentralAttribute +++ Description: +++ Central is true if, given an algebra over a ring R, the image of R +++ is the center of the algebra. For example, the set of members of the +++ algebra which commute with all others is precisely the image of R +++ in the algebra. + +CentralAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATCENRL.dotabb} +"ATCENRL" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCENRL"]; +"ATCENRL" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATCENRL.dotfull} +"CentralAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCENRL"]; +"CentralAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATCENRL.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"CentralAttribute()" [color=lightblue]; +"CentralAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{CoercibleTo}{KOERCE} \pagepic{ps/v102koerce.ps}{KOERCE}{1.00} @@ -1091,6 +1511,60 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{CommutativeStarAttribute}{ATCS} +\pagepic{ps/v102commutativestarattribute.eps}{ATCS}{1.00} +\begin{chunk}{CommutativeStarAttribute.input} +\end{chunk} +\begin{chunk}{CommutativeStarAttribute.help} +==================================================================== +CommutativeStarAttribute +==================================================================== + +The class of all commutative semigroups in multiplicative notation. +In other words domain D with "*": (D,D) -> D which is commutative. +Typially applied to rings. + +See Also: +o )show CommutativeStarAttribute + +\end{chunk} + +\begin{chunk}{category ATCS CommutativeStarAttribute} +)abbrev category ATCS CommutativeStarAttribute +++ Description: +++ The class of all commutative semigroups in multiplicative notation. +++ In other words domain \spad{D} with \spad{"*": (D,D) -> D} which is +++ commutative. Typially applied to rings. + +CommutativeStarAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATCS.dotabb} +"ATCS" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCS"]; +"ATCS" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATCS.dotfull} +"CommutativeStarAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCS"]; +"CommutativeStarAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATCS.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"CommutativeStarAttribute()" [color=lightblue]; +"CommutativeStarAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{ConvertibleTo}{KONVERT} \pagepic{ps/v102konvert.ps}{KONVERT}{1.00} @@ -1471,6 +1945,56 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{FiniteAggregateAttribute}{ATFINAG} +\pagepic{ps/v102finiteaggregateattribute.eps}{ATFINAG}{1.00} +\begin{chunk}{FiniteAggregateAttribute.input} +\end{chunk} +\begin{chunk}{FiniteAggregateAttribute.help} +==================================================================== +FiniteAggregateAttribute +==================================================================== + +The class of all aggregates with a finite number of arguments + +See Also: +o )show FiniteAggregateAttribute + +\end{chunk} + +\begin{chunk}{category ATFINAG FiniteAggregateAttribute} +)abbrev category ATFINAG FiniteAggregateAttribute +++ Description: +++ The class of all aggregates with a finite number of arguments + +FiniteAggregateAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATFINAG.dotabb} +"ATFINAG" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATFINAG"]; +"ATFINAG" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATFINAG.dotfull} +"FiniteAggregateAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATFINAG"]; +"FiniteAggregateAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATFINAG.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"FiniteAggregateAttribute()" [color=lightblue]; +"FiniteAggregateAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{HyperbolicFunctionCategory}{HYPCAT} \pagepic{ps/v102hyperbolicfunctioncategory.ps}{HYPCAT}{1.00} @@ -1735,6 +2259,158 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{JacobiIdentityAttribute}{ATJACID} +\pagepic{ps/v102jacobiidentityattribute.eps}{ATJACID}{1.00} +\begin{chunk}{JacobiIdentityAttribute.input} +\end{chunk} +\begin{chunk}{JacobiIdentityAttribute.help} +==================================================================== +JacobiIdentityAttribute +==================================================================== + +JacobiIdentity means that [x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0 holds. +See LieAlgebra. + +See Also: +o )show JacobiIdentityAttribute + +\end{chunk} + +\begin{chunk}{category ATJACID JacobiIdentityAttribute} +)abbrev category ATJACID JacobiIdentityAttribute +++ Description: +++ JacobiIdentity means that \spad{[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0} holds. +++ See LieAlgebra. + +JacobiIdentityAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATJACID.dotabb} +"ATJACID" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATJACID"]; +"ATJACID" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATJACID.dotfull} +"JacobiIdentityAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATJACID"]; +"JacobiIdentityAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATJACID.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"JacobiIdentityAttribute()" [color=lightblue]; +"JacobiIdentityAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{LazyRepresentationAttribute}{ATLR} +\pagepic{ps/v102lazyrepresentationattribute.eps}{ATLR}{1.00} +\begin{chunk}{LazyRepresentationAttribute.input} +\end{chunk} +\begin{chunk}{LazyRepresentationAttribute.help} +==================================================================== +LazyRepresentationAttribute +==================================================================== + +The class of all domains which have a lazy representation + +See Also: +o )show LazyRepresentationAttribute + +\end{chunk} + +\begin{chunk}{category ATLR LazyRepresentationAttribute} +)abbrev category ATLR LazyRepresentationAttribute +++ Description: +++ The class of all domains which have a lazy representation + +LazyRepresentationAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATLR.dotabb} +"ATLR" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLR"]; +"ATLR" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATLR.dotfull} +"LazyRepresentationAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLR"]; +"LazyRepresentationAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATLR.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"LazyRepresentationAttribute()" [color=lightblue]; +"LazyRepresentationAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{LeftUnitaryAttribute}{ATLUNIT} +\pagepic{ps/v102leftunitaryattribute.eps}{ATLUNIT}{1.00} +\begin{chunk}{LeftUnitaryAttribute.input} +\end{chunk} +\begin{chunk}{LeftUnitaryAttribute.help} +==================================================================== +LeftUnitaryAttribute +==================================================================== + +LeftUnitary is true if 1 * x = x for all x. + +See Also: +o )show LeftUnitaryAttribute + +\end{chunk} + +\begin{chunk}{category ATLUNIT LeftUnitaryAttribute} +)abbrev category ATLUNIT LeftUnitaryAttribute +++ Description: +++ LeftUnitary is true if \spad{1 * x = x} for all x. + +LeftUnitaryAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATLUNIT.dotabb} +"ATLUNIT" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLUNIT"]; +"ATLUNIT" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATLUNIT.dotfull} +"LeftUnitaryAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLUNIT"]; +"LeftUnitaryAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATLUNIT.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"LeftUnitaryAttribute()" [color=lightblue]; +"LeftUnitaryAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{ModularAlgebraicGcdOperations}{MAGCDOC} \pagepic{ps/v102modularalgebraicgcdoperations.ps}{MAGCDOC}{1.00} @@ -1883,6 +2559,210 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{MultiplicativeValuationAttribute}{ATMULVA} +\pagepic{ps/v102multiplicativevaluationattribute.eps}{ATMULVA}{1.00} +\begin{chunk}{MultiplicativeValuationAttribute.input} +\end{chunk} +\begin{chunk}{MultiplicativeValuationAttribute.help} +==================================================================== +MultiplicativeValuationAttribute +==================================================================== + +The class of all euclidean domains such that +euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b) + +See Also: +o )show MultiplicativeValuationAttribute + +\end{chunk} + +\begin{chunk}{category ATMULVA MultiplicativeValuationAttribute} +)abbrev category ATMULVA MultiplicativeValuationAttribute +++ Description: +++ The class of all euclidean domains such that +++ \spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)} + +MultiplicativeValuationAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATMULVA.dotabb} +"ATMULVA" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATMULVA"]; +"ATMULVA" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATMULVA.dotfull} +"MultiplicativeValuationAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATMULVA"]; +"MultiplicativeValuationAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATMULVA.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"MultiplicativeValuationAttribute()" [color=lightblue]; +"MultiplicativeValuationAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{NotherianAttribute}{ATNOTHR} +\pagepic{ps/v102notherianattribute.eps}{ATNOTHR}{1.00} +\begin{chunk}{NotherianAttribute.input} +\end{chunk} +\begin{chunk}{NotherianAttribute.help} +==================================================================== +NotherianAttribute +==================================================================== + +Notherian is true if all of its ideals are finitely generated. + +See Also: +o )show NotherianAttribute + +\end{chunk} + +\begin{chunk}{category ATNOTHR NotherianAttribute} +)abbrev category ATNOTHR NotherianAttribute +++ Description: +++ Notherian is true if all of its ideals are finitely generated. + +NotherianAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATNOTHR.dotabb} +"ATNOTHR" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNOTHR"]; +"ATNOTHR" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATNOTHR.dotfull} +"NotherianAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNOTHR"]; +"NotherianAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATNOTHR.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"NotherianAttribute()" [color=lightblue]; +"NotherianAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{NoZeroDivisorsAttribute}{ATNZDIV} +\pagepic{ps/v102nozerodivisorsattribute.eps}{ATNZDIV}{1.00} +\begin{chunk}{NoZeroDivisorsAttribute.input} +\end{chunk} +\begin{chunk}{NoZeroDivisorsAttribute.help} +==================================================================== +NoZeroDivisorsAttribute +==================================================================== + +The class of all semirings such that x * y ~= 0 implies +both x and y are non-zero. + +See Also: +o )show NoZeroDivisorsAttribute + +\end{chunk} + +\begin{chunk}{category ATNZDIV NoZeroDivisorsAttribute} +)abbrev category ATNZDIV NoZeroDivisorsAttribute +++ Description: +++ The class of all semirings such that \spad{x * y ~= 0} implies +++ both x and y are non-zero. + +NoZeroDivisorsAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATNZDIV.dotabb} +"ATNZDIV" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNZDIV"]; +"ATNZDIV" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATNZDIV.dotfull} +"NoZeroDivisorsAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNZDIV"]; +"NoZeroDivisorsAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATNZDIV.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"NoZeroDivisorsAttribute()" [color=lightblue]; +"NoZeroDivisorsAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{NullSquareAttribute}{ATNULSQ} +\pagepic{ps/v102nullsquareattribute.eps}{ATNULSQ}{1.00} +\begin{chunk}{NullSquareAttribute.input} +\end{chunk} +\begin{chunk}{NullSquareAttribute.help} +==================================================================== +NullSquareAttribute +==================================================================== + +NullSquare means that [x,x] = 0 holds. See LieAlgebra. + +See Also: +o )show NullSquareAttribute + +\end{chunk} + +\begin{chunk}{category ATNULSQ NullSquareAttribute} +)abbrev category ATNULSQ NullSquareAttribute +++ Description: +++ NullSquare means that \spad{[x,x] = 0} holds. See LieAlgebra. + +NullSquareAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATNULSQ.dotabb} +"ATNULSQ" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNULSQ"]; +"ATNULSQ" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATNULSQ.dotfull} +"NullSquareAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNULSQ"]; +"NullSquareAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATNULSQ.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"NullSquareAttribute()" [color=lightblue]; +"NullSquareAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{OpenMath}{OM} \pagepic{ps/v102openmath.ps}{OM}{1.00} @@ -1992,6 +2872,58 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{PartiallyOrderedSetAttribute}{ATPOSET} +\pagepic{ps/v102partiallyorderedsetattribute.eps}{ATPOSET}{1.00} +\begin{chunk}{PartiallyOrderedSetAttribute.input} +\end{chunk} +\begin{chunk}{PartiallyOrderedSetAttribute.help} +==================================================================== +PartiallyOrderedSetAttribute +==================================================================== + +PartiallyOrderedSet is true if a set with < is transitive, +but not(a "CATEGORY" + +\end{chunk} +\begin{chunk}{ATPOSET.dotfull} +"PartiallyOrderedSetAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATPOSET"]; +"PartiallyOrderedSetAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATPOSET.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"PartiallyOrderedSetAttribute()" [color=lightblue]; +"PartiallyOrderedSetAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{PartialTranscendentalFunctions}{PTRANFN} \pagepic{ps/v102partialtranscendentalfunctions.ps}{PTRANFN}{1.00} @@ -2746,6 +3678,110 @@ digraph pic { \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{RightUnitaryAttribute}{ATRUNIT} +\pagepic{ps/v102rightunitaryattribute.eps}{ATRUNIT}{1.00} +\begin{chunk}{RightUnitaryAttribute.input} +\end{chunk} +\begin{chunk}{RightUnitaryAttribute.help} +==================================================================== +RightUnitaryAttribute +==================================================================== + +RightUnitary is true if x * 1 = x for all x. + +See Also: +o )show RightUnitaryAttribute + +\end{chunk} + +\begin{chunk}{category ATRUNIT RightUnitaryAttribute} +)abbrev category ATRUNIT RightUnitaryAttribute +++ Description: +++ RightUnitary is true if \spad{x * 1 = x} for all x. + +RightUnitaryAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATRUNIT.dotabb} +"ATRUNIT" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATRUNIT"]; +"ATRUNIT" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATRUNIT.dotfull} +"RightUnitaryAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATRUNIT"]; +"RightUnitaryAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATRUNIT.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"RightUnitaryAttribute()" [color=lightblue]; +"RightUnitaryAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{ShallowlyMutableAttribute}{ATSHMUT} +\pagepic{ps/v102shallowlymutableattribute.eps}{ATSHMUT}{1.00} +\begin{chunk}{ShallowlyMutableAttribute.input} +\end{chunk} +\begin{chunk}{ShallowlyMutableAttribute.help} +==================================================================== +ShallowlyMutableAttribute +==================================================================== + +The class of all domains which have immediate components that +are updateable in place (mutable). The properties of any component +domain are irrevelant to the ShallowlyMutableAttribute. + +See Also: +o )show ShallowlyMutableAttribute + +\end{chunk} + +\begin{chunk}{category ATSHMUT ShallowlyMutableAttribute} +)abbrev category ATSHMUT ShallowlyMutableAttribute +++ Description: +++ The class of all domains which have immediate components that +++ are updateable in place (mutable). The properties of any component +++ domain are irrevelant to the ShallowlyMutableAttribute. + +ShallowlyMutableAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATSHMUT.dotabb} +"ATSHMUT" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATSHMUT"]; +"ATSHMUT" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATSHMUT.dotfull} +"ShallowlyMutableAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATSHMUT"]; +"ShallowlyMutableAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATSHMUT.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"ShallowlyMutableAttribute()" [color=lightblue]; +"ShallowlyMutableAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{SpecialFunctionCategory}{SPFCAT} \pagepic{ps/v102specialfunctioncategory.ps}{SPFCAT}{1.00} @@ -3087,6 +4123,60 @@ digraph pic { } \end{chunk} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{UnitsKnownAttribute}{ATUNIKN} +\pagepic{ps/v102unitsknownattribute.eps}{ATUNIKN}{1.00} +\begin{chunk}{UnitsKnownAttribute.input} +\end{chunk} +\begin{chunk}{UnitsKnownAttribute.help} +==================================================================== +UnitsKnownAttribute +==================================================================== + +The class of all monoids (multiplicative semigroups with a 1) +such that the operation recop can only return "failed" +if its argument is not a unit. + +See Also: +o )show UnitsKnownAttribute + +\end{chunk} + +\begin{chunk}{category ATUNIKN UnitsKnownAttribute} +)abbrev category ATUNIKN UnitsKnownAttribute +++ Description: +++ The class of all monoids (multiplicative semigroups with a 1) +++ such that the operation recop can only return "failed" +++ if its argument is not a unit. + +UnitsKnownAttribute(): Category == with nil + +\end{chunk} +\begin{chunk}{ATUNIKN.dotabb} +"ATUNIKN" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATUNIKN"]; +"ATUNIKN" -> "CATEGORY" + +\end{chunk} +\begin{chunk}{ATUNIKN.dotfull} +"UnitsKnownAttribute()" + [color=lightblue,href="bookvol10.2.pdf#nameddest=ATUNIKN"]; +"UnitsKnownAttribute()" -> "Category" + +\end{chunk} +\begin{chunk}{ATUNIKN.dotpic} +digraph pic { + fontsize=10; + bgcolor="#ECEA81"; + node [shape=box, color=white, style=filled]; + +"UnitsKnownAttribute()" [color=lightblue]; +"UnitsKnownAttribute()" -> "Category" + +"Category" [color=lightblue]; +} + +\end{chunk} \chapter{Category Layer 2} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{Aggregate}{AGG} @@ -91905,6 +92995,10 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category ALGEBRA Algebra} \getchunk{category ACF AlgebraicallyClosedField} \getchunk{category ACFS AlgebraicallyClosedFunctionSpace} +\getchunk{category ATADDVA AdditiveValuationAttribute} +\getchunk{category ATAPPRO ApproximateAttribute} +\getchunk{category ATARBEX ArbitraryExponentAttribute} +\getchunk{category ATARBPR ArbitraryPrecisionAttribute} \getchunk{category AHYP ArcHyperbolicFunctionCategory} \getchunk{category ATRIG ArcTrigonometricFunctionCategory} \getchunk{category ALAGG AssociationListAggregate} @@ -91920,12 +93014,17 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category CACHSET CachableSet} \getchunk{category CABMON CancellationAbelianMonoid} +\getchunk{category ATCANON CanonicalAttribute} +\getchunk{category ATCANCL CanonicalClosedAttribute} +\getchunk{category ATCUNOR CanonicalUnitNormalAttribute} +\getchunk{category ATCENRL CentralAttribute} \getchunk{category CHARNZ CharacteristicNonZero} \getchunk{category CHARZ CharacteristicZero} \getchunk{category KOERCE CoercibleTo} \getchunk{category CLAGG Collection} \getchunk{category CFCAT CombinatorialFunctionCategory} \getchunk{category COMBOPC CombinatorialOpsCategory} +\getchunk{category ATCS CommutativeStarAttribute} \getchunk{category COMPAR Comparable} \getchunk{category COMRING CommutativeRing} \getchunk{category COMPCAT ComplexCategory} @@ -91960,6 +93059,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category FNCAT FileNameCategory} \getchunk{category FINITE Finite} \getchunk{category FAMR FiniteAbelianMonoidRing} +\getchunk{category ATFINAG FiniteAggregateAttribute} \getchunk{category FAXF FiniteAlgebraicExtensionField} \getchunk{category FDIVCAT FiniteDivisorCategory} \getchunk{category FFIELDC FiniteFieldCategory} @@ -92003,11 +93103,15 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category INTDOM IntegralDomain} \getchunk{category INTCAT IntervalCategory} +\getchunk{category ATJACID JacobiIdentityAttribute} + \getchunk{category KDAGG KeyedDictionary} +\getchunk{category ATLR LazyRepresentationAttribute} \getchunk{category LZSTAGG LazyStreamAggregate} \getchunk{category LALG LeftAlgebra} \getchunk{category LMODULE LeftModule} +\getchunk{category ATLUNIT LeftUnitaryAttribute} \getchunk{category LIECAT LieAlgebra} \getchunk{category LNAGG LinearAggregate} \getchunk{category LINEXP LinearlyExplicitRingOver} @@ -92025,6 +93129,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category MLO MonogenicLinearOperator} \getchunk{category MONOID Monoid} \getchunk{category MDAGG MultiDictionary} +\getchunk{category ATMULVA MultiplicativeValuationAttribute} \getchunk{category MSETAGG MultisetAggregate} \getchunk{category MTSCAT MultivariateTaylorSeriesCategory} @@ -92032,6 +93137,9 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category NASRING NonAssociativeRing} \getchunk{category NARNG NonAssociativeRng} \getchunk{category NTSCAT NormalizedTriangularSetCategory} +\getchunk{category ATNOTHR NotherianAttribute} +\getchunk{category ATNZDIV NoZeroDivisorsAttribute} +\getchunk{category ATNULSQ NullSquareAttribute} \getchunk{category NUMINT NumericalIntegrationCategory} \getchunk{category OPTCAT NumericalOptimizationCategory} @@ -92054,6 +93162,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category PADICCT PAdicIntegerCategory} \getchunk{category PDECAT PartialDifferentialEquationsSolverCategory} \getchunk{category PDRING PartialDifferentialRing} +\getchunk{category ATPOSET PartiallyOrderedSetAttribute} \getchunk{category PTRANFN PartialTranscendentalFunctions} \getchunk{category PATAB Patternable} \getchunk{category PATMAB PatternMatchable} @@ -92089,6 +93198,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category RPOLCAT RecursivePolynomialCategory} \getchunk{category RSETCAT RegularTriangularSetCategory} \getchunk{category RETRACT RetractableTo} +\getchunk{category ATRUNIT RightUnitaryAttribute} \getchunk{category RMODULE RightModule} \getchunk{category RING Ring} \getchunk{category RNG Rng} @@ -92100,6 +93210,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category SETCAT SetCategory} \getchunk{category SETCATD SetCategoryWithDegree} \getchunk{category SEXCAT SExpressionCategory} +\getchunk{category ATSHMUT ShallowlyMutableAttribute} \getchunk{category SPFCAT SpecialFunctionCategory} \getchunk{category SNTSCAT SquareFreeNormalizedTriangularSetCategory} \getchunk{category SFRTCAT SquareFreeRegularTriangularSetCategory} @@ -92120,6 +93231,7 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{category URAGG UnaryRecursiveAggregate} \getchunk{category UFD UniqueFactorizationDomain} +\getchunk{category ATUNIKN UnitsKnownAttribute} \getchunk{category ULSCAT UnivariateLaurentSeriesCategory} \getchunk{category ULSCCAT UnivariateLaurentSeriesConstructorCategory} \getchunk{category UPOLYC UnivariatePolynomialCategory} @@ -92155,8 +93267,29 @@ digraph dotabb { \getchunk{ALGEBRA.dotabb} \getchunk{AMR.dotabb} \getchunk{ARR2CAT.dotabb} +\getchunk{ATADDVA.dotabb} +\getchunk{ATAPPRO.dotabb} +\getchunk{ATARBEX.dotabb} +\getchunk{ATARBPR.dotabb} +\getchunk{ATCANCL.dotabb} +\getchunk{ATCANON.dotabb} +\getchunk{ATCENRL.dotabb} +\getchunk{ATCS.dotabb} +\getchunk{ATCUNOR.dotabb} +\getchunk{ATFINAG.dotabb} +\getchunk{ATJACID.dotabb} +\getchunk{ATLUNIT.dotabb} +\getchunk{ATLR.dotabb} +\getchunk{ATMULVA.dotabb} +\getchunk{ATNOTHR.dotabb} +\getchunk{ATNULSQ.dotabb} +\getchunk{ATNZDIV.dotabb} +\getchunk{ATPOSET.dotabb} \getchunk{ATRIG.dotabb} +\getchunk{ATRUNIT.dotabb} +\getchunk{ATSHMUT.dotabb} \getchunk{ATTREG.dotabb} +\getchunk{ATUNIKN.dotabb} \getchunk{BASTYPE.dotabb} \getchunk{BGAGG.dotabb} \getchunk{BLMETCT.dotabb} @@ -92382,8 +93515,29 @@ digraph dotfull { \getchunk{ALGEBRA.dotfull} \getchunk{AMR.dotfull} \getchunk{ARR2CAT.dotfull} +\getchunk{ATADDVA.dotfull} +\getchunk{ATAPPRO.dotfull} +\getchunk{ATARBEX.dotfull} +\getchunk{ATARBPR.dotfull} +\getchunk{ATCANCL.dotfull} +\getchunk{ATCANON.dotfull} +\getchunk{ATCENRL.dotfull} +\getchunk{ATCS.dotfull} +\getchunk{ATCUNOR.dotfull} +\getchunk{ATFINAG.dotfull} +\getchunk{ATJACID.dotfull} +\getchunk{ATLUNIT.dotfull} +\getchunk{ATLR.dotfull} +\getchunk{ATMULVA.dotfull} +\getchunk{ATNOTHR.dotfull} +\getchunk{ATNULSQ.dotfull} +\getchunk{ATNZDIV.dotfull} +\getchunk{ATPOSET.dotfull} \getchunk{ATRIG.dotfull} +\getchunk{ATRUNIT.dotfull} +\getchunk{ATSHMUT.dotfull} \getchunk{ATTREG.dotfull} +\getchunk{ATUNIKN.dotfull} \getchunk{BASTYPE.dotfull} \getchunk{BGAGG.dotfull} \getchunk{BLMETCT.dotfull} diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index f25338b..5ba85df 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -24806,11 +24806,15 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|AbelianMonoid| . ABELMON) (|AbelianMonoidRing| . AMR) (|AbelianSemiGroup| . ABELSG) + (|AdditiveValuationAttribute| . ATADDVA) (|AffineSpaceCategory| . AFSPCAT) (|Aggregate| . AGG) (|Algebra| . ALGEBRA) (|AlgebraicallyClosedField| . ACF) (|AlgebraicallyClosedFunctionSpace| . ACFS) + (|ApproximateAttribute| . ATAPPRO) + (|ArbitraryExponentAttribute| . ATARBEX) + (|ArbitraryPrecisionAttribute| . ATARBPR) (|ArcHyperbolicFunctionCategory| . AHYP) (|ArcTrigonometricFunctionCategory| . ATRIG) (|AssociationListAggregate| . ALAGG) @@ -24824,6 +24828,10 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|BlowUpMethodCategory| . BLMETCT) (|CachableSet| . CACHSET) (|CancellationAbelianMonoid| . CABMON) + (|CanonicalAttribute| . ATCANON) + (|CanonicalClosedAttribute| . ATCANCL) + (|CanonicalUnitNormalAttribute| . ATCUNOR) + (|CentralAttribute| . ATCENRL) (|CharacteristicNonZero| . CHARNZ) (|CharacteristicZero| . CHARZ) (|CoercibleTo| . KOERCE) @@ -24831,6 +24839,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|CombinatorialFunctionCategory| . CFCAT) (|CombinatorialOpsCategory| . COMBOPC) (|CommutativeRing| . COMRING) + (|CommutativeStarAttribute| . ATCS) (|Comparable| . COMPAR) (|ComplexCategory| . COMPCAT) (|ConvertibleTo| . KONVERT) @@ -24861,6 +24870,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|FileCategory| . FILECAT) (|FileNameCategory| . FNCAT) (|FiniteAbelianMonoidRing| . FAMR) + (|FiniteAggregateAttribute| . ATFINAG) (|FiniteAlgebraicExtensionField| . FAXF) (|FiniteDivisorCategory| . FDIVCAT) (|FiniteFieldCategory| . FFIELDC) @@ -24895,9 +24905,12 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|IntegralDomain| . INTDOM) (|IntervalCategory| . INTCAT) (|KeyedDictionary| . KDAGG) + (|JacobiIdentityAttribute| . ATJACID) + (|LazyRepresentativeAttribute| . ATLR) (|LazyStreamAggregate| . LZSTAGG) (|LeftAlgebra| . LALG) (|LeftModule| . LMODULE) + (|LeftUnitaryAttribute| . ATLUNIT) (|LieAlgebra| . LIECAT) (|LinearAggregate| . LNAGG) (|LinearlyExplicitRingOver| . LINEXP) @@ -24915,12 +24928,16 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|MonogenicAlgebra| . MONOGEN) (|MonogenicLinearOperator| . MLO) (|MultiDictionary| . MDAGG) + (|MultiplicativeValuationAttribute| . ATMULVA) (|MultisetAggregate| . MSETAGG) (|MultivariateTaylorSeriesCategory| . MTSCAT) (|NonAssociativeAlgebra| . NAALG) (|NonAssociativeRing| . NASRING) (|NonAssociativeRng| . NARNG) (|NormalizedTriangularSetCategory| . NTSCAT) + (|NotherianAttribute| . ATNOTHR) + (|NullSquareAttribute| . ATNULSQ) + (|NoZeroDivisorsAttribute| . ATNZDIV) (|Object| . OBJECT) (|OctonionCategory| . OC) (|OneDimensionalArrayAggregate| . A1AGG) @@ -24938,6 +24955,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|OrderedSet| . ORDSET) (|PAdicIntegerCategory| . PADICCT) (|PartialDifferentialRing| . PDRING) + (|PartiallyOrderedSetAttribute| . ATPOSET) (|PartialTranscendentalFunctions| . PTRANFN) (|Patternable| . PATAB) (|PatternMatchable| . PATMAB) @@ -24984,6 +25002,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|SetCategory| . SETCAT) (|SetCategoryWithDegree| . SETCATD) (|SExpressionCategory| . SEXCAT) + (|ShallowlyMutableAttribute| . ATSHMUT) (|SpecialFunctionCategory| . SPFCAT) (|SquareFreeNormalizedTriangularSetCategory| . SNTSCAT) (|SquareFreeRegularTriangularSetCategory| . SFRTCAT) @@ -25003,6 +25022,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|Type| . TYPE) (|UnaryRecursiveAggregate| . URAGG) (|UniqueFactorizationDomain| . UFD) + (|UnitsKnownAttribute| . ATUNIKN) (|UnivariateLaurentSeriesCategory| . ULSCAT) (|UnivariateLaurentSeriesConstructorCategory| . ULSCCAT) (|UnivariatePolynomialCategory| . 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src/axiom-website/patches.html 20130426.01.tpd.patch +20130426 tpd src/share/algebra/dependents.daase/dependents.daase/index.kaf del +20130426 tpd src/share/algebra/users.daase/users.daase/index.kaf deleted +20130426 tpd src/share/algebra/operation.daase add Attributes as Categories +20130426 tpd src/share/algebra/interp.daase add Attributes as Categories +20130426 tpd src/share/algebra/compress.daase add Attributes as Categories +20130426 tpd src/share/algebra/category.daase add Attributes as Categories +20130426 tpd src/share/algebra/browse.daase add Attributes as Categories +20130426 tpd src/interp/temp.text deleted +20130426 tpd src/algebra/libdb.text add Attributes as Categories +20130426 tpd src/algebra/Makefile.pamphlet +20130426 tpd books/ps/v102unitsknownattribute.eps added +20130426 tpd books/ps/v102shallowlymutableattribute.eps added +20130426 tpd books/ps/v102rightunitaryattribute.eps added +20130426 tpd books/ps/v102partiallyorderedsetattribute.eps added +20130426 tpd books/ps/v102nullsquareattribute.eps added +20130426 tpd books/ps/v102nozerodivisorsattribute.eps added +20130426 tpd books/ps/v102notherianattribute.eps added +20130426 tpd books/ps/v102multiplicativevaluationattribute.eps added +20130426 tpd books/ps/v102leftunitaryattribute.eps added +20130426 tpd books/ps/v102lazyrepresentationattribute.eps added +20130426 tpd books/ps/v102jacobiidentityattribute.eps added +20130426 tpd books/ps/v102finiteaggregateattribute.eps added +20130426 tpd books/ps/v102commutativestarattribute.eps added +20130426 tpd books/ps/v102centralattribute.eps added +20130426 tpd books/ps/v102canonicalunitnormalattribute.eps added +20130426 tpd books/ps/v102canonicalclosedattribute.eps added +20130426 tpd books/ps/v102canonicalattribute.eps added +20130426 tpd books/ps/v102arbitraryprecisionattribute.eps added +20130426 tpd books/ps/v102arbitraryexponentattribute.eps added +20130426 tpd books/ps/v102approximateattribute.eps added +20130426 tpd books/ps/v102additivevaluationattribute.eps added +20130426 tpd books/bookvol5 add Attributes as Categories +20130426 tpd books/bookvol10.2 add Attributes as Categories 20130423 tpd src/axiom-website/patches.html 20130423.02.tpd.patch 20130423 tpd Makefile make clean removes all cruft 20130423 tpd src/axiom-website/patches.html 20130423.01.tpd.patch diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index e348280..4bbf51b 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -583,13 +583,21 @@ Used by next layer: BASTYPE CFCAT KOERCE KONVERT TYPE <>= LAYER0=\ - ${OUT}/AHYP.o ${OUT}/ATTREG.o ${OUT}/BASTYPE.o ${OUT}/BASTYPE-.o \ - ${OUT}/CFCAT.o ${OUT}/ELTAB.o ${OUT}/ESCONT1.o ${OUT}/GRDEF.o \ - ${OUT}/INTBIT.o ${OUT}/KOERCE.o ${OUT}/KONVERT.o \ + ${OUT}/AHYP.o ${OUT}/ATADDVA.o ${OUT}/ATCENRL.o ${OUT}/ATCS.o \ + ${OUT}/ATAPPRO.o ${OUT}/ATARBEX.o \ + ${OUT}/ATARBPR.o ${OUT}/ATCANCL.o ${OUT}/ATCANON.o ${OUT}/ATCUNOR.o \ + ${OUT}/ATFINAG.o ${OUT}/ATJACID.o ${OUT}/ATLR.o ${OUT}/ATLUNIT.o \ + ${OUT}/ATMULVA.o ${OUT}/ATNOTHR.o ${OUT}/ATNULSQ.o \ + ${OUT}/ATNZDIV.o ${OUT}/ATPOSET.o \ + ${OUT}/ATSHMUT.o \ + ${OUT}/ATTREG.o ${OUT}/ATUNIKN.o \ + ${OUT}/BASTYPE.o ${OUT}/BASTYPE-.o \ + ${OUT}/CFCAT.o ${OUT}/ELTAB.o ${OUT}/ESCONT1.o ${OUT}/GRDEF.o \ + ${OUT}/INTBIT.o ${OUT}/KOERCE.o ${OUT}/KONVERT.o \ ${OUT}/MAGCDOC.o ${OUT}/MSYSCMD.o \ - ${OUT}/ODEIFTBL.o ${OUT}/OM.o ${OUT}/OMCONN.o ${OUT}/OMDEV.o \ - ${OUT}/OUT.o ${OUT}/PRIMCAT.o ${OUT}/PRINT.o ${OUT}/PTRANFN.o \ - ${OUT}/RFDIST.o ${OUT}/RIDIST.o ${OUT}/SPFCAT.o ${OUT}/TYPE.o \ + ${OUT}/ODEIFTBL.o ${OUT}/OM.o ${OUT}/OMCONN.o ${OUT}/OMDEV.o \ + ${OUT}/OUT.o ${OUT}/PRIMCAT.o ${OUT}/PRINT.o ${OUT}/PTRANFN.o \ + ${OUT}/RFDIST.o ${OUT}/RIDIST.o ${OUT}/SPFCAT.o ${OUT}/TYPE.o \ layer0done @ @@ -601,9 +609,66 @@ LAYER0=\ "AHYP" [color="#4488FF",href="bookvol10.2.pdf#nameddest=AHYP"] "AHYP" -> "Category" +"ATADDVA" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATADDVA"]; +"ATADDVA" -> "Category" + +"ATCENRL" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCENRL"]; +"ATCENRL" -> "Category" + +"ATCS" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCS"]; +"ATCS" -> "Category" + +"ATAPPRO" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATAPPRO"]; +"ATAPPRO" -> "Category" + +"ATARBEX" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBEX"]; +"ATARBEX" -> "Category" + +"ATARBPR" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATARBPR"]; +"ATARBPR" -> "Category" + +"ATCANCL" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANCL"]; +"ATCANCL" -> "Category" + +"ATCANON" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCANON"]; +"ATCANON" -> "Category" + +"ATCUNOR" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATCUNOR"]; +"ATCUNOR" -> "Category" + +"ATFINAG" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATFINAG"]; +"ATFINAG" -> "Category" + +"ATJACID" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATJACID"]; +"ATJACID" -> "Category" + +"ATLR" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLR"]; +"ATLR" -> "Category" + +"ATLUNIT" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATLUNIT"]; +"ATLUNIT" -> "Category" + +"ATMULVA" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATMULVA"]; +"ATMULVA" -> "Category" + +"ATNOTHR" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNOTHR"]; +"ATNOTHR" -> "Category" + +"ATNULSQ" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNULSQ"]; +"ATNULSQ" -> "Category" + +"ATNZDIV" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATNZDIV"]; +"ATNZDIV" -> "Category" + +"ATSHMUT" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATSHMUT"]; +"ATSHMUT" -> "Category" + "ATTREG" [color="#4488FF",href="bookvol10.2.pdf#nameddest=ATTREG"] "ATTREG" -> "Category" +"ATUNIKN" [color=lightblue,href="bookvol10.2.pdf#nameddest=ATUNIKN"]; +"ATUNIKN" -> "Category" + /* nobody seems to go to bastype by itself */ /* we combine these two to minimize edges in the graph */ /* note that koerce is duplicated */ @@ -17807,6 +17872,7 @@ REGRESS= \ AbelianMonoid.regress \ AbelianMonoidRing.regress \ AbelianSemiGroup.regress \ + AdditiveValuationAttribute.regress \ AffineAlgebraicSetComputeWithGroebnerBasis.regress \ AffineAlgebraicSetComputeWithResultant.regress \ AffinePlane.regress \ @@ -17839,6 +17905,9 @@ REGRESS= \ ApplicationProgramInterface.regress \ ApplyRules.regress \ ApplyUnivariateSkewPolynomial.regress \ + ApproximateAttribute.regress \ + ArbitraryExponentAttribute.regress \ + ArbitraryPrecisionAttribute.regress \ ArcHyperbolicFunctionCategory.regress \ ArcTrigonometricFunctionCategory.regress \ ArrayStack.regress \ @@ -17912,9 +17981,13 @@ REGRESS= \ BrillhartTests.regress \ CachableSet.regress \ CancellationAbelianMonoid.regress \ + CanonicalAttribute.regress \ + CanonicalClosedAttribute.regress \ + CanonicalUnitNormalAttribute.regress \ CardinalNumber.regress \ CartesianTensor.regress \ CartesianTensorFunctions2.regress \ + CentralAttribute.regress \ ChangeOfVariable.regress \ Character.regress \ CharacterClass.regress \ @@ -17934,6 +18007,7 @@ REGRESS= \ CommonDenominator.regress \ CommonOperators.regress \ CommutativeRing.regress \ + CommutativeStarAttribute.regress \ Commutator.regress \ CommuteUnivariatePolynomialCategory.regress \ Comparable.regress \ @@ -18098,6 +18172,7 @@ REGRESS= \ Finite.regress \ FiniteAbelianMonoidRing.regress \ FiniteAbelianMonoidRingFunctions2.regress \ + FiniteAggregateAttribute.regress \ FiniteAlgebraicExtensionField.regress \ FiniteDivisor.regress \ FiniteDivisorCategory.regress \ @@ -18331,6 +18406,7 @@ REGRESS= \ InverseLaplaceTransform.regress \ IrredPolyOverFiniteField.regress \ IrrRepSymNatPackage.regress \ + JacobiIdentityAttribute.regress \ Kernel.regress \ KernelFunctions2.regress \ KeyedAccessFile.regress \ @@ -18338,11 +18414,13 @@ REGRESS= \ Kovacic.regress \ LaplaceTransform.regress \ LaurentPolynomial.regress \ + LazyRepresentativeAttribute.regress \ LazyStreamAggregate.regress \ LazardSetSolvingPackage.regress \ LeadingCoefDetermination.regress \ LeftAlgebra.regress \ LeftModule.regress \ + LeftUnitaryAttribute.regress \ LexTriangularPackage.regress \ Library.regress \ LieAlgebra.regress \ @@ -18431,6 +18509,7 @@ REGRESS= \ MultFiniteFactorize.regress \ MultiDictionary.regress \ MultipleMap.regress \ + MultiplicativeValuationAttribute.regress \ Multiset.regress \ MultisetAggregate.regress \ MultiVariableCalculusFunctions.regress \ @@ -18460,8 +18539,11 @@ REGRESS= \ NormalizedTriangularSetCategory.regress \ NormInMonogenicAlgebra.regress \ NormRetractPackage.regress \ + NotherianAttribute.regress \ NottinghamGroup.regress \ + NoZeroDivisors.regress \ NPCoef.regress \ + NullSquareAttribute.regress \ NumberFieldIntegralBasis.regress \ NumberFormats.regress \ NumberTheoreticPolynomialFunctions.regress \ @@ -18550,6 +18632,7 @@ REGRESS= \ PartialDifferentialRing.regress \ PartialFraction.regress \ PartialFractionPackage.regress \ + PartiallyOrderedSetAttribute.regress \ PartialTranscendentalFunctions.regress \ Partition.regress \ PartitionsAndPermutations.regress \ @@ -18731,6 +18814,7 @@ REGRESS= \ RewriteRule.regress \ RightModule.regress \ RightOpenIntervalRootCharacterization.regress \ + RightUnitaryAttribute.regress \ Ring.regress \ Rng.regress \ RomanNumeral.regress \ @@ -18757,6 +18841,7 @@ REGRESS= \ SExpression.regress \ SExpressionCategory.regress \ SExpressionOf.regress \ + ShallowlyMutableAttribute.regress \ SimpleAlgebraicExtension.regress \ SimpleAlgebraicExtensionAlgFactor.regress \ SimpleFortranProgram.regress \ @@ -18868,6 +18953,7 @@ REGRESS= \ TwoFactorize.regress \ UnaryRecursiveAggregate.regress \ UniqueFactorizationDomain.regress \ + UnitsKnownAttribute.regress \ UnivariateFactorize.regress \ UnivariateFormalPowerSeries.regress \ UnivariateFormalPowerSeriesFunctions.regress \ diff --git a/src/algebra/libdb.text b/src/algebra/libdb.text index e783613..125ea14 100755 --- a/src/algebra/libdb.text +++ b/src/algebra/libdb.text @@ -2,7 +2,9 @@ acanonicalUnitNormal`0`x``cIntegerNumberSystem`` acanonical`0`x``dSingleInteger``\spad{canonical} means that mathematical equality is implied by data structure equality. acanonicalsClosed`0`x``dSingleInteger``\spad{canonicalClosed} means two positives multiply to give positive. amultiplicativeValuation`0`x``cIntegerNumberSystem``euclideanSize(a*b) returns \spad{euclideanSize(a)*euclideanSize(b)}. +anil`0`x``cAdditiveValuationAttribute`` anoetherian`0`x``dSingleInteger``\spad{noetherian} all ideals are finitely generated (in fact principal). +cAdditiveValuationAttribute`0`x`()->Category``ATADDVA`The class of all euclidean domains such that cIntegerNumberSystem`0`x`()->Category``INS`An \spad{IntegerNumberSystem} is a model for the integers. dPlaneAlgebraicCurvePlot`0`x`()->Join(PlottablePlaneCurveCategory,etc)``ACPLOT`\indented{1}{Plot a NON-SINGULAR plane algebraic curve \spad{p}(\spad{x},{}\spad{y}) = 0.} Author: Clifton \spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References: dSingleInteger`0`x`()->Join(IntegerNumberSystem,etc)``SINT`SingleInteger is intended to support machine integer arithmetic. @@ -38,7 +40,7 @@ oinit`0`x`()->S`xIntegerNumberSystem&(S)`` oinvmod`2`x`(S,S)->S`xIntegerNumberSystem&(S)`` oinvmod`2`x`(_$,_$)->_$`cIntegerNumberSystem``\spad{invmod(a,{}b)},{} \spad{0<=a1},{} \spad{(a,{}b)=1} means \spad{1/a mod b}. olength`1`x`(_$)->_$`cIntegerNumberSystem``\spad{length(a)} length of \spad{a} in digits. -omakeSketch`5`x`(Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer)))->_$`dPlaneAlgebraicCurvePlot``\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \spad{p = 0} in the region {\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \spad{p = 0} in an rectangular region {\em xMin <= x <= xMax},{} {\em yMin <= y <= yMax}. The user inputs \spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax----)}. Here \spad{p} is a polynomial in the variables \spad{x} and \spad{y} with integer coefficients (\spad{p} belongs to the domain \spad{Polynomial Integer}). The case where \spad{p} is a polynomial in only one of the variables is allowed. The variables \spad{x} and \spad{y} are input to specify the the coordinate axes. The horizontal axis is the \spad{x}-axis and the vertical axis is the \spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the --cu--rve is to be plotted. +omakeSketch`5`x`(Polynomial(Integer),Symbol,Symbol,Segment(Fraction(Integer)),Segment(Fraction(Integer)))->_$`dPlaneAlgebraicCurvePlot``\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \spad{p = 0} in the region {\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \spad{p = 0} in an rectangular region {\em xMin <= x <= xMax},{} {\em yMin <= y <= yMax}. The user inputs \spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax------)}. Here \spad{p} is a polynomial in the variables \spad{x} and \spad{y} with integer coefficients (\spad{p} belongs to the domain \spad{Polynomial Integer}). The case where \spad{p} is a polynomial in only one of the variables is allowed. The variables \spad{x} and \spad{y} are input to specify the the coordinate axes. The horizontal axis is the \spad{x}-axis and the vertical axis is the \spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which th--e --cu--rve is to be plotted. omask`1`x`(S)->S`xIntegerNumberSystem&(S)`` omask`1`x`(_$)->_$`cIntegerNumberSystem``\spad{mask(n)} returns \spad{2**n-1} (an \spad{n} bit mask). omax`0`x`()->_$`dSingleInteger``\spad{max()} returns the largest single integer. diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 9d3067f..875c227 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4145,6 +4145,8 @@ books/bookvol10.2 add enumerate to FINITE books/bookvol10.2 add Comparable 20130423.02.tpd.patch Makefile make clean removes all cruft +20130426.01.tpd.patch +books/bookvol10.2 add Attributes as Categories diff --git a/src/interp/temp.text b/src/interp/temp.text deleted file mode 100755 index 9bbfdbf..0000000 --- a/src/interp/temp.text +++ /dev/null @@ -1,72 +0,0 @@ -dSingleInteger`0`x`()->Join(IntegerNumberSystem,etc)``SINT`SingleInteger is intended to support machine integer arithmetic. -o/\`2`x`(_$,_$)->_$`dSingleInteger``\spad{n} \spad{/\} \spad{m} returns the bit-by-bit logical {\em and} of the single integers \spad{n} and \spad{m}. -oAnd`2`x`(_$,_$)->_$`dSingleInteger``\spad{And(n,{}m)} returns the bit-by-bit logical {\em and} of the single integers \spad{n} and \spad{m}. -oNot`1`x`(_$)->_$`dSingleInteger``\spad{Not(n)} returns the bit-by-bit logical {\em not} of the single integer \spad{n}. -oOr`2`x`(_$,_$)->_$`dSingleInteger``\spad{Or(n,{}m)} returns the bit-by-bit logical {\em or} of the single integers \spad{n} and \spad{m}. -o\/`2`x`(_$,_$)->_$`dSingleInteger``\spad{n} \spad{\/} \spad{m} returns the bit-by-bit logical {\em or} of the single integers \spad{n} and \spad{m}. -omax`0`x`()->_$`dSingleInteger``\spad{max()} returns the largest single integer. -omin`0`x`()->_$`dSingleInteger``\spad{min()} returns the smallest single integer. -onot`1`x`(_$)->_$`dSingleInteger``\spad{not(n)} returns the bit-by-bit logical {\em not} of the single integer \spad{n}. -oxor`2`x`(_$,_$)->_$`dSingleInteger``\spad{xor(n,{}m)} returns the bit-by-bit logical {\em xor} of the single integers \spad{n} and \spad{m}. -o~`1`x`(_$)->_$`dSingleInteger``\spad{~ n} returns the bit-by-bit logical {\em not } of the single integer \spad{n}. -acanonical`0`x``dSingleInteger``\spad{canonical} means that mathematical equality is implied by data structure equality. -acanonicalsClosed`0`x``dSingleInteger``\spad{canonicalClosed} means two positives multiply to give positive. -anoetherian`0`x``dSingleInteger``\spad{noetherian} all ideals are finitely generated (in fact principal). -cIntegerNumberSystem`0`x`()->Category``INS`An \spad{IntegerNumberSystem} is a model for the integers. -oaddmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``\spad{addmod(a,{}b,{}p)},{} \spad{0<=a,{}b

1},{} means \spad{a+b mod p}. -obase`0`x`()->_$`cIntegerNumberSystem``\spad{base()} returns the base for the operations of \spad{IntegerNumberSystem}. -obit?`2`x`(_$,_$)->Boolean`cIntegerNumberSystem``\spad{bit?(n,{}i)} returns \spad{true} if and only if \spad{i}-th bit of \spad{n} is a 1. -ocopy`1`x`(_$)->_$`cIntegerNumberSystem``\spad{copy(n)} gives a copy of \spad{n}. -odec`1`x`(_$)->_$`cIntegerNumberSystem``\spad{dec(x)} returns \spad{x - 1}. -oeven?`1`x`(_$)->Boolean`cIntegerNumberSystem``\spad{even?(n)} returns \spad{true} if and only if \spad{n} is even. -ohash`1`x`(_$)->_$`cIntegerNumberSystem``\spad{hash(n)} returns the hash code of \spad{n}. -oinc`1`x`(_$)->_$`cIntegerNumberSystem``\spad{inc(x)} returns \spad{x + 1}. -oinvmod`2`x`(_$,_$)->_$`cIntegerNumberSystem``\spad{invmod(a,{}b)},{} \spad{0<=a1},{} \spad{(a,{}b)=1} means \spad{1/a mod b}. -olength`1`x`(_$)->_$`cIntegerNumberSystem``\spad{length(a)} length of \spad{a} in digits. -omask`1`x`(_$)->_$`cIntegerNumberSystem``\spad{mask(n)} returns \spad{2**n-1} (an \spad{n} bit mask). -omulmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``\spad{mulmod(a,{}b,{}p)},{} \spad{0<=a,{}b

1},{} means \spad{a*b mod p}. -oodd?`1`x`(_$)->Boolean`cIntegerNumberSystem``\spad{odd?(n)} returns \spad{true} if and only if \spad{n} is odd. -opositiveRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``\spad{positiveRemainder(a,{}b)} (where \spad{b > 1}) yields \spad{r} where \spad{0 <= r < b} and \spad{r == a rem b}. -opowmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``\spad{powmod(a,{}b,{}p)},{} \spad{0<=a,{}b

1},{} means \spad{a**b mod p}. -orandom`1`x`(_$)->_$`cIntegerNumberSystem``\spad{random(a)} creates a random element from 0 to \spad{n-1}. -orandom`0`x`()->_$`cIntegerNumberSystem``\spad{random()} creates a random element. -orational`1`x`(_$)->Fraction(Integer)`cIntegerNumberSystem``\spad{rational(n)} creates a rational number (see \spadtype{Fraction Integer}).. -orational?`1`x`(_$)->Boolean`cIntegerNumberSystem``\spad{rational?(n)} tests if \spad{n} is a rational number (see \spadtype{Fraction Integer}). -orationalIfCan`1`x`(_$)->Union(Fraction(Integer),"failed")`cIntegerNumberSystem``\spad{rationalIfCan(n)} creates a rational number,{} or returns "failed" if this is not possible. -oshift`2`x`(_$,_$)->_$`cIntegerNumberSystem``\spad{shift(a,{}i)} shift \spad{a} by \spad{i} digits. -osubmod`3`x`(_$,_$,_$)->_$`cIntegerNumberSystem``\spad{submod(a,{}b,{}p)},{} \spad{0<=a,{}b

1},{} means \spad{a-b mod p}. -osymmetricRemainder`2`x`(_$,_$)->_$`cIntegerNumberSystem``\spad{symmetricRemainder(a,{}b)} (where \spad{b > 1}) yields \spad{r} where \spad{ -b/2 <= r < b/2 }. -acanonicalUnitNormal`0`x``cIntegerNumberSystem`` -amultiplicativeValuation`0`x``cIntegerNumberSystem``euclideanSize(a*b) returns \spad{euclideanSize(a)*euclideanSize(b)}. -xIntegerNumberSystem&`1`x`(IntegerNumberSystem)->etc`(S)`INS-`An \spad{IntegerNumberSystem} is a model for the integers. -obinomial`2`x`(S,S)->S`xIntegerNumberSystem&(S)`` -obit?`2`x`(S,S)->Boolean`xIntegerNumberSystem&(S)`` -ocharacteristic`0`x`()->NonNegativeInteger`xIntegerNumberSystem&(S)`` -oconvert`1`x`(S)->DoubleFloat`xIntegerNumberSystem&(S)`` -oconvert`1`x`(S)->Float`xIntegerNumberSystem&(S)`` -oconvert`1`x`(S)->InputForm`xIntegerNumberSystem&(S)`` -oconvert`1`x`(S)->Integer`xIntegerNumberSystem&(S)`` -oconvert`1`x`(S)->Pattern(Integer)`xIntegerNumberSystem&(S)`` -ocopy`1`x`(S)->S`xIntegerNumberSystem&(S)`` -odifferentiate`2`x`(S,NonNegativeInteger)->S`xIntegerNumberSystem&(S)`` -odifferentiate`1`x`(S)->S`xIntegerNumberSystem&(S)`` -oeuclideanSize`1`x`(S)->NonNegativeInteger`xIntegerNumberSystem&(S)`` -oeven?`1`x`(S)->Boolean`xIntegerNumberSystem&(S)`` -ofactor`1`x`(S)->Factored(S)`xIntegerNumberSystem&(S)`` -ofactorial`1`x`(S)->S`xIntegerNumberSystem&(S)`` -oinit`0`x`()->S`xIntegerNumberSystem&(S)`` -oinvmod`2`x`(S,S)->S`xIntegerNumberSystem&(S)`` -omask`1`x`(S)->S`xIntegerNumberSystem&(S)`` -onextItem`1`x`(S)->Union(S,"failed")`xIntegerNumberSystem&(S)`` -opatternMatch`3`x`(S,Pattern(Integer),PatternMatchResult(Integer,S))->PatternMatchResult(Integer,S)`xIntegerNumberSystem&(S)`` -opermutation`2`x`(S,S)->S`xIntegerNumberSystem&(S)`` -opositive?`1`x`(S)->Boolean`xIntegerNumberSystem&(S)`` -opowmod`3`x`(S,S,S)->S`xIntegerNumberSystem&(S)`` -oprime?`1`x`(S)->Boolean`xIntegerNumberSystem&(S)`` -orational`1`x`(S)->Fraction(Integer)`xIntegerNumberSystem&(S)`` -orational?`1`x`(S)->Boolean`xIntegerNumberSystem&(S)`` -orationalIfCan`1`x`(S)->Union(Fraction(Integer),"failed")`xIntegerNumberSystem&(S)`` -oretract`1`x`(S)->Integer`xIntegerNumberSystem&(S)`` -oretractIfCan`1`x`(S)->Union(Integer,"failed")`xIntegerNumberSystem&(S)`` -osquareFree`1`x`(S)->Factored(S)`xIntegerNumberSystem&(S)`` -osymmetricRemainder`2`x`(S,S)->S`xIntegerNumberSystem&(S)`` diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d5e6557..55078ec 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2388726 . 3575591491) +(2388990 . 3575754975) (-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."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . 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\\br \\tab{5}\\spad{-(-x) = x}\\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|)) "\\spad{zerosOf(p, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. \\indented{1}{The yi'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 y1,...,yn are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} zerosOf(a,x)") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. \\indented{1}{The yi's are expressed in radicals if possible, and otherwise} \\indented{1}{as implicit algebraic quantities.} \\indented{1}{The returned symbols y1,...,yn are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} zerosOf(a)") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. \\indented{1}{The yi's are expressed in radicals if possible.} \\indented{1}{Otherwise they are implicit algebraic quantities.} \\indented{1}{The returned symbols y1,...,yn are bound in the interpreter} \\indented{1}{to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y.}} \\blankline \\spad{X} \\spad{a:Polynomial(Integer):=-3*x^2+2*x-13} \\spad{X} zerosOf(a)")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, \\spad{y)}} returns \\spad{y} such that \\spad{p(y) = 0}; \\indented{1}{if possible, \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity which} \\indented{1}{displays as \\spad{'y}.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} zeroOf(a,x)") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; \\indented{1}{if possible, \\spad{y} is expressed in terms of radicals.} \\indented{1}{Otherwise it is an implicit algebraic quantity.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} zeroOf(a)") (($ (|Polynomial| $)) "\\spad{zeroOf(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} \\spad{a:Polynomial(Integer):=-3*x^2+2*x-13} \\spad{X} zeroOf(a)")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; \\indented{1}{The returned roots display as \\spad{'y1},...,\\spad{'yn}.} \\indented{1}{Note that the returned symbols y1,...,yn are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootsOf(a,x)") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. \\indented{1}{Note that the returned symbols y1,...,yn are bound in the interpreter} \\indented{1}{to respective root values.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootsOf(a)") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. \\indented{1}{Note that the returned symbols y1,...,yn are bound in the} \\indented{1}{interpreter to respective root values.} \\indented{1}{Error: if \\spad{p} has more than one variable \\spad{y.}} \\blankline \\spad{X} \\spad{a:Polynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootsOf(a)")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, \\spad{y)}} returns \\spad{y} such that \\spad{p(y) = 0}. \\indented{1}{The object returned displays as \\spad{'y}.} \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootOf(a,x)") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. \\blankline \\spad{X} \\spad{a:SparseUnivariatePolynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootOf(a)") (($ (|Polynomial| $)) "\\spad{rootOf(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} \\spad{a:Polynomial(Integer):=-3*x^3+2*x+13} \\spad{X} rootOf(a)"))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The yi's are expressed in radicals if possible, and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols y1,...,yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The yi's are expressed in radicals if possible. The returned symbols y1,...,yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, \\spad{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, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},...,\\spad{'yn}. Note that the returned symbols y1,...,yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note that the returned symbols y1,...,yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y.}")) (|rootOf| (($ $ (|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, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The yi's are expressed in radicals if possible, and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols y1,...,yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The yi's are expressed in radicals if possible. The returned symbols y1,...,yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, \\spad{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, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},...,\\spad{'yn}. Note that the returned symbols y1,...,yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, \\spad{y)}} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note that the returned symbols y1,...,yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y.}")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y.}"))) -((-4597 . T) (-4595 . T) (-4594 . T) ((-4602 "*") . T) (-4593 . T) (-4598 . T) (-4592 . T) (-3348 . T)) +((-4599 . T) (-4597 . T) (-4596 . T) ((-4604 "*") . T) (-4595 . T) (-4600 . T) (-4594 . T) (-3389 . T)) NIL (-30) ((|constructor| (NIL "Plot a NON-SINGULAR plane algebraic curve p(x,y) = 0.")) (|refine| (($ $ (|DoubleFloat|)) "\\indented{1}{refine(p,x) is not documented} \\blankline \\spad{X} sketch:=makeSketch(x+y,x,y,-1/2..1/2,-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(p,x,y,a..b,c..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 x-axis and} \\indented{1}{the vertical axis is the 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,x,y,-1/2..1/2,-1/2..1/2)$ACPLOT"))) @@ -68,14 +68,14 @@ NIL ((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) NIL NIL -(-35 -3020 K) +(-35 -3465 K) ((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package"))) NIL NIL -(-36 R -3280) +(-36 R -3313) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, \\spad{n)}} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x \\spad{**} \\spad{q}} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, \\spad{x)}} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator, that is, an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator, that is, an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, \\spad{y)}} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571))))) +((|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572))))) (-37 K) ((|constructor| (NIL "The following is all the categories and domains related to projective space and part of the PAFF package")) (|pointValue| (((|List| |#1|) $) "\\spad{pointValue returns} the coordinates of the point or of the point of origin that represent an infinitly close point")) (|setelt| ((|#1| $ (|Integer|) |#1|) "\\spad{setelt sets} the value of a specified coordinates")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates")) (|list| (((|List| |#1|) $) "\\spad{list returns} the list of the coordinates")) (|rational?| (((|Boolean|) $) "\\spad{rational?(p)} test if the point is rational according to the characteristic of the ground field.") (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{rational?(p,n)} test if the point is rational according to \\spad{n.}")) (|removeConjugate| (((|List| $) (|List| $)) "\\spad{removeConjugate(lp)} returns removeConjugate(lp,n) where \\spad{n} is the characteristic of the ground field.") (((|List| $) (|List| $) (|NonNegativeInteger|)) "\\spad{removeConjugate(lp,n)} returns a list of points such that no points in the list is the conjugate (according to \\spad{n)} of another point.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns conjugate(p,n) where \\spad{n} is the characteristic of the ground field.") (($ $ (|NonNegativeInteger|)) "\\spad{conjugate(p,n)} returns p**n, that is all the coordinates of \\spad{p} to the power of \\spad{n}")) (|orbit| (((|List| $) $ (|NonNegativeInteger|)) "\\spad{orbit(p,n)} returns the orbit of the point \\spad{p} according to \\spad{n,} that is orbit(p,n) = \\spad{\\{} \\spad{p,} p**n, p**(n**2), p**(n**3), ..... \\spad{\\}}") (((|List| $) $) "\\spad{orbit(p)} returns the orbit of the point \\spad{p} according to the characteristic of \\spad{K,} that is, for \\spad{q=} char \\spad{K,} orbit(p) = \\spad{\\{} \\spad{p,} p**q, p**(q**2), p**(q**3), ..... \\spad{\\}}")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce a} list of \\spad{K} to a affine point.")) (|affinePoint| (($ (|List| |#1|)) "\\spad{affinePoint creates} a affine point from a list"))) NIL @@ -83,10 +83,10 @@ 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 r(x)\" An attribute \"finiteAggregate\" is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{# u} returns the number of items in u.")) (|sample| (($) "\\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()}$D creates an aggregate of type \\spad{D} with 0 elements. Note that The \\spad{$D} can be dropped if understood by context, for example \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of u. Note that for collections, \\axiom{copy(u) \\spad{==} \\spad{[x} for \\spad{x} in u]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4600))) +((|HasAttribute| |#1| (QUOTE -4602))) (-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 r(x)\" An attribute \"finiteAggregate\" is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{# u} returns the number of items in u.")) (|sample| (($) "\\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()}$D creates an aggregate of type \\spad{D} with 0 elements. Note that The \\spad{$D} can be dropped if understood by context, for example \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of u. Note that for collections, \\axiom{copy(u) \\spad{==} \\spad{[x} for \\spad{x} in u]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-3348 . T)) +((-3389 . T)) NIL (-40) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x.}")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x.}")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x.}")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x.}")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x.}")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x.}"))) @@ -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| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k,} or \"failed\" if \\spad{u} has no key \\spad{k.}"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL (-42 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline Axioms\\br \\tab{5}\\spad{(b+c)::% = (b::\\%) + (c::\\%)}\\br \\tab{5}\\spad{(b*c)::% = (b::\\%) * (c::\\%)}\\br \\tab{5}\\spad{(1::R)::% = 1::%}\\br \\tab{5}\\spad{b*x = (b::\\%)*x}\\br \\tab{5}\\spad{r*(a*b) = (r*a)*b = a*(r*b)}")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -102,20 +102,20 @@ NIL NIL (-43 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline Axioms\\br \\tab{5}\\spad{(b+c)::% = (b::\\%) + (c::\\%)}\\br \\tab{5}\\spad{(b*c)::% = (b::\\%) * (c::\\%)}\\br \\tab{5}\\spad{(1::R)::% = 1::%}\\br \\tab{5}\\spad{b*x = (b::\\%)*x}\\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."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . 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) / \\spad{(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 a1,...,an."))) NIL NIL -(-45 -3280 UP UPUP -4387) +(-45 -3313 UP UPUP -3195) ((|constructor| (NIL "Function field defined by f(x, \\spad{y)} = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} is not documented"))) -((-4593 |has| (-412 |#2|) (-367)) (-4598 |has| (-412 |#2|) (-367)) (-4592 |has| (-412 |#2|) (-367)) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-149))) (|HasCategory| (-412 |#2|) (QUOTE (-151))) (|HasCategory| (-412 |#2|) (QUOTE (-352))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (-1831 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-352)))) (|HasCategory| (-412 |#2|) (QUOTE (-373))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-373))) (-1831 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-1831 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-412 |#2|) (QUOTE (-352))))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-226))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-1831 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-226))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-352))))) -(-46 R -3280) +((-4595 |has| (-413 |#2|) (-368)) (-4600 |has| (-413 |#2|) (-368)) (-4594 |has| (-413 |#2|) (-368)) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-413 |#2|) (QUOTE (-149))) (|HasCategory| (-413 |#2|) (QUOTE (-151))) (|HasCategory| (-413 |#2|) (QUOTE (-353))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (-1841 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-353)))) (|HasCategory| (-413 |#2|) (QUOTE (-374))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-374))) (-1841 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-1841 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-353))))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-227))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-1841 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-227))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-353))))) +(-46 R -3313) ((|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 ai's which are algebraic from the denominators in \\spad{f.}") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the ai's which are algebraic kernels from the denominators in \\spad{f.}") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b.}")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -435) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -436) (|devaluate| |#1|))))) (-47 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list lan. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list lan."))) NIL @@ -123,34 +123,34 @@ NIL (-48 R A) ((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of va.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()}, if the algebra is associative, alternative or a Jordan algebra, then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid, \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note that right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note that left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},b in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},b in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},b in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},b in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},b in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x}, \\spad{x*bi}, \\spad{bi*x}, \\spad{bi*x*bj}, \\spad{i,j=1,...,n}, where \\spad{b=[b1,...,bn]} is a basis. Note that if \\spad{A} has a unit, then doubleRank, weakBiRank, and biRank coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj}, \\spad{i,j=1,...,n}, where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},...,\\spad{x*bn}, where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},...,\\spad{bn*x}, where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},...,\\spad{x*bn}, where \\spad{b=[b1,...,bn]} is a basis."))) NIL -((|HasCategory| |#1| (QUOTE (-302)))) +((|HasCategory| |#1| (QUOTE (-303)))) (-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 \\spad{k} in 1..rank()]} defined by \\spad{ai * aj = \\spad{gammaij1} * \\spad{a1} + \\spad{...} + 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."))) -((-4597 |has| |#1| (-561)) (-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) +((-4599 |has| |#1| (-562)) (-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-847)))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098)))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-848))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098)))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-848)))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))))) (-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 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 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p.}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) +((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (-52 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i, elements of the ordered abelian monoid, are thought of as exponents or monomials. The monomials commute with each other, and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least, only the non-zero terms are ever operated on.")) (/ (($ $ |#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 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 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p.}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL (-53) ((|constructor| (NIL "Algebraic closure of the rational numbers, with mathematical =")) (|norm| (($ $ (|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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| $ (QUOTE (-1053))) (|HasCategory| $ (LIST (QUOTE -1043) (QUOTE (-571))))) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| $ (QUOTE (-1054))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-572))))) (-54) ((|constructor| (NIL "This domain implements anonymous functions"))) 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(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} \\spad{...} 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.}"))) -((-4597 . T)) +((-4599 . 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}."))) @@ -168,7 +168,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, \\spad{f,} \\spad{m)}} returns \\spad{p(m)} where the action is given by \\spad{x \\spad{m} = f(m)}. \\spad{f} must be an R-pseudo linear map on \\spad{M.}"))) NIL NIL -(-60 |Base| R -3280) +(-60 |Base| R -3313) ((|constructor| (NIL "This package apply rewrite rules to expressions, calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, \\spad{n)}} applies the rules r1,...,rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules r1,...,rn to \\spad{f} an unlimited number of times, \\spadignore{i.e.} until none of r1,...,rn is applicable to the expression."))) NIL NIL @@ -178,7 +178,7 @@ NIL NIL (-62 R |Row| |Col|) ((|constructor| (NIL "Two dimensional array categories and domains")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map!(f,a)\\space{2}assign \\spad{a(i,j)} to \\spad{f(a(i,j))}} \\indented{1}{for all \\spad{i, \\spad{j}}} \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,4,10) \\spad{X} map!(-,arr)")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\indented{1}{map(f,a,b,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,arr1,arr2,17)") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\indented{1}{map(f,a,b) returns \\spad{c}, where \\spad{c(i,j) = f(a(i,j),b(i,j))}} \\indented{1}{for all \\spad{i, \\spad{j}}} \\blankline \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,4,10) \\spad{X} map(adder,arr,arr)") (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map(f,a) returns \\spad{b}, where \\spad{b(i,j) = f(a(i,j))}} \\indented{1}{for all \\spad{i, \\spad{j}}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,4,10) \\spad{X} map(-,arr) \\spad{X} map((x \\spad{+->} \\spad{x} + x),arr)")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\indented{1}{setColumn!(m,j,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} \\spad{acol:=construct([1,2,3,4,5]::List(INT))$T2} \\spad{X} \\spad{setColumn!(arr,1,acol)$T1}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\indented{1}{setRow!(m,i,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} \\spad{arow:=construct([1,2,3,4]::List(INT))$T2} \\spad{X} \\spad{setRow!(arr,1,arow)$T1}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\indented{1}{qsetelt!(m,i,j,r) sets the element in the \\spad{i}th row and jth} \\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(m,i,j,r) sets the element in the \\spad{i}th row and jth} \\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(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(m,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(m,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(m,i,j) returns the element in the \\spad{i}th row and jth} \\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(m,i,j,r) returns the element in the \\spad{i}th row and jth} \\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(m,i,j) returns the element in the \\spad{i}th row and jth} \\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(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(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(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(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(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|) $) "\\indented{1}{minRowIndex(m) returns the index of the 'first' row of the array \\spad{m}} \\blankline \\spad{X} arr : \\spad{ARRAY2} INT \\spad{:=} new(5,4,10) \\spad{X} minRowIndex(arr)")) (|fill!| (($ $ |#1|) "\\indented{1}{fill!(m,r) fills \\spad{m} with r'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(m,n,r) is an m-by-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"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . 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(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} T1:=OneDimensionalArrayFunctions2(Integer,Integer) \\spad{X} map(x+->x+2,[i for \\spad{i} in 1..10])$T1")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\indented{1}{reduce(f,a,r) applies function \\spad{f} to each} \\indented{1}{successive element of the} \\indented{1}{one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r.}} \\indented{1}{For example, \\spad{reduce(_+$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} T1:=OneDimensionalArrayFunctions2(Integer,Integer) \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} reduce(adder,[i for \\spad{i} in 1..10],0)$T1")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\indented{1}{scan(f,a,r) successively applies} \\indented{1}{\\spad{reduce(f,x,r)} to more and more leading sub-arrays} \\indented{1}{x of one-dimensional array \\spad{a}.} \\indented{1}{More precisely, if \\spad{a} is \\spad{[a1,a2,...]}, then} \\indented{1}{\\spad{scan(f,a,r)} returns} \\indented{1}{\\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.} \\blankline \\spad{X} T1:=OneDimensionalArrayFunctions2(Integer,Integer) \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} scan(adder,[i for \\spad{i} in 1..10],0)$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(n,s) creates an array from \\spad{n} copies of element \\spad{s}} \\blankline \\spad{X} oneDimensionalArray(10,0.0)") (($ (|List| |#1|)) "\\indented{1}{oneDimensionalArray(l) creates an array from a list of elements \\spad{l}} \\blankline \\spad{X} oneDimensionalArray \\spad{[i**2} for \\spad{i} in 1..10]"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) (-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's."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-66 -3159) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-66 -3201) ((|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(P,Q,DQDL,X,ELAM,JINT)\\br \\tab{5}DOUBLE PRECISION ELAM,P,Q,X,DQDL\\br \\tab{5}INTEGER JINT\\br \\tab{5}P=1.0D0\\br \\tab{5}Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)\\br \\tab{5}DQDL=1.0D0\\br \\tab{5}RETURN\\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 -3159) +(-67 -3201) ((|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)\\br \\tab{5}DOUBLE PRECISION ELAM,FINFO(15)\\br \\tab{5}INTEGER MAXIT,IFLAG\\br \\tab{5}IF(MAXIT.EQ.-1)THEN\\br \\tab{7}PRINT*,\"Output from Monit\"\\br \\tab{5}ENDIF\\br \\tab{5}PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)\\br \\tab{5}RETURN\\br \\tab{5}END\\")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-68 -3159) +(-68 -3201) ((|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 LSFUN2(M,N,XC,FVECC,FJACC,LJC)\\br \\tab{5}DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)\\br \\tab{5}INTEGER M,N,LJC\\br \\tab{5}INTEGER I,J\\br \\tab{5}DO 25003 I=1,LJC\\br \\tab{7}DO 25004 J=1,N\\br \\tab{9}FJACC(I,J)=0.0D0\\br 25004 CONTINUE\\br 25003 CONTINUE\\br \\tab{5}FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(\\br \\tab{4}&XC(3)+15.0D0*XC(2))\\br \\tab{5}FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(\\br \\tab{4}&XC(3)+7.0D0*XC(2))\\br \\tab{5}FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333\\br \\tab{4}&3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))\\br \\tab{5}FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(\\br \\tab{4}&XC(3)+3.0D0*XC(2))\\br \\tab{5}FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*\\br \\tab{4}&XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))\\br \\tab{5}FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333\\br \\tab{4}&3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))\\br \\tab{5}FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*\\br \\tab{4}&XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))\\br \\tab{5}FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+\\br \\tab{4}&XC(2))\\br \\tab{5}FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714\\br \\tab{4}&286D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666\\br \\tab{4}&6667D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)\\br \\tab{4}&+XC(2))\\br \\tab{5}FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)\\br \\tab{4}&+XC(2))\\br \\tab{5}FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333\\br \\tab{4}&3333D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X\\br \\tab{4}&C(2))\\br \\tab{5}FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3\\br \\tab{4}&)+XC(2))\\br \\tab{5}FJACC(1,1)=1.0D0\\br \\tab{5}FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)\\br \\tab{5}FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)\\br \\tab{5}FJACC(2,1)=1.0D0\\br \\tab{5}FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)\\br \\tab{5}FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)\\br \\tab{5}FJACC(3,1)=1.0D0\\br \\tab{5}FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(\\br \\tab{4}&XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666\\br \\tab{4}&666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)\\br \\tab{5}FJACC(4,1)=1.0D0\\br \\tab{5}FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)\\br \\tab{5}FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)\\br \\tab{5}FJACC(5,1)=1.0D0\\br \\tab{5}FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399\\br \\tab{4}&999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)\\br \\tab{5}FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999\\br \\tab{4}&999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)\\br \\tab{5}FJACC(6,1)=1.0D0\\br \\tab{5}FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(\\br \\tab{4}&XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333\\br \\tab{4}&333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)\\br \\tab{5}FJACC(7,1)=1.0D0\\br \\tab{5}FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(\\br \\tab{4}&XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428\\br \\tab{4}&571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)\\br \\tab{5}FJACC(8,1)=1.0D0\\br \\tab{5}FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(9,1)=1.0D0\\br \\tab{5}FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*\\br \\tab{4}&*2)\\br \\tab{5}FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*\\br \\tab{4}&*2)\\br \\tab{5}FJACC(10,1)=1.0D0\\br \\tab{5}FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(11,1)=1.0D0\\br \\tab{5}FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(12,1)=1.0D0\\br \\tab{5}FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(13,1)=1.0D0\\br \\tab{5}FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)\\br \\tab{4}&**2)\\br \\tab{5}FJACC(14,1)=1.0D0\\br \\tab{5}FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(15,1)=1.0D0\\br \\tab{5}FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)\\br \\tab{5}RETURN\\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 -3159) +(-69 -3201) ((|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 F(X)\\br \\tab{5}DOUBLE PRECISION X\\br \\tab{5}F=DSIN(X)\\br \\tab{5}RETURN\\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 -3159) +(-70 -3201) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs, for example: \\blankline \\tab{5}SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)\\br \\tab{5}DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)\\br \\tab{5}INTEGER JTHCOL,N,NROWH,NCOLH\\br \\tab{5}HX(1)=2.0D0*X(1)\\br \\tab{5}HX(2)=2.0D0*X(2)\\br \\tab{5}HX(3)=2.0D0*X(4)+2.0D0*X(3)\\br \\tab{5}HX(4)=2.0D0*X(4)+2.0D0*X(3)\\br \\tab{5}HX(5)=2.0D0*X(5)\\br \\tab{5}HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))\\br \\tab{5}HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))\\br \\tab{5}RETURN\\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 -3159) +(-71 -3201) ((|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 FUNCT1(N,XC,FC)\\br \\tab{5}DOUBLE PRECISION FC,XC(N)\\br \\tab{5}INTEGER N\\br \\tab{5}FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5\\br \\tab{4}&.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X\\br \\tab{4}&C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+\\br \\tab{4}&(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(\\br \\tab{4}&2)+10.0D0*XC(1)**4+XC(1)**2\\br \\tab{5}RETURN\\br \\tab{5}END\\br")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spadtype{FortranExpression} and turns it into an ASP. coerce(f) takes an object from the appropriate instantiation of"))) NIL NIL -(-72 -3159) +(-72 -3201) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs, needed for NAG routine f02fjf ,for example: \\blankline \\tab{5}FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)\\br \\tab{5}DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)\\br \\tab{5}INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)\\br \\tab{5}DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1\\br \\tab{4}&4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(\\br \\tab{4}&14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1\\br \\tab{4}&1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(\\br \\tab{4}&11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))\\br \\tab{4}&)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)\\br \\tab{4}&+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.\\br \\tab{4}&5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3\\br \\tab{4}&)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(\\br \\tab{4}&2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)\\br \\tab{5}RETURN\\br \\tab{5}END"))) NIL NIL -(-73 -3159) +(-73 -3201) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs, used in NAG routine f02fjf, for example: \\blankline \\tab{5}SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)\\br \\tab{5}DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)\\br \\tab{5}INTEGER N,LIWORK,IFLAG,LRWORK\\br \\tab{5}W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00\\br \\tab{4}&2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554\\br \\tab{4}&0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365\\br \\tab{4}&3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(\\br \\tab{4}&8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.\\br \\tab{4}&2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050\\br \\tab{4}&8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z\\br \\tab{4}&(1)\\br \\tab{5}W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010\\br \\tab{4}&94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136\\br \\tab{4}&72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D\\br \\tab{4}&0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)\\br \\tab{4}&)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532\\br \\tab{4}&5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056\\br \\tab{4}&67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1\\br \\tab{4}&))\\br \\tab{5}W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0\\br \\tab{4}&06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033\\br \\tab{4}&305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502\\br \\tab{4}&9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D\\br \\tab{4}&0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-\\br \\tab{4}&0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961\\br \\tab{4}&32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917\\br \\tab{4}&D0*Z(1))\\br \\tab{5}W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.\\br \\tab{4}&01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688\\br \\tab{4}&97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315\\br \\tab{4}&6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z\\br \\tab{4}&(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0\\br \\tab{4}&.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802\\br \\tab{4}&68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*\\br \\tab{4}&Z(1)\\br \\tab{5}W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(\\br \\tab{4}&-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014\\br \\tab{4}&45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966\\br \\tab{4}&3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352\\br \\tab{4}&4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))\\br \\tab{4}&+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718\\br \\tab{4}&5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851\\br \\tab{4}&6D0*Z(1)\\br \\tab{5}W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048\\br \\tab{4}&26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323\\br \\tab{4}&319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730\\br \\tab{4}&01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(\\br \\tab{4}&8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583\\br \\tab{4}&09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700\\br \\tab{4}&4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)\\br \\tab{5}W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0\\br \\tab{4}&2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843\\br \\tab{4}&8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017\\br \\tab{4}&95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(\\br \\tab{4}&8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136\\br \\tab{4}&2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015\\br \\tab{4}&423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1\\br \\tab{4}&)\\br \\tab{5}W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05\\br \\tab{4}&581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338\\br \\tab{4}&45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869\\br \\tab{4}&52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)\\br \\tab{4}&+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056\\br \\tab{4}&1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544\\br \\tab{4}&359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(\\br \\tab{4}&1)\\br \\tab{5}W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-\\br \\tab{4}&0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173\\br \\tab{4}&3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441\\br \\tab{4}&3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8\\br \\tab{4}&))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23\\br \\tab{4}&11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773\\br \\tab{4}&9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(\\br \\tab{4}&1)\\br \\tab{5}W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0\\br \\tab{4}&.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246\\br \\tab{4}&3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609\\br \\tab{4}&48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8\\br \\tab{4}&))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032\\br \\tab{4}&98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688\\br \\tab{4}&615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(\\br \\tab{4}&1)\\br \\tab{5}W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0\\br \\tab{4}&7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830\\br \\tab{4}&9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D\\br \\tab{4}&0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)\\br \\tab{4}&)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493\\br \\tab{4}&1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054\\br \\tab{4}&65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)\\br \\tab{5}W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-\\br \\tab{4}&0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162\\br \\tab{4}&3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889\\br \\tab{4}&45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8\\br \\tab{4}&)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.\\br \\tab{4}&01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226\\br \\tab{4}&501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763\\br \\tab{4}&75D0*Z(1)\\br \\tab{5}W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(\\br \\tab{4}&-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169\\br \\tab{4}&742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453\\br \\tab{4}&5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(\\br \\tab{4}&8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05\\br \\tab{4}&468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277\\br \\tab{4}&35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0\\br \\tab{4}&*Z(1)\\br \\tab{5}W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))\\br \\tab{4}&+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236\\br \\tab{4}&679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278\\br \\tab{4}&87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D\\br \\tab{4}&0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0\\br \\tab{4}&.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660\\br \\tab{4}&7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903\\br \\tab{4}&02D0*Z(1)\\br \\tab{5}W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0\\br \\tab{4}&.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325\\br \\tab{4}&555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556\\br \\tab{4}&9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D\\br \\tab{4}&0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.\\br \\tab{4}&0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122\\br \\tab{4}&10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z\\br \\tab{4}&(1)\\br \\tab{5}W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.\\br \\tab{4}&1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669\\br \\tab{4}&47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114\\br \\tab{4}&625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z\\br \\tab{4}&(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0\\br \\tab{4}&07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739\\br \\tab{4}&00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*\\br \\tab{4}&Z(1)\\br \\tab{5}RETURN\\br \\tab{5}END\\br"))) NIL NIL -(-74 -3159) +(-74 -3201) ((|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,K,F,D)\\br \\tab{5}DOUBLE PRECISION D(K),F(K)\\br \\tab{5}INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE\\br \\tab{5}CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)\\br \\tab{5}RETURN\\br \\tab{5}END\\br")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-75 -3159) +(-75 -3201) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs, needed for NAG routine f04qaf, for example: \\blankline \\tab{5}SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)\\br \\tab{5}DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)\\br \\tab{5}INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE\\br \\tab{5}DOUBLE PRECISION A(5,5)\\br \\tab{5}EXTERNAL F06PAF\\br \\tab{5}A(1,1)=1.0D0\\br \\tab{5}A(1,2)=0.0D0\\br \\tab{5}A(1,3)=0.0D0\\br \\tab{5}A(1,4)=-1.0D0\\br \\tab{5}A(1,5)=0.0D0\\br \\tab{5}A(2,1)=0.0D0\\br \\tab{5}A(2,2)=1.0D0\\br \\tab{5}A(2,3)=0.0D0\\br \\tab{5}A(2,4)=0.0D0\\br \\tab{5}A(2,5)=-1.0D0\\br \\tab{5}A(3,1)=0.0D0\\br \\tab{5}A(3,2)=0.0D0\\br \\tab{5}A(3,3)=1.0D0\\br \\tab{5}A(3,4)=-1.0D0\\br \\tab{5}A(3,5)=0.0D0\\br \\tab{5}A(4,1)=-1.0D0\\br \\tab{5}A(4,2)=0.0D0\\br \\tab{5}A(4,3)=-1.0D0\\br \\tab{5}A(4,4)=4.0D0\\br \\tab{5}A(4,5)=-1.0D0\\br \\tab{5}A(5,1)=0.0D0\\br \\tab{5}A(5,2)=-1.0D0\\br \\tab{5}A(5,3)=0.0D0\\br \\tab{5}A(5,4)=-1.0D0\\br \\tab{5}A(5,5)=4.0D0\\br \\tab{5}IF(MODE.EQ.1)THEN\\br \\tab{7}CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)\\br \\tab{5}ELSEIF(MODE.EQ.2)THEN\\br \\tab{7}CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)\\br \\tab{5}ENDIF\\br \\tab{5}RETURN\\br \\tab{5}END"))) NIL NIL -(-76 -3159) +(-76 -3201) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs, needed for NAG routine d02ejf, for example: \\blankline \\tab{5}SUBROUTINE PEDERV(X,Y,PW)\\br \\tab{5}DOUBLE PRECISION X,Y(*)\\br \\tab{5}DOUBLE PRECISION PW(3,3)\\br \\tab{5}PW(1,1)=-0.03999999999999999D0\\br \\tab{5}PW(1,2)=10000.0D0*Y(3)\\br \\tab{5}PW(1,3)=10000.0D0*Y(2)\\br \\tab{5}PW(2,1)=0.03999999999999999D0\\br \\tab{5}PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))\\br \\tab{5}PW(2,3)=-10000.0D0*Y(2)\\br \\tab{5}PW(3,1)=0.0D0\\br \\tab{5}PW(3,2)=60000000.0D0*Y(2)\\br \\tab{5}PW(3,3)=0.0D0\\br \\tab{5}RETURN\\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 -3159) +(-77 -3201) ((|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(X,V,JINT)\\br \\tab{5}DOUBLE PRECISION V(3),X\\br \\tab{5}INTEGER JINT\\br \\tab{5}RETURN\\br \\tab{5}END")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-78 -3159) +(-78 -3201) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs, needed for NAG routine f04mbf, for example: \\blankline \\tab{5}SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)\\br \\tab{5}DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)\\br \\tab{5}INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)\\br \\tab{5}DOUBLE PRECISION W1(3),W2(3),MS(3,3)\\br \\tab{5}IFLAG=-1\\br \\tab{5}MS(1,1)=2.0D0\\br \\tab{5}MS(1,2)=1.0D0\\br \\tab{5}MS(1,3)=0.0D0\\br \\tab{5}MS(2,1)=1.0D0\\br \\tab{5}MS(2,2)=2.0D0\\br \\tab{5}MS(2,3)=1.0D0\\br \\tab{5}MS(3,1)=0.0D0\\br \\tab{5}MS(3,2)=1.0D0\\br \\tab{5}MS(3,3)=2.0D0\\br \\tab{5}CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)\\br \\tab{5}IFLAG=-IFLAG\\br \\tab{5}RETURN\\br \\tab{5}END"))) NIL NIL -(-79 -3159) +(-79 -3201) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs, needed for NAG routines c05pbf, c05pcf, for example: \\blankline \\tab{5}SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)\\br \\tab{5}DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)\\br \\tab{5}INTEGER LDFJAC,N,IFLAG\\br \\tab{5}IF(IFLAG.EQ.1)THEN\\br \\tab{7}FVEC(1)=(-1.0D0*X(2))+X(1)\\br \\tab{7}FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)\\br \\tab{7}FVEC(3)=3.0D0*X(3)\\br \\tab{5}ELSEIF(IFLAG.EQ.2)THEN\\br \\tab{7}FJAC(1,1)=1.0D0\\br \\tab{7}FJAC(1,2)=-1.0D0\\br \\tab{7}FJAC(1,3)=0.0D0\\br \\tab{7}FJAC(2,1)=0.0D0\\br \\tab{7}FJAC(2,2)=2.0D0\\br \\tab{7}FJAC(2,3)=-1.0D0\\br \\tab{7}FJAC(3,1)=0.0D0\\br \\tab{7}FJAC(3,2)=0.0D0\\br \\tab{7}FJAC(3,3)=3.0D0\\br \\tab{5}ENDIF\\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 @@ -256,66 +256,66 @@ 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} Y(i) and also a continuation parameter EPS, for example: \\blankline \\tab{5}SUBROUTINE G(EPS,YA,YB,BC,N)\\br \\tab{5}DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)\\br \\tab{5}INTEGER N\\br \\tab{5}BC(1)=YA(1)\\br \\tab{5}BC(2)=YA(2)\\br \\tab{5}BC(3)=YB(2)-1.0D0\\br \\tab{5}RETURN\\br \\tab{5}END\\br \\tab{5}SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)\\br \\tab{5}DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)\\br \\tab{5}INTEGER N\\br \\tab{5}AJ(1,1)=1.0D0\\br \\tab{5}AJ(1,2)=0.0D0\\br \\tab{5}AJ(1,3)=0.0D0\\br \\tab{5}AJ(2,1)=0.0D0\\br \\tab{5}AJ(2,2)=1.0D0\\br \\tab{5}AJ(2,3)=0.0D0\\br \\tab{5}AJ(3,1)=0.0D0\\br \\tab{5}AJ(3,2)=0.0D0\\br \\tab{5}AJ(3,3)=0.0D0\\br \\tab{5}BJ(1,1)=0.0D0\\br \\tab{5}BJ(1,2)=0.0D0\\br \\tab{5}BJ(1,3)=0.0D0\\br \\tab{5}BJ(2,1)=0.0D0\\br \\tab{5}BJ(2,2)=0.0D0\\br \\tab{5}BJ(2,3)=0.0D0\\br \\tab{5}BJ(3,1)=0.0D0\\br \\tab{5}BJ(3,2)=1.0D0\\br \\tab{5}BJ(3,3)=0.0D0\\br \\tab{5}RETURN\\br \\tab{5}END\\br \\tab{5}SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)\\br \\tab{5}DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)\\br \\tab{5}INTEGER N\\br \\tab{5}BCEP(1)=0.0D0\\br \\tab{5}BCEP(2)=0.0D0\\br \\tab{5}BCEP(3)=0.0D0\\br \\tab{5}RETURN\\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 -3159) +(-82 -3201) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs, needed for NAG routines e04dgf, e04ucf, for example: \\blankline \\tab{5}SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)\\br \\tab{5}DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)\\br \\tab{5}INTEGER N,IUSER(*),MODE,NSTATE\\br \\tab{5}OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)\\br \\tab{4}&+(-1.0D0*X(2)*X(6))\\br \\tab{5}OBJGRD(1)=X(7)\\br \\tab{5}OBJGRD(2)=-1.0D0*X(6)\\br \\tab{5}OBJGRD(3)=X(8)+(-1.0D0*X(7))\\br \\tab{5}OBJGRD(4)=X(9)\\br \\tab{5}OBJGRD(5)=-1.0D0*X(8)\\br \\tab{5}OBJGRD(6)=-1.0D0*X(2)\\br \\tab{5}OBJGRD(7)=(-1.0D0*X(3))+X(1)\\br \\tab{5}OBJGRD(8)=(-1.0D0*X(5))+X(3)\\br \\tab{5}OBJGRD(9)=X(4)\\br \\tab{5}RETURN\\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 -3159) +(-83 -3201) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs, which take an expression in X(1) \\spad{..} X(NDIM) and produce a real function of the form: \\blankline \\tab{5}DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)\\br \\tab{5}DOUBLE PRECISION X(NDIM)\\br \\tab{5}INTEGER NDIM\\br \\tab{5}FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*\\br \\tab{4}&X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)\\br \\tab{5}RETURN\\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 -3159) +(-84 -3201) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs, needed for NAG routine e04fdf, for example: \\blankline \\tab{5}SUBROUTINE LSFUN1(M,N,XC,FVECC)\\br \\tab{5}DOUBLE PRECISION FVECC(M),XC(N)\\br \\tab{5}INTEGER I,M,N\\br \\tab{5}FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(\\br \\tab{4}&XC(3)+15.0D0*XC(2))\\br \\tab{5}FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X\\br \\tab{4}&C(3)+7.0D0*XC(2))\\br \\tab{5}FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666\\br \\tab{4}&66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))\\br \\tab{5}FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X\\br \\tab{4}&C(3)+3.0D0*XC(2))\\br \\tab{5}FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC\\br \\tab{4}&(2)+1.0D0)/(XC(3)+2.2D0*XC(2))\\br \\tab{5}FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X\\br \\tab{4}&C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))\\br \\tab{5}FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142\\br \\tab{4}&85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))\\br \\tab{5}FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999\\br \\tab{4}&99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999\\br \\tab{4}&99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666\\br \\tab{4}&67D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999\\br \\tab{4}&999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)\\br \\tab{4}&+XC(2))\\br \\tab{5}FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333\\br \\tab{4}&3333D0)/(XC(3)+XC(2))\\br \\tab{5}FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X\\br \\tab{4}&C(2))\\br \\tab{5}FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3\\br \\tab{4}&)+XC(2))\\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 -3159) +(-85 -3201) ((|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,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER\\br \\tab{4}&,USER)\\br \\tab{5}DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)\\br \\tab{5}INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE\\br \\tab{5}IF(NEEDC(1).GT.0)THEN\\br \\tab{7}C(1)=X(6)**2+X(1)**2\\br \\tab{7}CJAC(1,1)=2.0D0*X(1)\\br \\tab{7}CJAC(1,2)=0.0D0\\br \\tab{7}CJAC(1,3)=0.0D0\\br \\tab{7}CJAC(1,4)=0.0D0\\br \\tab{7}CJAC(1,5)=0.0D0\\br \\tab{7}CJAC(1,6)=2.0D0*X(6)\\br \\tab{5}ENDIF\\br \\tab{5}IF(NEEDC(2).GT.0)THEN\\br \\tab{7}C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2\\br \\tab{7}CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)\\br \\tab{7}CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))\\br \\tab{7}CJAC(2,3)=0.0D0\\br \\tab{7}CJAC(2,4)=0.0D0\\br \\tab{7}CJAC(2,5)=0.0D0\\br \\tab{7}CJAC(2,6)=0.0D0\\br \\tab{5}ENDIF\\br \\tab{5}IF(NEEDC(3).GT.0)THEN\\br \\tab{7}C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2\\br \\tab{7}CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)\\br \\tab{7}CJAC(3,2)=2.0D0*X(2)\\br \\tab{7}CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))\\br \\tab{7}CJAC(3,4)=0.0D0\\br \\tab{7}CJAC(3,5)=0.0D0\\br \\tab{7}CJAC(3,6)=0.0D0\\br \\tab{5}ENDIF\\br \\tab{5}RETURN\\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 -3159) +(-86 -3201) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs, needed for NAG routines c05nbf, c05ncf. These represent vectors of functions of X(i) and look like: \\blankline \\tab{5}SUBROUTINE FCN(N,X,FVEC,IFLAG) \\tab{5}DOUBLE PRECISION X(N),FVEC(N) \\tab{5}INTEGER N,IFLAG \\tab{5}FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 \\tab{5}FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. \\tab{4}&0D0 \\tab{5}FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. \\tab{4}&0D0 \\tab{5}FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. \\tab{4}&0D0 \\tab{5}FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. \\tab{4}&0D0 \\tab{5}FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. \\tab{4}&0D0 \\tab{5}FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. \\tab{4}&0D0 \\tab{5}FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. \\tab{4}&0D0 \\tab{5}FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+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 -3159) +(-87 -3201) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs, needed for NAG routine d03eef, for example: \\blankline \\tab{5}SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)\\br \\tab{5}DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI\\br \\tab{5}ALPHA=DSIN(X)\\br \\tab{5}BETA=Y\\br \\tab{5}GAMMA=X*Y\\br \\tab{5}DELTA=DCOS(X)*DSIN(Y)\\br \\tab{5}EPSOLN=Y+X\\br \\tab{5}PHI=X\\br \\tab{5}PSI=Y\\br \\tab{5}RETURN\\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 -3159) +(-88 -3201) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs, needed for NAG routine d03eef, for example: \\blankline \\tab{5} SUBROUTINE BNDY(X,Y,A,B,C,IBND)\\br \\tab{5} DOUBLE PRECISION A,B,C,X,Y\\br \\tab{5} INTEGER IBND\\br \\tab{5} IF(IBND.EQ.0)THEN\\br \\tab{7} A=0.0D0\\br \\tab{7} B=1.0D0\\br \\tab{7} C=-1.0D0*DSIN(X)\\br \\tab{5} ELSEIF(IBND.EQ.1)THEN\\br \\tab{7} A=1.0D0\\br \\tab{7} B=0.0D0\\br \\tab{7} C=DSIN(X)*DSIN(Y)\\br \\tab{5} ELSEIF(IBND.EQ.2)THEN\\br \\tab{7} A=1.0D0\\br \\tab{7} B=0.0D0\\br \\tab{7} C=DSIN(X)*DSIN(Y)\\br \\tab{5} ELSEIF(IBND.EQ.3)THEN\\br \\tab{7} A=0.0D0\\br \\tab{7} B=1.0D0\\br \\tab{7} C=-1.0D0*DSIN(Y)\\br \\tab{5} ENDIF\\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 -3159) +(-89 -3201) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs, needed for NAG routine d02gbf, for example: \\blankline \\tab{5}SUBROUTINE FCNF(X,F)\\br \\tab{5}DOUBLE PRECISION X\\br \\tab{5}DOUBLE PRECISION F(2,2)\\br \\tab{5}F(1,1)=0.0D0\\br \\tab{5}F(1,2)=1.0D0\\br \\tab{5}F(2,1)=0.0D0\\br \\tab{5}F(2,2)=-10.0D0\\br \\tab{5}RETURN\\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 -3159) +(-90 -3201) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs, needed for NAG routine d02gbf, for example: \\blankline \\tab{5}SUBROUTINE FCNG(X,G)\\br \\tab{5}DOUBLE PRECISION G(*),X\\br \\tab{5}G(1)=0.0D0\\br \\tab{5}G(2)=0.0D0\\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 -3159) +(-91 -3201) ((|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 FCN(X,Z,F)\\br \\tab{5}DOUBLE PRECISION F(*),X,Z(*)\\br \\tab{5}F(1)=DTAN(Z(3))\\br \\tab{5}F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)\\br \\tab{4}&**2))/(Z(2)*DCOS(Z(3)))\\br \\tab{5}F(3)=-0.03199999999999999D0/(X*Z(2)**2)\\br \\tab{5}RETURN\\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 -3159) +(-92 -3201) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs, needed for NAG routine d02kef, for example: \\blankline \\tab{5}SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)\\br \\tab{5}DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)\\br \\tab{5}YL(1)=XL\\br \\tab{5}YL(2)=2.0D0\\br \\tab{5}YR(1)=1.0D0\\br \\tab{5}YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))\\br \\tab{5}RETURN\\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 -3159) +(-93 -3201) ((|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,Y,COUNT,M,N,RESULT,FORWRD)\\br \\tab{5}DOUBLE PRECISION Y(N),RESULT(M,N),XSOL\\br \\tab{5}INTEGER M,N,COUNT\\br \\tab{5}LOGICAL FORWRD\\br \\tab{5}DOUBLE PRECISION X02ALF,POINTS(8)\\br \\tab{5}EXTERNAL X02ALF\\br \\tab{5}INTEGER I\\br \\tab{5}POINTS(1)=1.0D0\\br \\tab{5}POINTS(2)=2.0D0\\br \\tab{5}POINTS(3)=3.0D0\\br \\tab{5}POINTS(4)=4.0D0\\br \\tab{5}POINTS(5)=5.0D0\\br \\tab{5}POINTS(6)=6.0D0\\br \\tab{5}POINTS(7)=7.0D0\\br \\tab{5}POINTS(8)=8.0D0\\br \\tab{5}COUNT=COUNT+1\\br \\tab{5}DO 25001 I=1,N\\br \\tab{7} RESULT(COUNT,I)=Y(I)\\br 25001 CONTINUE\\br \\tab{5}IF(COUNT.EQ.M)THEN\\br \\tab{7}IF(FORWRD)THEN\\br \\tab{9}XSOL=X02ALF()\\br \\tab{7}ELSE\\br \\tab{9}XSOL=-X02ALF()\\br \\tab{7}ENDIF\\br \\tab{5}ELSE\\br \\tab{7} XSOL=POINTS(COUNT)\\br \\tab{5}ENDIF\\br \\tab{5}END"))) NIL NIL -(-94 -3159) +(-94 -3201) ((|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 G(X,Y)\\br \\tab{5}DOUBLE PRECISION X,Y(*)\\br \\tab{5}G=X+Y(1)\\br \\tab{5}RETURN\\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 (-95 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, \\spad{m)}} returns \\spad{[w, eq, \\spad{lw,} lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor, and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = \\spad{M} \\spad{y},} then \\spad{[$y_j',y_j'',...,y_j^{(n)}$] = $A_j \\spad{y$}} for all j's.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, \\spad{m)}} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = \\spad{M} \\spad{w}.}"))) NIL -((|HasCategory| |#1| (QUOTE (-367)))) +((|HasCategory| |#1| (QUOTE (-368)))) (-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(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} every?(x+->(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|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:ArrayStack INT:= arrayStack [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\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([x,y,...,z]) creates an array stack with first (top)} \\indented{1}{element \\spad{x,} second element y,...,and last element \\spad{z.}} \\blankline \\spad{E} c:ArrayStack INT:= arrayStack [1,2,3,4,5]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) (-97 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x.}")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x.}")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x.}")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x.}")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x.}")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x.}"))) NIL @@ -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,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,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(n)} sets the value of the steps for increasing and decreasing the button values. \\axiom{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\"."))) -((-4600 . T)) +((-4602 . 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, For example, 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 < \\spad{b} or a = \\spad{b)}} does not necessarily imply \\spad{b} \\spad{D}} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4600 . T) ((-4602 "*") . T) (-4601 . T) (-4597 . T) (-4595 . T) (-4594 . T) (-4593 . T) (-4598 . T) (-4592 . T) (-4591 . T) (-4590 . T) (-4589 . T) (-4588 . T) (-4596 . T) (-4599 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4587 . T) (-3367 . T)) +((-4602 . T) ((-4604 "*") . T) (-4603 . T) (-4599 . T) (-4597 . T) (-4596 . T) (-4595 . T) (-4600 . T) (-4594 . T) (-4593 . T) (-4592 . T) (-4591 . T) (-4590 . T) (-4598 . T) (-4601 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4589 . T) (-3410 . 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, \\spad{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.}"))) -((-4597 . T)) +((-4599 . T)) NIL (-102) ((|constructor| (NIL "This package provides a functions to support a web server for the new Axiom Browser functions."))) @@ -354,8 +354,8 @@ 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!(t,p,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 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}{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)$T1 \\spad{X} setleaves!(t2,[1,2,3,4]::List(Integer)) \\spad{X} adder3(i:Integer,j:Integer,k:Integer):List Integer \\spad{==} [i+j,j+k] \\spad{X} mapDown!(t2,4::INT,adder3) \\spad{X} \\spad{t2}") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\indented{1}{mapDown!(t,p,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{:=} f(p,x). The mapDown!(l,q,f) and} \\indented{1}{mapDown!(r,q,f) are evaluated for the left and right subtrees} \\indented{1}{l and \\spad{r} of \\spad{t.}} \\blankline \\spad{X} T1:=BalancedBinaryTree Integer \\spad{X} t2:=balancedBinaryTree(4, 0)$T1 \\spad{X} setleaves!(t2,[1,2,3,4]::List(Integer)) \\spad{X} adder(i:Integer,j:Integer):Integer \\spad{==} i+j \\spad{X} mapDown!(t2,4::INT,adder) \\spad{X} \\spad{t2}")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\indented{1}{mapUp!(t,t1,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 \\spad{by}} \\indented{1}{f(l,r,l1,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)$T1 \\spad{X} setleaves!(t2,[1,2,3,4]::List(Integer)) \\spad{X} adder4(i:INT,j:INT,k:INT,l:INT):INT \\spad{==} i+j+k+l \\spad{X} mapUp!(t2,t2,adder4) \\spad{X} \\spad{t2}") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\indented{1}{mapUp!(t,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 \\spad{by}} \\indented{1}{f(l,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)$T1 \\spad{X} setleaves!(t2,[1,2,3,4]::List(Integer)) \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} mapUp!(t2,adder) \\spad{X} \\spad{t2}")) (|setleaves!| (($ $ (|List| |#1|)) "\\indented{1}{setleaves!(t, \\spad{ls)} sets the leaves of \\spad{t} in left-to-right order} \\indented{1}{to the elements of ls.} \\blankline \\spad{X} t1:=balancedBinaryTree(4, 0) \\spad{X} setleaves!(t1,[1,2,3,4])")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\indented{1}{balancedBinaryTree(n, \\spad{s)} creates a balanced binary tree with} \\indented{1}{n nodes each with value \\spad{s.}} \\blankline \\spad{X} balancedBinaryTree(4, 0)"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) (-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=[x1,y1], the left-middle point b=[x2,y2],} \\indented{1}{the right-middle point c=[x3,y3] and an endpoint d=[x4,y4]} \\indented{1}{f(t) \\spad{==} \\spad{[(1-t)^3} \\spad{x1} + 3t(1-t)^2 \\spad{x2} + 3t^2 (1-t) \\spad{x3} + \\spad{t^3} x4,} \\indented{10}{(1-t)^3 \\spad{y1} + 3t(1-t)^2 \\spad{y2} + 3t^2 (1-t) \\spad{y3} + \\spad{t^3} y4]} \\blankline \\spad{X} n:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0]) \\spad{X} [n(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=[x1,y1], a middle point b=[x2,y2],} \\indented{1}{and an endpoint c=[x3,y3]} \\indented{1}{f(t) \\spad{==} \\spad{[(1-t)^2} \\spad{x1} + 2t(1-t) \\spad{x2} + \\spad{t^2} x3,} \\indented{10}{(1-t)^2 \\spad{y1} + 2t(1-t) \\spad{y2} + \\spad{t^2} y3]} \\blankline \\spad{X} n:=quadraticBezier([2.0,2.0],[4.0,4.0],[6.0,2.0]) \\spad{X} [n(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=[x1,y1] and an endpoint b=[x2,y2]} \\indented{1}{f(t) \\spad{==} \\spad{[(1-t)*x1} + t*x2, \\spad{(1-t)*y1} + t*y2]} \\blankline \\spad{X} n:=linearBezier([2.0,2.0],[4.0,4.0]) \\spad{X} [n(t/10.0) for \\spad{t} in 0..10 by 1]"))) NIL @@ -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 (-4602 "*")))) +((|HasAttribute| |#1| (QUOTE (-4604 "*")))) (-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"))) -((-4600 . T)) +((-4602 . 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 u.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag u.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements x,y,...,z.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -374,20 +374,20 @@ 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 u.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag u.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements x,y,...,z.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL (-112) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\indented{1}{binary(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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-571) (QUOTE (-909))) (|HasCategory| (-571) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-571) (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-151))) (|HasCategory| (-571) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-571) (QUOTE (-1027))) (|HasCategory| (-571) (QUOTE (-820))) (|HasCategory| (-571) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-1143))) (|HasCategory| (-571) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-571) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-571) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-571) (QUOTE (-226))) (|HasCategory| (-571) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-571) (LIST (QUOTE -526) (QUOTE (-1169)) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -282) (QUOTE (-571)) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-302))) (|HasCategory| (-571) (QUOTE (-553))) (|HasCategory| (-571) (QUOTE (-847))) (-1831 (|HasCategory| (-571) (QUOTE (-820))) (|HasCategory| (-571) (QUOTE (-847)))) (|HasCategory| (-571) (LIST (QUOTE -633) (QUOTE (-571)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-909)))) (|HasCategory| (-571) (QUOTE (-149))))) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-572) (QUOTE (-910))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-572) (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-151))) (|HasCategory| (-572) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-572) (QUOTE (-1028))) (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1144))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-227))) (|HasCategory| (-572) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-572) (LIST (QUOTE -527) (QUOTE (-1170)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -305) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -283) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-303))) (|HasCategory| (-572) (QUOTE (-554))) (|HasCategory| (-572) (QUOTE (-848))) (-1841 (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (QUOTE (-848)))) (|HasCategory| (-572) (LIST (QUOTE -634) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (|HasCategory| (-572) (QUOTE (-149))))) (-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 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}"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-121) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-121) (QUOTE (-847))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-121) (QUOTE (-1097))) (-12 (|HasCategory| (-121) (LIST (QUOTE -304) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1097))))) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-121) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-121) (QUOTE (-848))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-121) (QUOTE (-1098))) (-12 (|HasCategory| (-121) (LIST (QUOTE -305) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1098))))) (-115) ((|constructor| (NIL "This package provides an interface to the Blas library (level 1)")) (|zaxpy| (((|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|Complex| (|DoubleFloat|)) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) "\\spad{zaxpy(n,da,x,incx,y,incy)} computes a \\spad{y} = a*x + \\spad{y} for each of the chosen elements of the vectors \\spad{x} and \\spad{y} and a constant multiplier a Note that the vector \\spad{y} is modified with the results. \\blankline \\spad{X} a:PRIMARR(COMPLEX(DFLOAT)) \\spad{X} a:=[[3.+4.*\\%i, -4.+5.*\\%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*\\%i]] \\spad{X} b:PRIMARR(COMPLEX(DFLOAT)) \\spad{X} b:=[[3.+4.*\\%i, -4.+5.*\\%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*\\%i]] \\spad{X} zaxpy(3,2.0,a,1,b,1) \\spad{X} b:=[[3.+4.*\\%i, -4.+5.*\\%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*\\%i]] \\spad{X} zaxpy(5,2.0,a,1,b,1) \\spad{X} b:=[[3.+4.*\\%i, -4.+5.*\\%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*\\%i]] \\spad{X} zaxpy(3,2.0,a,3,b,3) \\spad{X} b:=[[3.+4.*\\%i, -4.+5.*\\%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*\\%i]] \\spad{X} zaxpy(4,2.0,a,2,b,2)")) (|izamax| (((|Integer|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) "\\spad{izamax computes} the largest absolute value of the elements of the array and returns the index of the first instance of the maximum. \\blankline \\spad{X} a:PRIMARR(COMPLEX(DFLOAT)) \\spad{X} a:=[[3.+4.*\\%i,-4.+5.*\\%i,5.+6.*\\%i,7.-8.*\\%i,-9.-2.*\\%i]] \\spad{X} izamax(5,a,1) \\spad{--} should be 3 \\spad{X} izamax(0,a,1) \\spad{--} should be \\spad{-1} \\spad{X} izamax(5,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} izamax(3,a,1) \\spad{--} should be 2 \\spad{X} izamax(3,a,2) \\spad{--} should be 1")) (|isamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|Float|)) (|Integer|)) "\\spad{isamax computes} the largest absolute value of the elements of the array and returns the index of the first instance of the maximum. \\blankline \\spad{X} a:PRIMARR(FLOAT):=[[3.0, 4.0, -3.0, 5.0, -1.0]] \\spad{X} isamax(5,a,1) \\spad{--} should be 3 \\spad{X} isamax(3,a,1) \\spad{--} should be 1 \\spad{X} isamax(0,a,1) \\spad{--} should be \\spad{-1} \\spad{X} isamax(-5,a,1) \\spad{--} should be \\spad{-1} \\spad{X} isamax(5,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} isamax(5,a,2) \\spad{--} should be 0 \\spad{X} isamax(1,a,0) \\spad{--} should be \\spad{-1} \\spad{X} isamax(1,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} a:PRIMARR(FLOAT):=[[3.0, 4.0, -3.0, -5.0, -1.0]] \\spad{X} isamax(5,a,1) \\spad{--} should be 3")) (|idamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|DoubleFloat|)) (|Integer|)) "\\spad{idamax computes} the largest absolute value of the elements of the array and returns the index of the first instance of the maximum. \\blankline \\spad{X} a:PRIMARR(DFLOAT):=[[3.0, 4.0, -3.0, 5.0, -1.0]] \\spad{X} idamax(5,a,1) \\spad{--} should be 3 \\spad{X} idamax(3,a,1) \\spad{--} should be 1 \\spad{X} idamax(0,a,1) \\spad{--} should be \\spad{-1} \\spad{X} idamax(-5,a,1) \\spad{--} should be \\spad{-1} \\spad{X} idamax(5,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} idamax(5,a,2) \\spad{--} should be 0 \\spad{X} idamax(1,a,0) \\spad{--} should be \\spad{-1} \\spad{X} idamax(1,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} a:PRIMARR(DFLOAT):=[[3.0, 4.0, -3.0, -5.0, -1.0]] \\spad{X} idamax(5,a,1) \\spad{--} should be 3")) (|icamax| (((|Integer|) (|Integer|) (|PrimitiveArray| (|Complex| (|Float|))) (|Integer|)) "\\spad{icamax computes} the largest absolute value of the elements of the array and returns the index of the first instance of the maximum \\blankline \\spad{X} a:PRIMARR(COMPLEX(FLOAT)) \\spad{X} a:=[[3.+4.*\\%i,-4.+5.*\\%i,5.+6.*\\%i,7.-8.*\\%i,-9.-2.*\\%i]] \\spad{X} icamax(5,a,1) \\spad{--} should be 3 \\spad{X} icamax(0,a,1) \\spad{--} should be \\spad{-1} \\spad{X} icamax(5,a,-1) \\spad{--} should be \\spad{-1} \\spad{X} icamax(3,a,1) \\spad{--} should be 2 \\spad{X} icamax(3,a,2) \\spad{--} should be 1")) (|dznrm2| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) "\\spad{dznrm2 returns} the norm of a complex vector. It computes sqrt(sum(v*conjugate(v))) \\blankline \\spad{X} a:PRIMARR(COMPLEX(DFLOAT)) \\spad{X} a:=[[3.+4.*\\%i,-4.+5.*\\%i,5.+6.*\\%i,7.-8.*\\%i,-9.-2.*\\%i]] \\spad{X} dznrm2(5,a,1) \\spad{--} should be 18.028 \\spad{X} dznrm2(3,a,2) \\spad{--} should be 13.077 \\spad{X} dznrm2(3,a,1) \\spad{--} should be 11.269 \\spad{X} dznrm2(3,a,-1) \\spad{--} should be 0.0 \\spad{X} dznrm2(-3,a,-1) \\spad{--} should be 0.0 \\spad{X} dznrm2(1,a,1) \\spad{--} should be 5.0 \\spad{X} dznrm2(1,a,2) \\spad{--} should be 5.0")) (|dzasum| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|Complex| (|DoubleFloat|))) (|SingleInteger|)) "\\spad{dzasum takes} the sum over all of the array where each element of the array sum is the sum of the absolute value of the real part and the absolute value of the imaginary part of each array element: \\indented{3}{for \\spad{i} in array do sum = sum + (real(a(i)) + imag(a(i)))} \\blankline \\spad{X} d:PRIMARR(COMPLEX(DFLOAT)):=[[1.0+2.0*\\%i,-3.0+4.0*\\%i,5.0-6.0*\\%i]] \\spad{X} dzasum(3,d,1) \\spad{--} 21.0 \\spad{X} dzasum(3,d,2) \\spad{--} 14.0 \\spad{X} dzasum(-3,d,1) \\spad{--} 0.0")) (|dswap| (((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{dswap swaps} elements from the first vector with the second Note that the arrays are modified in place. \\blankline \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dy:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dswap(5,dx,1,dy,1) \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dy:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dswap(3,dx,2,dy,2) \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dy:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dswap(5,dx,1,dy,-1)")) (|dscal| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{dscal scales} each element of the vector by the scalar so dscal(n,da,dx,incx) = da*dx for \\spad{n} elements, incremented by incx Note that the \\spad{dx} array is modified in place. \\blankline \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dscal(6,2.0,dx,1) \\spad{X} \\spad{dx} \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]] \\spad{X} dscal(3,0.5,dx,1) \\spad{X} \\spad{dx}")) (|drot| (((|List| (|PrimitiveArray| (|DoubleFloat|))) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{drot computes} a 2D plane Givens rotation spanned by two coordinate axes. It modifies the arrays in place. The call drot(n,dx,incx,dy,incy,c,s) has the \\spad{dx} array which contains the \\spad{y} axis locations and dy which contains the \\spad{y} axis locations. They are rotated in parallel where \\spad{c} is the cosine of the angle and \\spad{s} is the sine of the angle and \\spad{c^2+s^2} = 1 \\blankline \\spad{X} dx:PRIMARR(DFLOAT):=[[6,0, 1.0, 4.0, -1.0, -1.0]] \\spad{X} dy:PRIMARR(DFLOAT):=[[5.0, 1.0, -4.0, 4.0, -4.0]] \\spad{X} drot(5,dx,1,dy,1,0.707106781,0.707106781) \\spad{--} rotate by 45 degrees \\spad{X} \\spad{dx} \\spad{--} \\spad{dx} has been modified \\spad{X} dy \\spad{--} dy has been modified \\spad{X} drot(5,dx,1,dy,1,0.707106781,-0.707106781) \\spad{--} rotate by \\spad{-45} degrees \\spad{X} \\spad{dx} \\spad{--} \\spad{dx} has been modified \\spad{X} dy \\spad{--} dy has been modified")) (|drotg| (((|PrimitiveArray| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{drotg computes} a 2D plane Givens rotation spanned by two coordinate axes. \\blankline \\spad{X} a:MATRIX(DFLOAT):=[[6,5,0],[5,1,4],[0,4,3]] \\spad{X} drotg(elt(a,1,1),elt(a,1,2),0.0D0,0.0D0)")) (|dnrm2| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{dnrm2 takes} the norm of the vector, ||x|| \\blankline \\spad{X} a:PRIMARR(DFLOAT):=[[3.0, -4.0, 5.0, -7.0, 9.0]] \\spad{X} dnrm2(3,a,1) \\spad{--} 7.0710678118654755 = \\spad{sqrt(3.0^2} + \\spad{-4.0^2} + 5.0^2) \\spad{X} dnrm2(5,a,1) \\spad{--} 13.416407864998739 = sqrt(180.0) \\spad{X} dnrm2(3,a,2) \\spad{--} 10.72380529476361 = sqrt(115.0)")) (|ddot| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{ddot(n,x,incx,y,incy)} computes the vector dot product of elements from the vector \\spad{x} and the vector \\spad{y} If the indicies are negative the elements are taken relative to the far end of the vector. \\blankline \\spad{X} x:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0]] \\spad{X} y:PRIMARR(DFLOAT):=[[5.0,6.0,7.0,8.0,9.0]] \\spad{X} ddot(0,a,1,b,1) \\spad{--} handle 0 elements \\spad{==>} 0 \\spad{X} ddot(3,a,1,b,1) \\spad{--} (1,2,3) * (5,6,7) \\spad{==>} 38.0 \\spad{X} ddot(3,a,1,b,2) \\spad{--} increment = 2 in \\spad{b} (1,2,3) * (5,7,9) \\spad{==>} 46.0 \\spad{X} ddot(3,a,2,b,1) \\spad{--} increment = 2 in a (1,3,5) * (5,6,7) \\spad{==>} 58.0 \\spad{X} ddot(3,a,1,b,-2) \\spad{--} increment = \\spad{-2} in \\spad{b} (1,2,3) * (9,7,5) \\spad{==>} 38.0 \\spad{X} ddot(2,a,-2,b,1) \\spad{--} increment = \\spad{-2} in a (5,3,1) * (5,6,7) \\spad{==>} 50.0 \\spad{X} ddot(3,a,-2,b,-2) \\spad{--} (5,3,1) * (9,7,5) \\spad{==>} 71.0")) (|dcopy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{dcopy(n,x,incx,y,incy)} copies \\spad{y} from \\spad{x} for each of the chosen elements of the vectors \\spad{x} and \\spad{y} Note that the vector \\spad{y} is modified with the results. \\blankline \\spad{X} x:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0,6.0]] \\spad{X} y:PRIMARR(DFLOAT):=[[0.0,0.0,0.0,0.0,0.0,0.0]] \\spad{X} dcopy(6,x,1,y,1) \\spad{X} \\spad{y} \\spad{X} m:PRIMARR(DFLOAT):=[[1.0,2.0,3.0]] \\spad{X} n:PRIMARR(DFLOAT):=[[0.0,0.0,0.0,0.0,0.0,0.0]] \\spad{X} dcopy(3,m,1,n,2) \\spad{X} \\spad{n}")) (|daxpy| (((|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|DoubleFloat|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{daxpy(n,da,x,incx,y,incy)} computes a \\spad{y} = a*x + \\spad{y} for each of the chosen elements of the vectors \\spad{x} and \\spad{y} and a constant multiplier a Note that the vector \\spad{y} is modified with the results. \\blankline \\spad{X} x:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0,6.0]] \\spad{X} y:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0,6.0]] \\spad{X} daxpy(6,2.0,x,1,y,1) \\spad{X} \\spad{y} \\spad{X} m:PRIMARR(DFLOAT):=[[1.0,2.0,3.0]] \\spad{X} n:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0,6.0]] \\spad{X} daxpy(3,-2.0,m,1,n,2) \\spad{X} \\spad{n}")) (|dasum| (((|DoubleFloat|) (|SingleInteger|) (|PrimitiveArray| (|DoubleFloat|)) (|SingleInteger|)) "\\spad{dasum(n,array,incx)} computes the sum of \\spad{n} elements in \\spad{array} using a stride of \\spad{incx} \\blankline \\spad{X} dx:PRIMARR(DFLOAT):=[[1.0,2.0,3.0,4.0,5.0,6.0]] \\spad{X} dasum(6,dx,1) \\spad{X} dasum(3,dx,2)")) (|dcabs1| (((|DoubleFloat|) (|Complex| (|DoubleFloat|))) "\\spad{dcabs1(z)} computes \\spad{(+} (abs (realpart \\spad{z))} (abs (imagpart z))) \\blankline \\spad{X} t1:Complex DoubleFloat \\spad{:=} complex(1.0,0) \\spad{X} dcabs1(t1)"))) NIL @@ -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\\br \\tab{5}\\spad{r*(x*s) = (r*x)*s}")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = \\spad{x}}")) (|leftUnitary| ((|attribute|) "\\spad{1 * \\spad{x} = \\spad{x}}"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL (-121) ((|constructor| (NIL "\\spadtype{Boolean} is the elementary logic with 2 values: \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,b)} returns the logical implication of Boolean \\spad{a} and \\spad{b.}")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b.}")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b.}")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive or of Boolean \\spad{a} and \\spad{b.}")) (|or| (($ $ $) "\\spad{a or \\spad{b}} returns the logical inclusive or of Boolean \\spad{a} and \\spad{b.}")) (|and| (($ $ $) "\\spad{a and \\spad{b}} returns the logical and of Boolean \\spad{a} and \\spad{b.}")) (|not| (($ $) "\\spad{not \\spad{n}} returns the negation of \\spad{n.}")) (^ (($ $) "\\spad{^ \\spad{n}} returns the negation of \\spad{n.}")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -419,30 +419,30 @@ NIL (-122 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators, including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a}, \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one, and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of op. If \\spad{op} has an \"\\%diff\" property \\spad{f,} then applying a derivation \\spad{D} to op(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [foo1,...,foon] as the \"\\%diff\" property of op. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + \\spad{...} + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one, and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of op. If \\spad{op} has an \"\\%eval\" property \\spad{f,} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of op. If \\spad{op} has an \"\\%eval\" property \\spad{f,} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f.} If it has, then \\spad{f(a1,...,an)} is returned, and \"failed\" otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-847)))) +((|HasCategory| |#1| (QUOTE (-848)))) (-123) ((|constructor| (NIL "Basic system operators. A basic operator is an object that can be applied to a list of arguments from a set, the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, \\spad{l)}} sets the property list of \\spad{op} to \\spad{l.} Argument \\spad{op} is modified \"in place\", \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op, \\spad{s,} \\spad{v)}} attaches property \\spad{s} to op, and sets its value to \\spad{v.} Argument \\spad{op} is modified \"in place\", \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, \\spad{s)}} returns the value of property \\spad{s} if it is attached to op, and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op, \\spad{s)}} unattaches property \\spad{s} from op. Argument \\spad{op} is modified \"in place\", \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op, \\spad{s)}} attaches property \\spad{s} to op. Argument \\spad{op} is modified \"in place\", \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op, \\spad{s)}} tests if property \\spad{s} is attached to op.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op, \\spad{s)}} tests if the name of \\spad{op} is \\spad{s.}")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached, \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of op. If \\spad{op} has a \"\\%input\" property \\spad{f,} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of op. If \\spad{op} has a \"\\%display\" property \\spad{f,} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of op. If \\spad{op} has a \"\\%display\" property \\spad{f,} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached, and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to op. If \\spad{op1} and \\spad{op2} have the same name, and one of them has a \"\\%less?\" property \\spad{f,} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to op. If \\spad{op1} and \\spad{op2} have the same name, and one of them has an \"\\%equal?\" property \\spad{f,} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1} and \\spad{op2} should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, \\spad{n)}} attaches the weight \\spad{n} to op.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to op.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is n-ary, and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, \\spad{n)}} makes \\spad{f} into an n-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of op.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to op.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of op."))) NIL NIL -(-124 -3280 UP) +(-124 -3313 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p,} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-125 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} p-adic numbers are represented as sum(i = 0.., a[i] * p^i), where the a[i] lie in \\spad{-(p} - 1)/2,...,(p - 1)/2."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL (-126 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(i = k.., a[i] * p^i), where the a[i] lie in \\spad{-(p} - 1)/2,...,(p - 1)/2."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-125 |#1|) (QUOTE (-909))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-125 |#1|) (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-151))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-125 |#1|) (QUOTE (-1027))) (|HasCategory| (-125 |#1|) (QUOTE (-820))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-125 |#1|) (QUOTE (-1143))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| (-125 |#1|) (QUOTE (-226))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -526) (QUOTE (-1169)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -282) (LIST (QUOTE -125) (|devaluate| |#1|)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (QUOTE (-302))) (|HasCategory| (-125 |#1|) (QUOTE (-553))) (|HasCategory| (-125 |#1|) (QUOTE (-847))) (-1831 (|HasCategory| (-125 |#1|) (QUOTE (-820))) (|HasCategory| (-125 |#1|) (QUOTE (-847)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-909)))) (|HasCategory| (-125 |#1|) (QUOTE (-149))))) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-125 |#1|) (QUOTE (-910))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-125 |#1|) (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-151))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-125 |#1|) (QUOTE (-1028))) (|HasCategory| (-125 |#1|) (QUOTE (-821))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-125 |#1|) (QUOTE (-1144))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-125 |#1|) (QUOTE (-227))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -527) (QUOTE (-1170)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -305) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (LIST (QUOTE -283) (LIST (QUOTE -125) (|devaluate| |#1|)) (LIST (QUOTE -125) (|devaluate| |#1|)))) (|HasCategory| (-125 |#1|) (QUOTE (-303))) (|HasCategory| (-125 |#1|) (QUOTE (-554))) (|HasCategory| (-125 |#1|) (QUOTE (-848))) (-1841 (|HasCategory| (-125 |#1|) (QUOTE (-821))) (|HasCategory| (-125 |#1|) (QUOTE (-848)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-125 |#1|) (QUOTE (-910)))) (|HasCategory| (-125 |#1|) (QUOTE (-149))))) (-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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{b . right \\spad{:=} \\spad{b})} is equivalent to \\axiom{setright!(a,b)}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b})} is equivalent to \\axiom{setleft!(a,b)}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4601))) +((|HasAttribute| |#1| (QUOTE -4603))) (-128 S) ((|constructor| (NIL "A binary-recursive aggregate has 0, 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x.}")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b.}")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{b . right \\spad{:=} \\spad{b})} is equivalent to \\axiom{setright!(a,b)}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b})} is equivalent to \\axiom{setleft!(a,b)}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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."))) -((-3348 . T)) +((-3389 . T)) NIL (-129 UP) ((|constructor| (NIL "This package has no description")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer, \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart, \\spad{false} else. If \\spad{noLinears} is \\spad{true}, we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart, \\spad{false} is inconclusive."))) @@ -454,15 +454,15 @@ NIL NIL (-131 S) ((|constructor| (NIL "BinarySearchTree(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(S) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\indented{1}{split(x,b) splits binary tree \\spad{b} into two trees, one with elements} \\indented{1}{greater than \\spad{x,} the other with elements less than \\spad{x.}} \\blankline \\spad{X} t1:=binarySearchTree [1,2,3,4] \\spad{X} split(3,t1)")) (|insertRoot!| (($ |#1| $) "\\indented{1}{insertRoot!(x,b) inserts element \\spad{x} as a root of binary search tree \\spad{b.}} \\blankline \\spad{X} t1:=binarySearchTree [1,2,3,4] \\spad{X} insertRoot!(5,t1)")) (|insert!| (($ |#1| $) "\\indented{1}{insert!(x,b) inserts element \\spad{x} as leaves into binary search tree \\spad{b.}} \\blankline \\spad{X} t1:=binarySearchTree [1,2,3,4] \\spad{X} insert!(5,t1)")) (|binarySearchTree| (($ (|List| |#1|)) "\\indented{1}{binarySearchTree(l) is not documented} \\blankline \\spad{X} binarySearchTree [1,2,3,4]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) (-132 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{b}.")) (|or| (($ $ $) "\\spad{a or \\spad{b}} returns the logical or of bit aggregates \\axiom{a} and \\axiom{b}.")) (|and| (($ $ $) "\\spad{a and \\spad{b}} returns the logical and of bit aggregates \\axiom{a} and \\axiom{b}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{b}.")) (^ (($ $) "\\spad{^ \\spad{b}} returns the logical not of bit aggregate \\axiom{b}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{b}."))) NIL NIL (-133) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive-or of bit aggregates \\axiom{a} and \\axiom{b}.")) (|or| (($ $ $) "\\spad{a or \\spad{b}} returns the logical or of bit aggregates \\axiom{a} and \\axiom{b}.")) (|and| (($ $ $) "\\spad{a and \\spad{b}} returns the logical and of bit aggregates \\axiom{a} and \\axiom{b}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical nor of bit aggregates \\axiom{a} and \\axiom{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical nand of bit aggregates \\axiom{a} and \\axiom{b}.")) (^ (($ $) "\\spad{^ \\spad{b}} returns the logical not of bit aggregate \\axiom{b}.")) (|not| (($ $) "\\spad{not(b)} returns the logical not of bit aggregate \\axiom{b}."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL (-134 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right}, both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v}, a binary tree \\spad{left}, and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -470,16 +470,16 @@ NIL NIL (-135 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right}, both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v}, a binary tree \\spad{left}, and a binary tree \\spad{right}. \\blankline")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL (-136 S) ((|constructor| (NIL "BinaryTournament creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")) (|insert!| (($ |#1| $) "\\indented{1}{insert!(x,b) inserts element \\spad{x} as leaves into binary tournament \\spad{b.}} \\blankline \\spad{X} t1:=binaryTournament [1,2,3,4] \\spad{X} insert!(5,t1) \\spad{X} \\spad{t1}")) (|binaryTournament| (($ (|List| |#1|)) "\\indented{1}{binaryTournament(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]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) (-137 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| $) "\\indented{1}{binaryTree(l,v,r) creates a binary tree with} \\indented{1}{value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r.}} \\blankline \\spad{X} t1:=binaryTree([1,2,3]) \\spad{X} t2:=binaryTree([4,5,6]) \\spad{X} binaryTree(t1,[7,8,9],t2)") (($ |#1|) "\\indented{1}{binaryTree(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])"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) (-138) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property, \\spadignore{i.e.} \\tab{5}\\spad{ a+b = a+c \\spad{=>} \\spad{b=c} }.\\br This is formalised by the partial subtraction operator, which satisfies the Axioms\\br \\tab{5}\\spad{c = a+b \\spad{<=>} \\spad{c-b} = a}")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x, \\spad{y)}} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -490,32 +490,32 @@ NIL NIL (-140) ((|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 = \\spad{#X}} and \\spad{y = \\spad{#Y}} then\\br \\tab{5}\\spad{x+y = \\#(X+Y)} \\tab{5}disjoint union\\br \\tab{5}\\spad{x-y = \\#(X-Y)} \\tab{5}relative complement\\br \\tab{5}\\spad{x*y = \\#(X*Y)} \\tab{5}cartesian product\\br \\tab{5}\\spad{x**y = \\#(X**Y)} \\tab{4}\\spad{X**Y = \\spad{g|} g:Y->X} \\blankline The non-negative integers have a natural construction as cardinals\\br \\spad{0 = \\#\\{\\}}, \\spad{1 = \\{0\\}}, \\spad{2 = \\{0, 1\\}}, ..., \\spad{n = \\{i| 0 \\spad{<=} \\spad{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 \\spad{i} = Aleph(i+1)} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are\\br \\tab{5}\\spad{a = \\spad{#Z}} \\tab{5}countable infinity\\br \\tab{5}\\spad{c = \\spad{#R}} \\tab{5}the continuum\\br \\tab{5}\\spad{f = \\# \\spad{g} | g:[0,1]->R\\} \\blankline In this domain, these values are obtained using\\br \\tab{5}\\spad{a \\spad{:=} Aleph 0}, \\spad{c \\spad{:=} 2**a}, \\spad{f \\spad{:=} 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(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") $ $) "\\indented{1}{\\spad{x - \\spad{y}} returns an element \\spad{z} such that} \\indented{1}{\\spad{z+y=x} or \"failed\" if no such element exists.} \\blankline \\spad{X} c2:=2::CardinalNumber \\spad{X} \\spad{c2-c2} \\spad{X} A1:=Aleph 1 \\spad{X} \\spad{A1-c2}")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) \\spad{->} \\spad{D}} which is commutative."))) -(((-4602 "*") . T)) +(((-4604 "*") . T)) NIL -(-141 |minix| -3020 S T$) +(-141 |minix| -3465 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T.}")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts.}"))) NIL NIL -(-142 |minix| -3020 R) +(-142 |minix| -3465 R) ((|constructor| (NIL "CartesianTensor(minix,dim,R) provides Cartesian tensors with components belonging to a commutative ring \\spad{R.} These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\spad{%.}")) (|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|) $) "\\indented{1}{ravel(t) produces a list of components from a tensor such that} \\indented{3}{\\spad{unravel(ravel(t)) = t}.} \\blankline \\spad{X} n:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] \\spad{X} tn:CartesianTensor(1,2,Integer):=n \\spad{X} ravel \\spad{tn}")) (|leviCivitaSymbol| (($) "\\indented{1}{leviCivitaSymbol() is the rank \\spad{dim} tensor defined \\spad{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| (($) "\\indented{1}{kroneckerDelta() is the rank 2 tensor defined \\spad{by}} \\indented{4}{\\spad{kroneckerDelta()(i,j)}} \\indented{7}{\\spad{= 1\\space{2}if \\spad{i} = \\spad{j}}} \\indented{7}{\\spad{= 0 if\\space{2}i \\spad{\\^=} \\spad{j}}} \\blankline \\spad{X} delta:CartesianTensor(1,2,Integer):=kroneckerDelta()")) (|reindex| (($ $ (|List| (|Integer|))) "\\indented{1}{reindex(t,[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 \\spad{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):=n \\spad{X} p:=product(tn,tn) \\spad{X} reindex(p,[4,3,2,1])")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{transpose(t,i,j) exchanges the \\spad{i}-th and \\spad{j}-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 \\spad{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):=m \\spad{X} tn:CartesianTensor(1,2,Integer):=[tm,tm] \\spad{X} transpose(tn,1,2)") (($ $) "\\indented{1}{transpose(t) exchanges the first and last indices of \\spad{t.}} \\indented{1}{For example, if \\spad{r = transpose(t)} for a rank 4} \\indented{1}{tensor \\spad{t,} then \\spad{r} is the rank 4 tensor given \\spad{by}} \\indented{5}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.} \\blankline \\spad{X} m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] \\spad{X} Tm:CartesianTensor(1,2,Integer):=m \\spad{X} transpose(Tm)")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\indented{1}{contract(t,i,j) is the contraction of tensor \\spad{t} which} \\indented{1}{sums along the \\spad{i}-th and \\spad{j}-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 \\spad{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):=m \\spad{X} v:DirectProduct(2,Integer):=directProduct [3,4] \\spad{X} Tv:CartesianTensor(1,2,Integer):=v \\spad{X} Tmv:=contract(Tm,2,1)") (($ $ (|Integer|) $ (|Integer|)) "\\indented{1}{contract(t,i,s,j) is the inner product of tenors \\spad{s} and \\spad{t}} \\indented{1}{which sums along the \\spad{k1}-th index of} \\indented{1}{t and the \\spad{k2}-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 \\spad{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):=m \\spad{X} v:DirectProduct(2,Integer):=directProduct [3,4] \\spad{X} Tv:CartesianTensor(1,2,Integer):=v \\spad{X} Tmv:=contract(Tm,2,Tv,1)")) (* (($ $ $) "\\indented{1}{s*t is the inner product of the tensors \\spad{s} and \\spad{t} which contracts} \\indented{1}{the last index of \\spad{s} with the first index of \\spad{t,} that is,} \\indented{5}{\\spad{t*s = contract(t,rank \\spad{t,} \\spad{s,} 1)}} \\indented{5}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} \\indented{1}{This is compatible with the use of \\spad{M*v} to denote} \\indented{1}{the matrix-vector inner product.} \\blankline \\spad{X} m:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] \\spad{X} Tm:CartesianTensor(1,2,Integer):=m \\spad{X} v:DirectProduct(2,Integer):=directProduct [3,4] \\spad{X} Tv:CartesianTensor(1,2,Integer):=v \\spad{X} Tm*Tv")) (|product| (($ $ $) "\\indented{1}{product(s,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}{s and \\spad{t,} then \\spad{r} is a rank 4 tensor given \\spad{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):=m \\spad{X} n:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]] \\spad{X} Tn:CartesianTensor(1,2,Integer):=n \\spad{X} Tmn:=product(Tm,Tn)")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\indented{1}{elt(t,[i1,...,iN]) gives a component of a rank \\spad{N} tensor.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} tm:CartesianTensor(1,2,Integer):=[tv,tv] \\spad{X} tn:CartesianTensor(1,2,Integer):=[tm,tm] \\spad{X} tp:CartesianTensor(1,2,Integer):=[tn,tn] \\spad{X} tq:CartesianTensor(1,2,Integer):=[tp,tp] \\spad{X} elt(tq,[2,2,2,2,2])") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{elt(t,i,j,k,l) gives a component of a rank 4 tensor.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} tm:CartesianTensor(1,2,Integer):=[tv,tv] \\spad{X} tn:CartesianTensor(1,2,Integer):=[tm,tm] \\spad{X} tp:CartesianTensor(1,2,Integer):=[tn,tn] \\spad{X} elt(tp,2,2,2,2) \\spad{X} tp[2,2,2,2]") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{elt(t,i,j,k) gives a component of a rank 3 tensor.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} tm:CartesianTensor(1,2,Integer):=[tv,tv] \\spad{X} tn:CartesianTensor(1,2,Integer):=[tm,tm] \\spad{X} elt(tn,2,2,2) \\spad{X} tn[2,2,2]") ((|#3| $ (|Integer|) (|Integer|)) "\\indented{1}{elt(t,i,j) gives a component of a rank 2 tensor.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} tm:CartesianTensor(1,2,Integer):=[tv,tv] \\spad{X} elt(tm,2,2) \\spad{X} tm[2,2]") ((|#3| $ (|Integer|)) "\\indented{1}{elt(t,i) gives a component of a rank 1 tensor.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} elt(tv,2) \\spad{X} tv[2]") ((|#3| $) "\\indented{1}{elt(t) gives the component of a rank 0 tensor.} \\blankline \\spad{X} \\spad{tv:CartesianTensor(1,2,Integer):=8} \\spad{X} elt(tv) \\spad{X} tv[]")) (|rank| (((|NonNegativeInteger|) $) "\\indented{1}{rank(t) returns the tensorial rank of \\spad{t} (that is, the} \\indented{1}{number of indices).\\space{2}This is the same as the graded module} \\indented{1}{degree.} \\blankline \\spad{X} CT:=CARTEN(1,2,Integer) \\spad{X} \\spad{t0:CT:=8} \\spad{X} rank \\spad{t0}")) (|coerce| (($ (|List| $)) "\\indented{1}{coerce([t_1,...,t_dim]) allows tensors to be constructed} \\indented{1}{using lists.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v \\spad{X} tm:CartesianTensor(1,2,Integer):=[tv,tv]") (($ (|List| |#3|)) "\\indented{1}{coerce([r_1,...,r_dim]) allows tensors to be constructed} \\indented{1}{using lists.} \\blankline \\spad{X} v:=[2,3] \\spad{X} tv:CartesianTensor(1,2,Integer):=v") (($ (|SquareMatrix| |#2| |#3|)) "\\indented{1}{coerce(m) views a matrix as a rank 2 tensor.} \\blankline \\spad{X} v:SquareMatrix(2,Integer):=[[1,2],[3,4]] \\spad{X} tv:CartesianTensor(1,2,Integer):=v") (($ (|DirectProduct| |#2| |#3|)) "\\indented{1}{coerce(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):=v"))) NIL NIL (-143) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which alphanumeric? is true.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which alphabetic? is true.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which lowerCase? is true.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which upperCase? is true.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which hexDigit? is true.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which digit? is 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.}"))) -((-4600 . T) (-4590 . T) (-4601 . T)) -((|HasCategory| (-148) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-148) (QUOTE (-373))) (|HasCategory| (-148) (QUOTE (-847))) (|HasCategory| (-148) (QUOTE (-1097))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-373)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))))) +((-4602 . T) (-4592 . T) (-4603 . T)) +((|HasCategory| (-148) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-148) (QUOTE (-374))) (|HasCategory| (-148) (QUOTE (-848))) (|HasCategory| (-148) (QUOTE (-1098))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-374)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))))) (-144 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], \\spad{d]}} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the qi's.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the qi's.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for q1,...,qn."))) NIL NIL (-145) ((|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(n, \\spad{m)} creates a new uninitialized \\spad{n} by \\spad{m} matrix.} \\blankline \\spad{X} t1:CDFMAT:=qnew(3,4)"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-170 (-216)) (QUOTE (-1097))) (-12 (|HasCategory| (-170 (-216)) (LIST (QUOTE -304) (LIST (QUOTE -170) (QUOTE (-216))))) (|HasCategory| (-170 (-216)) (QUOTE (-1097)))) (|HasCategory| (-170 (-216)) (QUOTE (-302))) (|HasCategory| (-170 (-216)) (QUOTE (-561))) (|HasAttribute| (-170 (-216)) (QUOTE (-4602 "*"))) (|HasCategory| (-170 (-216)) (QUOTE (-173))) (|HasCategory| (-170 (-216)) (QUOTE (-367)))) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-171 (-217)) (QUOTE (-1098))) (-12 (|HasCategory| (-171 (-217)) (LIST (QUOTE -305) (LIST (QUOTE -171) (QUOTE (-217))))) (|HasCategory| (-171 (-217)) (QUOTE (-1098)))) (|HasCategory| (-171 (-217)) (QUOTE (-303))) (|HasCategory| (-171 (-217)) (QUOTE (-562))) (|HasAttribute| (-171 (-217)) (QUOTE (-4604 "*"))) (|HasCategory| (-171 (-217)) (QUOTE (-174))) (|HasCategory| (-171 (-217)) (QUOTE (-368)))) (-146) ((|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(l) converts the list \\spad{l} to a vector.} \\blankline \\spad{X} t1:List(Complex(DoubleFloat)):=[1+2*\\%i,3+4*\\%i,-5-6*\\%i] \\spad{X} t2:CDFVEC:=vector(t1)")) (|qnew| (($ (|Integer|)) "\\indented{1}{qnew(n) creates a new uninitialized vector of length \\spad{n.}} \\blankline \\spad{X} t1:CDFVEC:=qnew 7"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-170 (-216)) (QUOTE (-1097))) (|HasCategory| (-170 (-216)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-170 (-216)) (QUOTE (-847))) (-1831 (|HasCategory| (-170 (-216)) (QUOTE (-847))) (|HasCategory| (-170 (-216)) (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-170 (-216)) (QUOTE (-25))) (|HasCategory| (-170 (-216)) (QUOTE (-23))) (|HasCategory| (-170 (-216)) (QUOTE (-21))) (|HasCategory| (-170 (-216)) (QUOTE (-721))) (|HasCategory| (-170 (-216)) (QUOTE (-1053))) (-12 (|HasCategory| (-170 (-216)) (QUOTE (-1008))) (|HasCategory| (-170 (-216)) (QUOTE (-1053)))) (-12 (|HasCategory| (-170 (-216)) (LIST (QUOTE -304) (LIST (QUOTE -170) (QUOTE (-216))))) (|HasCategory| (-170 (-216)) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-170 (-216)) (LIST (QUOTE -304) (LIST (QUOTE -170) (QUOTE (-216))))) (|HasCategory| (-170 (-216)) (QUOTE (-847)))) (-12 (|HasCategory| (-170 (-216)) (LIST (QUOTE -304) (LIST (QUOTE -170) (QUOTE (-216))))) (|HasCategory| (-170 (-216)) (QUOTE (-1097)))))) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-171 (-217)) (QUOTE (-1098))) (|HasCategory| (-171 (-217)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-171 (-217)) (QUOTE (-848))) (-1841 (|HasCategory| (-171 (-217)) (QUOTE (-848))) (|HasCategory| (-171 (-217)) (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-171 (-217)) (QUOTE (-25))) (|HasCategory| (-171 (-217)) (QUOTE (-23))) (|HasCategory| (-171 (-217)) (QUOTE (-21))) (|HasCategory| (-171 (-217)) (QUOTE (-722))) (|HasCategory| (-171 (-217)) (QUOTE (-1054))) (-12 (|HasCategory| (-171 (-217)) (QUOTE (-1009))) (|HasCategory| (-171 (-217)) (QUOTE (-1054)))) (-12 (|HasCategory| (-171 (-217)) (LIST (QUOTE -305) (LIST (QUOTE -171) (QUOTE (-217))))) (|HasCategory| (-171 (-217)) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-171 (-217)) (LIST (QUOTE -305) (LIST (QUOTE -171) (QUOTE (-217))))) (|HasCategory| (-171 (-217)) (QUOTE (-848)))) (-12 (|HasCategory| (-171 (-217)) (LIST (QUOTE -305) (LIST (QUOTE -171) (QUOTE (-217))))) (|HasCategory| (-171 (-217)) (QUOTE (-1098)))))) (-147) ((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n, \\spad{m)}} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note that \\spad{permutation(n,m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note that \\spad{n! = \\spad{n} (n-1)! when \\spad{n} > 0}; also, \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\indented{1}{binomial(n,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 \\spad{>=} \\spad{r} \\spad{>=} 0}.} \\blankline \\spad{X} [binomial(5,i) for \\spad{i} in 0..5]"))) NIL @@ -526,7 +526,7 @@ NIL NIL (-149) ((|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."))) -((-4597 . T)) +((-4599 . T)) NIL (-150 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.}"))) @@ -534,9 +534,9 @@ NIL NIL (-151) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4597 . T)) +((-4599 . T)) NIL -(-152 -3280 UP UPUP) +(-152 -3313 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), \\spad{n]}} such that under the change of variable \\spad{x = c1(z)}, \\spad{y = \\spad{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, \\spad{y)} = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, \\spad{t)} = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), \\spad{y} * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, \\spad{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, \\spad{n)}} returns \\spad{[m, \\spad{c,} \\spad{P]}} such that \\spad{c * \\spad{g} \\spad{**} (1/n) = \\spad{P} \\spad{**} (1/m)} thus if \\spad{y**n = \\spad{g},} then \\spad{z**m = \\spad{P}} where \\spad{z = \\spad{c} * \\spad{y}.}")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), \\spad{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 = \\spad{c} * \\spad{y}} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, \\spad{y)} = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, \\spad{z)} = 0}."))) NIL NIL @@ -547,14 +547,14 @@ NIL (-154 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 construct. However, each collection provides its own special function with the same name as the data type, except with an initial lower case letter, For example, list for List, flexibleArray for FlexibleArray, and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{p(x)} is true. Note that \\axiom{select(p,u) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{u} | p(x)]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{y = \\spad{x}} removed. Note that \\axiom{remove(y,c) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} y]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{p(x)} is true. Note that \\axiom{remove(p,u) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{u} | not p(x)]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across u, stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(f,u,x)}, \\spad{x} is the identity operation of \\spad{f.} Same as \\axiom{reduce(f,u,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 u, where \\spad{x} is the identity operation of \\spad{f.} Same as \\axiom{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\axiom{f(x,y)} if \\spad{u} has one element \\spad{y,} \\spad{x} if \\spad{u} is empty. For example, \\axiom{reduce(+,u,0)} returns the sum of the elements of u.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across u. For example, if \\spad{u} is \\axiom{[x,y,...,z]} then \\axiom{reduce(f,u)} returns \\axiom{f(..f(f(x,y),...),z)}. Note that if \\spad{u} has one element \\spad{x,} \\axiom{reduce(f,u)} returns \\spad{x.} Error: if \\spad{u} is empty. \\blankline \\spad{C} )clear all \\spad{X} reduce(+,[C[i]*x**i for \\spad{i} in 1..5])")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\axiom{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{p(x)} is true, and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(x,y,...,z)} returns the collection of elements \\axiom{x,y,...,z} ordered as given. Equivalently written as \\axiom{[x,y,...,z]$D}, where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasAttribute| |#1| (QUOTE -4600))) +((|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-1098))) (|HasAttribute| |#1| (QUOTE -4602))) (-155 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named construct. However, each collection provides its own special function with the same name as the data type, except with an initial lower case letter, For example, list for List, flexibleArray for FlexibleArray, and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{p(x)} is true. Note that \\axiom{select(p,u) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{u} | p(x)]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{y = \\spad{x}} removed. Note that \\axiom{remove(y,c) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} y]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{p(x)} is true. Note that \\axiom{remove(p,u) \\spad{==} \\spad{[x} for \\spad{x} in \\spad{u} | not p(x)]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across u, stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(f,u,x)}, \\spad{x} is the identity operation of \\spad{f.} Same as \\axiom{reduce(f,u,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 u, where \\spad{x} is the identity operation of \\spad{f.} Same as \\axiom{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\axiom{f(x,y)} if \\spad{u} has one element \\spad{y,} \\spad{x} if \\spad{u} is empty. For example, \\axiom{reduce(+,u,0)} returns the sum of the elements of u.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across u. For example, if \\spad{u} is \\axiom{[x,y,...,z]} then \\axiom{reduce(f,u)} returns \\axiom{f(..f(f(x,y),...),z)}. Note that if \\spad{u} has one element \\spad{x,} \\axiom{reduce(f,u)} returns \\spad{x.} Error: if \\spad{u} is empty. \\blankline \\spad{C} )clear all \\spad{X} reduce(+,[C[i]*x**i for \\spad{i} in 1..5])")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\axiom{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{p(x)} is true, and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(x,y,...,z)} returns the collection of elements \\axiom{x,y,...,z} ordered as given. Equivalently written as \\axiom{[x,y,...,z]$D}, where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-3348 . T)) +((-3389 . T)) NIL (-156 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(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} 0.75 200 ``operation units'' \\spad{->} 0.5 83 ``operation units'' \\spad{->} 0.25 \\indent{15} exponentiation = 4 units ,{} function calls = 10 units.")) (|systemSizeIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{systemSizeIF(ode)} returns the intensity value of the size of the system of ODEs. 20 equations corresponds to the neutral value. It returns a value in the range [0,1].")) (|stiffnessAndStabilityOfODEIF| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityOfODEIF(ode)} calculates the intensity values of stiffness of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which O(10) equates to mildly stiff wheras stiffness ratios of O(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian). \\blankline It returns two values in the range [0,1].")) (|stiffnessAndStabilityFactor| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityFactor(me)} calculates the stability and stiffness factor of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which O(10) equates to mildly stiff wheras stiffness ratios of O(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian).")) (|eval| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Matrix| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{eval(mat,symbols,values)} evaluates a multivariable matrix at given \\spad{values} for each of a list of variables")) (|jacobian| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|))) "\\spad{jacobian(v,w)} is a local function to make a jacobian matrix")) (|sparsityIF| (((|Float|) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{sparsityIF(m)} calculates the sparsity of a jacobian matrix")) (|combineFeatureCompatibility| (((|Float|) (|Float|) (|List| (|Float|))) "\\spad{combineFeatureCompatibility(C1,L)} is for interacting attributes") (((|Float|) (|Float|) (|Float|)) "\\spad{combineFeatureCompatibility(C1,C2)} is for interacting attributes"))) NIL NIL -(-199) +(-200) ((|constructor| (NIL "\\axiomType{d02bbfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BBF, a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BBF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-200) +(-201) ((|constructor| (NIL "\\axiomType{d02bhfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BHF, a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BHF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-201) +(-202) ((|constructor| (NIL "\\axiomType{d02cjfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02CJF, a ODE routine which uses an Adams-Moulton-Bashworth method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02CJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-202) +(-203) ((|constructor| (NIL "\\axiomType{d02ejfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02EJF, a ODE routine which uses a backward differentiation formulae method to handle a stiff system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02EJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}."))) NIL NIL -(-203) +(-204) ((|constructor| (NIL "\\axiom{d03AgentsPackage} contains a set of computational agents for use with Partial Differential Equation solvers.")) (|elliptic?| (((|Boolean|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{elliptic?(r)} \\undocumented{}")) (|central?| (((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{central?(f,g,l)} \\undocumented{}")) (|subscriptedVariables| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{subscriptedVariables(e)} \\undocumented{}")) (|varList| (((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|)) "\\spad{varList(s,n)} \\undocumented{}"))) NIL NIL -(-204) +(-205) ((|constructor| (NIL "\\axiomType{d03eefAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routines D03EEF/D03EDF."))) NIL NIL -(-205) +(-206) ((|constructor| (NIL "\\axiomType{d03fafAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routine D03FAF."))) NIL NIL -(-206 S) +(-207 S) ((|constructor| (NIL "This domain implements a simple view of a database whose fields are indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end \\spad{)}} prints full details of entries in the range \\axiom{start..end} in \\axiom{db}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{db}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{db}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{s} field of each element of \\axiom{db}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{db} which satisfy \\axiom{q}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-207 -3280 UP UPUP R) +(-208 -3313 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, \\spad{')}} returns p(x) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-208 -3280 FP) +(-209 -3313 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus, modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of u**(2**i) for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v.}")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v.}")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by separateDegrees and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is true, the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p.}")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p.}"))) NIL NIL -(-209) +(-210) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-571) (QUOTE (-909))) (|HasCategory| (-571) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-571) (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-151))) (|HasCategory| (-571) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-571) (QUOTE (-1027))) (|HasCategory| (-571) (QUOTE (-820))) (|HasCategory| (-571) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-1143))) (|HasCategory| (-571) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-571) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-571) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-571) (QUOTE (-226))) (|HasCategory| (-571) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-571) (LIST (QUOTE -526) (QUOTE (-1169)) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (LIST (QUOTE -282) (QUOTE (-571)) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-302))) (|HasCategory| (-571) (QUOTE (-553))) (|HasCategory| (-571) (QUOTE (-847))) (-1831 (|HasCategory| (-571) (QUOTE (-820))) (|HasCategory| (-571) (QUOTE (-847)))) (|HasCategory| (-571) (LIST (QUOTE -633) (QUOTE (-571)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-909)))) (|HasCategory| (-571) (QUOTE (-149))))) -(-210 R -3280) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-572) (QUOTE (-910))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-572) (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-151))) (|HasCategory| (-572) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-572) (QUOTE (-1028))) (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1144))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-227))) (|HasCategory| (-572) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-572) (LIST (QUOTE -527) (QUOTE (-1170)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -305) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -283) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-303))) (|HasCategory| (-572) (QUOTE (-554))) (|HasCategory| (-572) (QUOTE (-848))) (-1841 (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (QUOTE (-848)))) (|HasCategory| (-572) (LIST (QUOTE -634) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (|HasCategory| (-572) (QUOTE (-149))))) +(-211 R -3313) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, \\spad{x,} a, \\spad{b,} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, \\spad{x} = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters), then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, \\spad{x} = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b.}"))) NIL NIL -(-211 R) +(-212 R) ((|constructor| (NIL "Definite integration of rational functions. \\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f, \\spad{x} = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters), then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f, \\spad{x} = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b.}") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f, \\spad{x} = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters), then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f, \\spad{x} = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b.} Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b.}"))) NIL NIL -(-212 R1 R2) +(-213 R1 R2) ((|constructor| (NIL "This package has no description")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) NIL NIL -(-213 S) +(-214 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|member?| (((|Boolean|) |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} member?(3,a)")) (|members| (((|List| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} members a")) (|parts| (((|List| |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} parts a")) (|#| (((|NonNegativeInteger|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} \\#a")) (|count| (((|NonNegativeInteger|) |#1| $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} count(4,a)") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} count(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} every?(x+->(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!(x+->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(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:Dequeue INT:= dequeue [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\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 \\spad{()}") (($ (|List| |#1|)) "\\indented{1}{dequeue([x,y,...,z]) creates a dequeue with first (top or front)} \\indented{1}{element \\spad{x,} second element y,...,and last (bottom or back) element \\spad{z.}} \\blankline \\spad{E} g:Dequeue INT:= dequeue [1,2,3,4,5]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-214 |CoefRing| |listIndVar|) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-215 |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(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.}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-215 R -3280) +(-216 R -3313) ((|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, \\spad{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 true, exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, \\spad{x,} a, \\spad{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 true, exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, \\spad{g,} a, \\spad{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 true, then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b}, provided that they are finite values. Otherwise, limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL -(-216) +(-217) ((|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{++} \\spad{+,} \\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 \\spad{+,} \\spad{*,} / 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|)) $) "\\spad{integerDecode(x)} returns the multiple values of the common lisp integer-decode-float function. See Steele, ISBN 0-13-152414-3 p354. This function can be used to ensure that the results are bit-exact and do not depend on the binary-to-decimal conversions. \\blankline \\spad{X} \\spad{a:DFLOAT:=-1.0/3.0} \\spad{X} integerDecode a")) (|machineFraction| (((|Fraction| (|Integer|)) $) "\\spad{machineFraction(x)} returns a bit-exact fraction of the machine floating point number using the common lisp integer-decode-float function. See Steele, ISBN 0-13-152414-3 \\spad{p354} This function can be used to print results which do not depend on binary-to-decimal conversions \\blankline \\spad{X} \\spad{a:DFLOAT:=-1.0/3.0} \\spad{X} machineFraction a")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, \\spad{n,} \\spad{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, \\spad{n)}} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "\\spad{doubleFloatFormat changes} 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...}.")) (** (($ $ $) "\\spad{x \\spad{**} \\spad{y}} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer i."))) -((-3367 . T) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3410 . T) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-217) -((|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(n, \\spad{m)} creates a new uninitialized \\spad{n} by \\spad{m} matrix.} \\blankline \\spad{X} t1:DFMAT:=qnew(3,4)"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-216) (QUOTE (-1097))) (-12 (|HasCategory| (-216) (LIST (QUOTE -304) (QUOTE (-216)))) (|HasCategory| (-216) (QUOTE (-1097)))) (|HasCategory| (-216) (QUOTE (-302))) (|HasCategory| (-216) (QUOTE (-561))) (|HasAttribute| (-216) (QUOTE (-4602 "*"))) (|HasCategory| (-216) (QUOTE (-173))) (|HasCategory| (-216) (QUOTE (-367)))) (-218) +((|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(n, \\spad{m)} creates a new uninitialized \\spad{n} by \\spad{m} matrix.} \\blankline \\spad{X} t1:DFMAT:=qnew(3,4)"))) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-217) (QUOTE (-1098))) (-12 (|HasCategory| (-217) (LIST (QUOTE -305) (QUOTE (-217)))) (|HasCategory| (-217) (QUOTE (-1098)))) (|HasCategory| (-217) (QUOTE (-303))) (|HasCategory| (-217) (QUOTE (-562))) (|HasAttribute| (-217) (QUOTE (-4604 "*"))) (|HasCategory| (-217) (QUOTE (-174))) (|HasCategory| (-217) (QUOTE (-368)))) +(-219) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|fresnelC| (((|Float|) (|Float|)) "\\indented{1}{fresnelC(f) denotes the Fresnel integral \\spad{C}} \\blankline \\spad{X} fresnelC(1.5)")) (|fresnelS| (((|Float|) (|Float|)) "\\indented{1}{fresnelS(f) denotes the Fresnel integral \\spad{S}} \\blankline \\spad{X} fresnelS(1.5)")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; \\spad{c;} z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; \\spad{c;} z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - \\spad{x} * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - \\spad{x} * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - \\spad{x} * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - \\spad{x} * 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) + \\spad{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*\\%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) + \\spad{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*\\%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) + \\spad{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) + \\spad{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) + \\spad{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*\\%pi) - J(-v,x))/sin(v*\\%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) + \\spad{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*\\%pi) - J(-v,x))/sin(v*\\%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) + \\spad{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) + \\spad{x} w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, \\spad{x)}} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, \\spad{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, \\spad{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, \\spad{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 x*\\%e^-x*Ei(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 x*\\%e^-x*Ei(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 x*\\%e^-x*Ei(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 (Ei(x)-log \\spad{|x|} - gamma)/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 x*\\%e^-x*Ei(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 x*\\%e^-x*Ei(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 -(-219) +(-220) ((|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(n) creates a new uninitialized vector of length \\spad{n.}} \\blankline \\spad{X} t1:DFVEC:=qnew(7)"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-216) (QUOTE (-1097))) (|HasCategory| (-216) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-216) (QUOTE (-847))) (-1831 (|HasCategory| (-216) (QUOTE (-847))) (|HasCategory| (-216) (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-216) (QUOTE (-25))) (|HasCategory| (-216) (QUOTE (-23))) (|HasCategory| (-216) (QUOTE (-21))) (|HasCategory| (-216) (QUOTE (-721))) (|HasCategory| (-216) (QUOTE (-1053))) (-12 (|HasCategory| (-216) (QUOTE (-1008))) (|HasCategory| (-216) (QUOTE (-1053)))) (-12 (|HasCategory| (-216) (LIST (QUOTE -304) (QUOTE (-216)))) (|HasCategory| (-216) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-216) (LIST (QUOTE -304) (QUOTE (-216)))) (|HasCategory| (-216) (QUOTE (-847)))) (-12 (|HasCategory| (-216) (LIST (QUOTE -304) (QUOTE (-216)))) (|HasCategory| (-216) (QUOTE (-1097)))))) -(-220 R) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-217) (QUOTE (-1098))) (|HasCategory| (-217) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-217) (QUOTE (-848))) (-1841 (|HasCategory| (-217) (QUOTE (-848))) (|HasCategory| (-217) (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-217) (QUOTE (-25))) (|HasCategory| (-217) (QUOTE (-23))) (|HasCategory| (-217) (QUOTE (-21))) (|HasCategory| (-217) (QUOTE (-722))) (|HasCategory| (-217) (QUOTE (-1054))) (-12 (|HasCategory| (-217) (QUOTE (-1009))) (|HasCategory| (-217) (QUOTE (-1054)))) (-12 (|HasCategory| (-217) (LIST (QUOTE -305) (QUOTE (-217)))) (|HasCategory| (-217) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-217) (LIST (QUOTE -305) (QUOTE (-217)))) (|HasCategory| (-217) (QUOTE (-848)))) (-12 (|HasCategory| (-217) (LIST (QUOTE -305) (QUOTE (-217)))) (|HasCategory| (-217) (QUOTE (-1098)))))) +(-221 R) ((|constructor| (NIL "4x4 Matrices for coordinate transformations\\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:\\br \\tab{5}\\spad{nx ox ax px}\\br \\tab{5}\\spad{ny oy ay py}\\br \\tab{5}\\spad{nz oz az pz}\\br \\tab{5}\\spad{0 0 0 1}\\br \\spad{(n,} 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}"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4602 "*"))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) -(-221 A S) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-303))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4604 "*"))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) +(-222 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 -(-222 S) +(-223 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."))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL -(-223 S R) +(-224 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R.} Given a differentiation on \\spad{R,} extend it to a differentiation on \\spad{%.}")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, \\spad{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, \\spad{n)}} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R.}") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R.}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226)))) -(-224 R) +((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227)))) +(-225 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R.} Given a differentiation on \\spad{R,} extend it to a differentiation on \\spad{%.}")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, \\spad{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, \\spad{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.}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-225 S) +(-226 S) ((|constructor| (NIL "An ordinary differential ring, that is, a ring with an operation \\spadfun{differentiate}. \\blankline Axioms\\br \\tab{5}\\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\\br \\tab{5}\\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, \\spad{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, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{x.}") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x.} This function is a simple differential operator where no variable needs to be specified."))) NIL NIL -(-226) +(-227) ((|constructor| (NIL "An ordinary differential ring, that is, a ring with an operation \\spadfun{differentiate}. \\blankline Axioms\\br \\tab{5}\\spad{differentiate(x+y) = differentiate(x)+differentiate(y)}\\br \\tab{5}\\spad{differentiate(x*y) = x*differentiate(y) + differentiate(x)*y}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, \\spad{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, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{x.}") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x.} This function is a simple differential operator where no variable needs to be specified."))) -((-4597 . T)) +((-4599 . T)) NIL -(-227 A S) +(-228 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{p(x)} is not true.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{p(x)} is true.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{y = \\spad{x}.}")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{x,y,...,z}.") (($) "\\spad{dictionary()}$D creates an empty dictionary of type \\spad{D.}"))) NIL -((|HasAttribute| |#1| (QUOTE -4600))) -(-228 S) +((|HasAttribute| |#1| (QUOTE -4602))) +(-229 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{p(x)} is not true.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{p(x)} is true.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{y = \\spad{x}.}")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{x,y,...,z}.") (($) "\\spad{dictionary()}$D creates an empty dictionary of type \\spad{D.}"))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL -(-229) +(-230) ((|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:\\br \\tab{5}1. all minimal inhomogeneous solutions\\br \\tab{5}2. all minimal homogeneous solutions\\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 u, then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-230 S -3020 R) +(-231 S -3465 R) ((|constructor| (NIL "This category represents a finite cartesian product of a given type. Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * \\spad{r}} multiplies each component of the vector \\spad{y} by the element \\spad{r.}") (($ |#3| $) "\\spad{r * \\spad{y}} multiplies the element \\spad{r} times each component of the vector \\spad{y.}")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y.}")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (QUOTE (-845))) (|HasAttribute| |#3| (QUOTE -4597)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-138))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1053))) (|HasCategory| |#3| (QUOTE (-1097)))) -(-231 -3020 R) +((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (QUOTE (-846))) (|HasAttribute| |#3| (QUOTE -4599)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-138))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1054))) (|HasCategory| |#3| (QUOTE (-1098)))) +(-232 -3465 R) ((|constructor| (NIL "This category represents a finite cartesian product of a given type. Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * \\spad{r}} multiplies each component of the vector \\spad{y} by the element \\spad{r.}") (($ |#2| $) "\\spad{r * \\spad{y}} multiplies the element \\spad{r} times each component of the vector \\spad{y.}")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y.}")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4594 |has| |#2| (-1053)) (-4595 |has| |#2| (-1053)) (-4597 |has| |#2| (-6 -4597)) ((-4602 "*") |has| |#2| (-173)) (-4600 . T) (-3348 . T)) +((-4596 |has| |#2| (-1054)) (-4597 |has| |#2| (-1054)) (-4599 |has| |#2| (-6 -4599)) ((-4604 "*") |has| |#2| (-174)) (-4602 . T) (-3389 . T)) NIL -(-232 -3020 A B) +(-233 -3465 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, \\spad{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 func. Argument \\spad{ident} is returned if the vector is empty.")) 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-305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-374)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-846)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))))) +(-235 |Coef|) ((|constructor| (NIL "DirichletRing is the ring of arithmetical functions with Dirichlet convolution as multiplication")) (|additive?| (((|Boolean|) $ (|PositiveInteger|)) "\\spad{additive?(a, \\spad{n)}} returns \\spad{true} if the first \\spad{n} coefficients of a are additive")) (|multiplicative?| (((|Boolean|) $ (|PositiveInteger|)) "\\spad{multiplicative?(a, \\spad{n)}} returns \\spad{true} if the first \\spad{n} coefficients of a are multiplicative")) (|zeta| (($) "\\spad{zeta()} returns the function which is constantly one"))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) ((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-173)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173)))) -(-235) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) ((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-174)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174)))) +(-236) ((|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 i, in which the other elements of the string are composed of as many replications as possible of the second indicated string, \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s.}")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings, \\spad{l,} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL NIL -(-236 S) +(-237 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(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} \\spad{].}")) (|degree| (((|Integer|) $) "\\spad{degree(d)} returns the degree of the divisor \\spad{d}"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-237 S) -((|constructor| (NIL "The following is part of the PAFF package"))) -((-4595 . T) (-4594 . T)) -((|HasCategory| (-571) (QUOTE (-792)))) (-238 S) +((|constructor| (NIL "The following is part of the PAFF package"))) +((-4597 . T) (-4596 . T)) +((|HasCategory| (-572) (QUOTE (-793)))) +(-239 S) ((|constructor| (NIL "A division ring (sometimes called a skew field), \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv \\spad{x}} returns the multiplicative inverse of \\spad{x.} Error: if \\spad{x} is 0.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n.}")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n.}"))) NIL NIL -(-239) +(-240) ((|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| (($ $) "\\spad{inv \\spad{x}} returns the multiplicative inverse of \\spad{x.} Error: if \\spad{x} is 0.")) (^ (($ $ (|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.}"))) -((-4593 . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-240 S) +(-241 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!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v,} returning \\spad{v.}")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v,} returning \\spad{v.}")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate u.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note that \\axiom{next(l) = rest(l)} and \\axiom{previous(next(l)) = \\spad{l}.}")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note that \\axiom{next(previous(l)) = \\spad{l}.}")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\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."))) -((-3348 . T)) +((-3389 . T)) NIL -(-241 S) +(-242 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{l.\"count\"} returns the number of elements in \\axiom{l}.") (($ $ "sort") "\\axiom{l.sort} returns \\axiom{l} with elements sorted. Note: \\axiom{l.sort = sort(l)}") (($ $ "unique") "\\axiom{l.unique} returns \\axiom{l} with duplicates removed. Note: \\axiom{l.unique = removeDuplicates(l)}.")) 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T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-243 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's algorithm. Note that this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x \\spad{**} \\spad{n}} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL -(-243 |vl| R) +(-244 |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 (-846)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1054)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1098)))))) +(-247 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, \\spad{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, \\spad{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, \\spad{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.n} where \\spad{z} \\spad{:=} makeVariable(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.n} where \\spad{z} :=makeVariable(s). Note that In the interpreter, \\spad{z} is given as an internal map, which may be ignored."))) NIL -((|HasCategory| |#2| (QUOTE (-226)))) -(-247 R S V E) +((|HasCategory| |#2| (QUOTE (-227)))) +(-248 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, \\spad{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, \\spad{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, \\spad{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.n} where \\spad{z} \\spad{:=} makeVariable(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.n} where \\spad{z} :=makeVariable(s). Note that In the interpreter, \\spad{z} is given as an internal map, which may be ignored."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-248 S) +(-249 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|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d.} Note that \\axiom{height(d) = \\# \\spad{d}.}")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x,} second element y,...,and last (bottom or back) element \\spad{z.}") (($) "\\spad{dequeue()}$D creates an empty dequeue of type \\spad{D.}"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-249) +(-250) ((|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), \\spad{y} = g(t), \\spad{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), \\spad{y} = g(t), \\spad{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), \\spad{y} = g(t), \\spad{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), \\spad{y} = g(t), \\spad{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), \\spad{y} = g(t), \\spad{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), \\spad{y} = g(t), \\spad{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), \\spad{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), \\spad{y} = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-250 R |Ex|) +(-251 R |Ex|) ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,y) = g(x,y),x,y,l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) NIL NIL -(-251) +(-252) ((|constructor| (NIL "\\axiomType{DrawComplex} provides some facilities for drawing complex functions.")) (|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x.}")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns i.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns i.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,rRange,iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-d viewport control panel. Sample call: \\indented{3}{\\spad{f \\spad{z} \\spad{==} sin \\spad{z}}} \\indented{3}{\\spad{drawComplexVectorField(f, -2..2, -2..2)}} Parameter descriptions: \\indented{2}{f : the function to draw} \\indented{2}{rRange : the range of the real values} \\indented{2}{iRange : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,rRange,iRange,arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value. Sample call: \\indented{2}{\\spad{f \\spad{z} \\spad{==} exp(1/z)}} \\indented{2}{\\spad{drawComplex(f, 0.3..3, 0..2*%pi, false)}} Parameter descriptions: \\indented{2}{f:\\space{2}the function to draw} \\indented{2}{rRange : the range of the real values} \\indented{2}{iRange : the range of imaginary values} \\indented{2}{arrows? : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) NIL NIL -(-252 R) +(-253 R) ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b.} This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables, but is meant for expressions involving \\%pi. Note that this package is meant for internal use only.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b.}"))) NIL NIL -(-253 |Ex|) +(-254 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)}, \\spad{y = g(u,v)}, \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)}, \\spad{y = g(u,v)}, \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)}, \\spad{y = g(u,v)}, \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)}, \\spad{y = g(u,v)}, \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), \\spad{y} = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), \\spad{y} = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title, and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) NIL NIL -(-254) +(-255) ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,lz,l)} draws the surface constructed by projecting the values in the \\axiom{lz} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly,lz)} draws the surface constructed by projecting the values in the \\axiom{lz} list onto the rectangular grid formed by the \\axiom{lx \\spad{x} ly}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,l)} plots the curve constructed from the list of points \\spad{lp.} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp.}") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,l)} plots the curve constructed of points (x,y) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly)} plots the curve constructed of points (x,y) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) NIL NIL -(-255) +(-256) ((|constructor| (NIL "This package has no description")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,u)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value, \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,p)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value, \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,n)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value, \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,n)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value, \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options, \\spad{l,} and checks to see if it contains the option \\spad{space}. If the the option doesn't exist, then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,n)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value, \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,n)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value, \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,r)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value, \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,p)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value, \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,p)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value, \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,b)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value, \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,s)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value, \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,s)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value, \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,ls)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist, the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,b)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value, \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,b)} takes the list of draw options, \\spad{l,} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value, \\spad{b} is returned."))) NIL NIL -(-256 S) +(-257 S) ((|constructor| (NIL "This package has no description")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,s)} determines whether the indicated drawing option, \\spad{s,} is contained in the list of drawing options, \\spad{l,} which is defined by the draw command."))) NIL NIL -(-257) +(-258) ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command, or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf.} This option is expressed in the form \\spad{unit \\spad{==} [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p.} This option is expressed in the form \\spad{coord \\spad{==} \\spad{p}.}")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points, \\spad{n,} defining the circle which creates the tube around a 3D curve, the default is 6. This option is expressed in the form \\spad{tubePoints \\spad{==} \\spad{n}.}")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions, \\spad{n,} of the second range variable. This option is expressed in the form \\spad{var2Steps \\spad{==} \\spad{n}.}")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions, \\spad{n,} of the first range variable. This option is expressed in the form \\spad{var1Steps \\spad{==} \\spad{n}.}")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l.} This option is expressed in the form \\spad{ranges \\spad{==} \\spad{l}.}")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range i. This option is expressed in the form \\spad{range \\spad{==} [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l.} This option is expressed in the form \\spad{range \\spad{==} [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius, \\spad{r,} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius \\spad{==} 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x,} \\spad{y,} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction \\spad{==} f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction \\spad{==} f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the z-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction \\spad{==} f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p.} This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color, \\spad{v,} for 2D graph curves. This option is expressed in the form \\spad{curveColor \\spad{==} \\spad{v}.}")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p.} This option is expressed in the form \\spad{pointColor \\spad{==} \\spad{p}.}") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color, \\spad{v,} for 2D graph points. This option is expressed in the form \\spad{pointColor \\spad{==} \\spad{v}.}")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p.} This option is expressed in the form \\spad{coordinates \\spad{==} \\spad{p}.}")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale, if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale \\spad{==} \\spad{b}.}")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s.} This option is expressed in the form \\spad{style \\spad{==} \\spad{s}.}")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s.} This option is expressed in the form \\spad{title \\spad{==} \\spad{s}.}")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta, phi, scale, scaleX, scaleY, scaleZ, deltaX, deltaY]. This option is expressed in the form \\spad{viewpoint \\spad{==} ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l.} This option is expressed in the form \\spad{clip \\spad{==} [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is true, or off if \\spad{b} is false. This option is expressed in the form \\spad{clip \\spad{==} \\spad{b}.}")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is true, or off if \\spad{b} is false. This option is expressed in the form \\spad{adaptive \\spad{==} \\spad{b}.}"))) NIL NIL -(-258 R S V) +(-259 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}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-259 S) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#3| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#3| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-260 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.}"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-260 S) +(-261 S) ((|constructor| (NIL "This category is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(b).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when true, a coerce to OutputForm yields the full output of \\spad{tr,} otherwise encode(tr) is output (see encode function). The default is 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"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-261 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-262 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) ((|constructor| (NIL "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 pol.")) (|initializeParamOfPlaces| (((|Void|) |#10| (|List| |#3|)) "initParLocLeaves(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(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 tr), computes the local exceptional divisor at each infinytly close points in the tree. This function is equivalent to the following called: initParLocLeaves(tr) initializeParamOfPlaces(tr) blowUpWithExcpDiv(tr)")) (|desingTree| (((|List| |#10|) |#3|) "\\spad{desingTree(pol)} returns all the desingularisation trees of all singular points on the curve defined by pol.")) (|desingTreeAtPoint| ((|#10| |#5| |#3|) "\\spad{desingTreeAtPoint(pt,pol)} computes the desingularisation tree at the point \\spad{pt} on the curve defined by pol. This function recursively compute the tree.")) (|adjunctionDivisor| ((|#8| |#10|) "\\spad{adjunctionDivisor(tr)} compute the local adjunction divisor of a desingularisation tree \\spad{tr} of a singular point.")) (|divisorAtDesingTree| ((|#8| |#3| |#10|) "\\spad{divisorAtDesingTree(f,tr)} computes the local divisor of \\spad{f} at a desingularisation tree \\spad{tr} of a singular point."))) NIL NIL -(-262 A S) +(-263 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If x,...,y is an ordered set of differential indeterminates, and the prime notation is used for differentiation, then the set of derivatives (including zero-th order) of the differential indeterminates is x,\\spad{x'},\\spad{x''},..., y,\\spad{y'},\\spad{y''},... (Note that in the interpreter, the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n.)} This set is viewed as a set of algebraic indeterminates, totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives, and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates, just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example, one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order}, then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates, Very often, a grading is the first step in ordering the set of monomials. For differential polynomial domains, this constructor provides a function \\spadfun{weight}, which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example, one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials, providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s,} viewed as the zero-th order derivative of \\spad{s.}")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{v.}") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v.}")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v.}")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s.}")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, \\spad{n)}} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL -(-263 S) +(-264 S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If x,...,y is an ordered set of differential indeterminates, and the prime notation is used for differentiation, then the set of derivatives (including zero-th order) of the differential indeterminates is x,\\spad{x'},\\spad{x''},..., y,\\spad{y'},\\spad{y''},... (Note that in the interpreter, the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n.)} This set is viewed as a set of algebraic indeterminates, totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives, and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates, just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example, one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order}, then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates, Very often, a grading is the first step in ordering the set of monomials. For differential polynomial domains, this constructor provides a function \\spadfun{weight}, which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example, one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials, providing a graded ring structure.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s,} viewed as the zero-th order derivative of \\spad{s.}")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{v.}") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v.}")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v.}")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s.}")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, \\spad{n)}} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL NIL -(-264) +(-265) ((|constructor| (NIL "\\axiomType{e04AgentsPackage} is a package of numerical agents to be used to investigate attributes of an input function so as to decide the \\axiomFun{measure} of an appropriate numerical optimization routine.")) (|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units''. It returns a value in the range [0,1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,r)} changes the name of item \\axiom{s} in \\axiom{r} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,n)} returns a list of \\axiom{n} indexed variables with name as in \\axiom{e}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{args.lfn}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{e} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\spad{l.}")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{l}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,n)} returns a matrix of coefficients of the linear functions in \\axiom{l}. If \\spad{l} is empty, the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{e} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course, it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,b)} repaces all instances of an infinite entry in \\axiom{l} by a finite entry \\axiom{b} or \\axiom{-b}."))) NIL NIL -(-265) +(-266) ((|constructor| (NIL "\\axiomType{e04dgfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04DGF, a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04DGF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-266) +(-267) ((|constructor| (NIL "\\axiomType{e04fdfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04FDF, a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04FDF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-267) +(-268) ((|constructor| (NIL "\\axiomType{e04gcfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04GCF, a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04GCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-268) +(-269) ((|constructor| (NIL "\\axiomType{e04jafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04JAF, a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04JAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-269) +(-270) ((|constructor| (NIL "\\axiomType{e04mbfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04MBF, an optimization routine for Linear functions. The function \\axiomFun{measure} measures the usefulness of the routine E04MBF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-270) +(-271) ((|constructor| (NIL "\\axiomType{e04nafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04NAF, an optimization routine for Quadratic functions. The function \\axiomFun{measure} measures the usefulness of the routine E04NAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-271) +(-272) ((|constructor| (NIL "\\axiomType{e04ucfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04UCF, a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04UCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) NIL NIL -(-272) +(-273) ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R.} This domain represents the set of all ordered subsets of the set \\spad{X,} assumed to be in correspondance with {1,2,3, ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X.} A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x,} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element, where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively, is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-273 R -3280) +(-274 R -3313) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-274 R -3280) +(-275 R -3313) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions, using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, \\spad{k)}} returns \\spad{f} rewriting either \\spad{k} which must be an nth-root in terms of radicals already in \\spad{f}, or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn}, and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, \\spad{x)}} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, \\spad{x)}} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, \\spad{x)}} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL -(-275 |Coef| UTS ULS) +(-276 |Coef| UTS ULS) ((|constructor| (NIL "This domain provides elementary functions on any Laurent series domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z.}")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z.}")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z.}")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z.}")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z.}")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z.}")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z.}")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z.}")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z.}")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z.}")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z.}")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z.}")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z.}")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z.}")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z.}")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z.}")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z.}")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z.}")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z.}")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z.}")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z.}")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z.}")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z.}")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z.}")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z.}")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z.}")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s \\spad{**} \\spad{r}} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-367)))) -(-276 |Coef| ULS UPXS EFULS) +((|HasCategory| |#1| (QUOTE (-368)))) +(-277 |Coef| ULS UPXS EFULS) ((|constructor| (NIL "This package provides elementary functions on any Laurent series domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z.}")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z.}")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z.}")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z.}")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z.}")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z.}")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z.}")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z.}")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z.}")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z.}")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z.}")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z.}")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z.}")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z.}")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z.}")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z.}")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z.}")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z.}")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z.}")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z.}")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z.}")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z.}")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z.}")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z.}")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z.}")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z.}")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z \\spad{**} \\spad{r}} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) NIL -((|HasCategory| |#1| (QUOTE (-367)))) -(-277 A S) +((|HasCategory| |#1| (QUOTE (-368)))) +(-278 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion, deletion, and concatenation efficient. However, access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from u.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{p(x)}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p.}")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position i.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position i.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from u.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{p(x)} is true.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements u.i through u.j.") (($ $ (|Integer|)) "\\indented{1}{delete!(u,i) destructively deletes the \\axiom{i}th element of u.} \\blankline \\spad{E} Data:=Record(age:Integer,gender:String) \\spad{E} a1:AssociationList(String,Data):=table() \\spad{E} a1.\"tim\":=[55,\"male\"]$Data \\spad{E} delete!(a1,1)")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of u. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of u."))) NIL -((|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097)))) -(-278 S) +((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098)))) +(-279 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!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from u.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{p(x)}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|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 i.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position i.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from u.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{p(x)} is true.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements u.i through u.j.") (($ $ (|Integer|)) "\\indented{1}{delete!(u,i) destructively deletes the \\axiom{i}th element of u.} \\blankline \\spad{E} Data:=Record(age:Integer,gender:String) \\spad{E} a1:AssociationList(String,Data):=table() \\spad{E} a1.\"tim\":=[55,\"male\"]$Data \\spad{E} delete!(a1,1)")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of u. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of u."))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL -(-279 S) +(-280 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y.}")) (|exp| (($ $) "\\spad{exp(x)} returns \\%e to the power \\spad{x.}")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x.}"))) NIL NIL -(-280) +(-281) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y.}")) (|exp| (($ $) "\\spad{exp(x)} returns \\%e to the power \\spad{x.}")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x.}"))) NIL NIL -(-281 |Coef| UTS) +(-282 |Coef| UTS) ((|constructor| (NIL "The elliptic functions \\spad{sn,} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) NIL NIL -(-282 S |Index|) +(-283 S |Index|) ((|constructor| (NIL "An eltable over domains \\spad{D} and \\spad{I} is a structure which can be viewed as a function from \\spad{D} to I. Examples of eltable structures range from data structures, For example, those of type List, to algebraic structures like Polynomial.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,i)} (also written: \\spad{u} . i) returns the element of \\spad{u} indexed by i. Error: if \\spad{i} is not an index of u."))) NIL NIL -(-283 S |Dom| |Im|) +(-284 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example, the list [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{x} to be \\axiom{y} under \\axiom{u}, without checking that \\axiom{x} is in the domain of \\axiom{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 u, assuming \\spad{x} is in the domain of u. Error: if \\spad{x} is not in the domain of u.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, \\spad{x)}} applies \\axiom{u} to \\axiom{x} without checking whether \\axiom{x} is in the domain of \\axiom{u}. If \\axiom{x} is not in the domain of \\axiom{u} a memory-access violation may occur. If a check on whether \\axiom{x} is in the domain of \\axiom{u} is required, use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, \\spad{x,} \\spad{y)}} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of u, and returns \\spad{y} otherwise. For example, if \\spad{u} is a polynomial in \\axiom{x} over the rationals, \\axiom{elt(u,n,0)} may define the coefficient of \\axiom{x} to the power \\spad{n,} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4601))) -(-284 |Dom| |Im|) +((|HasAttribute| |#1| (QUOTE -4603))) +(-285 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example, the list [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{x} to be \\axiom{y} under \\axiom{u}, without checking that \\axiom{x} is in the domain of \\axiom{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 u, assuming \\spad{x} is in the domain of u. Error: if \\spad{x} is not in the domain of u.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, \\spad{x)}} applies \\axiom{u} to \\axiom{x} without checking whether \\axiom{x} is in the domain of \\axiom{u}. If \\axiom{x} is not in the domain of \\axiom{u} a memory-access violation may occur. If a check on whether \\axiom{x} is in the domain of \\axiom{u} is required, use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, \\spad{x,} \\spad{y)}} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of u, and returns \\spad{y} otherwise. For example, if \\spad{u} is a polynomial in \\axiom{x} over the rationals, \\axiom{elt(u,n,0)} may define the coefficient of \\axiom{x} to the power \\spad{n,} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-285 S R |Mod| -2203 -3491 |exactQuo|) +(-286 S R |Mod| -4007 -4475 |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.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"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-286) +(-287) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains), \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline Axioms\\br \\tab{5}\\spad{ab=0 \\spad{=>} \\spad{a=0} or b=0} \\spad{--} known as noZeroDivisors\\br \\tab{5}\\spad{not(1=0)}")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4593 . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-287 R) +(-288 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 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 alpha. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue alpha. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m.}")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) NIL NIL -(-288 S R) +(-289 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL -(-289 S) +(-290 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 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| $)) "\\spad{eval(eqn, [x1=v1, \\spad{...} xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation eqn.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation eqn.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of eqn.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation eqn.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation eqn.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation eq.")) (|equation| (($ |#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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))))) -(-291) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098))))) +(-292) ((|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\\br \\tab{5}\\spad{f \\spad{x} \\spad{==} if \\spad{x} < 0 then error \"negative argument\" else x}\\br the call to error will actually be of the form\\br \\tab{5}\\spad{error(\"f\",\"negative argument\")}\\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):\\br \\spad{\\%l}\\tab{6}start a new line\\br \\spad{\\%b}\\tab{6}start printing in a bold font (where available)\\br \\spad{\\%d}\\tab{6}stop printing in a bold font (where available)\\br \\spad{\\%ceon}\\tab{3}start centering message lines\\br \\spad{\\%ceoff}\\tab{2}stop centering message lines\\br \\spad{\\%rjon}\\tab{3}start displaying lines \"ragged left\"\\br \\spad{\\%rjoff}\\tab{2}stop displaying lines \"ragged left\"\\br \\spad{\\%i}\\tab{6}indent following lines 3 additional spaces\\br \\spad{\\%u}\\tab{6}unindent following lines 3 additional spaces\\br \\spad{\\%xN}\\tab{5}insert \\spad{N} blanks (eg, \\spad{\\%x10} inserts 10 blanks) \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-292 -3280 S) +(-293 -3313 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set, using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, \\spad{p,} \\spad{k)}} uses the property \\spad{p} of the operator of \\spad{k,} in order to lift \\spad{f} and apply it to \\spad{k.}"))) NIL NIL -(-293 E -3280) +(-294 E -3313) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over E; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F;} Do not use this package with \\spad{E} = \\spad{F,} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, \\spad{k)}} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL -(-294 A B) +(-295 A B) ((|constructor| (NIL "\\spad{ExpertSystemContinuityPackage1} exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) NIL NIL -(-295) +(-296) ((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,var,range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,var,range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{u}"))) NIL NIL -(-296 S) +(-297 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? \\spad{x}} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? \\spad{x}} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},...,\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},...,\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},...,\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},...,\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, \\spad{s)}} tests if \\spad{x} does not contain any operator whose name is \\spad{s.}") (((|Boolean|) $ $) "\\spad{freeOf?(x, \\spad{y)}} tests if \\spad{x} does not contain any occurrence of \\spad{y,} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, \\spad{k)}} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, \\spad{x)}} constructs op(x) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, \\spad{s)}} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s.}") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{%.}")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f,} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f,} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f,} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level, or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f.} Constants have height 0. Symbols have height 1. For any operator op and expressions f1,...,fn, \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, \\spad{g)}} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them, and makes them applicable to a unary operator. For example, \\spad{atan(paren \\spad{[x,} 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (f). This prevents \\spad{f} from being evaluated when operators are applied to it. For example, \\spad{log(1)} returns 0, but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them, and makes them applicable to a unary operator. For example, \\spad{atan(box \\spad{[x,} 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example, \\spad{log(1)} returns 0, but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels k1,...,kn by g1,...,gn formally in \\spad{f.}") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, \\spad{[k1} = g1,...,kn = gn])} replaces the kernels k1,...,kn by g1,...,gn formally in \\spad{f.}") (($ $ (|Equation| $)) "\\spad{subst(f, \\spad{k} = \\spad{g)}} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f.}")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or op([x1,...,xn]) applies the n-ary operator \\spad{op} to x1,...,xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or op(x, \\spad{y,} \\spad{z,} \\spad{t)} applies the 4-ary operator \\spad{op} to \\spad{x,} \\spad{y,} \\spad{z} and \\spad{t.}") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or op(x, \\spad{y,} \\spad{z)} applies the ternary operator \\spad{op} to \\spad{x,} \\spad{y} and \\spad{z.}") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or op(x, \\spad{y)} applies the binary operator \\spad{op} to \\spad{x} and \\spad{y.}") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or op(x) applies the unary operator \\spad{op} to \\spad{x.}"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-1053)))) -(-297) +((|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1054)))) +(-298) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? \\spad{x}} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? \\spad{x}} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},...,\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},...,\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{f)}} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},...,\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},...,\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, \\spad{s)}} tests if \\spad{x} does not contain any operator whose name is \\spad{s.}") (((|Boolean|) $ $) "\\spad{freeOf?(x, \\spad{y)}} tests if \\spad{x} does not contain any occurrence of \\spad{y,} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, \\spad{k)}} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, \\spad{x)}} constructs op(x) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, \\spad{s)}} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s.}") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{%.}")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f,} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f,} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f,} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level, or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f.} Constants have height 0. Symbols have height 1. For any operator op and expressions f1,...,fn, \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, \\spad{g)}} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them, and makes them applicable to a unary operator. For example, \\spad{atan(paren \\spad{[x,} 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (f). This prevents \\spad{f} from being evaluated when operators are applied to it. For example, \\spad{log(1)} returns 0, but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them, and makes them applicable to a unary operator. For example, \\spad{atan(box \\spad{[x,} 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example, \\spad{log(1)} returns 0, but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels k1,...,kn by g1,...,gn formally in \\spad{f.}") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, \\spad{[k1} = g1,...,kn = gn])} replaces the kernels k1,...,kn by g1,...,gn formally in \\spad{f.}") (($ $ (|Equation| $)) "\\spad{subst(f, \\spad{k} = \\spad{g)}} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f.}")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or op([x1,...,xn]) applies the n-ary operator \\spad{op} to x1,...,xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or op(x, \\spad{y,} \\spad{z,} \\spad{t)} applies the 4-ary operator \\spad{op} to \\spad{x,} \\spad{y,} \\spad{z} and \\spad{t.}") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or op(x, \\spad{y,} \\spad{z)} applies the ternary operator \\spad{op} to \\spad{x,} \\spad{y} and \\spad{z.}") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or op(x, \\spad{y)} applies the binary operator \\spad{op} to \\spad{x} and \\spad{y.}") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or op(x) applies the unary operator \\spad{op} to \\spad{x.}"))) NIL NIL -(-298 R1) +(-299 R1) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) NIL NIL -(-299 R1 R2) +(-300 R1 R2) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,m)} applies a mapping \\spad{f:R1} \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) NIL NIL -(-300) +(-301) ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{p} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions, multiplications, exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) NIL NIL -(-301 S) +(-302 S) ((|constructor| (NIL "A constructive euclidean domain, \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes\\br \\tab{5}multiplicativeValuation\\tab{5}Size(a*b)=Size(a)*Size(b)\\br \\tab{5}additiveValuation\\tab{11}Size(a*b)=Size(a)+Size(b)")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ \\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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y.} The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem \\spad{y}} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo \\spad{y}} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder}, where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y.}")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x.} Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) NIL NIL -(-302) +(-303) ((|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\\br \\tab{5}multiplicativeValuation\\tab{5}Size(a*b)=Size(a)*Size(b)\\br \\tab{5}additiveValuation\\tab{11}Size(a*b)=Size(a)+Size(b)")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ \\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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y.} The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem \\spad{y}} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo \\spad{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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-303 S R) +(-304 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, \\spad{[x1} = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f.}") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = \\spad{v)}} replaces \\spad{x} by \\spad{v} in \\spad{f.}"))) NIL NIL -(-304 R) +(-305 R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, \\spad{[x1} = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f.}") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = \\spad{v)}} replaces \\spad{x} by \\spad{v} in \\spad{f.}"))) NIL NIL -(-305 -3280) +(-306 -3313) ((|constructor| (NIL "This package is to be used in conjuction with the CycleIndicators package. It provides an evaluation function for SymmetricPolynomials.")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL -(-306) +(-307) ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note that It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows, for example, errors to be raised in one half of a type-balanced \\spad{if}."))) NIL NIL -(-307) +(-308) ((|writeObj| (((|Void|) (|SubSpace| 3 (|DoubleFloat|)) (|String|)) "writes 3D SubSpace to a file in Wavefront (.OBJ) format"))) NIL NIL -(-308 R FE |var| |cen|) +(-309 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 \\spad{->} a+,f(var))}."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-151))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1027))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-1143))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-226))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1169)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -304) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (LIST (QUOTE -282) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1243) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-302))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-553))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-847))) (-1831 (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-847)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-909)))) (|HasCategory| (-1243 |#1| |#2| |#3| |#4|) (QUOTE (-149))))) -(-309 R S) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-910))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-151))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-1028))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-1144))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-227))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -527) (QUOTE (-1170)) (LIST (QUOTE -1244) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -305) (LIST (QUOTE -1244) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (LIST (QUOTE -283) (LIST (QUOTE -1244) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1244) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-303))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-554))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-848))) (-1841 (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-848)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-910)))) (|HasCategory| (-1244 |#1| |#2| |#3| |#4|) (QUOTE (-149))))) +(-310 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 e."))) NIL NIL -(-310 R FE) +(-311 R FE) ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of \\spad{(x} - a); terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of \\spad{(x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n.}") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f.} Note that \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-311 R) +(-312 R) ((|constructor| (NIL "Top-level mathematical expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} is not documented")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} is not documented")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(f,n) is not documented")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4597 -1831 (-3997 (|has| |#1| (-1053)) (|has| |#1| (-633 (-571)))) (-12 (|has| |#1| (-561)) (-1831 (-3997 (|has| |#1| (-1053)) (|has| |#1| (-633 (-571)))) (|has| |#1| (-1053)) (|has| |#1| (-481)))) (|has| |#1| (-1053)) (|has| |#1| (-481))) (-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) ((-4602 "*") |has| |#1| (-561)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-561)) 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(LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))))) (|HasCategory| $ (QUOTE (-1054))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-572))))) +(-313 R -3313) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, \\spad{y,} \\spad{x} = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, \\spad{y,} \\spad{x} = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, \\spad{y,} \\spad{x} = a, \\spad{y} a = \\spad{b)}} is equivalent to \\spad{seriesSolve(eq=0, \\spad{y,} x=a, \\spad{y} a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, \\spad{y,} \\spad{x} = a, \\spad{b)}} is equivalent to \\spad{seriesSolve(eq = 0, \\spad{y,} \\spad{x} = a, \\spad{y} a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, \\spad{b)}} is equivalent to \\spad{seriesSolve(eq, \\spad{y,} x=a, \\spad{y} a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "seriesSolve([eq1,...,eqn], [y1,...,yn], \\spad{x} = \\spad{a,[y1} a = b1,..., \\spad{yn} a = bn]) is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], \\spad{x} = a, \\spad{[y1} a = b1,..., \\spad{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], \\spad{x} = a, \\spad{[y1} a = b1,..., \\spad{yn} a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = \\spad{a,[y1} a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note that eqi must be of the form \\spad{fi(x, \\spad{y1} \\spad{x,} \\spad{y2} x,..., \\spad{yn} \\spad{x)} y1'(x) + gi(x, \\spad{y1} \\spad{x,} \\spad{y2} x,..., \\spad{yn} \\spad{x)} = h(x, \\spad{y1} \\spad{x,} \\spad{y2} x,..., \\spad{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, \\spad{y} \\spad{x,} y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y \\spad{x,} y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, \\spad{y} a = \\spad{b)}} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = \\spad{b}.} Note that \\spad{eq} must be of the form \\spad{f(x, \\spad{y} \\spad{x)} y'(x) + g(x, \\spad{y} \\spad{x)} = h(x, \\spad{y} x)}."))) NIL NIL -(-313 R -3280 UTSF UTSSUPF) +(-314 R -3313 UTSF UTSSUPF) ((|constructor| (NIL "This package has no description"))) NIL NIL -(-314) +(-315) ((|constructor| (NIL "Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\", the tube is considered to be closed; if \\spad{s} = \"open\", the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\", the tube is considered to be closed; if \\spad{s} = \"open\", the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius r(t) with \\spad{n} points on each circle about the curve \\spad{x = f(t)}, \\spad{y = g(t)}, \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s,} which may be a function of a constant, and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s.}"))) NIL NIL -(-315 FE |var| |cen|) +(-316 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 * \\spad{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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|))))) (|HasCategory| (-412 (-571)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-316 K) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasCategory| (-413 (-572)) (QUOTE (-1110))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-317 K) ((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) NIL NIL -(-317 M) +(-318 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + \\spad{...} + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, \\spad{n)}} returns \\spad{(p, \\spad{r,} [r1,...,rm])} such that the nth-root of \\spad{f} is equal to \\spad{r * \\spad{pth-root(r1} * \\spad{...} * rm)}, where r1,...,rm are distinct factors of \\spad{f,} each of which has an exponent smaller than \\spad{p} in \\spad{f.}"))) NIL NIL -(-318 K) +(-319 K) ((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) NIL NIL -(-319 E OV R P) +(-320 E OV R P) ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between \\spad{-k} and \\spad{k} as a member of \\spad{R.}")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R.} An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of upoly.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R.}"))) NIL NIL -(-320 S) +(-321 S) ((|constructor| (NIL "Free abelian group on any set of generators The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the si's are in \\spad{S,} and the ni's are integers. The operation is commutative."))) -((-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-571) (QUOTE (-792)))) -(-321 S E) +((-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| (-572) (QUOTE (-793)))) +(-322 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the si's are in \\spad{S,} and the ni's are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 \\spad{a1} + \\spad{...} + en an, \\spad{f1} \\spad{b1} + \\spad{...} + \\spad{fm} bm)} returns \\spad{reduce(+,[max(ei, fi) ci])} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, \\spad{e1} \\spad{a1} +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, \\spad{e1} \\spad{a1} +...+ en an)} returns \\spad{f(e1) \\spad{a1} +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, \\spad{e1} \\spad{a1} + \\spad{...} + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s,} or 0 if \\spad{s} is not one of the ai's.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, \\spad{n)}} returns the factor of the n^th term of \\spad{x.}")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, \\spad{n)}} returns the coefficient of the n^th term of \\spad{x.}")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 \\spad{a1} + \\spad{...} + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\indented{1}{size(x) returns the number of terms in \\spad{x.}} \\indented{1}{mapGen(f, \\spad{a1\\^e1} \\spad{...} an\\^en) returns} \\spad{f(a1)\\^e1 \\spad{...} f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * \\spad{s}} returns \\spad{e} times \\spad{s.}")) (+ (($ |#1| $) "\\spad{s + \\spad{x}} returns the sum of \\spad{s} and \\spad{x.}"))) NIL NIL -(-322 S) +(-323 S) ((|constructor| (NIL "Free abelian monoid on any set of generators The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the si's are in \\spad{S,} and the ni's are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-768) (QUOTE (-792)))) -(-323 E R1 A1 R2 A2) +((|HasCategory| (-769) (QUOTE (-793)))) +(-324 E R1 A1 R2 A2) ((|constructor| (NIL "This package provides a mapping function for \\spadtype{FiniteAbelianMonoidRing} The packages defined in this file provide fast fraction free rational interpolation algorithms. (see FAMR2, FFFG, FFFGF, NEWTON)")) (|map| ((|#5| (|Mapping| |#4| |#2|) |#3|) "\\spad{map}(f, a) applies the map \\spad{f} to each coefficient in a. It is assumed that \\spad{f} maps 0 to 0"))) NIL NIL -(-324 S R E) +(-325 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing, except that the sum is assumed to be finite. It is a useful model for polynomials, but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p.}")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p.}")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r,} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * \\spad{p2}} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial u.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p.} Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p.}")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p.}")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) -(-325 R E) +((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) +(-326 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing, except that the sum is assumed to be finite. It is a useful model for polynomials, but is somewhat more general.")) (|primitivePart| (($ $) "\\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| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * \\spad{p2}} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial 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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-326 S) +(-327 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."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-327 S -3280) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-328 S -3313) ((|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 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,} that is, for elements a from \\spad{K,} \\spad{c,d} from \\spad{F} and \\spad{f,g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,f) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,g). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from F[X]: \\spadfun{linearAssociatedExp}(a,monomial(1,k)\\$SUP(F)) is defined to be \\spadfun{Frobenius}(a,k) which is a**(q**k) where q=size()\\$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}(b,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(),g) equals a.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial \\spad{g} of least degree, such that \\spadfun{linearAssociatedExp}(a,g) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over \\spad{F,} that is, for elements a from \\spad{\\$,} \\spad{c,d} form \\spad{F} and \\spad{f,g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,f) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,g). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from F[X]: \\spadfun{linearAssociatedExp}(a,monomial(1,k)\\$SUP(F)) is defined to be \\spadfun{Frobenius}(a,k) which is a**(q**k), where q=size()\\$F.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F,} that is, \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} \\spad{<=} extensionDegree()-1} is an F-basis, where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element, normal over the ground field \\spad{F,} thus \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} < extensionDegree()} is an F-basis, where \\spad{q = size()\\$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| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F,} that is, \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} < extensionDegree()} is an F-basis, where \\spad{q = size()\\$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 \\spad{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,d) = reduce(*,[a**(q**(d*i)) for \\spad{i} in 0..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 + \\spad{...} + an*vn}, where v1,...,vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the vi'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 (-373)))) -(-328 -3280) +((|HasCategory| |#2| (QUOTE (-374)))) +(-329 -3313) ((|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 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,} that is, for elements a from \\spad{K,} \\spad{c,d} from \\spad{F} and \\spad{f,g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,f) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,g). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from F[X]: \\spadfun{linearAssociatedExp}(a,monomial(1,k)\\$SUP(F)) is defined to be \\spadfun{Frobenius}(a,k) which is a**(q**k) where q=size()\\$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}(b,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(),g) equals a.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial \\spad{g} of least degree, such that \\spadfun{linearAssociatedExp}(a,g) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over \\spad{F,} that is, for elements a from \\spad{\\$,} \\spad{c,d} form \\spad{F} and \\spad{f,g} univariate polynomials over \\spad{F} we have \\spadfun{linearAssociatedExp}(a,cf+dg) equals \\spad{c} times \\spadfun{linearAssociatedExp}(a,f) plus \\spad{d} times \\spadfun{linearAssociatedExp}(a,g). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from F[X]: \\spadfun{linearAssociatedExp}(a,monomial(1,k)\\$SUP(F)) is defined to be \\spadfun{Frobenius}(a,k) which is a**(q**k), where q=size()\\$F.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F,} that is, \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} \\spad{<=} extensionDegree()-1} is an F-basis, where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element, normal over the ground field \\spad{F,} thus \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} < extensionDegree()} is an F-basis, where \\spad{q = size()\\$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| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F,} that is, \\spad{a**(q**i), 0 \\spad{<=} \\spad{i} < extensionDegree()} is an F-basis, where \\spad{q = size()\\$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 \\spad{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,d) = reduce(*,[a**(q**(d*i)) for \\spad{i} in 0..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 + \\spad{...} + an*vn}, where v1,...,vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the vi'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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-329) +(-330) ((|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}'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}'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}'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}'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}'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}'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|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF \\spad{(s)} THEN e.")) (|returns| (($ (|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|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat \\spad{...} until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n.}") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) NIL NIL -(-330 E) +(-331 E) ((|constructor| (NIL "This domain creates kernels for use in Fourier series")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin, otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) NIL NIL -(-331) +(-332) ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and, where appropriate, naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1, I2, and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,b,d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,p,q)} uses loop variables in the Fortran, \\spad{I1} and \\spad{I2}")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,p)} \\undocumented{}"))) NIL NIL -(-332 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +(-333 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lift a map to finite divisors.")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-333 S -3280 UP UPUP R) +(-334 S -3313 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve, that is finite formal sums SUM(n * \\spad{P)} where the \\spad{n's} are integers and the \\spad{P's} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = \\spad{d},} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, \\spad{f]}} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, \\spad{d,} \\spad{d',} \\spad{g,} \\spad{r)}} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, \\spad{b,} \\spad{n)}} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, \\spad{y} = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, \\spad{b)}} makes the divisor \\spad{P:} \\spad{(x = a, \\spad{y} = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g.}") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal I.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D.}"))) NIL NIL -(-334 -3280 UP UPUP R) +(-335 -3313 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve, that is finite formal sums SUM(n * \\spad{P)} where the \\spad{n's} are integers and the \\spad{P's} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = \\spad{d},} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, \\spad{f]}} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, \\spad{d,} \\spad{d',} \\spad{g,} \\spad{r)}} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, \\spad{b,} \\spad{n)}} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, \\spad{y} = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, \\spad{b)}} makes the divisor \\spad{P:} \\spad{(x = a, \\spad{y} = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g.}") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal I.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D.}"))) NIL NIL -(-335 -3280 UP UPUP R) +(-336 -3313 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve, that is finite formal sums SUM(n * \\spad{P)} where the \\spad{n's} are integers and the \\spad{P's} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = \\spad{{f} | \\spad{(f)} \\spad{>=} -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over K[x]."))) NIL NIL -(-336 S R) +(-337 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex, applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -282) (|devaluate| |#2|) (|devaluate| |#2|)))) -(-337 R) +((|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -283) (|devaluate| |#2|) (|devaluate| |#2|)))) +(-338 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex, applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL -(-338 |basicSymbols| |subscriptedSymbols| R) +(-339 |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{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of 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."))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#3| (LIST (QUOTE -1043) (QUOTE (-384)))) (|HasCategory| $ (QUOTE (-1053))) (|HasCategory| $ (LIST (QUOTE -1043) (QUOTE (-571))))) -(-339 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-385)))) (|HasCategory| $ (QUOTE (-1054))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-572))))) +(-340 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, \\spad{p)}} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p.}"))) NIL NIL -(-340 S -3280 UP UPUP) +(-341 S -3313 UP UPUP) ((|constructor| (NIL "Function field of a curve This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,...,un of \\indented{1}{an affine non-singular model for the curve.}")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, \\spad{D)}} returns \\spad{[h,d,d',g]} such that \\indented{1}{\\spad{f=h/d},} \\indented{1}{\\spad{h} is integral at all the normal places w.r.t. \\spad{D},} \\indented{1}{\\spad{d' = Dd}, \\spad{g = gcd(d, discriminant())} and \\spad{D}} \\indented{1}{is the derivation to use. \\spad{f} must have at most simple finite} \\indented{1}{poles.}")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the \\indented{1}{hyperelliptic} \\indented{1}{defined by \\spad{y**2 = p(x)}, \"failed\" otherwise.}")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic \\indented{1}{defined by \\spad{y**2 = p(x)}, \"failed\" otherwise.}")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or f(a, \\spad{b)} returns the value of \\spad{f} \\indented{1}{at the point \\spad{(x = a, \\spad{y} = b)}} \\indented{1}{if it is not singular.}")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and \\indented{1}{the common content of the numerator of \\spad{f.}}")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, \\spad{d)}} extends the derivation \\spad{d} from UP to \\$ and \\indented{1}{applies it to \\spad{x.}}")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ \\indented{1}{and returns \\spad{(M,} \\spad{Q)} such that the i^th row of \\spad{M} divided by \\spad{Q} form} \\indented{1}{the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral basis returned} \\indented{1}{by integralBasis().}")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], \\spad{D)}} returns \\indented{1}{\\spad{(A1 w1+...+An wn)/D}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral} \\indented{1}{basis of \\spad{integralBasis()}.}")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], \\spad{D]}} such that \\indented{1}{\\spad{f = \\spad{(A1} \\spad{w1} +...+ An \\spad{wn)} / D}\\space{2}where \\spad{(w1,...,wn)} is the} \\indented{1}{integral basis returned by \\spad{integralBasis()}.}")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\indented{1}{\\spad{(A0 + \\spad{A1} \\spad{y} +...+ A(n-1)*y**(n-1))/D}.}") (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\indented{1}{\\spad{(A0 + \\spad{A1} \\spad{y} +...+ A(n-1)*y**(n-1))/D}.}")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], \\spad{D]}} such that \\indented{1}{\\spad{f = \\spad{(A1} + \\spad{A2} \\spad{y} +...+ An y**(n-1)) / D}.}")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such \\indented{1}{that \\spad{M (v1,...,vn) = \\spad{(1,} \\spad{y,} ..., y**(n-1))}} \\indented{1}{where \\spad{(v1,...,vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} inverseIntegralMatrixAtInfinity()$R")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\indented{1}{\\spad{(v1,...,vn) = \\spad{M} \\spad{(1,} \\spad{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(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralMatrixAtInfinity()$R")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\indented{1}{\\spad{M (w1,...,wn) = \\spad{(1,} \\spad{y,} ..., y**(n-1))}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} inverseIntegralMatrix()$R")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\indented{1}{\\spad{(w1,...,wn) = \\spad{M} \\spad{(1,} \\spad{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(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralMatrix()$R")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} \\indented{1}{for all i,j such that \\spad{x**i*bj} is locally integral} \\indented{1}{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 \\indented{1}{\\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.}")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, \\spad{p)}} tests whether \\spad{f} is locally integral at \\indented{1}{\\spad{p(x) = 0}}") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis \\indented{1}{at infinity} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralBasisAtInfinity()$R")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve. \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralBasis()$R")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point \\indented{1}{at infinity.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} branchPointAtInfinity?()$R \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} branchPointAtInfinity?()$R")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, \\spad{b)}} tests if \\spad{(x=a,y=b)} is on the curve. \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} rationalPoint?(0,0)$R \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} \\spad{rationalPoint?(0,0)$R2}")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible? \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} \\spad{absolutelyIrreducible?()$R2}")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} genus()$R")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible \\indented{1}{components.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} numberOfComponents()$R"))) NIL -((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-367)))) -(-341 -3280 UP UPUP) +((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-368)))) +(-342 -3313 UP UPUP) ((|constructor| (NIL "Function field of a curve This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,...,un of \\indented{1}{an affine non-singular model for the curve.}")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, \\spad{D)}} returns \\spad{[h,d,d',g]} such that \\indented{1}{\\spad{f=h/d},} \\indented{1}{\\spad{h} is integral at all the normal places w.r.t. \\spad{D},} \\indented{1}{\\spad{d' = Dd}, \\spad{g = gcd(d, discriminant())} and \\spad{D}} \\indented{1}{is the derivation to use. \\spad{f} must have at most simple finite} \\indented{1}{poles.}")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the \\indented{1}{hyperelliptic} \\indented{1}{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 \\indented{1}{defined by \\spad{y**2 = p(x)}, \"failed\" otherwise.}")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or f(a, \\spad{b)} returns the value of \\spad{f} \\indented{1}{at the point \\spad{(x = a, \\spad{y} = b)}} \\indented{1}{if it is not singular.}")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and \\indented{1}{the common content of the numerator of \\spad{f.}}")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, \\spad{d)}} extends the derivation \\spad{d} from UP to \\$ and \\indented{1}{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 \\$ \\indented{1}{and returns \\spad{(M,} \\spad{Q)} such that the i^th row of \\spad{M} divided by \\spad{Q} form} \\indented{1}{the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral basis returned} \\indented{1}{by integralBasis().}")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], \\spad{D)}} returns \\indented{1}{\\spad{(A1 w1+...+An wn)/D}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral} \\indented{1}{basis of \\spad{integralBasis()}.}")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], \\spad{D]}} such that \\indented{1}{\\spad{f = \\spad{(A1} \\spad{w1} +...+ An \\spad{wn)} / D}\\space{2}where \\spad{(w1,...,wn)} is the} \\indented{1}{integral basis returned by \\spad{integralBasis()}.}")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\indented{1}{\\spad{(A0 + \\spad{A1} \\spad{y} +...+ A(n-1)*y**(n-1))/D}.}") (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\indented{1}{\\spad{(A0 + \\spad{A1} \\spad{y} +...+ A(n-1)*y**(n-1))/D}.}")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], \\spad{D]}} such that \\indented{1}{\\spad{f = \\spad{(A1} + \\spad{A2} \\spad{y} +...+ An y**(n-1)) / D}.}")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such \\indented{1}{that \\spad{M (v1,...,vn) = \\spad{(1,} \\spad{y,} ..., y**(n-1))}} \\indented{1}{where \\spad{(v1,...,vn)} is the local integral basis at infinity} \\indented{1}{returned by \\spad{infIntBasis()}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} inverseIntegralMatrixAtInfinity()$R")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\indented{1}{\\spad{(v1,...,vn) = \\spad{M} \\spad{(1,} \\spad{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(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralMatrixAtInfinity()$R")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\indented{1}{\\spad{M (w1,...,wn) = \\spad{(1,} \\spad{y,} ..., y**(n-1))}} \\indented{1}{where \\spad{(w1,...,wn)} is the integral basis of} \\indented{1}{\\spadfunFrom{integralBasis}{FunctionFieldCategory}.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} inverseIntegralMatrix()$R")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\indented{1}{\\spad{(w1,...,wn) = \\spad{M} \\spad{(1,} \\spad{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(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralMatrix()$R")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} \\indented{1}{for all i,j such that \\spad{x**i*bj} is locally integral} \\indented{1}{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 \\indented{1}{\\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.}")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, \\spad{p)}} tests whether \\spad{f} is locally integral at \\indented{1}{\\spad{p(x) = 0}}") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis \\indented{1}{at infinity} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralBasisAtInfinity()$R")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve. \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} integralBasis()$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|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point \\indented{1}{at infinity.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} branchPointAtInfinity?()$R \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} branchPointAtInfinity?()$R")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, \\spad{b)}} tests if \\spad{(x=a,y=b)} is on the curve. \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} rationalPoint?(0,0)$R \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} \\spad{rationalPoint?(0,0)$R2}")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible? \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R2} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 2 * x**2, 4) \\spad{X} \\spad{absolutelyIrreducible?()$R2}")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} genus()$R")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible \\indented{1}{components.} \\blankline \\spad{X} \\spad{P0} \\spad{:=} UnivariatePolynomial(x, Integer) \\spad{X} \\spad{P1} \\spad{:=} UnivariatePolynomial(y, Fraction \\spad{P0)} \\spad{X} \\spad{R} \\spad{:=} RadicalFunctionField(INT, \\spad{P0,} \\spad{P1,} 1 - x**20, 20) \\spad{X} numberOfComponents()$R"))) -((-4593 |has| (-412 |#2|) (-367)) (-4598 |has| (-412 |#2|) (-367)) (-4592 |has| (-412 |#2|) (-367)) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 |has| (-413 |#2|) (-368)) (-4600 |has| (-413 |#2|) (-368)) (-4594 |has| (-413 |#2|) (-368)) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-342 |p| |extdeg|) +(-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(p,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-910 |#1|) (QUOTE (-151))) (|HasCategory| (-910 |#1|) (QUOTE (-373))) (|HasCategory| (-910 |#1|) (QUOTE (-149))) (-1831 (|HasCategory| (-910 |#1|) (QUOTE (-149))) (|HasCategory| (-910 |#1|) (QUOTE (-373))))) -(-343 GF |defpol|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-911 |#1|) (QUOTE (-151))) (|HasCategory| (-911 |#1|) (QUOTE (-374))) (|HasCategory| (-911 |#1|) (QUOTE (-149))) (-1841 (|HasCategory| (-911 |#1|) (QUOTE (-149))) (|HasCategory| (-911 |#1|) (QUOTE (-374))))) +(-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-344 GF |extdeg|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-345 K |PolK|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-346 K |PolK|) ((|constructor| (NIL "Part of the PAFF package"))) NIL NIL -(-346 K |PolK|) +(-347 K |PolK|) ((|constructor| (NIL "Part of the package for Algebraic Function Fields in one variable (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 -(-347 -1544 V VF) +(-348 -1557 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 FAMR2, FFFG, FFFGF, NEWTON)")) (|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#3|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalInterpolation(l, CA, \\spad{f,} sumEta, maxEta)} applies generalInterpolation(l, 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, \\spad{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 + e.i - [1,1,...,1], where the degree of zero is \\spad{-1.}"))) NIL NIL -(-348 -1544 V) +(-349 -1557 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 FAMR2, FFFG, FFFGF, NEWTON)")) (|qShiftC| (((|List| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{qShiftC} gives the coefficients c_{k,k} in the expansion \\spad{z} g(x) = sum_{i=0}^k c_{k,i} g(x), where \\spad{z} acts on g(x) by shifting. In fact, the result is [1,q,q^2,...]")) (|qShiftAction| ((|#1| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{qShiftAction(q, \\spad{k,} \\spad{l,} \\spad{g)}} gives the coefficient of \\spad{x^k} in \\spad{z^l} g(x), where 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(n)=q^n*u(n).")) (|DiffC| (((|List| |#1|) (|NonNegativeInteger|)) "\\spad{DiffC} gives the coefficients c_{k,k} in the expansion \\spad{z} g(x) = sum_{i=0}^k c_{k,i} g(x), where \\spad{z} acts on g(x) by shifting. In fact, the result is [0,0,0,...]")) (|DiffAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{DiffAction(k, \\spad{l,} \\spad{g)}} gives the coefficient of \\spad{x^k} in \\spad{z^l} g(x), where 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 c_{k,k} in the expansion \\spad{z} g(x) = sum_{i=0}^k c_{k,i} g(x), where \\spad{z} acts on g(x) by shifting. In fact, the result is [0,1,2,...]")) (|ShiftAction| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{ShiftAction(k, \\spad{l,} \\spad{g)}} gives the coefficient of \\spad{x^k} in \\spad{z^l} g(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(n)=n*u(n).")) (|generalCoefficient| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|Vector| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalCoefficient(action, \\spad{f,} \\spad{k,} \\spad{p)}} gives the coefficient of \\spad{x^k} in p(z)\\dot f(x), where the \\spad{action} of \\spad{z^l} on a polynomial in \\spad{x} is given by action, \\spadignore{i.e.} action(k, \\spad{l,} \\spad{f)} should return the coefficient of \\spad{x^k} in \\spad{z^l} f(x).")) (|generalInterpolation| (((|Stream| (|Matrix| (|SparseUnivariatePolynomial| |#1|))) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalInterpolation(C, CA, \\spad{f,} sumEta, maxEta)} applies \\spad{generalInterpolation(C, CA, \\spad{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 c_{k,k} in the expansion \\spad{z} g(x) = sum_{i=0}^k c_{k,i} g(x). \\blankline The second argument, CA(k, \\spad{l,} \\spad{f),} should return the coefficient of \\spad{x^k} in \\spad{z^l} f(x).") (((|Matrix| (|SparseUnivariatePolynomial| |#1|)) (|List| |#1|) (|Mapping| |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) (|Vector| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{generalInterpolation(C, CA, \\spad{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 + e.i - [1,1,...,1], where the degree of zero is \\spad{-1.} \\blankline The first argument \\spad{C} is the list of coefficients c_{k,k} in the expansion \\spad{z} g(x) = sum_{i=0}^k c_{k,i} g(x). \\blankline The second argument, CA(k, \\spad{l,} \\spad{f),} should return the coefficient of \\spad{x^k} in \\spad{z^l} f(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 c_{i,i}. These are the only values of \\spad{C} explicitely needed in \\spad{fffg}. \\blankline The second argument \\spad{c,} computes c_k(M), \\spadignore{i.e.} 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 -(-349 GF) +(-350 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field \\spad{GF,} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree \\spad{n} over \\spad{GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(n) to produce a normal polynomial of degree \\spad{n} over \\spad{GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree \\spad{n} over \\spad{GF} and returns its multiplication matrix Fails, if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table \\spad{m.}")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table \\spad{m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by \\spad{f.} This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP}, \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial f(x), \\spadignore{i.e.} \\spad{Z(i)}, defined by x**Z(i) = 1+x**i is stored at index i. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP}, \\spadtype{FFCGX}."))) NIL NIL -(-350 F1 GF F2) +(-351 F1 GF F2) ((|constructor| (NIL "FiniteFieldHomomorphisms(F1,GF,F2) exports coercion functions of elements between the fields \\spad{F1} and \\spad{F2,} which both must be finite simple algebraic extensions of the finite ground field \\spad{GF.}")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from \\spad{F2} in \\spad{F1,} where coerce is a field homomorphism between the fields extensions \\spad{F2} and \\spad{F1} both over ground field \\spad{GF} (the second argument to the package). Error: if the extension degree of \\spad{F2} doesn't divide the extension degree of \\spad{F1.} Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from \\spad{F1} in \\spad{F2.} Thus coerce is a field homomorphism between the fields extensions \\spad{F1} and \\spad{F2} both over ground field \\spad{GF} (the second argument to the package). Error: if the extension degree of \\spad{F1} doesn't divide the extension degree of \\spad{F2.} Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) NIL NIL -(-351 S) +(-352 S) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation, one of: \\spad{prime}, \\spad{polynomial}, \\spad{normal}, or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field, \\spadignore{i.e.} is a primitive element. Implementation Note that see ch.IX.1.3, \\spad{th.2} in \\spad{D.} Lipson.")) (|primitiveElement| (($) "\\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 \\spad{size()-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)}, given a matrix representing a homogeneous system of equations, returns a vector whose characteristic'th powers is a non-trivial solution, or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of a. Note that such a root is alway defined in finite fields."))) NIL NIL -(-352) +(-353) ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field, \\spadignore{i.e.} is a primitive element. Implementation Note that see ch.IX.1.3, \\spad{th.2} in \\spad{D.} Lipson.")) (|primitiveElement| (($) "\\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 \\spad{size()-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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-353 R UP -3280) +(-354 R UP -3313) ((|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 R-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{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 R-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-354 |p| |extdeg|) +(-355 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(p,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 (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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-910 |#1|) (QUOTE (-151))) (|HasCategory| (-910 |#1|) (QUOTE (-373))) (|HasCategory| (-910 |#1|) (QUOTE (-149))) (-1831 (|HasCategory| (-910 |#1|) (QUOTE (-149))) (|HasCategory| (-910 |#1|) (QUOTE (-373))))) -(-355 GF |uni|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-911 |#1|) (QUOTE (-151))) (|HasCategory| (-911 |#1|) (QUOTE (-374))) (|HasCategory| (-911 |#1|) (QUOTE (-149))) (-1841 (|HasCategory| (-911 |#1|) (QUOTE (-149))) (|HasCategory| (-911 |#1|) (QUOTE (-374))))) +(-356 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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 (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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-356 GF |extdeg|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-357 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,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 (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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-357 |p| |n|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-358 |p| |n|) ((|constructor| (NIL "FiniteField(p,n) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version, see \\spadtype{InnerFiniteField}."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-910 |#1|) (QUOTE (-151))) (|HasCategory| (-910 |#1|) (QUOTE (-373))) (|HasCategory| (-910 |#1|) (QUOTE (-149))) (-1831 (|HasCategory| (-910 |#1|) (QUOTE (-149))) (|HasCategory| (-910 |#1|) (QUOTE (-373))))) -(-358 GF |defpol|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-911 |#1|) (QUOTE (-151))) (|HasCategory| (-911 |#1|) (QUOTE (-374))) (|HasCategory| (-911 |#1|) (QUOTE (-149))) (-1841 (|HasCategory| (-911 |#1|) (QUOTE (-149))) (|HasCategory| (-911 |#1|) (QUOTE (-374))))) +(-359 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF, defpol) implements the extension of the finite field \\spad{GF} generated by the extension polynomial defpol which MUST be irreducible."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-359 -3280 GF) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-360 -3313 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(F,GF) exports some functions concerning finite fields, which depend on a finite field \\spad{GF} and an algebraic extension \\spad{F} of \\spad{GF,} \\spadignore{e.g.} a zero of a polynomial over \\spad{GF} in \\spad{F.}")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic, irreducible polynomial \\spad{f,} which degree must divide the extension degree of \\spad{F} over \\spad{GF,} \\spadignore{i.e.} \\spad{f} splits into linear factors over \\spad{F.}")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-360 GF) +(-361 GF) ((|constructor| (NIL "This package provides a number of functions for generating, counting and testing irreducible, normal, primitive, random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()$GF} and \\spad{n = degree \\spad{f}.}")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field \\spad{GF,} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q,} the size of \\spad{GF.}")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field \\spad{GF,} \\spad{d} between \\spad{m} and \\spad{n.}") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field \\spad{GF.}")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order, or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also, \\spad{f < \\spad{g}} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g} or, in case these numbers are equal, if the lookup of the coefficient of the term of degree \\spad{n-1} of \\spad{f} is less than this number for \\spad{g.} If these numbers are equals, \\spad{f < \\spad{g}} if the number of monomials of \\spad{f} is less than that for \\spad{g,} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g.} If these lists are also equal, the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup. This operation is equivalent to nextNormalPrimitivePoly(f).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order, or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also, \\spad{f < \\spad{g}} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g} or if lookup of the coefficient of the term of degree \\spad{n-1} of \\spad{f} is less than this number for \\spad{g.} Otherwise, \\spad{f < \\spad{g}} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g.} If these lists are also equal, the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup. This operation is equivalent to nextPrimitiveNormalPoly(f).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order, or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also, \\spad{f < \\spad{g}} if the lookup of the coefficient of the term of degree \\spad{n-1} of \\spad{f} is less than that for \\spad{g.} In case these numbers are equal, \\spad{f < \\spad{g}} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g.} If these lists are also equal, the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order, or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also, \\spad{f < \\spad{g}} if the lookup of the constant term of \\spad{f} is less than this number for \\spad{g.} If these values are equal, then \\spad{f < \\spad{g}} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g.} If these lists are also equal, the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field \\spad{GF} of the same degree as \\spad{f} in the following order, or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note that the input polynomial \\spad{f} is made monic. Also, \\spad{f < \\spad{g}} if the number of monomials of \\spad{f} is less than this number for \\spad{g.} If \\spad{f} and \\spad{g} have the same number of monomials, the lists of exponents are compared lexicographically. If these lists are also equal, the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of \\spad{GF} given by lookup.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field \\spad{GF.} polynomial of degree \\spad{n} over the field \\spad{GF.}")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field \\spad{GF.} Note that this function is equivalent to createPrimitiveNormalPoly(n)")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field \\spad{GF.}")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field \\spad{GF.}")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field \\spad{GF.}")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field \\spad{GF.}")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field \\spad{GF.}")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field \\spad{GF.}")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal, \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive, \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-361 -3280 FP FPP) +(-362 -3313 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], \\spad{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 ai's exists."))) NIL NIL -(-362 K |PolK|) +(-363 K |PolK|) ((|constructor| (NIL "Part of the package for Algebraic Function Fields in one variable (PAFF)"))) NIL NIL -(-363 GF |n|) +(-364 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-149))) (-1831 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373))))) -(-364 R |ls|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-149))) (-1841 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374))))) +(-365 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 \\spad{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(lq1)} returns the lexicographical Groebner basis of \\axiom{lq1}. If \\axiom{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(lq1)} returns the lexicographical Groebner basis of \\axiom{lq1} by using the FGLM strategy, if \\axiom{zeroDimensional?(lq1)} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(lq1)} returns \\spad{true} iff \\axiom{lq1} generates a zero-dimensional ideal w.r.t. the variables of \\axiom{ls}."))) NIL NIL -(-365 S) +(-366 S) ((|constructor| (NIL "Free group on any set of generators The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si \\spad{**} ni])} where the si's are in \\spad{S,} and the ni'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|) $) "\\spad{mapGen(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{f(a1)\\^e1 \\spad{...} f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{a1\\^f(e1) \\spad{...} an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, \\spad{n)}} returns the factor of the n^th monomial of \\spad{x.}")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, \\spad{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 \\spad{**} \\spad{n}} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * \\spad{s}} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * \\spad{x}} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4597 . T)) +((-4599 . T)) NIL -(-366 S) +(-367 S) ((|constructor| (NIL "The category of commutative fields, \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\br \\tab{5}\\spad{a*(b/a) = b}\\br \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0}, \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y.} Error: if \\spad{y} is 0."))) NIL NIL -(-367) +(-368) ((|constructor| (NIL "The category of commutative fields, \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline Axioms\\br \\tab{5}\\spad{a*(b/a) = b}\\br \\tab{5}\\spad{inv(a) = 1/a}")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0}, \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y.} Error: if \\spad{y} is 0."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-368 |Name| S) +(-369 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer's file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S.}")) (|flush| (((|Void|) $) "\\spad{flush(f)} makes sure that buffered data is written out")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f.} The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f.} The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f.} The input/output status of \\spad{f} may be \"input\", \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f.}")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) NIL NIL -(-369 S) +(-370 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f,} if possible. If \\spad{f} is not open for reading, or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) NIL NIL -(-370 S R) +(-371 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit, similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left, respectively right, minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique), or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique), or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique), or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra, or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra, or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note that the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities, that is, 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},b,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'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'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'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},b,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 \\spad{:=} 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},b,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 \\spad{:=} (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, that is, satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra, that is, 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},b,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'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'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'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't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative, that is, \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},b,c in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note that this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the left trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + \\spad{...} + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},...,\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},...,\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for \\spad{k} in 1..m]} defined by \\spad{vi * \\spad{vj} = \\spad{gammaij1} * \\spad{v1} + \\spad{...} + gammaijm * vm}, where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},...,\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-561)))) -(-371 R) +((|HasCategory| |#2| (QUOTE (-562)))) +(-372 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, that is, 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},b,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'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'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'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},b,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 \\spad{:=} 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},b,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 \\spad{:=} (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, that is, satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra, that is, 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},b,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'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'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'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't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative, that is, \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},b,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}-th row and \\spad{j}-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}-th row and \\spad{j}-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}-th row and \\spad{j}-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| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the left trace of the product \\spad{vi*vj}. Note that this is the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + \\spad{...} + 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{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 \\spad{k} in 1..m]} defined by \\spad{vi * \\spad{vj} = \\spad{gammaij1} * \\spad{v1} + \\spad{...} + 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."))) -((-4597 |has| |#1| (-561)) (-4595 . T) (-4594 . T)) +((-4599 |has| |#1| (-562)) (-4597 . T) (-4596 . T)) NIL -(-372 S) +(-373 S) ((|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")) (|enumerate| (((|List| $)) "\\indented{1}{enumerate() returns a list of elements of the set} \\blankline \\spad{X} enumerate()$OrderedVariableList([p,q])")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup \\spad{x}.}")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}-th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) NIL NIL -(-373) +(-374) ((|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")) (|enumerate| (((|List| $)) "\\indented{1}{enumerate() returns a list of elements of the set} \\blankline \\spad{X} enumerate()$OrderedVariableList([p,q])")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup \\spad{x}.}")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}-th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) NIL NIL -(-374 S R UP) +(-375 S R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free R-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the n-by-n matrix ( Tr(vi * \\spad{vj)} )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1+...+an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the vi's with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) NIL -((|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-367)))) -(-375 R UP) +((|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-368)))) +(-376 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free 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 n-by-n matrix ( Tr(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 vi'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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-376 S A R B) +(-377 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely, if \\spad{a} is \\spad{[a1,a2,...]}, then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r.} For example, \\spad{reduce(_+$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note that third argument \\spad{r} may be regarded as the identity element for the function \\spad{f.}")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) NIL NIL -(-377 A S) +(-378 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 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{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{p(x)} is 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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p.}")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note that \\axiom{sort(u) = sort(<=,u)}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p.}")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note that \\axiom{merge(u,v) = merge(<=,u,v)}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b.} The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{p(x,y)} is true, then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen, the next element of \\axiom{a} is examined, and so on. When all the elements of one aggregate are examined, the remaining elements of the other are appended. For example, \\axiom{merge(<,[1,3],[2,7,5])} returns \\axiom{[1,2,3,7,5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4601)) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097)))) -(-378 S) +((|HasAttribute| |#1| (QUOTE -4603)) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098)))) +(-379 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse}, \\spadfun{sort}, and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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 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{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{p(x)} is 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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p.}")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note that \\axiom{sort(u) = sort(<=,u)}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p.}")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note that \\axiom{merge(u,v) = merge(<=,u,v)}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b.} The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{p(x,y)} is true, then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen, the next element of \\axiom{a} is examined, and so on. When all the elements of one aggregate are examined, the remaining elements of the other are appended. For example, \\axiom{merge(<,[1,3],[2,7,5])} returns \\axiom{[1,2,3,7,5]}."))) -((-4600 . T) (-3348 . T)) +((-4602 . T) (-3389 . T)) NIL -(-379 |VarSet| R) +(-380 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}.")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(p, [x1,...,xn], [v1,...,vn])} replaces \\axiom{xi} by \\axiom{vi} in \\axiom{p}.") (($ $ |#1| $) "\\axiom{eval(p, \\spad{x,} \\spad{v)}} replaces \\axiom{x} by \\axiom{v} in \\axiom{p}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(x)} returns the list of distinct entries of \\axiom{x}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(p,n)} returns the polynomial \\axiom{p} truncated at order \\axiom{n}.")) (|mirror| (($ $) "\\axiom{mirror(x)} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{x} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(l)} returns the bracketed form of \\axiom{l} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(x,y)} returns the right simplification of \\axiom{x} by \\axiom{y}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(x,y)} returns the left simplification of \\axiom{x} by \\axiom{y}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(x)} returns the greatest length of a word in the support of \\axiom{x}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(x)} returns \\axiom{x} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(x)} returns \\axiom{x} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(x)} returns \\axiom{x} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(x,y)} returns the scalar product of \\axiom{x} by \\axiom{y}, the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4595 . T) (-4594 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4597 . T) (-4596 . T)) NIL -(-380 S V) +(-381 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates. Sort package (in-place) for shallowlyMutable Finite Linear Aggregates")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) NIL NIL -(-381 S R) +(-382 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver \\spad{R}} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver \\spad{R}} and, in addition, if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer}, then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571))))) -(-382 R) +((|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572))))) +(-383 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver \\spad{R}} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver \\spad{R}} and, in addition, if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer}, then so is \\spad{S}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-383 |Par|) +(-384 |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, \\spad{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 eq, with precision 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 eps.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp.}") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp.}"))) NIL NIL -(-384) +(-385) ((|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 \\spad{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, \\spad{n,} \\spad{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, \\spad{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|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - \\spad{y}} divided by \\spad{y,} when \\spad{y \\spad{\\^=} 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x \\spad{**} \\spad{y}} computes \\spad{exp(y log \\spad{x)}} where \\spad{x \\spad{>=} 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer i."))) -((-4583 . T) (-4591 . T) (-3367 . T) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4585 . T) (-4593 . T) (-3410 . T) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-385 |Par|) +(-386 |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 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 eq, with precision 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 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 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 eps."))) NIL NIL -(-386 R S) +(-387 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}"))) -((-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-173)))) -(-387 R |Basis|) +((-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-174)))) +(-388 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, \\spad{c:} \\spad{R)}} such that \\spad{x} equals \\spad{reduce(+, map(x \\spad{+->} 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}."))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-388) +(-389) ((|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}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-389) +(-390) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP, making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3348 . T)) +((-3389 . T)) NIL -(-390 R S) +(-391 R S) ((|constructor| (NIL "A 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."))) -((-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-173)))) -(-391 S) +((-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-174)))) +(-392 S) ((|constructor| (NIL "Free monoid on any set of generators The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si \\spad{**} ni])} where the si's are in \\spad{S,} and the ni's are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{f(a1)\\^e1 \\spad{...} f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{a1\\^f(e1) \\spad{...} an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, \\spad{n)}} returns the factor of the n^th monomial of \\spad{x.}")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, \\spad{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, \\spad{y)}} returns \\spad{[l, \\spad{m,} \\spad{r]}} such that \\spad{x = \\spad{l} * \\spad{m},} \\spad{y = \\spad{m} * \\spad{r}} and \\spad{l} and \\spad{r} have no overlap, \\spadignore{i.e.} \\spad{overlap(l, \\spad{r)} = \\spad{[l,} 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, \\spad{y)}} returns the left and right exact quotients of \\spad{x} by \\spad{y,} \\spadignore{i.e.} \\spad{[l, \\spad{r]}} such that \\spad{x = \\spad{l} * \\spad{y} * \\spad{r},} \"failed\" if \\spad{x} is not of the form \\spad{l * \\spad{y} * \\spad{r}.}")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, \\spad{y)}} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = \\spad{q} * \\spad{y},} \"failed\" if \\spad{x} is not of the form \\spad{q * \\spad{y}.}")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, \\spad{y)}} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = \\spad{y} * \\spad{q},} \"failed\" if \\spad{x} is not of the form \\spad{y * \\spad{q}.}")) (|hcrf| (($ $ $) "\\spad{hcrf(x, \\spad{y)}} returns the highest common right factor of \\spad{x} and \\spad{y,} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a \\spad{d}} and \\spad{y = \\spad{b} \\spad{d}.}")) (|hclf| (($ $ $) "\\spad{hclf(x, \\spad{y)}} returns the highest common left factor of \\spad{x} and \\spad{y,} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = \\spad{d} a} and \\spad{y = \\spad{d} \\spad{b}.}")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s \\spad{**} \\spad{n}} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * \\spad{s}} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * \\spad{x}} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL -((|HasCategory| |#1| (QUOTE (-847)))) -(-392) +((|HasCategory| |#1| (QUOTE (-848)))) +(-393) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-393) +(-394) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL NIL -(-394) +(-395) ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory, \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string, a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory, \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string, a default is used.")) (|coerce| (((|String|) $) "\\spad{coerce(fn)} produces a string for a file name according to operating system-dependent conventions.") (($ (|String|)) "\\spad{coerce(s)} converts a string to a file name according to operating system-dependent conventions."))) NIL NIL -(-395 |n| |class| R) +(-396 |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"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-396) +(-397) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-397 -3280 UP UPUP R) +(-398 -3313 UP UPUP R) ((|constructor| (NIL "Finds the order of a divisor over a finite field")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-398 S) +(-399 S) ((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) NIL NIL -(-399) +(-400) ((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue, a formula part and an epilogue. The functions \\spadfun{prologue}, \\spadfun{formula} and \\spadfun{epilogue} extract these parts, respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!}, \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example, the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a formatted object \\spad{t} to strings.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,strings)} sets the formula section of a formatted object \\spad{t} to strings.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a formatted object \\spad{t} to strings.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t.}")) (|new| (($) "\\spad{new()} create a new, empty object. Use \\spadfun{setPrologue!}, \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t.}")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t.}")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{width}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to SCRIPT formula format."))) NIL NIL -(-400) +(-401) ((|constructor| (NIL "FortranProgramCategory provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(u)} translates \\axiom{u} into a legal FORTRAN subprogram."))) -((-3348 . T)) +((-3389 . T)) NIL -(-401) +(-402) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP, making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3348 . T)) +((-3389 . T)) NIL -(-402) +(-403) ((|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 -(-403 -3159 |returnType| |arguments| |symbols|) +(-404 -3201 |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 -(-404 -3280 UP) +(-405 -3313 UP) ((|constructor| (NIL "Full partial fraction expansion of rational functions")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{f.}") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f.}")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, \\spad{n)}} returns the \\spad{n}-th derivative of \\spad{f.}") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f.}")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f.}")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, \\spad{Dj,} Hj]...]]} such that \\spad{f = p(x) + sum_{[j,Dj,Hj] in \\spad{l}} sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + \\spad{x}} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL -(-405 R) +(-406 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-3348 . T)) +((-3389 . T)) NIL -(-406 S) +(-407 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic, \\spadignore{e.g.} finite fields, algebraic closures of fields of prime characteristic, transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a**p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) NIL NIL -(-407) +(-408) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic, \\spadignore{e.g.} finite fields, algebraic closures of fields of prime characteristic, transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-408 S) +(-409 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact, it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline 1: base of the exponent where the actual implemenations are usually binary or decimal)\\br 2: precision of the mantissa (arbitrary or fixed)\\br 3: rounding error for operations \\blankline Because a Float is an approximation to the real numbers, even though it is defined to be a join of a Field and OrderedRing, some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x.}")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x.}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order \\spad{x}} is the order of magnitude of \\spad{x.} Note that \\spad{base \\spad{**} order \\spad{x} \\spad{<=} \\spad{|x|} < base \\spad{**} \\spad{(1} + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * \\spad{b} \\spad{**} e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() \\spad{**} e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4583)) (|HasAttribute| |#1| (QUOTE -4591))) -(-409) +((|HasAttribute| |#1| (QUOTE -4585)) (|HasAttribute| |#1| (QUOTE -4593))) +(-410) ((|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)\\br 2: precision of the mantissa (arbitrary or fixed)\\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(\"+\") 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'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's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x.}")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x.}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order \\spad{x}} is the order of magnitude of \\spad{x.} Note that \\spad{base \\spad{**} order \\spad{x} \\spad{<=} \\spad{|x|} < base \\spad{**} \\spad{(1} + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * \\spad{b} \\spad{**} e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() \\spad{**} e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3367 . T) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3410 . T) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-410 R S) +(-411 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{fn} to every factor of \\spadvar{u}. The new factored object will have all its information flags set to \"nil\". This function is used, for example, to coerce every factor base to another type."))) NIL NIL -(-411 A B) +(-412 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction frac."))) NIL NIL -(-412 S) +(-413 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4587 -12 (|has| |#1| (-6 -4598)) (|has| |#1| (-456)) (|has| |#1| (-6 -4587))) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -282) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-553))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828)))) (-12 (|HasAttribute| |#1| (QUOTE -4598)) (|HasAttribute| |#1| (QUOTE -4587)) (|HasCategory| |#1| (QUOTE (-456)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-828))))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-413 S R UP) +((-4589 -12 (|has| |#1| (-6 -4600)) (|has| |#1| (-457)) (|has| |#1| (-6 -4589))) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -283) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-303))) (|HasCategory| |#1| (QUOTE (-554))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829)))) (-12 (|HasAttribute| |#1| (QUOTE -4600)) (|HasAttribute| |#1| (QUOTE -4589)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-829))))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-414 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed R-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the n-by-n matrix ( \\spad{Tr(vi * vj)} \\spad{),} where \\spad{v1,} ..., \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + \\spad{...} + an*vn}, where \\spad{v1,} ..., \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed R-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + \\spad{...} + 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 vi'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 R-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed R-module basis."))) NIL NIL -(-414 R UP) +(-415 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed R-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the n-by-n matrix ( \\spad{Tr(vi * vj)} \\spad{),} where \\spad{v1,} ..., \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + \\spad{...} + an*vn}, where \\spad{v1,} ..., \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed R-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + \\spad{...} + 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 vi'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 R-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed R-module basis."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-415 A S) +(-416 A S) ((|constructor| (NIL "A is fully retractable to \\spad{B} means that A is retractable to \\spad{B} and if \\spad{B} is retractable to the integers or rational numbers then so is A. In particular, what we are asserting is that there are no integers (rationals) in A which don't retract into \\spad{B.}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571))))) -(-416 S) +((|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572))))) +(-417 S) ((|constructor| (NIL "A is fully retractable to \\spad{B} means that A is retractable to \\spad{B} and if \\spad{B} is retractable to the integers or rational numbers then so is A. In particular, what we are asserting is that there are no integers (rationals) in A which don't retract into \\spad{B.}"))) NIL NIL -(-417 R1 F1 U1 A1 R2 F2 U2 A2) +(-418 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "Lifting of morphisms to fractional ideals.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-418 R -3280 UP A) +(-419 R -3313 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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 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)}."))) -((-4597 . T)) +((-4599 . T)) NIL -(-419 R -3280 UP A |ibasis|) +(-420 R -3313 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R.}") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R.}")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f.}")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1043) (|devaluate| |#2|)))) -(-420 AR R AS S) +((|HasCategory| |#4| (LIST (QUOTE -1044) (|devaluate| |#2|)))) +(-421 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL NIL -(-421 S R) +(-422 S R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(R) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication, this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra, defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra, defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by left trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the left trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + \\spad{...} + an*vn}, where \\spad{v1}, ..., \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + \\spad{...} + an*vn}, where \\spad{v1}, ..., \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for \\spad{k} in 1..rank()]} defined by \\spad{vi * \\spad{vj} = \\spad{gammaij1} * \\spad{v1} + \\spad{...} + gammaijn * vn}, where \\spad{v1},...,\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-367)))) -(-422 R) +((|HasCategory| |#2| (QUOTE (-368)))) +(-423 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(R) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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'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|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by left trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the right trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}-th row and \\spad{j}-th column is given by the left trace of the product \\spad{vi*vj}, where \\spad{v1},...,\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note that the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + \\spad{...} + 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 + \\spad{...} + 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 \\spad{k} in 1..rank()]} defined by \\spad{vi * \\spad{vj} = \\spad{gammaij1} * \\spad{v1} + \\spad{...} + 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{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."))) -((-4597 |has| |#1| (-561)) (-4595 . T) (-4594 . T)) +((-4599 |has| |#1| (-562)) (-4597 . T) (-4596 . T)) NIL -(-423 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{u} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{u} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map(fn,u) maps the function \\userfun{fn} across the factors of} \\indented{1}{\\spadvar{u} and creates a new factored object. Note: this clears} \\indented{1}{the information flags (sets them to \"nil\") because the effect of} \\indented{1}{\\userfun{fn} is clearly not known in general.} \\blankline \\spad{X} m(a:Factored Polynomial Integer):Factored Polynomial Integer \\spad{==} \\spad{a^2} \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} map(m,f) \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} map(m,g)")) (|unitNormalize| (($ $) "\\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| $) "\\indented{1}{unit(u) extracts the unit part of the factorization.} \\blankline \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} unit \\spad{f} \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} unit \\spad{g}")) (|flagFactor| (($ |#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 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(u) returns the number of factors in \\spadvar{u}.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} numberOfFactors a")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\indented{1}{nthFlag(u,n) returns the information flag of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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(u,n) returns the base of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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{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(u,n) returns the exponent of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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|)))) $) "\\indented{1}{factors(u) returns a list of the factors in a form suitable} \\indented{1}{for iteration. That is, it returns a list where each element} \\indented{1}{is a record containing a base and exponent.\\space{2}The original} \\indented{1}{object is the product of all the factors and the unit (which} \\indented{1}{can be extracted by \\axiom{unit(u)}).} \\blankline \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} factors \\spad{f} \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} factors \\spad{g}")) (|nilFactor| (($ |#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(x-y,3)")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\indented{1}{factorList(u) returns the list of factors with flags (for} \\indented{1}{use by factoring code).} \\blankline \\spad{X} f:=nilFactor(x-y,3) \\spad{X} factorList \\spad{f}")) (|makeFR| (($ |#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(x-y,3) \\spad{X} g:=factorList \\spad{f} \\spad{X} makeFR(z,g)")) (|exponent| (((|Integer|) $) "\\indented{1}{exponent(u) returns the exponent of the first factor of} \\indented{1}{\\spadvar{u}, or 0 if the factored form consists solely of a unit.} \\blankline \\spad{X} f:=nilFactor(y-x,3) \\spad{X} exponent(f)")) (|expand| ((|#1| $) "\\indented{1}{expand(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(y-x,3) \\spad{X} expand(f)"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -304) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -282) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1213))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -282) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-1213))))) (-424 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{u} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{u} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\indented{1}{map(fn,u) maps the function \\userfun{fn} across the factors of} \\indented{1}{\\spadvar{u} and creates a new factored object. Note: this clears} \\indented{1}{the information flags (sets them to \"nil\") because the effect of} \\indented{1}{\\userfun{fn} is clearly not known in general.} \\blankline \\spad{X} m(a:Factored Polynomial Integer):Factored Polynomial Integer \\spad{==} \\spad{a^2} \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} map(m,f) \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} map(m,g)")) (|unitNormalize| (($ $) "\\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| $) "\\indented{1}{unit(u) extracts the unit part of the factorization.} \\blankline \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} unit \\spad{f} \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} unit \\spad{g}")) (|flagFactor| (($ |#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 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(u) returns the number of factors in \\spadvar{u}.} \\blankline \\spad{X} a:=factor 9720000 \\spad{X} numberOfFactors a")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\indented{1}{nthFlag(u,n) returns the information flag of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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(u,n) returns the base of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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{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(u,n) returns the exponent of the \\spad{n}th factor of} \\indented{1}{\\spadvar{u}.\\space{2}If \\spadvar{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|)))) $) "\\indented{1}{factors(u) returns a list of the factors in a form suitable} \\indented{1}{for iteration. That is, it returns a list where each element} \\indented{1}{is a record containing a base and exponent.\\space{2}The original} \\indented{1}{object is the product of all the factors and the unit (which} \\indented{1}{can be extracted by \\axiom{unit(u)}).} \\blankline \\spad{X} \\spad{f:=x*y^3-3*x^2*y^2+3*x^3*y-x^4} \\spad{X} factors \\spad{f} \\spad{X} g:=makeFR(z,factorList \\spad{f)} \\spad{X} factors \\spad{g}")) (|nilFactor| (($ |#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(x-y,3)")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\indented{1}{factorList(u) returns the list of factors with flags (for} \\indented{1}{use by factoring code).} \\blankline \\spad{X} f:=nilFactor(x-y,3) \\spad{X} factorList \\spad{f}")) (|makeFR| (($ |#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(x-y,3) \\spad{X} g:=factorList \\spad{f} \\spad{X} makeFR(z,g)")) (|exponent| (((|Integer|) $) "\\indented{1}{exponent(u) returns the exponent of the first factor of} \\indented{1}{\\spadvar{u}, or 0 if the factored form consists solely of a unit.} \\blankline \\spad{X} f:=nilFactor(y-x,3) \\spad{X} exponent(f)")) (|expand| ((|#1| $) "\\indented{1}{expand(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(y-x,3) \\spad{X} expand(f)"))) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -305) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -283) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -283) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1214))))) +(-425 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{u} and \\spadvar{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{fn} to each factor of \\spadvar{u} and then build a new factored object from the results. For example, if \\spadvar{u} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL NIL -(-425 R FE |x| |cen|) +(-426 R FE |x| |cen|) ((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function, but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is true, log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is false, these are allowed."))) NIL NIL -(-426 R A S B) +(-427 R A S B) ((|constructor| (NIL "Lifting of maps to function spaces This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S;}")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) NIL NIL -(-427 R FE |Expon| UPS TRAN |x|) +(-428 R FE |Expon| UPS TRAN |x|) ((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x.} The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function, but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is true, log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is false, these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))}, where \\spad{f(x)} has a pole, will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"}, \\spad{\"real: two sides\"}, \\spad{\"real: left side\"}, \\spad{\"real: right side\"}, and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"}, then no series expansion will be computed because, viewed as a function of a complex variable, \\spad{atan(f(x))} has an essential singularity. Otherwise, the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined, a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator), then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"}, no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series, we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a, the user should perform the substitution \\spad{x \\spad{->} \\spad{x} + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is true, log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is false, these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))}, where \\spad{f(x)} has a pole, will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"}, \\spad{\"real: two sides\"}, \\spad{\"real: left side\"}, \\spad{\"real: right side\"}, and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"}, then no series expansion will be computed because, viewed as a function of a complex variable, \\spad{atan(f(x))} has an essential singularity. Otherwise, the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined, a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator), then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"}, no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series, a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a, the user should perform the substitution \\spad{x \\spad{->} \\spad{x} + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")) (|coerce| (($ |#3|) "\\spad{coerce(e)} converts an 'exponent' \\spad{e} to an 'expression'"))) NIL NIL -(-428 S A R B) +(-429 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers, where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely, if \\spad{a} is \\spad{[a1,a2,...]}, then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r.} For example, \\spad{reduce(_+$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note that third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a}, creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-429 A S) +(-430 A S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set, that is, a collection of elements characterized by membership, but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate u.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate u.")) (|universe| (($) "\\spad{universe()}$D returns the universal set for finite set aggregate \\spad{D.}")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set u, that is, the set of all values not in u.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of u. Note that \\axiom{cardinality(u) = \\#u}."))) NIL -((|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-373)))) -(-430 S) +((|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-374)))) +(-431 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 u.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate u.")) (|universe| (($) "\\spad{universe()}$D returns the universal set for finite set aggregate \\spad{D.}")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set u, that is, the set of all values not in u.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of u. Note that \\axiom{cardinality(u) = \\#u}."))) -((-4600 . T) (-4590 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4592 . T) (-4603 . T) (-3389 . T)) NIL -(-431 R -3280) +(-432 R -3313) ((|constructor| (NIL "Top-level complex function integration \\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, \\spad{x)}} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function, but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, \\spad{x)}} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL -(-432 R E) +(-433 R E) ((|constructor| (NIL "This domain converts terms into Fourier series")) (|makeCos| (($ |#2| |#1|) "\\indented{1}{makeCos(e,r) makes a sin expression with given} argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4587 -12 (|has| |#1| (-6 -4587)) (|has| |#2| (-6 -4587))) (-4594 . T) (-4595 . T) (-4597 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4587)) (|HasAttribute| |#2| (QUOTE -4587)))) -(-433 R -3280) +((-4589 -12 (|has| |#1| (-6 -4589)) (|has| |#2| (-6 -4589))) (-4596 . T) (-4597 . T) (-4599 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4589)) (|HasAttribute| |#2| (QUOTE -4589)))) +(-434 R -3313) ((|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, \\spad{x)}} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-434 S R) +(-435 S R) ((|constructor| (NIL "Category for formal functions A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, \\spad{k)}} returns \\spad{f} viewed as a univariate fraction in \\spad{k.}")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\spad{%.}")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\spad{%.}")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R.}")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 \\spad{...} fm\\^em)} returns \\spad{(f1)\\^e1 \\spad{...} (fm)\\^em} as an element of \\spad{%,} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\spad{%.}")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not, then numer(f) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R.}")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\spad{%.}") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\spad{%.}") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\spad{%.}") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\spad{%.}")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, \\spad{x]}} if \\spad{p = \\spad{n} * \\spad{x}} and \\spad{n \\spad{<>} 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = \\spad{m1} +...+ \\spad{mn}} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 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{...} * \\spad{x} \\spad{(n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{n,} \\spad{f)}} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{n,} \\spad{f)}} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,...,am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,...,am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], \\spad{y)}} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, \\spad{s,} \\spad{f,} \\spad{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}'s in \\spad{f.}") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f.}")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y,} \\spad{z,} \\spad{t)}} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y,} \\spad{z)}} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y)}} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, \\spad{x)}} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f.}")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R.} An error occurs if \\spad{f} is not an element of \\spad{R.}")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R.}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544))))) -(-435 R) +((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-1110))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545))))) +(-436 R) ((|constructor| (NIL "Category for formal functions A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, \\spad{k)}} returns \\spad{f} viewed as a univariate fraction in \\spad{k.}")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\spad{%.}")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\spad{%.}")) (|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 \\spad{...} fm\\^em)} returns \\spad{(f1)\\^e1 \\spad{...} (fm)\\^em} as an element of \\spad{%,} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\spad{%.}")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not, then numer(f) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R.}")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\spad{%.}") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\spad{%.}") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\spad{%.}") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\spad{%.}")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, \\spad{x]}} if \\spad{p = \\spad{n} * \\spad{x}} and \\spad{n \\spad{<>} 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = \\spad{m1} +...+ \\spad{mn}} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 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{...} * \\spad{x} \\spad{(n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, \\spad{s,} \\spad{n,} \\spad{f)}} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, \\spad{s,} \\spad{n,} \\spad{f)}} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,...,am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,...,am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], \\spad{y)}} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, \\spad{s,} \\spad{f,} \\spad{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}'s in \\spad{f.}") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f.}")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y,} \\spad{z,} \\spad{t)}} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y,} \\spad{z)}} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, \\spad{x,} \\spad{y)}} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, \\spad{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.}"))) -((-4597 -1831 (|has| |#1| (-1053)) (|has| |#1| (-481))) (-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) ((-4602 "*") |has| |#1| (-561)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-561)) (-4592 |has| |#1| (-561)) (-3348 . T)) +((-4599 -1841 (|has| |#1| (-1054)) (|has| |#1| (-482))) (-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) ((-4604 "*") |has| |#1| (-562)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-562)) (-4594 |has| |#1| (-562)) (-3389 . T)) NIL -(-436 R -3280) +(-437 R -3313) ((|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|)) "\\spad{iiBeta(x)} should be local but conditional.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F;} error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-437 R -3280) +(-438 R -3313) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, \\spad{q1,} \\spad{q2,} \\spad{q]}} such that \\spad{k(a1, a2) = k(a)}, \\spad{ai = qi(a)}, and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve a1, but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], \\spad{q]}} such that then \\spad{k(a1,...,an) = k(a)}, \\spad{ai = qi(a)}, and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-438 R -3280) +(-439 R -3313) ((|constructor| (NIL "Reduction from a function space to the rational numbers This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL -(-439) +(-440) ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL, INTEGER, COMPLEX, LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the s-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real, complex,double precision, logical, integer, character, REAL, COMPLEX, LOGICAL, INTEGER, CHARACTER, DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\", \"double precision\", \"complex\", \"logical\", \"integer\", \"character\", \"REAL\", \"COMPLEX\", \"LOGICAL\", \"INTEGER\", \"CHARACTER\", \"DOUBLE PRECISION\""))) NIL NIL -(-440 R -3280 UP) +(-441 R -3313 UP) ((|constructor| (NIL "This package is used internally by IR2F")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers, returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers, returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-53))))) -(-441) +((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-53))))) +(-442) ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream, followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp,} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,fn)} processes the template \\spad{tp,} writing the result out to \\spad{fn.}"))) NIL NIL -(-442) +(-443) ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types, including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER, an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX, an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX, an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL, an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER, an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION, an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL, an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type") (((|OutputForm|) $) "\\spad{coerce(x)} provides a printable form for \\spad{x}"))) NIL NIL -(-443 |f|) +(-444 |f|) ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-444) +(-445) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP, making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-445) +(-446) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP, checking that \\indented{1}{legal \\spad{Fortran-77} is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP, making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3348 . T)) +((-3389 . T)) NIL -(-446 UP) +(-447 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p,} the result is a Record such that \\spad{contp=}content \\spad{p,} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p.} Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p,} the result is a Record such that \\spad{contp=}content \\spad{p,} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree listOfDegrees, and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree listOfDegrees, and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree listOfDegrees.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d.}")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm, knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm, knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree listOfDegrees. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm, knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm, knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree listOfDegrees.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion, \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it, \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound, \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization, \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by completeHensel. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or -1). \\spad{f} shall be primitive (\\spadignore{i.e.} content(p)=1) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by ddFact for some prime \\spad{p.}")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by ddFact for some prime \\spad{p.}")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-447 R UP -3280) +(-448 R UP -3313) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p.}")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p.}")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f.}")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f.}")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f.}")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p.} \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p.}")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p.}") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p.}")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p.}"))) NIL NIL -(-448 R UP) +(-449 R UP) ((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored}")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f.}")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f.} Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f.}")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p.}")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p.}")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p.}")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) NIL NIL -(-449 R) +(-450 R) ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) NIL -((|HasCategory| |#1| (QUOTE (-409)))) -(-450) +((|HasCategory| |#1| (QUOTE (-410)))) +(-451) ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p,} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer zi."))) NIL NIL -(-451 |Dom| |Expon| |VarSet| |Dpol|) +(-452 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given, a computational summary is given for each s-polynomial. If \"redcrit\" is given, the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial}, \\spadtype{HomogeneousDistributedMultivariatePolynomial}, \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\indented{1}{euclideanGroebner(lp, \"info\", \"redcrit\") computes a groebner basis} \\indented{1}{for a polynomial ideal generated by the list of polynomials lp.} \\indented{1}{If the second argument is \"info\",} \\indented{1}{a summary is given of the critical pairs.} \\indented{1}{If the third argument is \"redcrit\", critical pairs are printed.} \\blankline \\spad{X} a1:DMP([y,x],INT):= \\spad{(9*x**2} + 5*x - 3)+ \\spad{y*(3*x**2} + 2*x + 1) \\spad{X} a2:DMP([y,x],INT):= \\spad{(6*x**3} - 2*x**2 - 3*x \\spad{+3)} + \\spad{y*(2*x**3} - \\spad{x} - 1) \\spad{X} a3:DMP([y,x],INT):= \\spad{(3*x**3} + 2*x**2) + \\spad{y*(x**3} + x**2) \\spad{X} an:=[a1,a2,a3] \\spad{X} euclideanGroebner(an,\"info\",\"redcrit\")") (((|List| |#4|) (|List| |#4|) (|String|)) "\\indented{1}{euclideanGroebner(lp, infoflag) computes a groebner basis} \\indented{1}{for a polynomial ideal over a euclidean domain} \\indented{1}{generated by the list of polynomials lp.} \\indented{1}{During computation, additional information is printed out} \\indented{1}{if infoflag is given as} \\indented{1}{either \"info\" (for summary information) or} \\indented{1}{\"redcrit\" (for reduced critical pairs)} \\blankline \\spad{X} a1:DMP([y,x],INT):= \\spad{(9*x**2} + 5*x - 3)+ \\spad{y*(3*x**2} + 2*x + 1) \\spad{X} a2:DMP([y,x],INT):= \\spad{(6*x**3} - 2*x**2 - 3*x \\spad{+3)} + \\spad{y*(2*x**3} - \\spad{x} - 1) \\spad{X} a3:DMP([y,x],INT):= \\spad{(3*x**3} + 2*x**2) + \\spad{y*(x**3} + x**2) \\spad{X} an:=[a1,a2,a3] \\spad{X} euclideanGroebner(an,\"redcrit\") \\spad{X} euclideanGroebner(an,\"info\")") (((|List| |#4|) (|List| |#4|)) "\\indented{1}{euclideanGroebner(lp) computes a groebner basis for a polynomial} \\indented{1}{ideal over a euclidean domain generated by the list of polys lp.} \\blankline \\spad{X} a1:DMP([y,x],INT):= \\spad{(9*x**2} + 5*x - 3)+ \\spad{y*(3*x**2} + 2*x + 1) \\spad{X} a2:DMP([y,x],INT):= \\spad{(6*x**3} - 2*x**2 - 3*x \\spad{+3)} + \\spad{y*(2*x**3} - \\spad{x} - 1) \\spad{X} a3:DMP([y,x],INT):= \\spad{(3*x**3} + 2*x**2) + \\spad{y*(x**3} + x**2) \\spad{X} an:=[a1,a2,a3] \\spad{X} euclideanGroebner(an)")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) NIL NIL -(-452 |Dom| |Expon| |VarSet| |Dpol|) +(-453 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of Axiom to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact, that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases, whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial}, \\spadtype{HomogeneousDistributedMultivariatePolynomial}, \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by listOfPolys. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next S-polynomial) is factorized. For each irreducible factors of \\spad{p,} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p.} If info is true, information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\indented{1}{groebnerFactorize(listOfPolys) returns} \\indented{1}{a list of groebner bases. The union of their solutions} \\indented{1}{is the solution of the system of equations given by listOfPolys.} \\indented{1}{At each stage the polynomial \\spad{p} under consideration (either from} \\indented{1}{the given basis or obtained from a reduction of the next S-polynomial)} \\indented{1}{is factorized. For each irreducible factors of \\spad{p,} a} \\indented{1}{new createGroebnerBasis is started} \\indented{1}{doing the usual updates with the factor} \\indented{1}{in place of \\spad{p.}} \\blankline \\spad{X} mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) \\spad{:=} \\spad{++X} [ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], \\spad{++X} [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] \\spad{X} eq \\spad{:=} determinant mfzn \\spad{X} groebnerFactorize \\spad{++X} [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])]") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by \\spad{listOfPolys} under the restriction that the polynomials of \\spad{nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next S-polynomial) is factorized. For each irreducible factors of \\spad{p} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p.} If argument info is true, information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by \\spad{listOfPolys} under the restriction that the polynomials of nonZeroRestrictions don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next S-polynomial) is factorized. For each irreducible factors of \\spad{p,} a new createGroebnerBasis is started doing the usual updates with the factor in place of \\spad{p.}")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the basis. If argument \\spad{info} is true, information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the basis."))) NIL NIL -(-453 |Dom| |Expon| |VarSet| |Dpol|) +(-454 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) NIL NIL -(-454 |Dom| |Expon| |VarSet| |Dpol|) +(-455 |Dom| |Expon| |VarSet| |Dpol|) ((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain, Dom, is not a field, the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients, but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each s-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial}, \\spadtype{HomogeneousDistributedMultivariatePolynomial}, \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\indented{1}{groebner(lp, \"info\", \"redcrit\") computes a groebner basis} \\indented{1}{for a polynomial ideal generated by the list of polynomials lp,} \\indented{1}{displaying both a summary of the critical pairs considered (\"info\")} \\indented{1}{and the result of reducing each critical pair (\"redcrit\").} \\indented{1}{If the second or third arguments have any other string value,} \\indented{1}{the indicated information is suppressed.} \\blankline \\spad{X} s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[s1,s2,s3,s4,s5,s6,s7] \\spad{X} groebner(sn7,\"info\",\"redcrit\")") (((|List| |#4|) (|List| |#4|) (|String|)) "\\indented{1}{groebner(lp, infoflag) computes a groebner basis} \\indented{1}{for a polynomial ideal} \\indented{1}{generated by the list of polynomials lp.} \\indented{1}{Argument infoflag is used to get information on the computation.} \\indented{1}{If infoflag is \"info\", then summary information} \\indented{1}{is displayed for each s-polynomial generated.} \\indented{1}{If infoflag is \"redcrit\", the reduced critical pairs are displayed.} \\indented{1}{If infoflag is any other string,} \\indented{1}{no information is printed during computation.} \\blankline \\spad{X} s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[s1,s2,s3,s4,s5,s6,s7] \\spad{X} groebner(sn7,\"info\") \\spad{X} groebner(sn7,\"redcrit\")") (((|List| |#4|) (|List| |#4|)) "\\indented{1}{groebner(lp) computes a groebner basis for a polynomial ideal} \\indented{1}{generated by the list of polynomials lp.} \\blankline \\spad{X} s1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 \\spad{X} s2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s \\spad{X} s3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 \\spad{X} s4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s \\spad{X} s5:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{w*p} + 2*z*t - 11*b**3 \\spad{X} s6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 \\spad{X} s7:DMP([w,p,z,t,s,b],FRAC(INT)):= \\spad{b**2} + 33/50*b + 2673/10000 \\spad{X} sn7:=[s1,s2,s3,s4,s5,s6,s7] \\spad{X} groebner(sn7)"))) NIL -((|HasCategory| |#1| (QUOTE (-367)))) -(-455 S) +((|HasCategory| |#1| (QUOTE (-368)))) +(-456 S) ((|constructor| (NIL "This category describes domains where \\spadfun{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| $)) "\\spad{gcdPolynomial(p,q)} returns the greatest common divisor (gcd) of univariate polynomials over the domain")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l.}") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y.}")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l.}") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y.}"))) NIL NIL -(-456) +(-457) ((|constructor| (NIL "This category describes domains where \\spadfun{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| $)) "\\spad{gcdPolynomial(p,q)} returns the greatest common divisor (gcd) of univariate polynomials over the domain")) (|lcm| (($ (|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.}"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-457 R |n| |ls| |gamma|) +(-458 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"))) -((-4597 |has| (-412 (-958 |#1|)) (-561)) (-4595 . T) (-4594 . T)) -((|HasCategory| (-412 (-958 |#1|)) (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-412 (-958 |#1|)) (QUOTE (-561)))) -(-458 |vl| R E) +((-4599 |has| (-413 (-959 |#1|)) (-562)) (-4597 . T) (-4596 . T)) +((|HasCategory| (-413 (-959 |#1|)) (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-413 (-959 |#1|)) (QUOTE (-562)))) +(-459 |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"))) -(((-4602 "*") |has| |#2| (-173)) (-4593 |has| |#2| (-561)) (-4598 |has| |#2| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-367))) (-1831 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#2| (QUOTE -4598)) (|HasCategory| |#2| (QUOTE (-456))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-149))))) -(-459) +(((-4604 "*") |has| |#2| (-174)) (-4595 |has| |#2| (-562)) (-4600 |has| |#2| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-368))) (-1841 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#2| (QUOTE -4600)) (|HasCategory| |#2| (QUOTE (-457))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-149))))) +(-460) ((|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(x)*cos(y),x=-6..4,y=-4..6,\"out3d.dat\") \\spad{X} )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(x)*cos(y),x=-6..4,y=-4..6,\"out3d.dat\",title==\"out3d\") \\spad{X} )sys gnuplot -persist out3d.dat") (((|Void|) (|Expression| (|Float|)) (|SegmentBinding| (|Float|)) (|String|)) "\\indented{1}{\\spad{gnuDraw} provides 2d plotting, default options} \\blankline \\spad{X} gnuDraw(D(cos(exp(z))/exp(z^2),z),z=-5..5,\"out2d.dat\") \\spad{X} )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(D(cos(exp(z))/exp(z^2),z),z=-5..5,\"out2d.dat\",title==\"out2d\") \\spad{X} )sys gnuplot -persist out2d.dat"))) NIL NIL -(-460 R BP) +(-461 R BP) ((|constructor| (NIL "\\indented{1}{Author : P.Gianni.} Date Created: January 1990 Description:")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp,} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h.}")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for lpol. Here the right side is \\spad{x**k}, for \\spad{k} less or equal to maxdeg. The operation returns \"failed\" when the elements are not coprime modulo prime.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p,} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R.} Note that this function is exported only because it's conditional."))) NIL NIL -(-461 OV E S R P) +(-462 OV E S R P) ((|constructor| (NIL "This is the top level package for doing multivariate factorization over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-462 E OV R P) +(-463 E OV R P) ((|constructor| (NIL "Description:")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{GCD} of \\spad{p} and \\spad{q}"))) NIL NIL -(-463 R) +(-464 R) ((|constructor| (NIL "This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) NIL NIL -(-464 R FE) +(-465 R FE) ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = \\spad{r0,r0} + \\spad{r,r0} + 2*r..., \\spad{a(n)} * \\spad{(x} - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = \\spad{r0} + \\spad{k*r} while \\spad{n} \\spad{<=} \\spad{r1,} \\spad{a(n)} * \\spad{(x} - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n \\spad{+->} a(n),x = a,r0..,r)} returns \\spad{sum(n = \\spad{r0,r0} + \\spad{r,r0} + 2*r..., a(n) * \\spad{(x} - a)**n)}; \\spad{series(n \\spad{+->} a(n),x = a,r0..r1,r)} returns \\spad{sum(n = \\spad{r0} + \\spad{k*r} while \\spad{n} \\spad{<=} \\spad{r1,} a(n) * \\spad{(x} - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * \\spad{(x} - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * \\spad{(x} - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n \\spad{+->} a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * \\spad{(x} - a)**n)}; \\spad{series(n \\spad{+->} a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * \\spad{(x} - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n \\spad{+->} a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = \\spad{r0,r0} + \\spad{r,r0} + 2*r..., \\spad{a(n)} * \\spad{(x} - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = \\spad{r0} + \\spad{k*r} while \\spad{n} \\spad{<=} \\spad{r1,} \\spad{a(n)} * \\spad{(x} - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n \\spad{+->} a(n),x = a,r0..,r)} returns \\spad{sum(n = \\spad{r0,r0} + \\spad{r,r0} + 2*r..., a(n) * \\spad{(x} - a)**n)}; \\spad{puiseux(n \\spad{+->} a(n),x = a,r0..r1,r)} returns \\spad{sum(n = \\spad{r0} + \\spad{k*r} while \\spad{n} \\spad{<=} \\spad{r1,} a(n) * \\spad{(x} - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * \\spad{(x} - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * \\spad{(x} - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n \\spad{+->} a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * \\spad{(x} - a)**n)}; \\spad{laurent(n \\spad{+->} a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * \\spad{(x} - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n \\spad{+->} a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n \\spad{+->} a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n \\spad{+->} a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}."))) NIL NIL -(-465 RP TP) +(-466 RP TP) ((|constructor| (NIL "General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts lfact, the factorization mod \\spad{prime} of pol, to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts lfacts, that are the factors of \\spad{pol} mod prime, to factors of \\spad{pol} mod prime**k > bound. No recombining is done ."))) NIL NIL -(-466 |vl| R IS E |ff| P) +(-467 |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"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-467) +(-468) ((|constructor| (NIL "\\spad{GuessOptionFunctions0} provides operations that extract the values of options for Guess.")) (|checkOptions| (((|Void|) (|List| (|GuessOption|))) "\\spad{checkOptions checks} whether the given options are consistent, and yields an error otherwise")) (|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 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}")) (|one| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{one returns} whether we need only one solution, default being true.")) (|checkExtraValues| (((|Boolean|) (|List| (|GuessOption|))) "\\spad{checkExtraValues(d)} specifies whether we want to check the solution beyond the order given by the degree bounds. The default is true.")) (|check| (((|Union| "skip" "MonteCarlo" "deterministic") (|List| (|GuessOption|))) "\\spad{check(d)} specifies how we want to check the solution. If the value is \"skip\", we return the solutions found by the interpolation routine without checking. If the value is \"MonteCarlo\", we use a probabilistic check. The default is \"deterministic\".")) (|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 false.")) (|maxMixedDegree| (((|NonNegativeInteger|) (|List| (|GuessOption|))) "\\spad{maxMixedDegree returns} the specified maxMixedDegree.")) (|maxDegree| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxDegree returns} the specified maxDegree.")) (|maxLevel| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxLevel returns} the specified maxLevel.")) (|Somos| (((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|))) "\\spad{Somos returns} whether we allow only Somos-like operators, default being \\spad{false}")) (|homogeneous| (((|Union| (|PositiveInteger|) (|Boolean|)) (|List| (|GuessOption|))) "\\spad{homogeneous returns} whether we allow only homogeneous algebraic differential equations, default being \\spad{false}")) (|maxPower| (((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxPower returns} the specified maxPower.")) (|maxSubst| (((|Union| (|PositiveInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxSubst returns} the specified maxSubst.")) (|maxShift| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxShift returns} the specified maxShift.")) (|maxDerivative| (((|Union| (|NonNegativeInteger|) "arbitrary") (|List| (|GuessOption|))) "\\spad{maxDerivative returns} the specified maxDerivative."))) NIL NIL -(-468) +(-469) ((|constructor| (NIL "GuessOption is a domain whose elements are various options used by Guess.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option(l, option)} returns which options are given.")) (|displayKind| (($ (|Symbol|)) "\\spad{displayKind(d)} specifies kind of the result: generating function, recurrence or equation. This option should not be set by the user, but rather by the HP-specification.")) (|indexName| (($ (|Symbol|)) "\\spad{indexName(d)} specifies the index variable used for the formulas. This option is expressed in the form \\spad{indexName \\spad{==} \\spad{d}.}")) (|variableName| (($ (|Symbol|)) "\\spad{variableName(d)} specifies the variable used in by the algebraic differential equation. This option is expressed in the form \\spad{variableName \\spad{==} \\spad{d}.}")) (|functionNames| (($ (|List| (|Symbol|))) "\\spad{functionNames(d)} specifies the names for the function in algebraic dependence. This option is expressed in the form \\spad{functionNames \\spad{==} \\spad{d}.}")) (|functionName| (($ (|Symbol|)) "\\spad{functionName(d)} specifies the name of the function given by the algebraic differential equation or recurrence. This option is expressed in the form \\spad{functionName \\spad{==} \\spad{d}.}")) (|debug| (($ (|Boolean|)) "\\spad{debug(d)} specifies whether we want additional output on the progress. This option is expressed in the form \\spad{debug \\spad{==} \\spad{d}.}")) (|one| (($ (|Boolean|)) "\\spad{one(d)} specifies whether we are happy with one solution. This option is expressed in the form \\spad{one \\spad{==} \\spad{d}.}")) (|checkExtraValues| (($ (|Boolean|)) "\\spad{checkExtraValues(d)} specifies whether we want to check the solution beyond the order given by the degree bounds. This option is expressed in the form \\spad{checkExtraValues \\spad{==} \\spad{d}}")) (|check| (($ (|Union| "skip" "MonteCarlo" "deterministic")) "\\spad{check(d)} specifies how we want to check the solution. If the value is \"skip\", we return the solutions found by the interpolation routine without checking. If the value is \"MonteCarlo\", we use a probabilistic check. This option is expressed in the form \\spad{check \\spad{==} \\spad{d}}")) (|safety| (($ (|NonNegativeInteger|)) "\\spad{safety(d)} specifies the number of values reserved for testing any solutions found. This option is expressed in the form \\spad{safety \\spad{==} \\spad{d}.}")) (|allDegrees| (($ (|Boolean|)) "\\spad{allDegrees(d)} specifies whether all possibilities of the degree vector - taking into account maxDegree - should be tried. This is mainly interesting for rational interpolation. This option is expressed in the form \\spad{allDegrees \\spad{==} \\spad{d}.}")) (|maxMixedDegree| (($ (|NonNegativeInteger|)) "\\spad{maxMixedDegree(d)} specifies the maximum q-degree of the coefficient polynomials in a recurrence with polynomial coefficients, in the case of mixed shifts. Although slightly inconsistent, maxMixedDegree(0) specifies that no mixed shifts are allowed. This option is expressed in the form \\spad{maxMixedDegree \\spad{==} \\spad{d}.}")) (|maxDegree| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) "\\spad{maxDegree(d)} specifies the maximum degree of the coefficient polynomials in an algebraic differential equation or a recursion with polynomial coefficients. For rational functions with an exponential term, \\spad{maxDegree} bounds the degree of the denominator polynomial. This option is expressed in the form \\spad{maxDegree \\spad{==} \\spad{d}.}")) (|maxLevel| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) "\\spad{maxLevel(d)} specifies the maximum number of recursion levels operators guessProduct and guessSum will be applied. This option is expressed in the form spad{maxLevel \\spad{==} \\spad{d}.}")) (|Somos| (($ (|Union| (|PositiveInteger|) (|Boolean|))) "\\spad{Somos(d)} specifies whether we want that the total degree of the differential operators is constant, and equal to \\spad{d,} or maxDerivative if true. If true, maxDerivative must be set, too.")) (|homogeneous| (($ (|Union| (|PositiveInteger|) (|Boolean|))) "\\spad{homogeneous(d)} specifies whether we allow only homogeneous algebraic differential equations. This option is expressed in the form \\spad{homogeneous \\spad{==} \\spad{d}.} If true, then maxPower must be set, too, and ADEs with constant total degree are allowed. If a PositiveInteger is given, only ADE's with this total degree are allowed.")) (|maxPower| (($ (|Union| (|PositiveInteger|) "arbitrary")) "\\spad{maxPower(d)} specifies the maximum degree in an algebraic differential equation. For example, the degree of \\spad{(f'')^3} \\spad{f'} is 4. maxPower(-1) specifies that the maximum exponent can be arbitrary. This option is expressed in the form \\spad{maxPower \\spad{==} \\spad{d}.}")) (|maxSubst| (($ (|Union| (|PositiveInteger|) "arbitrary")) "\\spad{maxSubst(d)} specifies the maximum degree of the monomial substituted into the function we are looking for. That is, if \\spad{maxSubst \\spad{==} \\spad{d},} we look for polynomials such that $p(f(x), f(x^2), ..., f(x^d))=0$. equation. This option is expressed in the form \\spad{maxSubst \\spad{==} \\spad{d}.}")) (|maxShift| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) "\\spad{maxShift(d)} specifies the maximum shift in a recurrence equation. This option is expressed in the form \\spad{maxShift \\spad{==} \\spad{d}.}")) (|maxDerivative| (($ (|Union| (|NonNegativeInteger|) "arbitrary")) "\\spad{maxDerivative(d)} specifies the maximum derivative in an algebraic differential equation. This option is expressed in the form \\spad{maxDerivative \\spad{==} \\spad{d}.}"))) NIL NIL -(-469 E V R P Q) +(-470 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, \\spad{n,} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n}, \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)}, where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note that \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) NIL NIL -(-470 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +(-471 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) ((|constructor| (NIL "A package that implements the Brill-Noether algorithm. Part of the PAFF package.")) (|ZetaFunction| (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|) (|PositiveInteger|)) "Returns the Zeta function of the curve in constant field extension. Calculated by using the L-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the L-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(d, \\spad{n)} returns the number of places of degree \\spad{d} in the constant field extension of degree \\spad{n}")) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) "\\spad{numberRatPlacesExtDeg(n)} returns the number of rational places in the constant field extenstion of degree \\spad{n}")) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) "returns the number of places of the given degree")) (|placesOfDegree| (((|List| |#7|) (|PositiveInteger|)) "\\spad{placesOfDegree(d)} returns all places of degree \\spad{d} of the curve.")) (|classNumber| (((|Integer|)) "Returns the class number of the curve.")) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) "\\spad{LPolynomial(d)} returns the L-Polynomial of the curve in constant field extension of degree \\spad{d.}") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the L-Polynomial of the curve.")) (|rationalPlaces| (((|List| |#7|)) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| ((|#5| |#7|) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl.}")) (|adjunctionDivisor| ((|#8|) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial crv.")) (|intersectionDivisor| ((|#8| |#3|) "\\spad{intersectionDivisor(pol)} compute the intersection divisor (the Cartier divisor) of the form \\spad{pol} with the curve. If some intersection points lie in an extension of the ground field, an error message is issued specifying the extension degree needed to find all the intersection points. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| |#3|) |#7|) "\\spad{evalIfCan(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") |#3| |#3| |#7|) "\\spad{evalIfCan(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") |#3| |#7|) "\\spad{evalIfCan(f,pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| |#3|) |#7|) "\\spad{eval(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl.}") ((|#1| |#3| |#3| |#7|) "\\spad{eval(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl.}") ((|#1| |#3| |#7|) "\\spad{eval(f,pl)} evaluate \\spad{f} at the place \\spad{pl.}")) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|)) "\\spad{interpolateForms(d,n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d.}")) (|lBasis| (((|Record| (|:| |num| (|List| |#3|)) (|:| |den| |#3|)) |#8|) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| ((|#6| |#3| |#7|) "\\spad{parametrize(f,pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl.}")) (|singularPoints| (((|List| |#5|)) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|setSingularPoints| (((|List| |#5|) (|List| |#5|)) "\\spad{setSingularPoints(lpt)} sets the singular points to be used. Beware: no attempt is made to check if the points are singular or not, nor if all of the singular points are presents. Hence, results of some computation maybe false. It is intend to be use when one want to compute the singular points are computed by other means than to use the function singularPoints.")) (|desingTreeWoFullParam| (((|List| |#10|)) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|desingTree| (((|List| |#10|)) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| ((|#3|) "\\spad{theCurve returns} the specified polynomial for the package.")) (|printInfo| (((|Void|) (|List| (|Boolean|))) "\\spad{printInfo(lbool)} prints some information comming from various package and domain used by this package."))) NIL -((|HasCategory| |#1| (QUOTE (-373)))) -(-471 R E |VarSet| P) +((|HasCategory| |#1| (QUOTE (-374)))) +(-472 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1097))) (-12 (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561)))) -(-472 S R E) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#4| (QUOTE (-1098))) (-12 (|HasCategory| |#4| (LIST (QUOTE -305) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562)))) +(-473 S R E) ((|constructor| (NIL "GradedAlgebra(R,E) denotes ``E-graded R-algebra''. A graded algebra is a graded module together with a degree preserving R-linear map, called the product. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving R-linear product: \\blankline \\spad{degree product(a,b) = degree a + degree \\spad{b}} \\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)} \\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)} \\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)} \\spad{product(a,product(b,c)) = product(product(a,b),c)}")) ((|One|) (($) "\\spad{1} is the identity for \\spad{product}."))) NIL NIL -(-473 R E) +(-474 R E) ((|constructor| (NIL "GradedAlgebra(R,E) denotes ``E-graded R-algebra''. A graded algebra is a graded module together with a degree preserving R-linear map, called the product. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving R-linear product: \\blankline \\spad{degree product(a,b) = degree a + degree \\spad{b}} \\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)} \\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)} \\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)} \\spad{product(a,product(b,c)) = product(product(a,b),c)}")) ((|One|) (($) "\\spad{1} is the identity for \\spad{product}."))) NIL NIL -(-474) +(-475) ((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set, only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector \\spad{ww} to start a loop using nextSubsetGray(ww,n)")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector \\spad{vv} whose components have the following meanings:\\br vv.1: a vector of length \\spad{n} whose entries are 0 or 1. This can be interpreted as a code for a subset of the set 1,...,n; \\spad{vv.1} differs from \\spad{ww.1} by exactly one entry;\\br \\spad{vv.2.1} is the number of the entry of \\spad{vv.1} which will be changed next time;\\br \\spad{vv.2.1} = \\spad{n+1} means that \\spad{vv.1} is the last subset; trying to compute nextSubsetGray(vv) if \\spad{vv.2.1} = \\spad{n+1} will produce an error!\\br \\blankline The other components of \\spad{vv.2} are needed to compute nextSubsetGray efficiently. Note that this is an implementation of [Williamson, Topic II, 3.54, \\spad{p.} 112] for the special case \\spad{r1} = \\spad{r2} = \\spad{...} = \\spad{rn} = 2; Note that nextSubsetGray produces a side-effect, \\spadignore{i.e.} nextSubsetGray(vv) and \\spad{vv} \\spad{:=} nextSubsetGray(vv) will have the same effect."))) NIL NIL -(-475) +(-476) ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n.}") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n.}")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is false.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is true.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) NIL NIL -(-476) +(-477) ((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points, \\spad{llp}, and returns the points with their hue and shade components set according to the list of palette colors, \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph, \\spad{gi}, of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(gi,pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp}, and whose point colors, line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault}, \\spadfun{lineColorDefault}, and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component, \\spad{pt} whose point color is set to be the palette color \\spad{pal}, and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph, \\spad{gi}, which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component, \\spad{pt} whose point color is set to the palette color \\spad{pal1}, line color is set to the palette color \\spad{pal2}, and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component, \\spad{pt} whose point color, line color and point size are determined by the default functions \\spadfun{pointColorDefault}, \\spadfun{lineColorDefault}, and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph, \\spad{gi} of the domain \\spadtype{GraphImage}, to the values given. The point list for \\spad{gi} is set to the list \\spad{lp}, the color of the points in \\spad{lp} is set to the palette color \\spad{pal1}, the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2}, and the size of the points in \\spad{lp} is given by the integer \\spad{p.}")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph, \\spad{gi} of the domain \\spadtype{GraphImage}, to be that of the list of unit increments, \\spad{lu}, and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph, \\spad{gi}, of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph, \\spad{gi} of the domain \\spadtype{GraphImage}, to be that of the list of range segments, \\spad{lr}, and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph, \\spad{gi}, of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph, \\spad{gi}, of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph, \\spad{gi}, of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points, \\spad{llp}, whose point colors are indicated by the list of palette colors, \\spad{lpal1}, and whose lines are colored according to the list of palette colors, \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points, and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points, \\spad{llp}, whose point colors are indicated by the list of palette colors, \\spad{lpal1}, and whose lines are colored according to the list of palette colors, \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points, \\spad{llp}, with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph, \\spad{gi} of the domain \\spadtype{GraphImage}, and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph, and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions, not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) NIL NIL -(-477 S R E) +(-478 S R E) ((|constructor| (NIL "GradedModule(R,E) denotes ``E-graded R-module'', that is, collection of R-modules indexed by an abelian monoid E. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with degree \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h.} Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h.} Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g.}")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "\\spad{0} denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g.} The set of all elements of a given degree form an R-module."))) NIL NIL -(-478 R E) +(-479 R E) ((|constructor| (NIL "GradedModule(R,E) denotes ``E-graded R-module'', that is, collection of R-modules indexed by an abelian monoid E. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with degree \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h.} Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h.} Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g.}")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "\\spad{0} denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g.} The set of all elements of a given degree form an R-module."))) NIL NIL -(-479 |lv| -3280 R) +(-480 |lv| -3313 R) ((|constructor| (NIL "Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position, for system \\spad{lp} in variables \\spad{lv.}")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL -(-480 S) +(-481 S) ((|constructor| (NIL "The class of multiplicative groups, that is, monoids with multiplicative inverses. \\blankline Axioms\\br \\tab{5}\\spad{leftInverse(\"*\":(\\%,\\%)->\\%,inv)}\\tab{5}\\spad{inv(x)*x = 1}\\br \\tab{5}\\spad{rightInverse(\"*\":(\\%,\\%)->\\%,inv)}\\tab{4}\\spad{x*inv(x) = 1}")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * \\spad{p} * \\spad{q}.}")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * \\spad{p} * \\spad{q};} this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n.}")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n.}")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y.}")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x.}"))) NIL NIL -(-481) +(-482) ((|constructor| (NIL "The class of multiplicative groups, that is, monoids with multiplicative inverses. \\blankline Axioms\\br \\tab{5}\\spad{leftInverse(\"*\":(\\%,\\%)->\\%,inv)}\\tab{5}\\spad{inv(x)*x = 1}\\br \\tab{5}\\spad{rightInverse(\"*\":(\\%,\\%)->\\%,inv)}\\tab{4}\\spad{x*inv(x) = 1}")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * \\spad{p} * \\spad{q}.}")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * \\spad{p} * \\spad{q};} this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|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.}")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y.}")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x.}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-482 |Coef| |var| |cen|) +(-483 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]}, where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . 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T) (-4597 . T) (-4599 . 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T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097))))) -(-484 R E V P) +((-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098))))) +(-485 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 w.r.t. the main variables of their members but they are displayed in reverse order."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1097))) (-12 (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-373)))) -(-485) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#4| (QUOTE (-1098))) (-12 (|HasCategory| |#4| (LIST (QUOTE -305) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-374)))) +(-486) ((|constructor| (NIL "This package exports guessing of sequences of rational functions"))) NIL -((|HasCategory| (-53) (LIST (QUOTE -1043) (QUOTE (-1169))))) -(-486 -3280) +((|HasCategory| (-53) (LIST (QUOTE -1044) (QUOTE (-1170))))) +(-487 -3313) ((|constructor| (NIL "This package exports guessing of sequences of numbers in a finite field"))) NIL NIL -(-487 -3280) +(-488 -3313) ((|constructor| (NIL "This package exports guessing of sequences of numbers in a finite field"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-1169))))) -(-488) +((|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1170))))) +(-489) ((|constructor| (NIL "This package exports guessing of sequences of rational numbers"))) NIL -((-12 (|HasCategory| (-412 (-571)) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-571) (LIST (QUOTE -1043) (QUOTE (-1169)))))) -(-489 -3280 S EXPRR R -1316 -3942) +((-12 (|HasCategory| (-413 (-572)) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-1170)))))) +(-490 -3313 S EXPRR R -1318 -3972) ((|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 $q$-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 $q$-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 \\spad{q}} returns a guesser that tries to find a 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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessRat \\spad{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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} 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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.")) (|guessPRec| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessPRec \\spad{q}} returns a guesser that tries to find a linear 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 \\spad{==} 1}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessPRec \\spad{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 \\spad{==} 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 \\spad{==} 1}.")) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRec \\spad{q}} returns a guesser that finds an ordinary 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 \\spad{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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} 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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} 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 \\spad{==} 1}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessHolo \\spad{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 \\spad{==} 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}(l, options) with \\spad{maxDerivative \\spad{==} 0}.") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessAlg \\spad{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}(l, maxDerivative \\spad{==} 0).")) (|guessADE| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessADE \\spad{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 \\spad{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 \\spad{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 \\spad{q}} returns a guesser that tries to find a function of the form n+->qbinomial(a+b \\spad{n,} \\spad{n)} r(n), where r(q^n) is a 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 n+->binomial(a+b \\spad{n,} \\spad{n)} r(n), where r(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 n+->binomial(a+b \\spad{n,} \\spad{n)} r(n), where r(n) is a rational function, that fits \\spad{l.}")) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessExpRat \\spad{q}} returns a guesser that tries to find a function of the form n+->(a+b q^n)^n r(q^n), where r(q^n) is a 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 n+->(a+b n)^n r(n), where r(n) is a rational function, that fits \\spad{l.}") (((|List| (|Record| (|:| |function| |#3|) (|:| |order| (|NonNegativeInteger|)))) (|List| |#1|)) "\\spad{guessExpRat \\spad{l}} tries to find a function of the form n+->(a+b n)^n r(n), where r(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 \\spad{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 -1043) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169)))))) -(-490) +((-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170)))))) +(-491) ((|constructor| (NIL "This package exports guessing of sequences of rational functions"))) NIL -((-12 (|HasCategory| (-412 (-958 (-571))) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-958 (-571)) (LIST (QUOTE -1043) (QUOTE (-1169)))))) -(-491 |q|) +((-12 (|HasCategory| (-413 (-959 (-572))) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-959 (-572)) (LIST (QUOTE -1044) (QUOTE (-1170)))))) +(-492 |q|) ((|constructor| (NIL "This package exports guessing of sequences of univariate rational functions")) (|shiftHP| (((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|)) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the $q$-shift operator") ((HPSPEC (|List| (|GuessOption|))) "\\spad{shiftHP options} returns a specification for Hermite-Pade approximation with the shift operator")) (|diffHP| (((|Mapping| HPSPEC (|List| (|GuessOption|))) (|Symbol|)) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the $q$-dilation operator") ((HPSPEC (|List| (|GuessOption|))) "\\spad{diffHP options} returns a specification for Hermite-Pade approximation with the differential operator")) (|guessRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRat \\spad{q}} returns a guesser that tries to find a 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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessRat \\spad{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 \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessRat(l, options)} tries to find a rational function whose first values are given by \\spad{l,} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l, maxShift \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.")) (|guessPRec| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessPRec \\spad{q}} returns a guesser that tries to find a linear 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 \\spad{==} 1}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessPRec \\spad{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 \\spad{==} 1)}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessPRec(l, options)} tries to find a linear recurrence with polynomial coefficients whose first values are given by \\spad{l,} using the given options. It is equivalent to \\spadfun{guessRec}\\spad{(l, options)} with \\spad{maxPower \\spad{==} 1}.")) (|guessRec| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessRec \\spad{q}} returns a guesser that finds an ordinary q-difference equation whose first values are given by \\spad{l,} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessRec(l, options)} tries to find an ordinary difference equation whose first values are given by \\spad{l,} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessRec \\spad{l}} tries to find an ordinary difference equation whose first values are given by \\spad{l,} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessPade| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessPade(l, options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l,} using the default options described in \\spadtype{GuessOptionFunctions0}. It is equivalent to \\spadfun{guessADE}\\spad{(l, options)} with \\spad{maxDerivative \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessPade(l, options)} tries to find a rational function whose first Taylor coefficients are given by \\spad{l,} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l, maxDerivative \\spad{==} 0, maxPower \\spad{==} 1, allDegrees \\spad{==} true)}.")) (|guessHolo| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessHolo(l, options)} tries to find an ordinary linear differential equation for a generating function whose first Taylor coefficients are given by \\spad{l,} using the given options. It is equivalent to \\spadfun{guessADE}\\spad{(l, options)} with \\spad{maxPower \\spad{==} 1}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessHolo \\spad{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 \\spad{==} 1)}.")) (|guessAlg| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessAlg(l, options)} tries to find an algebraic equation for a generating function whose first Taylor coefficients are given by \\spad{l,} using the given options. It is equivalent to \\spadfun{guessADE}(l, options) with \\spad{maxDerivative \\spad{==} 0}.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessAlg \\spad{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}(l, maxDerivative \\spad{==} 0).")) (|guessADE| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessADE \\spad{q}} returns a guesser that tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l,} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessADE(l, options)} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l,} using the given options.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessADE \\spad{l}} tries to find an algebraic differential equation for a generating function whose first Taylor coefficients are given by \\spad{l,} using the default options described in \\spadtype{GuessOptionFunctions0}.")) (|guessHP| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Mapping| HPSPEC (|List| (|GuessOption|)))) "\\spad{guessHP \\spad{f}} constructs an operation that applies Hermite-Pade approximation to the series generated by the given function \\spad{f.}")) (|guessBinRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessBinRat \\spad{q}} returns a guesser that tries to find a function of the form n+->qbinomial(a+b \\spad{n,} \\spad{n)} r(n), where r(q^n) is a q-rational function, that fits \\spad{l.}") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessBinRat(l, options)} tries to find a function of the form n+->binomial(a+b \\spad{n,} \\spad{n)} r(n), where r(n) is a rational function, that fits \\spad{l.}") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessBinRat(l, options)} tries to find a function of the form n+->binomial(a+b \\spad{n,} \\spad{n)} r(n), where r(n) is a rational function, that fits \\spad{l.}")) (|guessExpRat| (((|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) (|Symbol|)) "\\spad{guessExpRat \\spad{q}} returns a guesser that tries to find a function of the form n+->(a+b q^n)^n r(q^n), where r(q^n) is a q-rational function, that fits \\spad{l.}") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guessExpRat(l, options)} tries to find a function of the form n+->(a+b n)^n r(n), where r(n) is a rational function, that fits \\spad{l.}") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guessExpRat \\spad{l}} tries to find a function of the form n+->(a+b n)^n r(n), where r(n) is a rational function, that fits \\spad{l.}")) (|guess| (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|)) (|List| (|GuessOption|))) "\\spad{guess(l, guessers, ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol \\spad{guessSum} and quotients if ops contains the symbol \\spad{guessProduct} to the list. The given options are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|Mapping| (|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|)))) (|List| (|Symbol|))) "\\spad{guess(l, guessers, ops)} applies recursively the given \\spad{guessers} to the successive differences if ops contains the symbol guessSum and quotients if ops contains the symbol guessProduct to the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|)))) (|List| (|GuessOption|))) "\\spad{guess(l, options)} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. The given options are used.") (((|List| (|Record| (|:| |function| (|MyExpression| |#1| (|Integer|))) (|:| |order| (|NonNegativeInteger|)))) (|List| (|Fraction| (|MyUnivariatePolynomial| |#1| (|Integer|))))) "\\spad{guess \\spad{l}} applies recursively \\spadfun{guessRec} and \\spadfun{guessADE} to the successive differences and quotients of the list. Default options as described in \\spadtype{GuessOptionFunctions0} are used."))) NIL NIL -(-492) +(-493) ((|constructor| (NIL "Symbolic fractions in \\%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{pi()} returns the symbolic \\%pi."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-493 |Key| |Entry| |hashfn|) +(-494 |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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))))) -(-494) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098))))) +(-495) ((|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'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. 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T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-498 -3280 UP UPUP R) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-499 -3313 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve, that is finite formal sums SUM(n * \\spad{P)} where the \\spad{n's} are integers and the \\spad{P's} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = f(x) and \\spad{f} must have odd degree."))) NIL NIL -(-499 BP) +(-500 BP) ((|constructor| (NIL "This package provides the functions for the heuristic integer gcd. 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T) (-4594 . T) (-4595 . T) (-4597 . 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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 u. For collections, \\axiom{member?(x,u) = reduce(or,[x=y for \\spad{y} in u],false)}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of u. For collections, \\axiom{parts([x,y,...,z]) = (x,y,...,z)}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of u. For collections, \\axiom{parts([x,y,...,z]) = (x,y,...,z)}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in u. For collections, \\axiom{count(x,u) = reduce(+,[x=y for \\spad{y} in u],0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{p(x)} is true. For collections, \\axiom{count(p,u) = \\spad{reduce(+,[1} for \\spad{x} in \\spad{u} | p(x)],0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if p(x) is \\spad{true} for all elements \\spad{x} of u. Note that for collections, \\axiom{every?(p,u) = reduce(and,map(f,u),true,false)}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{p(x)} is \\spad{true} for any element \\spad{x} of u. Note that for collections, \\axiom{any?(p,u) = reduce(or,map(f,u),false,true)}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{f(x)}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by f(x). For collections, \\axiom{map(f,u) = [f(x) for \\spad{x} in u]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4600)) (|HasAttribute| |#1| (QUOTE -4601)) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) -(-502 S) +((|HasAttribute| |#1| (QUOTE -4602)) (|HasAttribute| |#1| (QUOTE -4603)) (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) +(-503 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 u. For collections, \\axiom{member?(x,u) = reduce(or,[x=y for \\spad{y} in u],false)}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of u. For collections, \\axiom{parts([x,y,...,z]) = (x,y,...,z)}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of u. For collections, \\axiom{parts([x,y,...,z]) = (x,y,...,z)}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in u. For collections, \\axiom{count(x,u) = reduce(+,[x=y for \\spad{y} in u],0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{p(x)} is true. For collections, \\axiom{count(p,u) = \\spad{reduce(+,[1} for \\spad{x} in \\spad{u} | p(x)],0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if p(x) is \\spad{true} for all elements \\spad{x} of u. Note that for collections, \\axiom{every?(p,u) = reduce(and,map(f,u),true,false)}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{p(x)} is \\spad{true} for any element \\spad{x} of u. Note that for collections, \\axiom{any?(p,u) = reduce(or,map(f,u),false,true)}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{f(x)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by f(x). For collections, \\axiom{map(f,u) = [f(x) for \\spad{x} in u]}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-503) +(-504) ((|constructor| (NIL "HtmlFormat provides a coercion from OutputForm to html.")) (|display| (((|Void|) (|String|)) "\\indented{1}{display(o) prints the string returned by coerce.} \\blankline \\spad{X} display(coerce(sqrt(3+x)::OutputForm)$HTMLFORM)$HTMLFORM")) (|exprex| (((|String|) (|OutputForm|)) "\\indented{1}{exprex(o) coverts \\spadtype{OutputForm} to \\spadtype{String}} \\blankline \\spad{X} exprex(sqrt(3+x)::OutputForm)$HTMLFORM")) (|coerceL| (((|String|) (|OutputForm|)) "\\indented{1}{coerceL(o) changes \\spad{o} in the standard output format to html} \\indented{1}{format and displays result as one long string.} \\blankline \\spad{X} coerceL(sqrt(3+x)::OutputForm)$HTMLFORM")) (|coerceS| (((|String|) (|OutputForm|)) "\\indented{1}{coerceS(o) changes \\spad{o} in the standard output format to html} \\indented{1}{format and displays formatted result.} \\blankline \\spad{X} coerceS(sqrt(3+x)::OutputForm)$HTMLFORM")) (|coerce| (((|String|) (|OutputForm|)) "\\indented{1}{coerce(o) changes \\spad{o} in the standard output format to html format.} \\blankline \\spad{X} coerce(sqrt(3+x)::OutputForm)$HTMLFORM"))) NIL NIL -(-504 S) +(-505 S) ((|constructor| (NIL "\\indented{1}{Date Last Updated: 14 May 1991} Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x.}")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x.}")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x.}")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x.}")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x.}")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x.}"))) NIL NIL -(-505) +(-506) ((|constructor| (NIL "\\indented{1}{Date Last Updated: 14 May 1991} Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x.}")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x.}")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x.}")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x.}")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x.}")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x.}"))) NIL NIL -(-506 -3280 UP |AlExt| |AlPol|) +(-507 -3313 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorisation in a simple algebraic extension Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, \\spad{f)}} returns a prime factorisation of \\spad{p;} \\spad{f} is a factorisation map for elements of UP."))) NIL NIL -(-507) +(-508) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| $ (QUOTE (-1053))) (|HasCategory| $ (LIST (QUOTE -1043) (QUOTE (-571))))) -(-508 S |mn|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| $ (QUOTE (-1054))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-572))))) +(-509 S |mn|) ((|constructor| (NIL "This is the basic one dimensional array data type."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-509 R |mnRow| |mnCol|) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-510 R |mnRow| |mnCol|) ((|constructor| (NIL "This domain implements two dimensional arrays"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-510 K R UP) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-511 K R UP) ((|constructor| (NIL "This package has no description")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]}, where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-511 R UP -3280) +(-512 R UP -3313) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with R-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{j} = 1..n)}, \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly, the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2.}")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns e, where \\spad{e} is the smallest integer such that \\spad{p **e \\spad{>=} \\spad{n}}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful, 1 is returned and if not, \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-512 |mn|) +(-513 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical And of \\spad{n} and \\spad{m.}")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical Or of \\spad{n} and \\spad{m.}")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical Not of \\spad{n.}"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-121) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-121) (QUOTE (-847))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-121) (QUOTE (-1097))) (-12 (|HasCategory| (-121) (LIST (QUOTE -304) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1097))))) -(-513 K R UP L) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-121) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-121) (QUOTE (-848))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-121) (QUOTE (-1098))) (-12 (|HasCategory| (-121) (LIST (QUOTE -305) (QUOTE (-121)))) (|HasCategory| (-121) (QUOTE (-1098))))) +(-514 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for mapping functions on the coefficients of univariate and bivariate polynomials.")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible, and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}, if possible, and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL NIL -(-514) +(-515) ((|constructor| (NIL "This domain implements a container of information about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{s} into an \\axiom{IndexCard}. Warning: if \\axiom{s} is not of the right format then an error will occur")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{ic}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of information contained in \\axiom{ic}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{ic}. Valid fields are \\axiom{name, nargs, exposed, type, abbreviation, kind, origin, params, condition, doc}."))) NIL NIL -(-515 R Q A B) +(-516 R Q A B) ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], \\spad{d]}} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the qi's.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the qi's.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for q1,...,qn."))) NIL NIL -(-516 K |symb| BLMET) +(-517 K |symb| BLMET) ((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(b).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when true, a coerce to OutputForm yields the full output of \\spad{tr,} otherwise encode(tr) is output (see encode function). The default is false.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) NIL NIL -(-517 -3280 |Expon| |VarSet| |DPoly|) +(-518 -3313 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations, including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in polyList.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f.}")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal I.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials polyList.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal I.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal I. in the ring \\spad{F[lvar]}, where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal I, in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by generalPosition from PolynomialIdeals and performs the inverse transformation, returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = I.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for I.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f,} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J,} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals LI.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J.}")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional, \\spadignore{i.e.} all its associated primes are maximal, in the ring \\spad{F[lvar]}, where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional, \\spadignore{i.e.} all its associated primes are maximal, in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal I.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J.}")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal I.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal, \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J.}")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal I.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J.}"))) NIL -((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1169))))) -(-518 |vl| |nv|) +((|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-1170))))) +(-519 |vl| |nv|) ((|constructor| (NIL "This package provides functions for the primary decomposition of polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain, and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal I.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal I.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL NIL -(-519 A S) +(-520 A S) ((|constructor| (NIL "Indexed direct products of abelian groups over an abelian group \\spad{A} of generators indexed by the ordered set \\spad{S.} All items have finite support: only non-zero terms are stored."))) NIL NIL -(-520 A S) +(-521 A S) ((|constructor| (NIL "Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of generators indexed by the ordered set \\spad{S.} All items have finite support. Only non-zero terms are stored."))) NIL NIL -(-521 A S) +(-522 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z.} Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z.} Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z.} Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z.}"))) NIL NIL -(-522 A S) +(-523 A S) ((|constructor| (NIL "Indexed direct products of ordered abelian monoids \\spad{A} of generators indexed by the ordered set \\spad{S.} The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL NIL -(-523 A S) +(-524 A S) ((|constructor| (NIL "Indexed direct products of ordered abelian monoid sups \\spad{A}, generators indexed by the ordered set \\spad{S.} All items have finite support: only non-zero terms are stored."))) NIL NIL -(-524 A S) +(-525 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S.} All items have finite support."))) NIL NIL -(-525 S A B) +(-526 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f.}") (($ $ |#2| |#3|) "\\spad{eval(f, \\spad{x,} \\spad{v)}} replaces \\spad{x} by \\spad{v} in \\spad{f.}"))) NIL NIL -(-526 A B) +(-527 A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f.}") (($ $ |#1| |#2|) "\\spad{eval(f, \\spad{x,} \\spad{v)}} replaces \\spad{x} by \\spad{v} in \\spad{f.}"))) NIL NIL -(-527 S E |un|) +(-528 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid on any set of generators"))) NIL -((|HasCategory| |#2| (QUOTE (-792)))) -(-528 S |mn|) +((|HasCategory| |#2| (QUOTE (-793)))) +(-529 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\\br \\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}\\br \\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}\\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(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} \\spad{shrinkable(false)$T1}")) (|physicalLength!| (($ $ (|Integer|)) "\\indented{1}{physicalLength!(x,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([i for \\spad{i} in 1..10])$T1 \\spad{X} physicalLength!(t2,15)")) (|physicalLength| (((|NonNegativeInteger|) $) "\\indented{1}{physicalLength(x) returns the number of elements \\spad{x} can} \\indented{1}{accomodate before growing} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,20) \\spad{X} t2:=flexibleArray([i for \\spad{i} in 1..10])$T1 \\spad{X} physicalLength \\spad{t2}")) (|flexibleArray| (($ (|List| |#1|)) "\\indented{1}{flexibleArray(l) creates a flexible array from the list of elements \\spad{l}} \\blankline \\spad{X} T1:=IndexedFlexibleArray(Integer,20) \\spad{X} flexibleArray([i for \\spad{i} in 1..10])$T1"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-529 |p| |n|) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-530 |p| |n|) ((|constructor| (NIL "InnerFiniteField(p,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}."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-584 |#1|) (QUOTE (-151))) (|HasCategory| (-584 |#1|) (QUOTE (-373))) (|HasCategory| (-584 |#1|) (QUOTE (-149))) (-1831 (|HasCategory| (-584 |#1|) (QUOTE (-149))) (|HasCategory| (-584 |#1|) (QUOTE (-373))))) -(-530 R |mnRow| |mnCol| |Row| |Col|) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-585 |#1|) (QUOTE (-151))) (|HasCategory| (-585 |#1|) (QUOTE (-374))) (|HasCategory| (-585 |#1|) (QUOTE (-149))) (-1841 (|HasCategory| (-585 |#1|) (QUOTE (-149))) (|HasCategory| (-585 |#1|) (QUOTE (-374))))) +(-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "There is no description for this domain"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-531 S |mn|) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-532 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."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-532 R |Row| |Col| M) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-533 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 -4601))) -(-533 R |Row| |Col| M QF |Row2| |Col2| M2) +((|HasAttribute| |#3| (QUOTE -4603))) +(-534 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 -4601))) -(-534 R |mnRow| |mnCol|) +((|HasAttribute| |#7| (QUOTE -4603))) +(-535 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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4602 "*"))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) -(-535 GF) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-303))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4604 "*"))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) +(-536 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(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 \\spad{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{**}{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 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 T.Itoh and S.Tsujii, \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\", Information and Computation 78, 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 D.R.Stinson, \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\", Siam \\spad{J.} Computation, Vol.19, No.4, 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+ \\spad{...} + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic, where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF.}"))) NIL NIL -(-536 R) +(-537 R) ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example, if \\spad{{f} \\spad{:=} increment(n)} then \\spad{f \\spad{x}} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example, if \\spad{{f} \\spad{:=} increment()} then \\spad{f \\spad{x}} is \\spad{x+1}."))) NIL NIL -(-537 |Varset|) +(-538 |Varset|) ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-538 K -3280 |Par|) +(-539 K -3313 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m.} The parameter \\spad{eps} determines the type of the output, \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned, if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K.} This function returns a polynomial over \\spad{K,} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL -(-539 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) +(-540 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) ((|constructor| (NIL "This category is part of the PAFF package")) (|excpDivV| ((|#8| $) "\\spad{excpDivV returns} the exceptional divisor of the infinitly close point.")) (|chartV| ((|#9| $) "chartV is the chart of the infinitly close point. The first integer correspond to variable defining the exceptional line, the last one the affine neighboorhood and the second one is the remaining integer. For example [1,2,3] means that Z=1, \\spad{X=X} and Y=XY. [2,3,1] means that X=1, \\spad{Y=Y} and Z=YZ.")) (|multV| (((|NonNegativeInteger|) $) "\\spad{multV returns} the multiplicity of the infinitly close point.")) (|localPointV| (((|AffinePlane| |#1|) $) "\\spad{localPointV returns} the coordinates of the local infinitly close point")) (|curveV| (((|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) $) "\\spad{curveV(p)} returns the defining polynomial of the strict transform on which lies the corresponding infinitly close point.")) (|pointV| ((|#5| $) "\\spad{pointV returns} the infinitly close point.")) (|create| (($ |#5| (|DistributedMultivariatePolynomial| (|construct| (QUOTE X) (QUOTE Y)) |#1|) (|AffinePlane| |#1|) (|NonNegativeInteger|) |#9| (|NonNegativeInteger|) |#8| |#1| (|Symbol|)) "\\spad{create an} infinitly close point"))) NIL NIL -(-540 K |symb| BLMET) +(-541 K |symb| BLMET) ((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(b).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when true, a coerce to OutputForm \\indented{1}{yields the full output of \\spad{tr,} otherwise encode(tr) is output} (see encode function). The default is false.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) NIL NIL -(-541 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) +(-542 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR BLMET) ((|constructor| (NIL "This domain is part of the PAFF package")) (|fullOutput| (((|Boolean|)) "\\spad{fullOutput returns} the value of the flag set by fullOutput(b).") (((|Boolean|) (|Boolean|)) "\\spad{fullOutput(b)} sets a flag such that when true, a coerce to OutputForm yields the full output of \\spad{tr,} otherwise encode(tr) is output (see encode function). The default is false.")) (|fullOut| (((|OutputForm|) $) "\\spad{fullOut(tr)} yields a full output of \\spad{tr} (see function fullOutput)."))) NIL NIL -(-542) +(-543) ((|constructor| (NIL "Top-level infinity Default infinity signatures for the interpreter.")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-543 R) +(-544 R) ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter, and transforms the result into an object of type \\spad{R.}")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to f$R."))) NIL NIL -(-544) +(-545) ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) \\spad{->} \\spad{?}.} returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter, or if the ti's are not valid types, or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t,} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parse| (($ (|String|)) "\\spad{parse(s)} is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f.} Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code, this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a \\spad{**} \\spad{b}} returns the input form corresponding to \\spad{a \\spad{**} \\spad{b}.}") (($ $ (|NonNegativeInteger|)) "\\spad{a \\spad{**} \\spad{b}} returns the input form corresponding to \\spad{a \\spad{**} \\spad{b}.}")) (/ (($ $ $) "\\spad{a / \\spad{b}} returns the input form corresponding to \\spad{a / \\spad{b}.}")) (* (($ $ $) "\\spad{a * \\spad{b}} returns the input form corresponding to \\spad{a * \\spad{b}.}")) (+ (($ $ $) "\\spad{a + \\spad{b}} returns the input form corresponding to \\spad{a + \\spad{b}.}")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) \\spad{+->} code} if \\spad{n > 1}, or to \\spad{x1 \\spad{+->} code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], \\spad{f)}} returns the input form corresponding to \\spad{f(x1,...,xn) \\spad{==} code}.")) (|binary| (($ $ (|List| $)) "\\indented{1}{\\spad{binary(op, [a1,...,an])} returns the input form} \\indented{1}{corresponding \\spad{to\\space{2}\\spad{a1} op \\spad{a2} op \\spad{...} op an}.} \\blankline \\spad{X} a:=[1,2,3]::List(InputForm) \\spad{X} binary(_+::InputForm,a)")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL -(-545 |Coef| UTS) +(-546 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-546 K -3280 |Par|) +(-547 K -3313 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float}, \\spad{Fraction(Integer)}, \\spad{Complex(Float)}, \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and lsol.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials lnum, with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by eps.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision eps.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision eps."))) NIL NIL -(-547 R BP |pMod| |nextMod|) +(-548 R BP |pMod| |nextMod|) ((|constructor| (NIL "This file contains the functions for modular \\spad{gcd} algorithm for univariate polynomials with coefficients in a non-trivial euclidean domain (\\spadignore{i.e.} not a field). The package parametrised by the coefficient domain, the polynomial domain, a prime, and a function for choosing the next prime")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p.}")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) NIL NIL -(-548 OV E R P) +(-549 OV E R P) ((|constructor| (NIL "This is an inner package for factoring multivariate polynomials over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer ufact. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer ufact."))) NIL NIL -(-549 K UP |Coef| UTS) +(-550 K UP |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-550 |Coef| UTS) +(-551 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-551 R UP) +(-552 R UP) ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL -(-552 S) +(-553 S) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)}, \\spad{0<=a1}, \\spad{(a,b)=1} means \\spad{1/a mod \\spad{b}.}")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)}, \\spad{0<=a,b

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

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

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

1}, means \\spad{a+b mod \\spad{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|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ \\spad{-b/2} \\spad{<=} \\spad{r} < \\spad{b/2} \\spad{}.}")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 \\spad{<=} \\spad{r} < \\spad{b}} and \\spad{r \\spad{==} a rem \\spad{b}.}")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) NIL NIL -(-553) +(-554) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)}, \\spad{0<=a1}, \\spad{(a,b)=1} means \\spad{1/a mod \\spad{b}.}")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)}, \\spad{0<=a,b

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

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

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

1}, means \\spad{a+b mod \\spad{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|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ \\spad{-b/2} \\spad{<=} \\spad{r} < \\spad{b/2} \\spad{}.}")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 \\spad{<=} \\spad{r} < \\spad{b}} and \\spad{r \\spad{==} a rem \\spad{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."))) -((-4598 . T) (-4599 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4600 . T) (-4601 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-554 |Key| |Entry| |addDom|) +(-555 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))))) -(-555 R -3280) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098))))) +(-556 R -3313) ((|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, \\spad{x,} \\spad{y,} \\spad{d)}} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x;} \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-556 R0 -3280 UP UPUP R) +(-557 R0 -3313 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, \\spad{d)}} returns an algebraic function \\spad{g} such that \\spad{dg = \\spad{f}} if such a \\spad{g} exists, \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, \\spad{d)}} integrates \\spad{f} with respect to the derivation \\spad{d.} Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, \\spad{d)}} integrates \\spad{f} with respect to the derivation \\spad{d.}"))) NIL NIL -(-557) +(-558) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(n) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(n)")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(n)"))) NIL NIL -(-558 R) +(-559 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{f} is contained within the interval \\axiom{i}, \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{true} if every element of \\spad{u} is negative, \\axiom{false} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{true} if every element of \\spad{u} is positive, \\axiom{false} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(u) - inf(u)}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{u}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{u}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[inf,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{[inf,sup]} if \\axiom{inf \\spad{<=} sup} or \\axiom{[sup,in]} otherwise."))) -((-3367 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3410 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-559 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR |InfClsPoint| |DesTree| BLMET) +(-560 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, \\spad{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 pol. \\spad{listOfTree} must contain all the desingularisation trees of all singular points on the curve \\indented{1}{defined by pol.}"))) NIL NIL -(-560 S) +(-561 S) ((|constructor| (NIL "The category of commutative integral domains, \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes\\br canonicalUnitNormal\\tab{5}the canonical field is the same for all associates\\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 = \\spad{x},} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) NIL NIL -(-561) +(-562) ((|constructor| (NIL "The category of commutative integral domains, \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes\\br canonicalUnitNormal\\tab{5}the canonical field is the same for all associates\\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 = \\spad{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."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-562 R -3280) +(-563 R -3313) ((|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, \\spad{c]}} such that \\spad{dh/dx = \\spad{f} - \\spad{c} dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and k1,...,kn (the ki's must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, \\spad{x)}} = \\spad{g} such that \\spad{dg/dx = \\spad{f}.}")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, \\spad{x)}} returns a function \\spad{g} such that \\spad{dg/dx = \\spad{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,[[ci, gi]]]} such that the gi's are among \\spad{[g1,...,gn]}, and \\spad{d(h+sum(ci log(gi)))/dx = \\spad{f},} if possible, \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, \\spad{x,} \\spad{g)}} returns functions \\spad{[h, \\spad{c]}} such that \\spad{dh/dx = \\spad{f} - cg}, if \\spad{(h,} \\spad{c)} exist, \"failed\" otherwise."))) NIL NIL -(-563 K |symb| E OV R) +(-564 K |symb| E OV R) ((|constructor| (NIL "Part of the Package for Algebraic Function Fields in one variable PAFF"))) NIL NIL -(-564 I) +(-565 I) ((|constructor| (NIL "This Package contains basic methods for integer factorization. The factor operation employs trial division up to 10,000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail, the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-565 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR) +(-566 K |symb| |PolyRing| E |ProjPt| PCS |Plc| DIVISOR) ((|constructor| (NIL "The following is part of the PAFF package")) (|interpolateForms| (((|List| |#3|) |#8| (|NonNegativeInteger|) |#3| (|List| |#3|)) "\\spad{interpolateForms(D,n,pol,base)} compute the basis of the sub-vector space \\spad{W} of \\spad{V} = , such that for all \\spad{G} in \\spad{W,} the divisor \\spad{(G)} \\spad{>=} \\spad{D.} All the elements in \\spad{base} must be homogeneous polynomial of degree \\spad{n.} Typicaly, \\spad{base} is the set of all monomial of degree \\spad{n:} in that case, interpolateForms(D,n,pol,base) returns the basis of the vector space of all forms of degree \\spad{d} that interpolated \\spad{D.} The argument \\spad{pol} must be the same polynomial that defined the curve form which the divisor \\spad{D} is defined."))) NIL NIL -(-566) +(-567) ((|constructor| (NIL "There is no description for this domain")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} is not documented")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} is not documented")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} is not documented")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l.}")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-567 R -3280 L) +(-568 R -3313 L) ((|constructor| (NIL "Rationalization of several types of genus 0 integrands; This internal package rationalises integrands on curves of the form:\\br \\tab{5}\\spad{y\\^2 = a \\spad{x\\^2} + \\spad{b} \\spad{x} + c}\\br \\tab{5}\\spad{y\\^2 = (a \\spad{x} + \\spad{b)} / \\spad{(c} \\spad{x} + d)}\\br \\tab{5}\\spad{f(x, \\spad{y)} = 0} where \\spad{f} has degree 1 in x\\br The rationalization is done for integration, limited integration, extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op \\spad{f} = \\spad{g}} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = \\spad{c} f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y.}") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, \\spad{g,} \\spad{x,} \\spad{y,} \\spad{d,} \\spad{p)}} returns the solution of \\spad{op \\spad{f} = \\spad{g}.} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, \\spad{g,} \\spad{x,} \\spad{y,} foo, \\spad{t,} \\spad{c)}} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + \\spad{n} * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists, and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = \\spad{c} f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y.} Argument \\spad{foo}, called by \\spad{foo(a, \\spad{b,} x)}, is a function that solves \\spad{du/dx + \\spad{n} * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y.}") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, \\spad{g,} \\spad{x,} \\spad{y,} foo, \\spad{d,} \\spad{p)}} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + \\spad{n} * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists, and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument foo, called by \\spad{foo(a, \\spad{b,} x)}, is a function that solves \\spad{du/dx + \\spad{n} * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y.}")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, \\spad{x,} \\spad{y,} [u1,...,un], \\spad{z,} \\spad{t,} \\spad{c)}} returns functions \\spad{[h,[[ci, ui]]]} such that the ui's are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist, and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = \\spad{c} f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y.}") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, \\spad{x,} \\spad{y,} [u1,...,un], \\spad{d,} \\spad{p)}} returns functions \\spad{[h,[[ci, ui]]]} such that the ui's are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist, and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, \\spad{x,} \\spad{y,} \\spad{g,} \\spad{z,} \\spad{t,} \\spad{c)}} returns functions \\spad{[h, \\spad{d]}} such that \\spad{dh/dx = f(x,y) - \\spad{d} \\spad{g},} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = \\spad{c} f(t,y) dy}, and \\spad{c} and \\spad{t} are rational functions of \\spad{y.} Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, \\spad{x,} \\spad{y,} \\spad{g,} \\spad{d,} \\spad{p)}} returns functions \\spad{[h, \\spad{c]}} such that \\spad{dh/dx = f(x,y) - \\spad{c} \\spad{g},} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 \\spad{y(x)\\^2} = P(x)}, or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, \\spad{x,} \\spad{y,} \\spad{z,} \\spad{t,} \\spad{c)}} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = \\spad{c} f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y.} Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, \\spad{x,} \\spad{y,} \\spad{d,} \\spad{p)}} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 \\spad{y(x)\\^2} = P(x)}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -649) (|devaluate| |#2|)))) -(-568) +((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|)))) +(-569) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n.} the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n.} The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n.} The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1,0} or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1, \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod \\spad{p}} \\spad{(p} prime), which is 0 if \\spad{a} is 0, 1 if \\spad{a} is a quadratic residue \\spad{mod \\spad{p}} and \\spad{-1} otherwise. Note that because the primality test is expensive, if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd, \\spad{J(a/b) = product(L(a/p) for \\spad{p} in factor \\spad{b} \\spad{)}.} Note that by convention, 0 is returned if \\spad{gcd(a,b) \\spad{^=} 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth, The Art of Computer Programming Vol 2, Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n.} This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)}, where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n.}")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w,} where \\spad{w} is such that \\spad{w = \\spad{x1} mod \\spad{m1}} and \\spad{w = \\spad{x2} mod m2}. Note that \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)}, where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-569 -3280 UP UPUP R) +(-570 -3313 UP UPUP R) ((|constructor| (NIL "Algebraic Hermite reduction.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, \\spad{')}} returns \\spad{[g,h]} such that \\spad{f = \\spad{g'} + \\spad{h}} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-570 -3280 UP) +(-571 -3313 UP) ((|constructor| (NIL "Hermite integration, transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, \\spad{D)}} returns \\spad{[g, \\spad{h,} \\spad{s,} \\spad{p]}} such that \\spad{f = \\spad{Dg} + \\spad{h} + \\spad{s} + \\spad{p},} \\spad{h} has a squarefree denominator normal w.r.t. \\spad{D,} and all the squarefree factors of the denominator of \\spad{s} are special w.r.t. \\spad{D.} Furthermore, \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL -(-571) +(-572) ((|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}."))) -((-4582 . T) (-4588 . T) (-4592 . T) (-4587 . T) (-4598 . T) (-4599 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4584 . T) (-4590 . T) (-4594 . T) (-4589 . T) (-4600 . T) (-4601 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-572) +(-573) ((|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{prob}. \\blankline It calls each \\axiom{domain} listed in \\axiom{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{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, \\spad{x} = a..b, numerical)} is a top level ANNA function to integrate an expression, {\\tt exp}, over a given range, {\\tt a} to {\\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 {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, \\spad{x} = a..b, \"numerical\")} is a top level ANNA function to integrate an expression, {\\tt exp}, over a given range, {\\tt a} to {\\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 {\\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, {\\tt 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, {\\tt 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, {\\tt 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, {\\tt 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, {\\tt exp}, over a given range {\\tt a} to {\\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, {\\tt exp}, over a given range {\\tt a} to {\\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, {\\tt exp}, over a given range {\\tt a} to {\\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, {\\tt exp}, over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-573 R -3280 L) +(-574 R -3313 L) ((|constructor| (NIL "Integration of pure algebraic functions; This package provides functions for integration, limited integration, extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, \\spad{g,} \\spad{kx,} \\spad{y,} \\spad{x)}} returns the solution of \\spad{op \\spad{f} = \\spad{g}.} \\spad{y} is an algebraic function of \\spad{x.}")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, \\spad{f,} \\spad{g,} \\spad{x,} \\spad{y,} foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + \\spad{n} * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists, \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x;} \\spad{foo(a, \\spad{b,} \\spad{x)}} is a function that solves \\spad{du/dx + \\spad{n} * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y.} \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, \\spad{x,} \\spad{y,} [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the ui's are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist, \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x.}")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, \\spad{x,} \\spad{y,} \\spad{g)}} returns functions \\spad{[h, \\spad{c]}} such that \\spad{dh/dx = f(x,y) - \\spad{c} \\spad{g},} where \\spad{y} is an algebraic function of \\spad{x;} returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, \\spad{x,} \\spad{y)}} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x.}"))) NIL -((|HasCategory| |#3| (LIST (QUOTE -649) (|devaluate| |#2|)))) -(-574 R -3280) +((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|)))) +(-575 R -3313) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, \\spad{x} = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, \\spad{x)}} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = \\spad{g} + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, \\spad{x)}} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = \\spad{g} + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, \\spad{x)}} returns \\spad{[c, \\spad{g]}} such that \\spad{f = \\spad{c} * \\spad{g}} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-623))))) -(-575 -3280 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-624))))) +(-576 -3313 UP) ((|constructor| (NIL "Rational function integration This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the gi's are among \\spad{[g1,...,gn]}, \\spad{ci' = 0}, and \\spad{(h+sum(ci log(gi)))' = \\spad{f},} if possible, \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, \\spad{g)}} returns fractions \\spad{[h, \\spad{c]}} such that \\spad{c' = 0} and \\spad{h' = \\spad{f} - cg}, if \\spad{(h, \\spad{c)}} exist, \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = \\spad{f}} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = \\spad{f}.}"))) NIL NIL -(-576 S) +(-577 S) ((|constructor| (NIL "Provides integer testing and retraction functions.")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer, \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer, \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-577 -3280) +(-578 -3313) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, \\spad{x,} \\spad{g)}} returns fractions \\spad{[h, \\spad{c]}} such that \\spad{dc/dx = 0} and \\spad{dh/dx = \\spad{f} - cg}, if \\spad{(h, \\spad{c)}} exist, \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, \\spad{x,} [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the gi's are among \\spad{[g1,...,gn]}, \\spad{dci/dx = 0}, and \\spad{d(h + sum(ci log(gi)))/dx = \\spad{f}} if possible, \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, \\spad{x)}} returns a fraction \\spad{g} such that \\spad{dg/dx = \\spad{f}} if \\spad{g} exists, \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, \\spad{x)}} returns \\spad{g} such that \\spad{dg/dx = \\spad{f}.}"))) NIL NIL -(-578 R) +(-579 R) ((|constructor| (NIL "This domain is an implementation of interval arithmetic and transcendental functions over intervals."))) -((-3367 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3410 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-579) +(-580) ((|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], \\spad{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 ai's exists."))) NIL NIL -(-580 R -3280) +(-581 R -3313) ((|constructor| (NIL "Tools for the integrator")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, \\spad{x,} int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int}, and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, \\spad{x)}} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x.}")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, \\spad{x)}} returns \\spad{f} minus any additive constant with respect to \\spad{x.}")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2.}")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], \\spad{x)}} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x.}")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], \\spad{x)}} returns the \\spad{ki} which involve \\spad{x.}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-280))) (|HasCategory| |#2| (QUOTE (-623)))) (-12 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-280)))) (|HasCategory| |#1| (QUOTE (-561)))) -(-581 -3280 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-281))) (|HasCategory| |#2| (QUOTE (-624)))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-281)))) (|HasCategory| |#1| (QUOTE (-562)))) +(-582 -3313 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, \\spad{')}} returns \\spad{[q,} \\spad{r]} such that \\spad{p = \\spad{q'} + \\spad{r}} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, \\spad{')}} returns \\spad{[ir, \\spad{s,} \\spad{p]}} such that \\spad{f = ir' + \\spad{s} + \\spad{p}} and all the squarefree factors of the denominator of \\spad{s} are special w.r.t the derivation \\spad{'.}")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = \\spad{q}} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F.}")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, \\spad{',} t')} returns \\spad{q} such that \\spad{p' = \\spad{q}} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, \\spad{',} [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = \\spad{v'} + +/[ci * ui'/ui]}. Error: if \\spad{degree numer \\spad{f} \\spad{>=} degree denom \\spad{f}.}")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, \\spad{',} \\spad{g)}} returns \\spad{[v, \\spad{c]}} such that \\spad{f = \\spad{v'} + \\spad{c} \\spad{g}} and \\spad{c' = 0}. Error: if \\spad{degree numer \\spad{f} \\spad{>=} degree denom \\spad{f}} or if \\spad{degree numer \\spad{g} \\spad{>=} degree denom \\spad{g}} or if \\spad{denom \\spad{g}} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, \\spad{',} foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0}, \\spad{f = \\spad{v'} + a + reduce(+,[ci * ui'/ui])}, and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F.} Returns \"failed\" if no such \\spad{v,} ci, a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F.}")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, \\spad{',} foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0}, \\spad{f = \\spad{v'} + a + reduce(+,[ci * ui'/ui])}, and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v,} ci, a exist. Argument \\spad{foo} is an extended integration function on \\spad{F.}")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, \\spad{',} foo, \\spad{g)}} returns either \\spad{[v, \\spad{c]}} such that \\spad{f = \\spad{v'} + \\spad{c} \\spad{g}} and \\spad{c' = 0}, or \\spad{[v, a]} such that \\spad{f = \\spad{g'} + a}, and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F.} Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F.}")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, \\spad{',} foo, \\spad{g)}} returns either \\spad{[v, \\spad{c]}} such that \\spad{f = \\spad{v'} + \\spad{c} \\spad{g}} and \\spad{c' = 0}, or \\spad{[v, a]} such that \\spad{f = \\spad{g'} + a}, and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F.}")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, \\spad{',} foo)} returns \\spad{[g, a]} such that \\spad{f = \\spad{g'} + a}, and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F;} Argument foo is a Risch differential system solver on \\spad{F;}")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, \\spad{',} foo)} returns \\spad{[g, a]} such that \\spad{f = \\spad{g'} + a}, and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F;} Argument foo is a Risch differential equation solver on \\spad{F;}")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, \\spad{',} foo)} returns \\spad{[g, a]} such that \\spad{f = \\spad{g'} + a}, and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F.}"))) NIL NIL -(-582 R -3280) +(-583 R -3313) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, \\spad{s,} \\spad{t)}} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form. Handles only rational \\spad{f(s)}."))) NIL NIL -(-583 |p| |unBalanced?|) +(-584 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp,} the p-adic completion of the integers. This is an internal domain."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-584 |p|) +(-585 |p|) ((|constructor| (NIL "InnerPrimeField(p) implements the field with \\spad{p} elements."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| $ (QUOTE (-151))) (|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-373)))) -(-585) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| $ (QUOTE (-151))) (|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-374)))) +(-586) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(s)} prints \\axiom{s} at the current position of the cursor."))) NIL NIL -(-586 R -3280) +(-587 R -3313) ((|constructor| (NIL "Conversion of integration results to top-level expressions This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents, provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to i.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to i.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + \\spad{...} + sum_{Pn(a)=0} Q(a,x)} where P1,...,Pn are the factors of \\spad{P.}"))) NIL NIL -(-587 E -3280) +(-588 E -3313) ((|constructor| (NIL "Internally used by the integration packages")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL -(-588 -3280) +(-589 -3313) ((|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 = \\spad{h} + \\spad{c1} log(u1) + \\spad{c2} log(u2) + \\spad{...} + \\spad{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) + \\spad{...} \\spad{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 ne."))) -((-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-1169))))) -(-589 I) +((-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1170))))) +(-590 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 < \\spad{x} - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < \\spad{s} - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( \\spad{log(n)**2} \\spad{)}.}")) (|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 < \\spad{x} - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]}, where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL NIL -(-590 GF) +(-591 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-591 R) +(-592 R) ((|constructor| (NIL "Conversion of integration results to top-level expressions. This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents, provided that the indexing polynomial can be factored into quadratics.")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, \\spad{x)}} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, \\spad{x)}} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to i.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to i.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + \\spad{...} + sum_{Pn(a)=0} Q(a,x)} where P1,...,Pn are the factors of \\spad{P.}"))) NIL ((|HasCategory| |#1| (QUOTE (-151)))) -(-592) +(-593) ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {1,2,...,n} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n,} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n,} \\spadignore{e.g.} [3,3,3,1] labels an irreducible representation for \\spad{n} equals 10. Note that whenever a \\spadtype{List Integer} appears in a signature, a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to \\spad{lambda} in Young's natural form for the list of permutations given by listOfPerm.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition \\spad{lambda} in Young's natural form for the following two generators of the symmetric group, whose elements permute {1,2,...,n}, namely \\spad{(1} 2) (2-cycle) and \\spad{(1} 2 \\spad{...} \\spad{n)} (n-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition \\spad{lambda} in Young's natural form of the permutation \\spad{pi} in the symmetric group, whose elements permute {1,2,...,n}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to lambda. Note that the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-593 R E V P TS) +(-594 R E V P TS) ((|constructor| (NIL "\\indented{1}{Author: Marc Moreno Maza} Date Created: 01/1999 Date Last Updated: 23/01/1999 References: \\indented{1}{[1] \\spad{D.} LAZARD \"Solving Zero-dimensional Algebraic Systems\"} \\indented{5}{Journal of Symbolic Computation, 1992, 13, 117-131} Description:")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-594 |mn|) +(-595 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-148) (QUOTE (-1097))) (|HasCategory| (-148) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-148) (QUOTE (-847))) (-1831 (|HasCategory| (-148) (QUOTE (-847))) (|HasCategory| (-148) (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-847)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))))) -(-595 E V R P) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-148) (QUOTE (-1098))) (|HasCategory| (-148) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-148) (QUOTE (-848))) (-1841 (|HasCategory| (-148) (QUOTE (-848))) (|HasCategory| (-148) (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-848)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))))) +(-596 E V R P) ((|constructor| (NIL "Tools for the summation packages of polynomials")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), \\spad{n)}} returns \\spad{P(n)}, the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n,} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), \\spad{n} = a..b)} returns \\spad{p(a) + p(a+1) + \\spad{...} + p(b)}."))) NIL NIL -(-596 |Coef|) -((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain used for creating sparse Taylor and Laurent series.")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f.} For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns \\spad{a1 + \\spad{a2} \\spad{x} + \\spad{a3} \\spad{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) \\spad{>=} 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}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-571)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-571)) (|devaluate| |#1|))))) (|HasCategory| (-571) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-367))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-571))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169))))))) (-597 |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 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns \\spad{a1 + \\spad{a2} \\spad{x} + \\spad{a3} \\spad{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) \\spad{>=} 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}."))) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-572) (QUOTE (-1110))) (|HasCategory| |#1| (QUOTE (-368))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170))))))) +(-598 |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.}"))) -((-4595 |has| |#1| (-561)) (-4594 |has| |#1| (-561)) ((-4602 "*") |has| |#1| (-561)) (-4593 |has| |#1| (-561)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-561)))) -(-598 A B) +((-4597 |has| |#1| (-562)) (-4596 |has| |#1| (-562)) ((-4604 "*") |has| |#1| (-562)) (-4595 |has| |#1| (-562)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-562)))) +(-599 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-599 A B C) +(-600 A B C) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-600 R -3280 FG) +(-601 R -3313 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms, and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's}, in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) \\spad{b)}} returns \\spad{a + \\spad{i} \\spad{b}.}")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + \\spad{i} \\spad{b)}} returns \\spad{a + sqrt(-1) \\spad{b}.}")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + \\spad{i} \\spad{b)}} returns \\spad{a + \\spad{i} \\spad{b}} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL -(-601 S) +(-602 S) ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for \\spad{x} in \\spad{t} | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for \\spad{x} in \\spad{t} while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for \\spad{x} in \\spad{t} while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for \\spad{x} in t]}."))) NIL NIL -(-602 R |mn|) +(-603 R |mn|) ((|constructor| (NIL "This type represents vector like objects with varying lengths and a user-specified initial index."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-603 S |Index| |Entry|) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1009))) (|HasCategory| |#1| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-604 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 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 u. Note that for collections, \\axiom{first([x,y,...,z]) = \\spad{x}.} Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate u. Note that in general, \\axiom{minIndex(a) = reduce(min,[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 u. Note that in general, \\axiom{maxIndex(u) = reduce(max,[i for \\spad{i} in indices u])}; if \\spad{u} is a list, \\axiom{maxIndex(u) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{u . i} for some index 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 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 -4601)) (|HasCategory| |#2| (QUOTE (-847))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#3| (QUOTE (-1097)))) -(-604 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -4603)) (|HasCategory| |#2| (QUOTE (-848))) (|HasAttribute| |#1| (QUOTE -4602)) (|HasCategory| |#3| (QUOTE (-1098)))) +(-605 |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 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 u. Note that for collections, \\axiom{first([x,y,...,z]) = \\spad{x}.} Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate u. Note that in general, \\axiom{minIndex(a) = reduce(min,[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 u. Note that in general, \\axiom{maxIndex(u) = reduce(max,[i for \\spad{i} in indices u])}; if \\spad{u} is a list, \\axiom{maxIndex(u) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{u . i} for some index 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 u.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-3348 . T)) +((-3389 . T)) NIL -(-605 R A) +(-606 R A) ((|constructor| (NIL "AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*$A} to define the new multiplications \\spad{a*b \\spad{:=} (a *$A \\spad{b} + \\spad{b} *$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?()$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free R-module of finite rank, together with a fixed R-module basis), then the same is \\spad{true} for the associated Jordan algebra. Moreover, if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free R-module of finite rank), then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(R,A)."))) -((-4597 -1831 (-3997 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4595 . T) (-4594 . T)) -((|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (-1831 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))))) -(-606 |Entry|) +((-4599 -1841 (-4028 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4597 . T) (-4596 . T)) +((|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (-1841 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))))) +(-607 |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''. 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 s-expression for the value of the key.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-1151) (QUOTE (-847))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (QUOTE (-1097))))) -(-607 S |Key| |Entry|) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-1152) (QUOTE (-848))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (QUOTE (-1098))))) +(-608 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(k,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!(k,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 -(-608 |Key| |Entry|) +(-609 |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(k,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!(k,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.}"))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL -(-609 R S) +(-610 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) NIL NIL -(-610 S) +(-611 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S.}")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), \\spad{s)}} tests if the name of op is \\spad{s.}") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), \\spad{f)}} tests if op = \\spad{f.}")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol, and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], \\spad{m)}} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m.} Error: if \\spad{op} is k-ary for some \\spad{k} not equal to \\spad{m.}")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k.}")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,...,an))} returns the name of op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) -(-611 S) +((|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) +(-612 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S.}"))) NIL NIL -(-612 S) +(-613 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B,} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S.}"))) NIL NIL -(-613 -3280 UP) +(-614 -3313 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or P(u) such that \\spad{$e^{\\int(-a_1/2a_2)} e^{\\int u}$} is a solution of \\indented{5}{\\spad{$a_2 \\spad{y''} + \\spad{a_1} \\spad{y'} + \\spad{a0} \\spad{y} = 0$}} whenever \\spad{u} is a solution of \\spad{P \\spad{u} = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or P(u) such that \\spad{$e^{\\int(-a_1/2a_2)} e^{\\int u}$} is a solution of \\indented{5}{\\spad{a_2 \\spad{y''} + \\spad{a_1} \\spad{y'} + \\spad{a0} \\spad{y} = 0}} whenever \\spad{u} is a solution of \\spad{P \\spad{u} = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL -(-614 S R) +(-615 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-615 R) +(-616 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."))) -((-4597 . T)) +((-4599 . T)) NIL -(-616 A R S) +(-617 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 \\spad{x}} returns the denominator of \\spad{x.}")) (|numer| ((|#1| $) "\\spad{numer \\spad{x}} returns the numerator of \\spad{x.}")) (/ (($ |#1| |#3|) "\\spad{a / \\spad{d}} divides the element \\spad{a} by \\spad{d.}") (($ $ |#3|) "\\spad{x / \\spad{d}} divides the element \\spad{x} by \\spad{d.}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-845)))) -(-617 R -3280) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-846)))) +(-618 R -3313) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, \\spad{t,} \\spad{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), \\spad{t} = 0..%plusInfinity)}. Returns the formal object \\spad{laplace(f, \\spad{t,} \\spad{s)}} if it cannot compute the transform."))) NIL NIL -(-618 R UP) +(-619 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"))) -((-4595 . T) (-4594 . T) ((-4602 "*") . T) (-4593 . T) (-4597 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571))))) -(-619 R E V P TS ST) +((-4597 . T) (-4596 . T) ((-4604 "*") . T) (-4595 . T) (-4599 . T)) +((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572))))) +(-620 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(lp,clos?)} has the same specifications as zeroSetSplit(lp,clos?) from RegularTriangularSetCategory.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) NIL NIL -(-620 OV E Z P) +(-621 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)}, where \\spad{contm} is the content of the evaluated polynomial, \\spad{unilist} is the list of factors of the evaluated polynomial, \\spad{plead} is the complete factorization of the leading coefficient, \\spad{vl} is the list of factors of the leading coefficient evaluated, \\spad{lvar} is the list of variables, \\spad{lval} is the list of values, returns a record giving the list of leading coefficients to impose on the univariate factors.")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)}, where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial, \\spad{numFacts} is the number of factors of the leadingCoefficient, and evallcs is the list of the evaluated factors of the leadingCoefficient, returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-621 |VarSet| R |Order|) +(-622 |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(g,h)} returns the list of equations \\axiom{g_i = h_i}, where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{g} (resp. \\axiom{h}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(g)} returns the exponential coordinates of \\axiom{g}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(g)} returns the list of variables of \\axiom{g}.")) (|mirror| (($ $) "\\axiom{mirror(g)} is the mirror of the internal representation of \\axiom{g}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(g)} returns the internal representation of \\axiom{g}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(g)} returns the internal representation of \\axiom{g}.")) (|listOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{listOfTerms(p)} returns the internal representation of \\axiom{p}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(p)} returns the logarithm of \\axiom{p}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(p)} returns the exponential of \\axiom{p}."))) -((-4597 . T)) +((-4599 . T)) NIL -(-622 R |ls|) +(-623 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 \\spad{[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(lp, norm?)} decomposes the variety associated with \\axiom{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{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{true} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp, norm?)} decomposes the variety associated with \\axiom{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{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{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{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{true} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the FGLM strategy, if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal w.r.t. the variables involved in \\axiom{lp}."))) NIL NIL -(-623) +(-624) ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|fresnelC| (($ $) "\\spad{fresnelC(x)} is the Fresnel integral \\spad{C,} defined by C(x) = integrate(cos(t^2),t=0..x)")) (|fresnelS| (($ $) "\\spad{fresnelS(x)} is the Fresnel integral \\spad{S,} defined by S(x) = integrate(sin(t^2),t=0..x)")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x,} that is, \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x,} that is, the integral of \\spad{log(x) / \\spad{(1} - \\spad{x)} dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x,} that is, the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x,} that is, the integral of \\spad{cos(x) / \\spad{x} dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x,} that is, the integral of \\spad{sin(x) / \\spad{x} dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x,} that is, the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-624 R -3280) +(-625 R -3313) ((|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{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\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 -(-625 |lv| -3280) +(-626 |lv| -3313) ((|constructor| (NIL "Given a Groebner basis \\spad{B} with respect to the total degree ordering for a zero-dimensional ideal I, compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL -(-626) +(-627) ((|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 \\spad{:=} \\spad{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 lib.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."))) -((-4601 . T)) -((|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 (-57))) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-1151) (QUOTE (-847))) (|HasCategory| (-57) (QUOTE (-1097))) (-12 (|HasCategory| (-57) (LIST (QUOTE -304) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 (-57))) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 (-57))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -4279) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 (-57))) (QUOTE (-1097)))) (-1831 (|HasCategory| (-57) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 (-57))) (QUOTE (-1097))))) -(-627 S R) +((-4603 . T)) +((|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 (-57))) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-1152) (QUOTE (-848))) (|HasCategory| (-57) (QUOTE (-1098))) (-12 (|HasCategory| (-57) (LIST (QUOTE -305) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1098)))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 (-57))) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 (-57))) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -4320) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 (-57))) (QUOTE (-1098)))) (-1841 (|HasCategory| (-57) (QUOTE (-1098))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 (-57))) (QUOTE (-1098))))) +(-628 S R) ((|constructor| (NIL "The category of Lie Algebras. It is used by the domains of non-commutative algebra, LiePolynomial and XPBWPolynomial.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{x} by \\axiom{r}.")) (|construct| (($ $ $) "\\axiom{construct(x,y)} returns the Lie bracket of \\axiom{x} and \\axiom{y}."))) NIL -((|HasCategory| |#2| (QUOTE (-367)))) -(-628 R) +((|HasCategory| |#2| (QUOTE (-368)))) +(-629 R) ((|constructor| (NIL "The category of Lie Algebras. It is used by the domains of non-commutative algebra, LiePolynomial and XPBWPolynomial.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{x} by \\axiom{r}.")) (|construct| (($ $ $) "\\axiom{construct(x,y)} returns the Lie bracket of \\axiom{x} and \\axiom{y}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4595 . T) (-4594 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4597 . T) (-4596 . T)) NIL -(-629 R A) +(-630 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*$A} to define the Lie bracket \\spad{a*b \\spad{:=} (a *$A \\spad{b} - \\spad{b} *$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?()$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank, together with a fixed \\spad{R}-module basis), then the same is \\spad{true} for the associated Lie algebra. Also, if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free R-module of finite rank), then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(R,A)."))) -((-4597 -1831 (-3997 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4595 . T) (-4594 . T)) -((|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (-1831 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))))) -(-630 R FE) +((-4599 -1841 (-4028 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4597 . T) (-4596 . T)) +((|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (-1841 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))))) +(-631 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 \\spad{->} 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 \\spad{->} a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x \\spad{->} 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 \\spad{->} a,f(x))}."))) NIL NIL -(-631 R) +(-632 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(f(x),x,a,\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-632 S R) +(-633 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 + \\spad{...} + cn*vn = u}, \"failed\" if no such ci'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 + \\spad{...} + cn*vn = u}, \"failed\" if no such ci's exist in \\spad{S.}")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + \\spad{...} + cn*vn = 0} and not all the ci's are 0, \"failed\" if the vi's are linearly independent over \\spad{S.}")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the vi's are linearly dependent over \\spad{S,} \\spad{false} otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-367))) (-2931 (|HasCategory| |#1| (QUOTE (-367))))) -(-633 R) +((|HasCategory| |#1| (QUOTE (-368))) (-2959 (|HasCategory| |#1| (QUOTE (-368))))) +(-634 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, \\spad{v)}} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A \\spad{x} = \\spad{v}} and \\spad{B \\spad{x} = \\spad{w}} have the same solutions in \\spad{R.}") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A \\spad{x} = 0} and \\spad{B \\spad{x} = 0} have the same solutions in \\spad{R.}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-634 A B) +(-635 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, \\spad{lb,} a, \\spad{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 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, \\spad{lb,} \\spad{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, \\spad{lb,} a, \\spad{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 la. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, \\spad{lb,} \\spad{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, \\spad{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 la."))) NIL NIL -(-635 A B) +(-636 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists, each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * \\spad{(2} * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = \\spad{[2} * 1, 3 * \\spad{(2} * 1)]}."))) NIL NIL -(-636 A B C) +(-637 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists, each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is, the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-637 S) +(-638 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| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and u2, then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-638 K PCS) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-639 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(s,n) and apply an appropriate shift (mult by a power of \\spad{t).}"))) NIL NIL -(-639 S) +(-640 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's} with \\spad{y's} in dictionary \\spad{d.}")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) -(-640 R) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) +(-641 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline Axioms\\br \\tab{5}\\spad{ (a*b)*x = a*(b*x) }\\br \\tab{5}\\spad{ (a+b)*x = (a*x)+(b*x) }\\br \\tab{5}\\spad{ a*(x+y) = (a*x)+(a*y) }")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r.}"))) NIL NIL -(-641 S E |un|) +(-642 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not, with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{f(a1)\\^e1 \\spad{...} f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, \\spad{a1\\^e1} \\spad{...} an\\^en)} returns \\spad{a1\\^f(e1) \\spad{...} an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, \\spad{y)}} returns \\spad{x + \\spad{y}} where \\spad{+} is the monoid operation, which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, \\spad{x)}} returns \\spad{e * \\spad{s} + \\spad{x}} where \\spad{+} is the monoid operation, which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation, which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, \\spad{s)}} returns \\spad{a * \\spad{s}} where \\spad{*} is the monoid operation, which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l.}")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l,} destroying the element \\spad{l.}")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l.} This has some effect if the monoid is non-abelian, \\spadignore{i.e.} \\spad{reverse(a1\\^e1 \\spad{...} an\\^en) = an\\^en \\spad{...} a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, \\spad{n)}} returns the factor of the n^th monomial of \\spad{l.}")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, \\spad{n)}} returns the exponent of the n^th monomial of \\spad{l.}")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l.}")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s).}")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l.}")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1), \\spad{fop(a, \\spad{b)}} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + \\spad{b},} \\spad{a * \\spad{b},} \\spad{ab}), and \\spad{fexp(a, \\spad{n)}} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a}, \\spad{n * a}, \\spad{a \\spad{**} \\spad{n},} \\spad{a\\^n})."))) NIL NIL -(-642 A S) +(-643 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{u(i..j) \\spad{:=} \\spad{x})} destructively replaces each element in the segment \\axiom{u(i..j)} by \\spad{x.} The value \\spad{x} is returned. Note that \\spad{u} is destructively change so that \\axiom{u.k \\spad{:=} \\spad{x} for \\spad{k} in i..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{i}th element. Note that \\axiom{insert(v,u,k) = concat( u(0..k-1), \\spad{v,} u(k..) \\spad{)}.}") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{i}th element. Note that \\axiom{insert(x,a,k) = concat(concat(a(0..k-1),x),a(k..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{i}th through \\axiom{j}th element deleted. Note that \\axiom{delete(a,i..j) = concat(a(0..i-1),a(j+1..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{i}th element deleted. Note that for lists, \\axiom{delete(a,i) \\spad{==} concat(a(0..i - 1),a(i + 1,..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(i..j)}) returns the aggregate of elements \\axiom{u} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note that in general, \\axiom{a.s = [a.k for \\spad{i} in s]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{z = f(x,y)} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v.} Note that for linear aggregates, \\axiom{w.i = f(u.i,v.i)}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)}, where \\spad{u} is a lists of aggregates \\axiom{[a,b,...,c]}, returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed \\spad{...} by the elements of \\spad{c.} Note that \\axiom{concat(a,b,...,c) = concat(a,concat(b,...,c))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v.} Note that if \\axiom{w = concat(u,v)} then \\axiom{w.i = u.i for \\spad{i} in indices u} and \\axiom{w.(j + maxIndex u) = \\spad{v.j} for \\spad{j} in indices \\spad{v}.}") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note that for lists: \\axiom{concat(x,u) \\spad{==} concat([x],u)}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note that for lists, \\axiom{concat(u,x) \\spad{==} concat(u,[x])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new n,x)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4601))) -(-643 S) +((|HasAttribute| |#1| (QUOTE -4603))) +(-644 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{u(i..j) \\spad{:=} \\spad{x})} destructively replaces each element in the segment \\axiom{u(i..j)} by \\spad{x.} The value \\spad{x} is returned. Note that \\spad{u} is destructively change so that \\axiom{u.k \\spad{:=} \\spad{x} for \\spad{k} in i..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{i}th element. Note that \\axiom{insert(v,u,k) = concat( u(0..k-1), \\spad{v,} u(k..) \\spad{)}.}") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{i}th element. Note that \\axiom{insert(x,a,k) = concat(concat(a(0..k-1),x),a(k..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{i}th through \\axiom{j}th element deleted. Note that \\axiom{delete(a,i..j) = concat(a(0..i-1),a(j+1..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{i}th element deleted. Note that for lists, \\axiom{delete(a,i) \\spad{==} concat(a(0..i - 1),a(i + 1,..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(i..j)}) returns the aggregate of elements \\axiom{u} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note that in general, \\axiom{a.s = [a.k for \\spad{i} in s]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{z = f(x,y)} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v.} Note that for linear aggregates, \\axiom{w.i = f(u.i,v.i)}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)}, where \\spad{u} is a lists of aggregates \\axiom{[a,b,...,c]}, returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed \\spad{...} by the elements of \\spad{c.} Note that \\axiom{concat(a,b,...,c) = concat(a,concat(b,...,c))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v.} Note that if \\axiom{w = concat(u,v)} then \\axiom{w.i = u.i for \\spad{i} in indices u} and \\axiom{w.(j + maxIndex u) = \\spad{v.j} for \\spad{j} in indices \\spad{v}.}") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note that for lists: \\axiom{concat(x,u) \\spad{==} concat([x],u)}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note that for lists, \\axiom{concat(u,x) \\spad{==} concat(u,[x])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new n,x)}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-644 K) +(-645 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{<-} 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| $) (|List| (|NonNegativeInteger|)) (|Integer|)) "\\spad{monomial2series(ls,le,n)} returns t**n * reduce(\"*\",[s \\spad{**} \\spad{e} for \\spad{s} in \\spad{ls} for \\spad{e} in le])")) (|delay| (($ (|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.}"))) -(((-4602 "*") . T) (-4593 . T) (-4592 . T) (-4598 . T) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") . T) (-4595 . T) (-4594 . T) (-4600 . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-645 R -3280 L) +(-646 R -3313 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, \\spad{g,} \\spad{x,} a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op \\spad{y} = \\spad{g,} y(a) = \\spad{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, \\spad{g,} \\spad{x)}} returns either a solution of the ordinary differential equation \\spad{op \\spad{y} = \\spad{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 \\spad{y} = 0}. A full basis for the solutions of the homogenuous equation is not always returned, only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-646 A) +(-647 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:\\br \\spad{(L1 * L2).(f) = \\spad{L1} \\spad{L2} \\spad{f}}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-367)))) -(-647 A M) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-368)))) +(-648 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:\\br \\spad{(L1 * L2).(f) = \\spad{L1} \\spad{L2} \\spad{f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-367)))) -(-648 S A) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-368)))) +(-649 S A) ((|constructor| (NIL "LinearOrdinaryDifferentialOperatorCategory is the category of differential operators with coefficients in a ring A with a given derivation. \\blankline Multiplication of operators corresponds to functional composition:\\br \\spad{(L1} * L2).(f) = \\spad{L1} \\spad{L2} \\spad{f}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL -((|HasCategory| |#2| (QUOTE (-367)))) -(-649 A) +((|HasCategory| |#2| (QUOTE (-368)))) +(-650 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:\\br \\spad{(L1} * L2).(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}."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-650 -3280 UP) +(-651 -3313 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)))) -(-651 A -1408) +(-652 A -3903) ((|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:\\br \\spad{(L1 * L2).(f) = \\spad{L1} \\spad{L2} \\spad{f}}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-367)))) -(-652 A L) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-368)))) +(-653 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-653 S) +(-654 S) ((|constructor| (NIL "Logic provides the basic operations for lattices, for example, boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{\\/} returns the logical `join', for example, `or'.")) (|/\\| (($ $ $) "\\spadignore{/\\} returns the logical `meet', for example, `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x.}"))) NIL NIL -(-654) +(-655) ((|constructor| (NIL "Logic provides the basic operations for lattices, for example, boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{\\/} returns the logical `join', for example, `or'.")) (|/\\| (($ $ $) "\\spadignore{/\\} returns the logical `meet', for example, `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x.}"))) NIL NIL -(-655 M R S) +(-656 M R S) ((|constructor| (NIL "Localize(M,R,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 \\spad{x}} returns the denominator of \\spad{x.}")) (|numer| ((|#1| $) "\\spad{numer \\spad{x}} returns the numerator of \\spad{x.}")) (/ (($ |#1| |#3|) "\\spad{m / \\spad{d}} divides the element \\spad{m} by \\spad{d.}") (($ $ |#3|) "\\spad{x / \\spad{d}} divides the element \\spad{x} by \\spad{d.}"))) -((-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-791)))) -(-656 K) +((-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-792)))) +(-657 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-a*v1} where \\indented{1}{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's almost the rowEchelon form except that no permution of lines is performed."))) NIL NIL -(-657 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) +(-658 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) ((|constructor| (NIL "This package is part of the PAFF package")) (|localize| (((|Record| (|:| |fnc| |#3|) (|:| |crv| |#3|) (|:| |chart| (|List| (|Integer|)))) |#3| |#5| |#3| (|Integer|)) "\\spad{localize(f,pt,crv,n)} returns a record containing the polynomials \\spad{f} and \\spad{crv} translate to the origin with respect to \\spad{pt.} The last element of the records, consisting of three integers contains information about the local parameter that will be used (either \\spad{x} or \\spad{y):} the first integer correspond to the variable that will be used as a local parameter.")) (|pointDominateBy| ((|#5| |#7|) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl.}")) (|localParamOfSimplePt| (((|List| |#6|) |#5| |#3| (|Integer|)) "\\spad{localParamOfSimplePt(pt,pol,n)} computes the local parametrization of the simple point \\spad{pt} on the curve defined by pol. This local parametrization is done according to the standard open affine plane set by \\spad{n}")) (|pointToPlace| ((|#7| |#5| |#3|) "\\spad{pointToPlace(pt,pol)} takes for input a simple point \\spad{pt} on the curve defined by \\spad{pol} and set the local parametrization of the point.")) (|printInfo| (((|Boolean|)) "returns the value of the \\spad{printInfo} flag.") (((|Boolean|) (|Boolean|)) "\\spad{printInfo(b)} set a flag such that when \\spad{true} \\spad{(b} \\spad{<-} true) prints some information during some critical computation."))) NIL NIL -(-658 R) +(-659 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring, this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation, by moving into the field of fractions, and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], \\spad{g)}} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-659 |VarSet| R) +(-660 |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(x,y)} returns the Lie bracket \\axiom{[x,y]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(x,y)} returns the Lie bracket \\axiom{[x,y]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(x,y)} returns the Lie bracket \\axiom{[x,y]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(p)} returns \\axiom{p} in Lyndon basis if \\axiom{p} is a Lie polynomial, otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4595 . T) (-4594 . T)) -((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-173)))) -(-660 A S) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4597 . T) (-4596 . T)) +((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-174)))) +(-661 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x.}"))) NIL NIL -(-661 S) +(-662 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.}"))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-662 -3280) +(-663 -3313) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = \\spad{B}.} It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package'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 = \\spad{B}.}")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = \\spad{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 = \\spad{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 = \\spad{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 = \\spad{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 = \\spad{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 = \\spad{B}} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-663 -3280 |Row| |Col| M) +(-664 -3313 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = \\spad{B}.}")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = \\spad{B}.}")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = \\spad{B}} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = \\spad{B}.}")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = \\spad{B}} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB.}") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = \\spad{B}} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-664 R E OV P) +(-665 R E OV P) ((|constructor| (NIL "This package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols lvar."))) NIL NIL -(-665 |n| R) +(-666 |n| R) ((|constructor| (NIL "LieSquareMatrix(n,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\\br \\spad{a*b \\spad{:=} (a *$SQMATRIX(n,R) \\spad{b} - \\spad{b} *$SQMATRIX(n,R) a)},\\br where \\spadfun{*$SQMATRIX(n,R)} is the usual matrix multiplication."))) -((-4597 . T) (-4600 . T) (-4594 . T) (-4595 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226))) (|HasAttribute| |#2| (QUOTE (-4602 "*"))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561))) (-1831 (|HasAttribute| |#2| (QUOTE (-4602 "*"))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-226)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))))) (|HasCategory| |#2| (QUOTE (-173)))) -(-666 |VarSet|) +((-4599 . T) (-4602 . T) (-4596 . T) (-4597 . T)) +((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4604 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-303))) (|HasCategory| |#2| (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-1841 (|HasAttribute| |#2| (QUOTE (-4604 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098))))) (|HasCategory| |#2| (QUOTE (-174)))) +(-667 |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 w.r.t. the pure lexicographical ordering. If \\axiom{a} and \\axiom{b} are two Lyndon words such that \\axiom{a < \\spad{b}} holds w.r.t lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule:\\br \\axiom{[[a,b],c]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds.\\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(vl, \\spad{n)}} returns the list of Lyndon words over the alphabet \\axiom{vl}, up to order \\axiom{n}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(vl, \\spad{n)}} returns an array of lists of Lyndon words over the alphabet \\axiom{vl}, up to order \\axiom{n}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(x)} returns the list of distinct entries of \\axiom{x}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(w)} convert \\axiom{w} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(w)} convert \\axiom{w} into a Lyndon word, error if \\axiom{w} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(w)} test if \\axiom{w} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(x)} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(x)} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{x}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(x)} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{x}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(x,y)} returns \\axiom{true} iff \\axiom{x} is smaller than \\axiom{y} w.r.t. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(x)} returns the number of entries in \\axiom{x}.")) (|right| (($ $) "\\axiom{right(x)} returns right subtree of \\axiom{x} or error if retractable?(x) is true.")) (|left| (($ $) "\\axiom{left(x)} returns left subtree of \\axiom{x} or error if retractable?(x) is true.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(x)} tests if \\axiom{x} is a tree with only one entry."))) NIL NIL -(-667 A S) +(-668 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?', for example 'first' and 'rest', will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. \\indented{1}{this function should only be called on streams which are} \\indented{1}{known to be finite.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} n:=filterUntil(i+->i>100,m) \\spad{X} numberOfComputedEntries \\spad{n} \\spad{X} complete \\spad{n} \\spad{X} numberOfComputedEntries \\spad{n}")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed, if necessary, \\indented{1}{so that 'st' will have at least \\spad{'n'} explicit entries or so} \\indented{1}{that all entries of 'st' will be computed if 'st' is finite} \\indented{1}{with length \\spad{<=} \\spad{n.}} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m} \\spad{X} extend(m,20) \\spad{X} numberOfComputedEntries \\spad{m}")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly \\indented{1}{computed entries of stream \\spad{st} which exist immediately prior to the} \\indented{1}{time this function is called.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m}")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s.} \\indented{1}{Cautrion: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} \\spad{rst} \\spad{m}")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} frst \\spad{m}")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s.} \\indented{1}{Caution: the first node must be a lazy evaluation mechanism} \\indented{1}{(satisfies \\spad{lazy?(s) = true}) as there is no error check.} \\indented{1}{Note that a call to this function may} \\indented{1}{or may not produce an explicit first entry}")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} \\indented{1}{is a lazy evaluation mechanism which could produce an} \\indented{1}{additional entry to \\spad{s.}} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} lazy? \\spad{m}")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an \\indented{1}{(explicitly) empty stream.} \\indented{1}{Note that this is a null test which will not cause lazy evaluation.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} explicitlyEmpty? \\spad{m}")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has \\indented{1}{explicitly computed entries, and \\spad{false} otherwise.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} explicitEntries? \\spad{m}")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\indented{1}{st satisfying the predicate \\spad{f.}} \\indented{1}{Note that \\spad{select(f,st) = \\spad{[x} for \\spad{x} in \\spad{st} | f(x)]}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} select(x+->prime? x,m)")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\indented{1}{st which do not satisfy the predicate \\spad{f.}} \\indented{1}{Note that \\spad{remove(f,st) = \\spad{[x} for \\spad{x} in \\spad{st} | not f(x)]}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} f(i:PositiveInteger):Boolean \\spad{==} even? \\spad{i} \\spad{X} remove(f,m)"))) NIL NIL -(-668 S) +(-669 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?', for example 'first' and 'rest', will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. \\indented{1}{this function should only be called on streams which are} \\indented{1}{known to be finite.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} n:=filterUntil(i+->i>100,m) \\spad{X} numberOfComputedEntries \\spad{n} \\spad{X} complete \\spad{n} \\spad{X} numberOfComputedEntries \\spad{n}")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed, if necessary, \\indented{1}{so that 'st' will have at least \\spad{'n'} explicit entries or so} \\indented{1}{that all entries of 'st' will be computed if 'st' is finite} \\indented{1}{with length \\spad{<=} \\spad{n.}} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m} \\spad{X} extend(m,20) \\spad{X} numberOfComputedEntries \\spad{m}")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly \\indented{1}{computed entries of stream \\spad{st} which exist immediately prior to the} \\indented{1}{time this function is called.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} numberOfComputedEntries \\spad{m}")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s.} \\indented{1}{Cautrion: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} \\spad{rst} \\spad{m}")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s.} \\indented{1}{Caution: this function should only be called after a \\spad{empty?}} \\indented{1}{test has been made since there no error check.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} frst \\spad{m}")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s.} \\indented{1}{Caution: the first node must be a lazy evaluation mechanism} \\indented{1}{(satisfies \\spad{lazy?(s) = true}) as there is no error check.} \\indented{1}{Note that a call to this function may} \\indented{1}{or may not produce an explicit first entry}")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} \\indented{1}{is a lazy evaluation mechanism which could produce an} \\indented{1}{additional entry to \\spad{s.}} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} lazy? \\spad{m}")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an \\indented{1}{(explicitly) empty stream.} \\indented{1}{Note that this is a null test which will not cause lazy evaluation.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} explicitlyEmpty? \\spad{m}")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has \\indented{1}{explicitly computed entries, and \\spad{false} otherwise.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} explicitEntries? \\spad{m}")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\indented{1}{st satisfying the predicate \\spad{f.}} \\indented{1}{Note that \\spad{select(f,st) = \\spad{[x} for \\spad{x} in \\spad{st} | f(x)]}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 0..] \\spad{X} select(x+->prime? x,m)")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\indented{1}{st which do not satisfy the predicate \\spad{f.}} \\indented{1}{Note that \\spad{remove(f,st) = \\spad{[x} for \\spad{x} in \\spad{st} | not f(x)]}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} f(i:PositiveInteger):Boolean \\spad{==} even? \\spad{i} \\spad{X} remove(f,m)"))) -((-3348 . T)) +((-3389 . T)) NIL -(-669 R) +(-670 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-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 x.i.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-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 (-1097))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-670 MPT MD) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-671 MPT MD) ((|constructor| (NIL "This category specifies operations needed by ModularAlgebraicGcd package. Since we have multiple implementations we specify interface here and put implementations in separate packages. Most operations are done using special purpose abstract representation. Apropriate types are passesd as parametes: \\spad{MPT} is type of modular polynomials in one variable with coefficients in some algebraic extension. \\spad{MD} is type of modulus. Final results are converted to packed representation, with coefficients (from prime field) stored in one array and exponents (in main variable and in auxilary variables representing generators of algebrac extension) stored in parallel array.")) (|repack1| (((|Void|) |#1| (|U32Vector|) (|Integer|) |#2|) "\\spad{repack1(x, a, \\spad{d,} \\spad{m)}} stores coefficients of \\spad{x} in a. \\spad{d} is degree of \\spad{x.} Corresponding exponents are given by packExps.")) (|packExps| ((|SortedExponentVector| (|Integer|) (|Integer|) |#2|) "\\spad{packExps(d, \\spad{s,} \\spad{m)}} produces vector of exponents up to degree \\spad{d.} \\spad{s} is size (degree) of algebraic extension. Use together with repack1.")) (|degree| (((|Integer|) |#1|) "\\spad{degree(x)} gives degree of \\spad{x.}")) (|zero?| (((|Boolean|) |#1|) "\\spad{zero?(x)} checks if \\spad{x} is zero.")) (|MPtoMPT| ((|#1| (|Polynomial| (|Integer|)) (|Symbol|) (|List| (|Symbol|)) |#2|) "\\spad{MPtoMPT(p, \\spad{s,} \\spad{ls,} \\spad{m)}} coverts \\spad{p} to packed represntation.")) (|packModulus| (((|Union| |#2| "failed") (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Integer|)) "\\spad{packModulus(lp, \\spad{ls,} \\spad{p)}} converts \\spad{lp,} \\spad{ls} and prime \\spad{p} which together describe algebraic extension to packed representation.")) (|canonicalIfCan| (((|Union| |#1| "failed") |#1| |#2|) "\\spad{canonicalIfCan(x, \\spad{m)}} tries to divide \\spad{x} by its leading coefficient modulo \\spad{m.}")) (|pseudoRem| ((|#1| |#1| |#1| |#2|) "\\spad{pseudoRem(x, \\spad{y,} \\spad{m)}} computes pseudoremainder of \\spad{x} by \\spad{y} modulo \\spad{m.}"))) NIL NIL -(-671 |VarSet|) +(-672 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(x)} returns the list of distinct entries of \\axiom{x}.")) (|right| (($ $) "\\axiom{right(x)} returns right subtree of \\axiom{x} or error if retractable?(x) is true.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(x)} tests if \\axiom{x} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(x)} return \\axiom{x} without the first entry or error if retractable?(x) is true.")) (|mirror| (($ $) "\\axiom{mirror(x)} returns the reversed word of \\axiom{x}. That is \\axiom{x} itself if retractable?(x) is \\spad{true} and \\axiom{mirror(z) * mirror(y)} if \\axiom{x} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(x,y)} returns \\axiom{true} iff \\axiom{x} is smaller than \\axiom{y} w.r.t. the lexicographical ordering induced by \\axiom{VarSet}. N.B. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(x)} returns the number of entries in \\axiom{x}.")) (|left| (($ $) "\\axiom{left(x)} returns left subtree of \\axiom{x} or error if retractable?(x) is true.")) (|first| ((|#1| $) "\\axiom{first(x)} returns the first entry of the tree \\axiom{x}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\indented{1}{\\axiom{coerce(x)} returns the element of} \\axiomType{OrderedFreeMonoid}(VarSet) \\indented{1}{corresponding to \\axiom{x} by removing parentheses.}")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[x,y]}."))) NIL NIL -(-672 R |Row| |Col| M) +(-673 R |Row| |Col| M) ((|constructor| (NIL "Some functions for manipulating (dense) matrices. Supported are various kinds of slicing, splitting and stacking of matrices. The functions resemble operations often used in numerical linear algebra algorithms.")) (|blockSplit| (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|List| (|PositiveInteger|))) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|List| (|PositiveInteger|)) (|PositiveInteger|)) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.") (((|List| (|List| |#4|)) |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\spad{blockSplit} splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.")) (|horizSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\spad{horizSplit} splits a matrix into multiple submatrices column wise.") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\spad{horizSplit} splits a matrix into multiple submatrices column wise.")) (|vertSplit| (((|List| |#4|) |#4| (|List| (|PositiveInteger|))) "\\spad{vertSplit} splits a matrix into multiple submatrices row wise.") (((|List| |#4|) |#4| (|PositiveInteger|)) "\\spad{vertSplit} splits a matrix into multiple submatrices row wise.")) (|blockConcat| ((|#4| (|List| (|List| |#4|))) "\\spad{blockConcat} concatenates matrices row and column wise, building a block matrix. The order is row major as in \\spad{matrix}.")) (|vertConcat| ((|#4| (|List| |#4|)) "\\spad{vertConcat} concatenates matrices row wise.")) (|horizConcat| ((|#4| (|List| |#4|)) "\\spad{horizConcat} concatenates matrices column wise.")) (|bandMatrix| ((|#4| |#4| (|Segment| (|Integer|))) "\\spad{bandMatrix} returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.") ((|#4| |#4| (|List| (|Integer|))) "\\spad{bandMatrix} returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.")) (|diagonalMatrix| ((|#4| |#4|) "\\spad{diagonalMatrix} returns the main diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one.") ((|#4| |#4| (|Integer|)) "\\spad{diagonalMatrix} returns a diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.")) (|subMatrix| ((|#4| |#4| (|Segment| (|PositiveInteger|)) (|Segment| (|PositiveInteger|))) "\\spad{subMatrix} returns several elements out of a matrix. The elements are stacked into a submatrix.") ((|#4| |#4| (|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{subMatrix} returns several elements out of a matrix. The elements are stacked into a submatrix.")) (|columns| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\spad{columns} returns several columns out of a matrix. The columns are stacked into a matrix.") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\spad{columns} returns several columns out of a matrix. The columns are stacked into a matrix.")) (|aColumn| ((|#4| |#4| (|PositiveInteger|)) "\\spad{aColumn} returns a single column out of a matrix. The column is put into a one by \\spad{N} matrix.")) (|rows| ((|#4| |#4| (|Segment| (|PositiveInteger|))) "\\spad{rows} returns several rows out of a matrix. The rows are stacked into a matrix.") ((|#4| |#4| (|List| (|PositiveInteger|))) "\\spad{rows} returns several rows out of a matrix. The rows are stacked into a matrix.")) (|aRow| ((|#4| |#4| (|PositiveInteger|)) "\\spad{aRow} returns a single row out of a matrix. The row is put into a one by \\spad{N} matrix.")) (|element| ((|#4| |#4| (|PositiveInteger|) (|PositiveInteger|)) "\\spad{element} returns a single element out of a matrix. The element is put into a one by one matrix."))) NIL NIL -(-673 A) +(-674 A) ((|constructor| (NIL "Various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f \\spad{n}} times to \\spad{x}."))) NIL NIL -(-674 A C) +(-675 A C) ((|constructor| (NIL "Various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) NIL NIL -(-675 A B C) +(-676 A B C) ((|constructor| (NIL "Various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) NIL NIL -(-676 A) +(-677 A) ((|constructor| (NIL "Various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the n-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id \\spad{x}} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint \\spad{f}} is the fixed point of function \\spad{f}. \\indented{1}{that is, such that \\spad{fixedPoint \\spad{f} = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-677 A C) +(-678 A C) ((|constructor| (NIL "Various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= \\spad{f} ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g \\spad{()=} \\spad{f} a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const \\spad{c}} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-678 A B C) +(-679 A B C) ((|constructor| (NIL "Various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h \\spad{x=} \\spad{f(g} x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= \\spad{f} b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= \\spad{f} a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g \\spad{b} = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) NIL NIL -(-679 A B) +(-680 A B) ((|constructor| (NIL "Functional Composition. Given functions \\spad{f} and \\spad{g,} returns the applicable closure")) (/ (((|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|) (|Mapping| (|Expression| (|Integer|)) |#1|)) "\\indented{1}{\\spad(+) does functional addition} \\blankline \\spad{X} p:=(x:EXPR(INT)):EXPR(INT)+->3*x \\spad{X} \\spad{q:=(x:EXPR(INT)):EXPR(INT)+->2*x+3} \\spad{X} (p/q)(4) \\spad{X} (p/q)(x)")) (* (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}{\\spad(+) does functional addition} \\blankline \\spad{X} f:=(x:INT):INT \\spad{+->} 3*x \\spad{X} g:=(x:INT):INT \\spad{+->} 2*x+3 \\spad{X} (f*g)(4)")) (- (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}{\\spad(+) does functional addition} \\blankline \\spad{X} f:=(x:INT):INT \\spad{+->} 3*x \\spad{X} g:=(x:INT):INT \\spad{+->} 2*x+3 \\spad{X} (f-g)(4)")) (+ (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|) (|Mapping| |#2| |#1|)) "\\indented{1}{\\spad(+) does functional addition} \\blankline \\spad{X} f:=(x:INT):INT \\spad{+->} 3*x \\spad{X} g:=(x:INT):INT \\spad{+->} 2*x+3 \\spad{X} (f+g)(4)"))) NIL NIL -(-680 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-681 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j.}")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m.}") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m.}"))) NIL NIL -(-681 S R |Row| |Col|) +(-682 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m.} \\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| $) "\\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],[-1,0,0,0],[0,0,0,1],[0,0,-1,0]]")) (|minordet| ((|#2| $) "\\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| $) "\\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|) $) "\\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|) $) "\\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|) $) "\\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|) $) "\\spad{columnSpace(m)} returns a sublist of columns of the matrix \\spad{m} \\indented{1}{forming a basis of its column space} \\blankline \\spad{X} columnSpace matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m.} \\blankline \\spad{X} rowEchelon matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (/ (($ $ |#2|) "\\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|) "\\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(m,2)")) (** (($ $ (|Integer|)) "\\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|)) "\\spad{x \\spad{**} \\spad{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| $) "\\spad{r * \\spad{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|) "\\spad{x * \\spad{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|) $) "\\spad{n * \\spad{x}} is an integer multiple. \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 3*m") (($ $ |#2|) "\\spad{x * \\spad{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| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the \\indented{1}{matrix \\spad{x.}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 1/3*m") (($ $ $) "\\spad{x * \\spad{y}} is the product of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*m}")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{-m}") (($ $ $) "\\spad{x - \\spad{y}} is the difference of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m-m}")) (+ (($ $ $) "\\spad{x + \\spad{y}} is the sum of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m+m}")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix!(x,i1,j1,y)} destructively alters the \\indented{1}{matrix \\spad{x.} Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for} \\indented{1}{\\spad{i = i1,...,i1-1+nrows \\spad{y}} and \\spad{j = j1,...,j1-1+ncols y}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setsubMatrix!(m,2,2,matrix [[3,3],[3,3]])")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\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(m,1,3,2,4)")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\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!(m,2,4)")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\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!(m,2,4)")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x.} \\indented{1}{If \\spad{y} is \\spad{m}-by-\\spad{n}, \\spad{rowList = [i<1>,i<2>,...,i]}} \\indented{1}{and \\spad{colList = [j<1>,j<2>,...,j]}, then \\spad{x(i,j)}} \\indented{1}{is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setelt(m,3,3,10)")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an m-by-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 \\spad{=}} \\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(m,3,3)")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list \\indented{1}{of lists.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} listOfLists \\spad{m}")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an \\indented{1}{equal number of columns. The entries of \\spad{y} appear below} \\indented{1}{of the entries of x.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of columns.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} vertConcat(m,m)")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with \\indented{1}{an equal number of rows. The entries of \\spad{y} appear to the right} \\indented{1}{of the entries of x.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of rows.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} horizConcat(m,m)")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an n-by-n matrix consisting of the first \\indented{1}{n rows of the m-by-n matrix \\spad{m.} Error: if} \\indented{1}{\\spad{m < n}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..2] for \\spad{j} in 1..5] \\spad{X} squareTop \\spad{m}")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} transpose \\spad{m}") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix. \\blankline \\spad{X} transpose([1,2,3])@Matrix(INT)")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix. \\blankline \\spad{X} coerce([1,2,3])@Matrix(INT)")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\indented{1}{M with block matrices m1,...,mk down the diagonal,} \\indented{1}{with 0 block matrices elsewhere.} \\indented{1}{More precisly: if \\spad{ri \\spad{:=} nrows mi}, \\spad{ci \\spad{:=} ncols mi},} \\indented{1}{then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix\\space{2}with entries} \\indented{1}{\\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))}, if} \\indented{1}{\\spad{(r1+..+r(l-1)) < \\spad{i} \\spad{<=} r1+..+rl} and} \\indented{1}{\\spad{(c1+..+c(l-1)) < \\spad{i} \\spad{<=} c1+..+cl},} \\indented{1}{\\spad{m.i.j} = 0\\space{2}otherwise.} \\blankline \\spad{X} diagonalMatrix [matrix [[1,2],[3,4]], matrix [[4,5],[6,7]]]") (($ (|List| |#2|)) "\\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|) "\\spad{scalarMatrix(n,r)} returns an n-by-n matrix with \\spad{r's} on the \\indented{1}{diagonal and zeroes elsewhere.} \\blankline \\spad{X} z:Matrix(INT):=scalarMatrix(3,5)")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} constructs an \\spad{n * \\spad{m}} matrix with \\indented{1}{the \\spad{(i,j)} entry equal to \\spad{f(i,j)}} \\blankline \\spad{X} f(i:INT,j:INT):INT \\spad{==} i+j \\spad{X} matrix(3,4,f)") (($ (|List| (|List| |#2|))) "\\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|)) "\\spad{zero(m,n)} returns an m-by-n zero matrix. \\blankline \\spad{X} z:Matrix(INT):=zero(3,3)")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{antisymmetric (that is, \\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|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{symmetric (that is, \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j)} and 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|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{diagonal (that is, all entries of \\spad{m} not on the diagonal are zero) and} \\indented{1}{false otherwise.} \\blankline \\spad{X} diagonal? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|square?| (((|Boolean|) $) "\\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 (-173))) (|HasAttribute| |#2| (QUOTE (-4602 "*"))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561)))) -(-682 R |Row| |Col|) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE (-4604 "*"))) (|HasCategory| |#2| (QUOTE (-303))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562)))) +(-683 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m.} \\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| $) "\\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],[-1,0,0,0],[0,0,0,1],[0,0,-1,0]]")) (|minordet| ((|#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| $) "\\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|) $) "\\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|) $) "\\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|) $) "\\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|) $) "\\spad{columnSpace(m)} returns a sublist of columns of the matrix \\spad{m} \\indented{1}{forming a basis of its column space} \\blankline \\spad{X} columnSpace matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]]")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m.} \\blankline \\spad{X} rowEchelon matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (/ (($ $ |#1|) "\\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|) "\\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(m,2)")) (** (($ $ (|Integer|)) "\\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|)) "\\spad{x \\spad{**} \\spad{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| $) "\\spad{r * \\spad{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|) "\\spad{x * \\spad{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|) $) "\\spad{n * \\spad{x}} is an integer multiple. \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 3*m") (($ $ |#1|) "\\spad{x * \\spad{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| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the \\indented{1}{matrix \\spad{x.}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} 1/3*m") (($ $ $) "\\spad{x * \\spad{y}} is the product of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m*m}")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{-m}") (($ $ $) "\\spad{x - \\spad{y}} is the difference of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m-m}")) (+ (($ $ $) "\\spad{x + \\spad{y}} is the sum of the matrices \\spad{x} and \\spad{y.} \\indented{1}{Error: if the dimensions are incompatible.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} \\spad{m+m}")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix!(x,i1,j1,y)} destructively alters the \\indented{1}{matrix \\spad{x.} Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for} \\indented{1}{\\spad{i = i1,...,i1-1+nrows \\spad{y}} and \\spad{j = j1,...,j1-1+ncols y}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setsubMatrix!(m,2,2,matrix [[3,3],[3,3]])")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\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(m,1,3,2,4)")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\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!(m,2,4)")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\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!(m,2,4)")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x.} \\indented{1}{If \\spad{y} is \\spad{m}-by-\\spad{n}, \\spad{rowList = [i<1>,i<2>,...,i]}} \\indented{1}{and \\spad{colList = [j<1>,j<2>,...,j]}, then \\spad{x(i,j)}} \\indented{1}{is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} setelt(m,3,3,10)")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an m-by-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 \\spad{=}} \\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(m,3,3)")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list \\indented{1}{of lists.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} listOfLists \\spad{m}")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an \\indented{1}{equal number of columns. The entries of \\spad{y} appear below} \\indented{1}{of the entries of x.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of columns.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} vertConcat(m,m)")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with \\indented{1}{an equal number of rows. The entries of \\spad{y} appear to the right} \\indented{1}{of the entries of x.\\space{2}Error: if the matrices} \\indented{1}{do not have the same number of rows.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} horizConcat(m,m)")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an n-by-n matrix consisting of the first \\indented{1}{n rows of the m-by-n matrix \\spad{m.} Error: if} \\indented{1}{\\spad{m < n}.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..2] for \\spad{j} in 1..5] \\spad{X} squareTop \\spad{m}")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m.} \\blankline \\spad{X} m:=matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5] \\spad{X} transpose \\spad{m}") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix. \\blankline \\spad{X} transpose([1,2,3])@Matrix(INT)")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix. \\blankline \\spad{X} coerce([1,2,3])@Matrix(INT)")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\indented{1}{M with block matrices m1,...,mk down the diagonal,} \\indented{1}{with 0 block matrices elsewhere.} \\indented{1}{More precisly: if \\spad{ri \\spad{:=} nrows mi}, \\spad{ci \\spad{:=} ncols mi},} \\indented{1}{then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix\\space{2}with entries} \\indented{1}{\\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))}, if} \\indented{1}{\\spad{(r1+..+r(l-1)) < \\spad{i} \\spad{<=} r1+..+rl} and} \\indented{1}{\\spad{(c1+..+c(l-1)) < \\spad{i} \\spad{<=} c1+..+cl},} \\indented{1}{\\spad{m.i.j} = 0\\space{2}otherwise.} \\blankline \\spad{X} diagonalMatrix [matrix [[1,2],[3,4]], matrix [[4,5],[6,7]]]") (($ (|List| |#1|)) "\\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|) "\\spad{scalarMatrix(n,r)} returns an n-by-n matrix with \\spad{r's} on the \\indented{1}{diagonal and zeroes elsewhere.} \\blankline \\spad{X} z:Matrix(INT):=scalarMatrix(3,5)")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} constructs an \\spad{n * \\spad{m}} matrix with \\indented{1}{the \\spad{(i,j)} entry equal to \\spad{f(i,j)}} \\blankline \\spad{X} f(i:INT,j:INT):INT \\spad{==} i+j \\spad{X} matrix(3,4,f)") (($ (|List| (|List| |#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|)) "\\spad{zero(m,n)} returns an m-by-n zero matrix. \\blankline \\spad{X} z:Matrix(INT):=zero(3,3)")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{antisymmetric (that is, \\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|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{symmetric (that is, \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j)} and 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|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and \\indented{1}{diagonal (that is, all entries of \\spad{m} not on the diagonal are zero) and} \\indented{1}{false otherwise.} \\blankline \\spad{X} diagonal? matrix [[j**i for \\spad{i} in 0..4] for \\spad{j} in 1..5]")) (|square?| (((|Boolean|) $) "\\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"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-683 R |Row| |Col| M) +(-684 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(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(m,j) : elementary operation of second kind. \\spad{(i} ^=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(m,j) : elementary operation of second kind. \\spad{(i} ^=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m.} an error message is returned if the matrix is not square."))) NIL -((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-561)))) -(-684 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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4602 "*"))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) +((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-303))) (|HasCategory| |#1| (QUOTE (-562)))) (-685 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."))) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-303))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4604 "*"))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-686 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 \\spad{**} \\spad{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 * \\spad{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 * \\spad{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 - \\spad{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 + \\spad{b}} and stores the result in the matrix \\spad{c.} Error: if \\spad{a}, \\spad{b,} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c.} Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-686 S -3280 FLAF FLAS) +(-687 S -3313 FLAF FLAS) ((|constructor| (NIL "\\spadtype{MultiVariableCalculusFunctions} Package provides several functions for multivariable calculus. These include gradient, hessian and jacobian, divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian, the matrix of first partial derivatives, of the vector field \\spad{vf,} \\spad{vf} a vector function of the variables listed in xlist, \\spad{kl} is the number of nonzero subdiagonals, \\spad{ku} is the number of nonzero superdiagonals, \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix, dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows, the diagonal is in row ku+1, the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to \\spad{LAPACK/NAG-F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian, the matrix of first partial derivatives, of the vector field \\spad{vf,} \\spad{vf} a vector function of the variables listed in xlist.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian, the matrix of second partial derivatives, of the scalar field \\spad{v,} \\spad{v} a function of the variables listed in xlist, \\spad{k} is the semi-bandwidth, the number of nonzero subdiagonals, 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix, dimensions \\spad{k+1} by \\#xlist, whose rows are the vectors formed by diagonal, subdiagonal, etc. of the real, full-matrix, hessian. (The notation conforms to \\spad{LAPACK/NAG-F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian, the matrix of second partial derivatives, of the scalar field \\spad{v,} \\spad{v} a function of the variables listed in xlist.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v,} \\spad{v} a function of the variables listed in xlist.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf,} \\spad{vf} a vector function of the variables listed in xlist.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient, the vector of first partial derivatives, of the scalar field \\spad{v,} \\spad{v} a function of the variables listed in xlist."))) NIL NIL -(-687 R Q) +(-688 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, \\spad{d]}} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q.}")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q.}")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q.}"))) NIL NIL -(-688) +(-689) ((|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"))) -((-4593 . T) (-4598 |has| (-693) (-367)) (-4592 |has| (-693) (-367)) (-3331 . T) (-4599 |has| (-693) (-6 -4599)) (-4596 |has| (-693) (-6 -4596)) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-693) (QUOTE (-151))) (|HasCategory| (-693) (QUOTE (-149))) (|HasCategory| (-693) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-693) (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| (-693) (QUOTE (-373))) (|HasCategory| (-693) (QUOTE (-367))) (|HasCategory| (-693) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-693) (QUOTE (-226))) (|HasCategory| (-693) (QUOTE (-352))) (-1831 (|HasCategory| (-693) (QUOTE (-367))) (|HasCategory| (-693) (QUOTE (-352)))) (|HasCategory| (-693) (LIST (QUOTE -282) (QUOTE (-693)) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -304) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -526) (QUOTE (-1169)) (QUOTE (-693)))) (|HasCategory| (-693) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-693) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-693) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-693) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-693) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-693) (QUOTE (-1027))) (|HasCategory| (-693) (QUOTE (-1189))) (-12 (|HasCategory| (-693) (QUOTE (-1008))) (|HasCategory| (-693) (QUOTE (-1189)))) (|HasCategory| (-693) (QUOTE (-553))) (|HasCategory| (-693) (QUOTE (-1062))) (-12 (|HasCategory| (-693) (QUOTE (-1062))) (|HasCategory| (-693) (QUOTE (-1189)))) (-1831 (|HasCategory| (-693) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-693) (QUOTE (-367)))) (|HasCategory| (-693) (QUOTE (-302))) (-1831 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-367))) (|HasCategory| (-693) (QUOTE (-352)))) (|HasCategory| (-693) (QUOTE (-909))) (-12 (|HasCategory| (-693) (QUOTE (-226))) (|HasCategory| (-693) (QUOTE (-367)))) (-12 (|HasCategory| (-693) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-693) (QUOTE (-367)))) (|HasCategory| (-693) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-693) (QUOTE (-847))) (|HasCategory| (-693) (QUOTE (-561))) (|HasAttribute| (-693) (QUOTE -4599)) (|HasAttribute| (-693) (QUOTE -4596)) (-12 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (|HasCategory| (-693) (QUOTE (-367))) (-12 (|HasCategory| (-693) (QUOTE (-352))) (|HasCategory| (-693) (QUOTE (-909))))) (-1831 (-12 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (-12 (|HasCategory| (-693) (QUOTE (-367))) (|HasCategory| (-693) (QUOTE (-909)))) (-12 (|HasCategory| (-693) (QUOTE (-352))) (|HasCategory| (-693) (QUOTE (-909))))) (-1831 (-12 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (|HasCategory| (-693) (QUOTE (-367)))) (-1831 (-12 (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (|HasCategory| (-693) (QUOTE (-561)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (|HasCategory| (-693) (QUOTE (-149)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-693) (QUOTE (-302))) (|HasCategory| (-693) (QUOTE (-909)))) (|HasCategory| (-693) (QUOTE (-352))))) -(-689 S) +((-4595 . T) (-4600 |has| (-694) (-368)) (-4594 |has| (-694) (-368)) (-3363 . T) (-4601 |has| (-694) (-6 -4601)) (-4598 |has| (-694) (-6 -4598)) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-694) (QUOTE (-151))) (|HasCategory| (-694) (QUOTE (-149))) (|HasCategory| (-694) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-694) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-694) (QUOTE (-374))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-694) (QUOTE (-227))) (|HasCategory| (-694) (QUOTE (-353))) (-1841 (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-353)))) (|HasCategory| (-694) (LIST (QUOTE -283) (QUOTE (-694)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -305) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -527) (QUOTE (-1170)) (QUOTE (-694)))) (|HasCategory| (-694) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-694) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-694) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-694) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-694) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-694) (QUOTE (-1028))) (|HasCategory| (-694) (QUOTE (-1190))) (-12 (|HasCategory| (-694) (QUOTE (-1009))) (|HasCategory| (-694) (QUOTE (-1190)))) (|HasCategory| (-694) (QUOTE (-554))) (|HasCategory| (-694) (QUOTE (-1063))) (-12 (|HasCategory| (-694) (QUOTE (-1063))) (|HasCategory| (-694) (QUOTE (-1190)))) (-1841 (|HasCategory| (-694) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-694) (QUOTE (-368)))) (|HasCategory| (-694) (QUOTE (-303))) (-1841 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-353)))) (|HasCategory| (-694) (QUOTE (-910))) (-12 (|HasCategory| (-694) (QUOTE (-227))) (|HasCategory| (-694) (QUOTE (-368)))) (-12 (|HasCategory| (-694) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-694) (QUOTE (-368)))) (|HasCategory| (-694) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-694) (QUOTE (-848))) (|HasCategory| (-694) (QUOTE (-562))) (|HasAttribute| (-694) (QUOTE -4601)) (|HasAttribute| (-694) (QUOTE -4598)) (-12 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (|HasCategory| (-694) (QUOTE (-368))) (-12 (|HasCategory| (-694) (QUOTE (-353))) (|HasCategory| (-694) (QUOTE (-910))))) (-1841 (-12 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (-12 (|HasCategory| (-694) (QUOTE (-368))) (|HasCategory| (-694) (QUOTE (-910)))) (-12 (|HasCategory| (-694) (QUOTE (-353))) (|HasCategory| (-694) (QUOTE (-910))))) (-1841 (-12 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (|HasCategory| (-694) (QUOTE (-368)))) (-1841 (-12 (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (|HasCategory| (-694) (QUOTE (-562)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (|HasCategory| (-694) (QUOTE (-149)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-694) (QUOTE (-303))) (|HasCategory| (-694) (QUOTE (-910)))) (|HasCategory| (-694) (QUOTE (-353))))) +(-690 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.}"))) -((-4601 . T) (-3348 . T)) +((-4603 . T) (-3389 . T)) NIL -(-690 U) +(-691 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, \\spad{p)}} refines the distinct degree factorization produced by ddFact to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p,} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p.}")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p.} Error: if \\spad{f1} is not square-free modulo \\spad{p.}")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p.} Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p.}")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p.}"))) NIL NIL -(-691) +(-692) ((|constructor| (NIL "This package has no description")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-692 OV E -3280 PG) +(-693 OV E -3313 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL -(-693) +(-694) ((|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}"))) -((-3367 . T) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3410 . T) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-694 R) +(-695 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, \\spad{d,} \\spad{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, \\spad{d)}} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[d\\space{5}]} \\indented{3}{[\\space{2}d\\space{3}]} \\indented{3}{[\\space{4}. \\spad{]}} \\indented{3}{[\\space{5}d]} \\indented{3}{[\\space{3}M\\space{2}]} where \\spad{M = \\spad{m} mod \\spad{d}.}")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m,} finding an appropriate modulus."))) NIL NIL -(-695) +(-696) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4599 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4601 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-696 S D1 D2 I) +(-697 S D1 D2 I) ((|constructor| (NIL "Tools and transforms for making compiled functions from top-level expressions")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, \\spad{D2)} \\spad{->} I} defined by \\spad{f(x, \\spad{y)} \\spad{==} expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-697 S) +(-698 S) ((|constructor| (NIL "MakeCachableSet(S) returns a cachable set which is equal to \\spad{S} as a set.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s} viewed as an element of \\spad{%.}"))) NIL NIL -(-698 S) +(-699 S) ((|constructor| (NIL "Tools for making compiled functions from top-level expressions MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the Axiom compiler and interpreter, thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, \\spad{x,} \\spad{y)}} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) \\spad{->} \\axiomType{DoubleFloat}} defined by \\spad{f(x, \\spad{y)} \\spad{==} expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, \\spad{x)}} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} \\spad{->} \\axiomType{DoubleFloat}} defined by \\spad{f(x) \\spad{==} expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-699 S) +(-700 S) ((|constructor| (NIL "Tools for making interpreter functions from top-level expressions Transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) \\spad{==} e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, \\spad{x,} \\spad{y)}} creates a function \\spad{foo(x, \\spad{y)} = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, \\spad{x)}} creates a function \\spad{foo(x) \\spad{==} e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() \\spad{==} e}."))) NIL NIL -(-700 S T$) +(-701 S T$) ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S, part2:R), where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-701 S -1544 I) +(-702 S -1557 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, \\spad{x)}} returns a function \\spad{f: \\spad{D} \\spad{->} I} defined by \\spad{f(x) \\spad{==} 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 -(-702 E OV R P) +(-703 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\", using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F,} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) NIL NIL -(-703 R) +(-704 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, \\spad{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 \\spad{\\^=} 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), \\spad{i} = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\spad{\\^=} 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-704 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-705 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, \\spad{p)}} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p.}"))) NIL NIL -(-705) +(-706) ((|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(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(o) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-706 R |Mod| -2203 -3491 |exactQuo|) +(-707 R |Mod| -4007 -4475 |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| $) "\\spad{modulus(x)} is not documented"))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-707 R |Rep|) +(-708 R |Rep|) ((|constructor| (NIL "This package has not been documented")) (|frobenius| (($ $) "\\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"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4596 |has| |#1| (-367)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-352))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-708 IS E |ff|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4598 |has| |#1| (-368)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-353))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-709 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| $) "\\spad{exponent(x)} is not documented"))) NIL NIL -(-709 R M) +(-710 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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, \\spad{u} \\spad{+->} \\spad{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 + \\spad{b)} = g(a) + g(b)} for any \\spad{a}, \\spad{b} in \\spad{M.} This implies that \\spad{g(n a) = \\spad{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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151)))) -(-710 R |Mod| -2203 -3491 |exactQuo|) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151)))) +(-711 R |Mod| -4007 -4475 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4597 . T)) +((-4599 . T)) NIL -(-711 S R) +(-712 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline Axioms\\br \\tab{5}\\spad{1*x = x}\\br \\tab{5}\\spad{(a*b)*x = a*(b*x)}\\br \\tab{5}\\spad{(a+b)*x = (a*x)+(b*x)}\\br \\tab{5}\\spad{a*(x+y) = (a*x)+(a*y)}"))) NIL NIL -(-712 R) +(-713 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline Axioms\\br \\tab{5}\\spad{1*x = x}\\br \\tab{5}\\spad{(a*b)*x = a*(b*x)}\\br \\tab{5}\\spad{(a+b)*x = (a*x)+(b*x)}\\br \\tab{5}\\spad{a*(x+y) = (a*x)+(a*y)}"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-713 -3280) +(-714 -3313) ((|constructor| (NIL "MoebiusTransform(F) is the domain of fractional linear (Moebius) transformations over \\spad{F.} This a domain of 2-by-2 matrices acting on P1(F).")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + \\spad{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 + \\spad{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 \\spad{->} 1 / \\spad{x}.}")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * \\spad{m}} (see shift from MoebiusTransform).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x \\spad{->} \\spad{k} * \\spad{x}.}")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * \\spad{m}} (see shift from MoebiusTransform).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x \\spad{->} \\spad{x} + \\spad{k}.}")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) -((-4597 . T)) +((-4599 . T)) NIL -(-714 S) +(-715 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads, that is sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}-th power of \\spad{a}, defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}-th left power of \\spad{a}, that is, \\spad{leftPower(a,n) \\spad{:=} a * leftPower(a,n-1)} and \\spad{leftPower(a,1) \\spad{:=} a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}-th right power of \\spad{a}, that is, \\spad{rightPower(a,n) \\spad{:=} rightPower(a,n-1) * a} and \\spad{rightPower(a,1) \\spad{:=} a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-715) +(-716) ((|constructor| (NIL "Monad is the class of all multiplicative monads, that is sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}-th power of \\spad{a}, defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}-th left power of \\spad{a}, that is, \\spad{leftPower(a,n) \\spad{:=} a * leftPower(a,n-1)} and \\spad{leftPower(a,1) \\spad{:=} a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}-th right power of \\spad{a}, that is, \\spad{rightPower(a,n) \\spad{:=} rightPower(a,n-1) * a} and \\spad{rightPower(a,1) \\spad{:=} a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-716 S) +(-717 S) ((|constructor| (NIL "MonadWithUnit is the class of multiplicative monads with unit, that is, sets with a binary operation and a unit element. \\blankline Axioms\\br \\tab{5}leftIdentity(\"*\":(\\%,\\%)->\\%,1) for example, 1*x=x\\br \\tab{5}rightIdentity(\"*\":(\\%,\\%)->\\%,1) for example, x*1=x \\blankline Common Additional Axioms\\br \\tab{5}unitsKnown - if \"recip\" says \"failed\", it PROVES input wasn't a unit")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element, which is a right inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element, which is a left inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element, which is both a left and a right inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}-th power of \\spad{a}, defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}-th left power of \\spad{a}, that is, \\spad{leftPower(a,n) \\spad{:=} a * leftPower(a,n-1)} and \\spad{leftPower(a,0) \\spad{:=} 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}-th right power of \\spad{a}, that is, \\spad{rightPower(a,n) \\spad{:=} rightPower(a,n-1) * a} and \\spad{rightPower(a,0) \\spad{:=} 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "\\spad{1} returns the unit element, denoted by 1."))) NIL NIL -(-717) +(-718) ((|constructor| (NIL "MonadWithUnit is the class of multiplicative monads with unit, that is, sets with a binary operation and a unit element. \\blankline Axioms\\br \\tab{5}leftIdentity(\"*\":(\\%,\\%)->\\%,1) for example, 1*x=x\\br \\tab{5}rightIdentity(\"*\":(\\%,\\%)->\\%,1) for example, x*1=x \\blankline Common Additional Axioms\\br \\tab{5}unitsKnown - if \"recip\" says \"failed\", it PROVES input wasn't a unit")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element, which is a right inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element, which is a left inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element, which is both a left and a right inverse of \\spad{a}, or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}-th power of \\spad{a}, defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}-th left power of \\spad{a}, that is, \\spad{leftPower(a,n) \\spad{:=} a * leftPower(a,n-1)} and \\spad{leftPower(a,0) \\spad{:=} 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}-th right power of \\spad{a}, that is, \\spad{rightPower(a,n) \\spad{:=} rightPower(a,n-1) * a} and \\spad{rightPower(a,0) \\spad{:=} 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "\\spad{1} returns the unit element, denoted by 1."))) NIL NIL -(-718 S R UP) +(-719 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, \\spad{')}} returns \\spad{M} such that \\spad{b' = \\spad{M} \\spad{b}.}")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element, reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element, reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL -((|HasCategory| |#2| (QUOTE (-352))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-373)))) -(-719 R UP) +((|HasCategory| |#2| (QUOTE (-353))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-374)))) +(-720 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, \\spad{')}} returns \\spad{M} such that \\spad{b' = \\spad{M} \\spad{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."))) -((-4593 |has| |#1| (-367)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 |has| |#1| (-368)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-720 S) +(-721 S) ((|constructor| (NIL "The class of multiplicative monoids, \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline Axioms\\br \\tab{5}\\spad{leftIdentity(\"*\":(\\%,\\%)->\\%,1)}\\tab{5}\\spad{1*x=x}\\br \\tab{5}\\spad{rightIdentity(\"*\":(\\%,\\%)->\\%,1)}\\tab{4}\\spad{x*1=x} \\blankline Conditional attributes\\br \\tab{5}unitsKnown - \\spadfun{recip} only returns \"failed\" on non-units")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times, \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times, \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-721) +(-722) ((|constructor| (NIL "The class of multiplicative monoids, \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline Axioms\\br \\tab{5}\\spad{leftIdentity(\"*\":(\\%,\\%)->\\%,1)}\\tab{5}\\spad{1*x=x}\\br \\tab{5}\\spad{rightIdentity(\"*\":(\\%,\\%)->\\%,1)}\\tab{4}\\spad{x*1=x} \\blankline Conditional attributes\\br \\tab{5}unitsKnown - \\spadfun{recip} only returns \"failed\" on non-units")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times, \\spadignore{i.e.} exponentiation.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times, \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-722 -3280 UP) +(-723 -3313 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, \\spad{D)}} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s}, all the squarefree factors of \\spad{denom(n)} are normal w.r.t. \\spad{D,} \\spad{denom(s)} is special w.r.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, \\spad{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, \\spad{D)}} returns \\spad{[n_1 \\spad{n_2\\^2} \\spad{...} n_m\\^m, \\spad{s_1} \\spad{s_2\\^2} \\spad{...} s_q\\^q]} such that \\spad{p = \\spad{n_1} \\spad{n_2\\^2} \\spad{...} n_m\\^m \\spad{s_1} \\spad{s_2\\^2} \\spad{...} s_q\\^q}, each \\spad{n_i} is normal w.r.t. \\spad{D} and each \\spad{s_i} is special w.r.t \\spad{D.} \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, \\spad{D)}} returns \\spad{[n,s]} such that \\spad{p = \\spad{n} \\spad{s},} all the squarefree factors of \\spad{n} are normal w.r.t. \\spad{D,} and \\spad{s} is special w.r.t. \\spad{D.} \\spad{D} is the derivation to use."))) NIL NIL -(-723 |VarSet| -1370 E2 R S PR PS) +(-724 |VarSet| -3670 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 -(-724 |Vars1| |Vars2| -1370 E2 R PR1 PR2) +(-725 |Vars1| |Vars2| -3670 E2 R PR1 PR2) ((|constructor| (NIL "This package has no description")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-725 E OV R PPR) +(-726 E OV R PPR) ((|constructor| (NIL "This package exports a factor operation for multivariate polynomials with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-726 |vl| R) +(-727 |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."))) -(((-4602 "*") |has| |#2| (-173)) (-4593 |has| |#2| (-561)) (-4598 |has| |#2| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-857 |#1|) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-367))) (-1831 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#2| (QUOTE -4598)) (|HasCategory| |#2| (QUOTE (-456))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-149))))) -(-727 E OV R PRF) +(((-4604 "*") |has| |#2| (-174)) (-4595 |has| |#2| (-562)) (-4600 |has| |#2| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-368))) (-1841 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#2| (QUOTE -4600)) (|HasCategory| |#2| (QUOTE (-457))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-149))))) +(-728 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 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 prf.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-728 E OV R P) +(-729 E OV R P) ((|constructor| (NIL "MRationalFactorize contains the factor function for multivariate polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R.}")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R.}"))) NIL NIL -(-729 R S M) +(-730 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b.}"))) NIL NIL -(-730 R M) +(-731 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(R,M), implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over f(a)g(b) such that ab = \\spad{c.} Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M.} Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol}, one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G,} where modules over \\spadtype{MonoidRing}(R,G) are studied.")) (|reductum| (($ $) "\\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 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.}"))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) (-4597 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-847)))) -(-731 S) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) (-4599 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-848)))) +(-732 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4590 . T) (-4601 . T) (-3348 . T)) +((-4592 . T) (-4603 . T) (-3389 . T)) NIL -(-732 S) +(-733 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{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{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.}") (($) "\\spad{multiset()}$D creates an empty multiset of domain \\spad{D.}"))) -((-4600 . T) (-4590 . T) (-4601 . T)) -((|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-733) +((-4602 . T) (-4592 . T) (-4603 . T)) +((|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-734) ((|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, for example, the \"what\" commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{cmd} and passes it to the runtime environment for execution as a system command. Although various things may be printed, no usable value is returned."))) NIL NIL -(-734 S) +(-735 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2.} Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1.}"))) NIL NIL -(-735 |Coef| |Var|) +(-736 |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 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= \\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 * \\spad{x1^n1} * \\spad{...} * 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{<= \\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 * \\spad{...} * xk^nk} in \\spad{f.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f.}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4595 . T) (-4594 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-736 OV E R P) +(-737 OV E R P) ((|constructor| (NIL "This is the top level package for doing multivariate factorization over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-737 E OV R P) +(-738 E OV R P) ((|constructor| (NIL "This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + \\spad{Bg} = \\spad{h}} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p.}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") 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T) (-4594 . T) (-4597 . 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NIL NIL -(-741 R) +(-742 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs).\\br \\blankline Axioms\\br \\tab{5}r*(a*b) = (r*a)*b = a*(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}."))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-742) +(-743) ((|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'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's Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) NIL NIL -(-743) +(-744) ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.)")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,ldfjac,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,b,eps,eta,ifail,f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation, extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) NIL NIL -(-744) +(-745) ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values, and applies it to calculate convolutions and correlations.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,n,x,ifail)} takes \\spad{m} Hermitian sequences, each containing \\spad{n} data values, and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,n,x,ifail)} forms the complex conjugates, each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,y,ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,x,ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,n,init,x,y,trigm,trign,ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,n,init,x,y,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences, each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences, each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences, each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,n,x,y,ifail)} calculates the circular convolution of two real vectors of period \\spad{n.} No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,x,y,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,x,ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,x,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) NIL NIL -(-745) +(-746) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,a,b,maxcls,eps,lenwrk,mincls,wrkstr,ifail,functn)} returns an approximation to the integral of a function over a hyper-rectangular region, using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,y,n,ifail)} integrates a function which is specified numerically at four or more points, over the whole of its specified range, using third-order finite-difference formulae with error estimates, according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,a,b,maxpts,eps,lenwrk,minpts,ifail,functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions), with constant and finite limits, to a specified relative accuracy, using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,b,itype,n,gtype,ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre, Gauss-Rational, Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,omega,key,epsabs,limlst,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,b,c,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the Hilbert transform of a function g(x) over [a,b]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,b,alfa,beta,key,epsabs,epsrel,lw,liw,ifail,g)} is an adaptive integrator which calculates an approximation to the integral of a function g(x)w(x) over a finite interval [a,b]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,b,omega,key,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,b]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,inf,epsabs,epsrel,lw,liw,ifail,f)} calculates an approximation to the integral of a function f(x) over an infinite or semi-infinite interval [a,b]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,b,npts,points,epsabs,epsrel,lw,liw,ifail,f)} is a general purpose integrator which calculates an approximation to the integral of a function f(x) over a finite interval [a,b]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is an adaptive integrator, especially suited to oscillating, non-singular integrands, which calculates an approximation to the integral of a function f(x) over a finite interval [a,b]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is a general-purpose integrator which calculates an approximation to the integral of a function f(x) over a finite interval [a,b]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) NIL NIL -(-746) +(-747) ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem, those in which all boundary conditions are specified at one point (initial-value problems), and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems, two-point boundary-value problems and Sturm-Liouville eigenvalue problems.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "d02raf(n,mnp,numbeg,nummix,tol,init,iy,ijac,lwork, \\indented{7}{liwork,np,x,y,deleps,ifail,fcn,g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations, using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "d02kef(xpoint,m,k,tol,maxfun,match,elam,delam, \\indented{7}{hmax,maxit,ifail,coeffn,bdyval,monit,report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range, using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "d02kef(xpoint,m,k,tol,maxfun,match,elam,delam, \\indented{7}{hmax,maxit,ifail,coeffn,bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range, using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains \\spad{Asp12} and \\spad{Asp33} are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,b,n,tol,mnp,lw,liw,c,d,gam,x,np,ifail,fcnf,fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,v,n,a,b,tol,mnp,lw,liw,x,np,ifail,fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations, using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,m,n,relabs,iw,x,y,tol,ifail,g,fcn,pederv,output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions, using a variable-order, variable-step method implementing the Backward Differentiation Formulae (BDF), until a user-specified function, if supplied, of the solution is zero, and returns the solution at points specified by the user, if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,m,n,tol,relabs,x,y,ifail,g,fcn,output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions, using a variable-order, variable-step Adams method until a user-specified function, if supplied, of the solution is zero, and returns the solution at points specified by the user, if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,n,irelab,hmax,x,y,tol,ifail,g,fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions, using a Runge-Kutta-Merson method, until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,m,n,irelab,x,y,tol,ifail,fcn,output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions, using a Runge-Kutta-Merson method, and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) NIL NIL -(-747) +(-748) ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "d03faf(xs,xf,l,lbdcnd,bdxs,bdxf,ys,yf,m,mbdcnd,bdys,bdyf,zs, \\indented{7}{zf,n,nbdcnd,bdzs,bdzf,lambda,ldimf,mdimf,lwrk,f,ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,xmax,ymin,ymax,ngx,ngy,lda,scheme,ifail,pdef,bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,ngy,lda,maxit,acc,iout,a,rhs,ub,ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) NIL NIL -(-748) +(-749) ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(s), the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions, there are supporting routines to evaluate, differentiate or integrate them.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,x,y,f,rnw,fnodes,px,py,ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,x,y,f,nw,nq,rnw,rnq,ifail)} generates a two-dimensional surface interpolating a set of scattered data points, using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,x,y,f,triang,grads,px,py,ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,x,y,f,ifail)} generates a two-dimensional surface interpolating a set of scattered data points, using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,my,x,y,f,ifail)} computes a bicubic spline interpolating surface through a set of data values, given on a rectangular grid in the x-y plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,x,f,d,a,b,ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,b]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,x,f,ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,x,y,lck,lwrk,ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) NIL NIL -(-749) +(-750) ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors, as of experimental measurement, which need to be smoothed out. To seek an approximation to the data, it is first necessary to specify for the approximating function a mathematical form (a polynomial, for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function, since these cover the most common needs. However, fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating, differentiating and integrating polynomial and spline curves and surfaces, once the numerical values of their coefficients have been determined.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,py,lamda,mu,m,x,y,npoint,nadres,ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,la,nplus2,toler,a,b,ifail)} calculates an \\spad{l} solution to an over-determined system of linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,my,px,py,x,y,lamda,mu,c,lwrk,liwrk,ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,px,py,x,y,lamda,mu,c,ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,m,x,y,f,w,s,nxest,nyest,lwrk,liwrk,nx, \\spad{++} lamda,ny,mu,wrk,ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically, but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,mx,x,my,y,f,s,nxest,nyest,lwrk,liwrk,nx, \\spad{++} lamda,ny,mu,wrk,iwrk,ifail)} computes a bicubic spline approximation to a set of data values, given on a rectangular grid in the x-y plane. The knots of the spline are located automatically, but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,px,py,x,y,f,w,mu,point,npoint,nc,nws,eps,lamda,ifail)} forms a minimal, weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,m,x,y,w,s,nest,lwrk,n,lamda,ifail,wrk,iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically, but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,lamda,c,ifail)} computes the definite integral from its B-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,lamda,c,x,left,ifail)} evaluates a cubic spline and its first three derivatives from its B-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,lamda,c,x,ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,ncap7,x,y,w,lamda,ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,xmin,xmax,a,ia1,la,x,ifail)} evaluates a polynomial from its Chebyshev-series representation, allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,xmin,xmax,a,ia1,la,qatm1,iaint1,laint,ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,xmin,xmax,a,ia1,la,iadif1,ladif,ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,kplus1,nrows,xmin,xmax,x,y,w,mf,xf,yf,lyf,ip,lwrk,liwrk,ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,a,xcap,ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,kplus1,nrows,x,y,w,ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) NIL NIL -(-750) +(-751) ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables, possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only, since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1.}")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,m,n,fsumsq,s,lv,v,ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function f(x) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "e04ucf(n,nclin,ncnln,nrowa,nrowj,nrowr,a,bl,bu,liwork,lwork,sta, \\indented{7}{cra,der,fea,fun,hes,infb,infs,linf,lint,list,maji,majp,mini,} \\indented{7}{minp,mon,nonf,opt,ste,stao,stac,stoo,stoc,ve,istate,cjac,} \\indented{7}{clamda,r,x,ifail,confun,objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables, linear constraints. (E04UCF may be used for unconstrained, bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense, and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "e04naf(itmax,msglvl,n,nclin,nctotl,nrowa,nrowh,ncolh,bigbnd,a,bl, bu,cvec,featol,hess,cold,lpp,orthog,liwork,lwork,x,istate,ifail,qphess) is a comprehensive programming (QP) or linear programming (LP) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "e04mbf(itmax,msglvl,n,nclin,nctotl,nrowa,a,bl,bu, \\indented{7}{cvec,linobj,liwork,lwork,x,ifail)} is an easy-to-use routine for solving linear programming problems, or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,ibound,liw,lw,bl,bu,x,ifail,funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F(x} \\spad{,x} ,...,x \\spad{),} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}n} lower bounds of the independent variables \\spad{x} \\spad{,x} ,...,x ,{} using \\indented{43}{1\\space{2}2\\space{6}n} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,n,liw,lw,x,ifail,lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,n,liw,lw,x,ifail,lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,es,fu,it,lin,list,ma,op,pr,sta,sto,ve,x,ifail,objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned, limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) NIL NIL -(-751) +(-752) ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,m,n,ncolq,lda,theta,a,ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q,} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,wheret,m,n,a,lda,theta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,n,lda,a,ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A, where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,m,n,ncolq,lda,zeta,a,ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q,} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,wheret,m,n,a,lda,zeta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,n,lda,a,ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A, where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,avals,lal,nrow,ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,nz,licn,lirn,abort,avals,irn,icn,droptl,densw,ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "f01bsf(n,nz,licn,ivect,jvect,icn,ikeep,grow, \\indented{7}{eta,abort,idisp,avals,ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,nz,licn,lirn,pivot,lblock,grow,abort,a,irn,icn,ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix, or, optionally, first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) NIL NIL -(-752) +(-753) ((|constructor| (NIL "This package uses the NAG Library to compute\\br \\tab{5}eigenvalues and eigenvectors of a matrix\\br \\tab{5} eigenvalues and eigenvectors of generalized matrix eigenvalue problems\\br \\tab{5}singular values and singular vectors of a matrix.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldph,a,b,ifail)} returns all, or part, of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldpt,a,b,ifail)} returns all, or part, of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "f02fjf(n,k,tol,novecs,nrx,lwork,lrwork, \\indented{7}{liwork,m,noits,x,ifail,dot,image,monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "f02fjf(n,k,tol,novecs,nrx,lwork,lrwork, \\indented{7}{liwork,m,noits,x,ifail,dot,image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,ia,ib,eps1,matv,iv,a,b,ifail)} calculates all the eigenvalues and, if required, all the eigenvectors of the generalized eigenproblem Ax=(lambda)Bx where A and \\spad{B} are real, square matrices, using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,n,alb,ub,m,iv,a,ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form, bisection and inverse iteration, where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,iar,ai,iai,n,ivr,ivi,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,iai,n,ivr,ivi,ar,ai,ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,n,ivr,ivi,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,n,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,ib,n,iv,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)Bx, where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,ib,n,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)Bx, where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,ia,n,iv,ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,n,a,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) NIL NIL -(-753) +(-754) ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\spad{\\br} \\tab{5}\\axiom{AX=B}, where \\axiom{B}\\br may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real, complex, symmetric, Hermitian positive- definite, or sparse. It may also be rectangular, in which case a least-squares solution is obtained.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "f04qaf(m,n,damp,atol,btol,conlim,itnlim,msglvl, \\indented{7}{lrwork,liwork,b,ifail,aprod)} solves sparse unsymmetric equations, sparse linear least- squares problems and sparse damped linear least-squares problems, using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,al,lal,d,nrow,ir,b,nrb,iselct,nrx,ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides, AX=B, where A is a symmetric positive-definite variable-bandwidth matrix, which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,b,precon,shift,itnlim,msglvl,lrwork, \\spad{++} liwork,rtol,ifail,aprod,msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "f04maf(n,nz,avals,licn,irn,lirn,icn,wkeep,ikeep, \\indented{7}{inform,b,acc,noits,ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations, Ax=b, using a pre-conditioned conjugate gradient method, where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,n,nra,tol,lwork,a,b,ifail)} finds the solution of a linear least-squares problem, Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank, then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,n,d,e,b,ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,a,licn,icn,ikeep,mtype,idisp,rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side, Ax=b or \\indented{1}{T} A x=b, where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,ia,b,n,iaa,ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side, using an LU factorization with partial pivoting, and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,b,n,a,ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side, Ax=b, using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,b,n,a,ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side, using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,b,ib,n,m,ic,a,ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides, using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) NIL NIL -(-754) +(-755) ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations, and to solve systems of linear equations following the matrix factorizations.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,n,nrhs,a,lda,ldb,b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides, AX=B, where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,n,lda,a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,n,nrhs,a,lda,ipiv,ldb,b)} (DGETRS) solves a real system of linear equations with \\indented{36}{T} multiple right-hand sides, AX=B or A X=B, where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,n,lda,a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) NIL NIL -(-755) +(-756) ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,y,z,r,ifail)} returns a value of the symmetrised elliptic integral of the third kind, via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the second kind, via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the first kind, via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,y,ifail)} returns a value of an elementary integral, which occurs as a degenerate case of an elliptic integral of the first kind, via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,ifail)} returns a value for the Fresnel Integral C(x), via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,ifail)} returns a value for the Fresnel Integral S(x), via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,ifail)} returns a value for the Kelvin function kei(x) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,ifail)} returns a value for the Kelvin function ker(x), via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,ifail)} returns a value for the Kelvin function bei(x) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,ifail)} returns a value for the Kelvin function ber(x) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{I\\space{6}(z) for complex \\spad{z,} non-negative (nu) and} \\indented{2}{(nu)+n} n=0,1,...,N-1, with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{K\\space{6}(z) for complex \\spad{z,} non-negative (nu) and} \\indented{2}{(nu)+n} n=0,1,...,N-1, with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,ifail)} returns a value for the modified Bessel Function \\indented{1}{I (x), via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{I (x), via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{K (x), via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{K (x), via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,fnu,z,n,scale,ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{H\\space{6}(z) or H\\space{6}(z) for complex \\spad{z,} non-negative (nu) and} \\indented{2}{(nu)+n\\space{8}(nu)+n} n=0,1,...,N-1, with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,z,scale,ifail)} returns the value of the Airy function Bi(z) or its derivative Bi'(z) for complex \\spad{z,} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,z,scale,ifail)} returns the value of the Airy function Ai(z) or its derivative Ai'(z) for complex \\spad{z,} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{J\\space{6}(z) for complex \\spad{z,} non-negative (nu) and n=0,1,...,N-1,} \\indented{2}{(nu)+n} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{Y\\space{6}(z) for complex \\spad{z,} non-negative (nu) and n=0,1,...,N-1,} \\indented{2}{(nu)+n} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,ifail)} returns a value for the derivative of the Airy function Bi(x), via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,ifail)} returns a value of the derivative of the Airy function Ai(x), via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,ifail)} returns a value of the Airy function, Bi(x), via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,ifail)} returns a value for the Airy function, Ai(x), via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,ifail)} returns the value of the Bessel Function \\indented{1}{J (x), via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,ifail)} returns the value of the Bessel Function \\indented{1}{J (x), via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,ifail)} returns the value of the Bessel Function \\indented{1}{Y (x), via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,ifail)} returns the value of the Bessel Function \\indented{1}{Y (x), via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,ifail)} returns the value of the error function erf(x), via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,ifail)} returns the value of the complementary error function, erfc(x), via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,x,tol,ifail)} computes values for the incomplete gamma functions P(a,x) and Q(a,x). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,ifail)} returns a value for the log, ln(Gamma(x)), via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,ifail)} returns the value of the Gamma function (Gamma)(x), via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,ifail)} returns the value of the exponential integral \\indented{1}{E (x), via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,ifail)} S01EAF evaluates the exponential function exp(z) ,{} for complex \\spad{z.} See \\downlink{Manual Page}{manpageXXs01eaf}."))) NIL NIL -(-756) +(-757) ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) NIL NIL -(-757 S) +(-758 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure, not necessarily commutative or associative, and not necessarily with unit.\\br Axioms\\br \\tab{5}x*(y+z) = x*y + x*z\\br \\tab{5}(x+y)*z = \\spad{x*z} + y*z\\br \\blankline Common Additional Axioms\\br \\tab{5}noZeroDivisors\\tab{5} ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-758) +(-759) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure, not necessarily commutative or associative, and not necessarily with unit.\\br Axioms\\br \\tab{5}x*(y+z) = x*y + x*z\\br \\tab{5}(x+y)*z = \\spad{x*z} + y*z\\br \\blankline Common Additional Axioms\\br \\tab{5}noZeroDivisors\\tab{5} ab = 0 \\spad{=>} \\spad{a=0} or \\spad{b=0}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-759 S) +(-760 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit, the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-760) +(-761) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit, the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-761 |Par|) +(-762 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue, its algebraic multiplicity, and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision eps. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x.}") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-762 -3280) +(-763 -3313) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions for converting floating point numbers to continued fractions.")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-763 P -3280) +(-764 P -3313) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}s over a \\spadtype{Field}. Since the multiplication is in general non-commutative, these operations all have left- and right-hand versions. This package provides the operations based on left-division.\\br \\tab{5}[q,r] = leftDivide(a,b) means a=b*q+r")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q}, if it exists, \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL -(-764 -3280) +(-765 -3313) ((|constructor| (NIL "This package exports Newton interpolation for the special case where the result is known to be in the original integral domain The packages defined in this file provide fast fraction free rational interpolation algorithms. (see FAMR2, FFFG, FFFGF, NEWTON)")) (|newton| (((|SparseUnivariatePolynomial| |#1|) (|List| |#1|)) "\\spad{newton}(l) returns the interpolating polynomial for the values \\spad{l,} where the x-coordinates are assumed to be [1,2,3,...,n] and the coefficients of the interpolating polynomial are known to be in the domain \\spad{F.} I.e., it is a very streamlined version for a special case of interpolation."))) NIL NIL -(-765 UP -3280) +(-766 UP -3313) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F.}")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F,} where \\spad{F} is a framed algebra with Z-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F,} where \\spad{F} is a framed algebra with Z-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F.}"))) NIL NIL -(-766) +(-767) ((|constructor| (NIL "\\axiomType{NumericalIntegrationProblem} is a \\axiom{domain} for the representation of Numerical Integration problems for use by ANNA. \\blankline The representation is a Union of two record types - one for integration of a function of one variable: \\blankline \\axiomType{Record}(var:\\axiomType{Symbol},\\br fn:\\axiomType{Expression DoubleFloat},\\br range:\\axiomType{Segment OrderedCompletion DoubleFloat},\\br abserr:\\axiomType{DoubleFloat},\\br relerr:\\axiomType{DoubleFloat},) \\blankline and one for multivariate integration: \\blankline \\axiomType{Record}(fn:\\axiomType{Expression DoubleFloat},\\br range:\\axiomType{List Segment OrderedCompletion DoubleFloat},\\br abserr:\\axiomType{DoubleFloat},\\br relerr:\\axiomType{DoubleFloat},). \\blankline")) (|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-767 R) +(-768 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp.}") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv.}")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp.}") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv.}"))) NIL NIL -(-768) +(-769) ((|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| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b.}")) (|rem| (($ $ $) "\\spad{a rem \\spad{b}} returns the remainder of \\spad{a} and \\spad{b.}")) (|quo| (($ $ $) "\\spad{a quo \\spad{b}} returns the quotient of \\spad{a} and \\spad{b,} forgetting the remainder."))) -(((-4602 "*") . T)) +(((-4604 "*") . T)) NIL -(-769 R -3280) +(-770 R -3313) ((|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), \\spad{y,} \\spad{x)}} returns \\spad{F(x,y)} such that \\spad{F(x,y) = \\spad{c}} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) \\spad{dx} + N(x,y) dy = 0}, or \"failed\" if no first-integral can be found."))) NIL NIL -(-770 S) +(-771 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-771) +(-772) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-772 R |PolR| E |PolE|) +(-773 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm \\spad{q}} returns the norm of \\spad{q,} \\spadignore{i.e.} the product of all the conjugates of \\spad{q.}"))) NIL NIL -(-773 R E V P TS) +(-774 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(p,ts)} is an internal subroutine, exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(s1,s2,p,ts)} is an internal subroutine, exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(p,ts)} normalizes \\axiom{p} w.r.t \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(p,ts)} returns a normalized polynomial \\axiom{n} w.r.t. \\spad{ts} such that \\axiom{n} and \\axiom{p} are associates w.r.t \\spad{ts} and assuming that \\axiom{p} is invertible w.r.t \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(p,ts)} returns the inverse of \\axiom{p} w.r.t \\spad{ts} assuming that \\axiom{p} is invertible w.r.t \\spad{ts}."))) NIL NIL -(-774 -3280 |ExtF| |SUEx| |ExtP| |n|) +(-775 -3313 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package has no description")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL -(-775 -3280) +(-776 -3313) ((|constructor| (NIL "This is an implmenentation of the Nottingham Group"))) -((-4597 . T)) +((-4599 . T)) NIL -(-776 BP E OV R P) +(-777 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 -(-777 K |PolyRing| E -3020) +(-778 K |PolyRing| E -3465) ((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-778 |Par|) +(-779 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue, its algebraic multiplicity, and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision eps. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x.} Fraction \\spad{P} \\spad{RN.}") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) NIL NIL -(-779 K) +(-780 K) ((|constructor| (NIL "This domain is part of the PAFF package"))) -(((-4602 "*") . T) (-4593 . T) (-4592 . T) (-4598 . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| (-571) (QUOTE (-1109))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-571)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-571)) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-571)) (|:| |c| |#1|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-571))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-2 (|:| |k| (-571)) (|:| |c| |#1|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| |k| (-571)) (|:| |c| |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE |k|) (QUOTE (-571))) (LIST (QUOTE |:|) (QUOTE |c|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-571)) (|:| |c| |#1|)) (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571)))))) -(-780 R |VarSet|) +(((-4604 "*") . T) (-4595 . T) (-4594 . T) (-4600 . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-1110))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-572)) (|:| |c| |#1|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-2 (|:| |k| (-572)) (|:| |c| |#1|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| |k| (-572)) (|:| |c| |#1|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE |k|) (QUOTE (-572))) (LIST (QUOTE |:|) (QUOTE |c|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| |k| (-572)) (|:| |c| |#1|)) (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572)))))) +(-781 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . 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(|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 -(-782 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{halfExtendedResultant2(a,b)} returns \\axiom{[r,ca]} such that \\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca, cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,b)} returns \\axiom{[r,ca]} such that \\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca, cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca,cb]} such that \\axiom{r} is the resultant of \\axiom{a} and \\axiom{b} and \\axiom{r = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,b)} returns \\axiom{[g,cb]} such that \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,b)} returns \\axiom{[g,ca]} such that \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]} such that \\axiom{g} is a \\spad{gcd} of \\axiom{a} and \\axiom{b} in \\axiom{R^(-1) \\spad{P}} and \\axiom{g = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,b)} returns \\axiom{resultant(a,b)} if \\axiom{a} and \\axiom{b} has no non-trivial \\spad{gcd} in \\axiom{R^(-1) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,b)} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{b} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,b)} returns \\axiom{q} if \\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]} such that \\axiom{c^n * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]} where \\axiom{n + \\spad{g} = max(0, degree(b) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,b)} returns \\axiom{r} if \\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]}. This lazy pseudo-remainder is computed by means of the fmecg from NewSparseUnivariatePolynomial operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]} such that \\axiom{r} is reduced w.r.t. \\axiom{b} and \\axiom{b} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{c} is \\axiom{leadingCoefficient(b)} and \\axiom{n} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,b)} returns \\axiom{r} such that \\axiom{r} is reduced w.r.t. \\axiom{b} and \\axiom{b} divides \\axiom{a \\spad{-r}} where \\axiom{b} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(p1,e,r,p2)} returns \\axiom{p1 - \\spad{r} * x**e * \\spad{p2}} where \\axiom{x} is \\axiom{monomial(1,1)}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4596 |has| |#1| (-367)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) (-783 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{halfExtendedResultant2(a,b)} returns \\axiom{[r,ca]} such that \\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca, cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,b)} returns \\axiom{[r,ca]} such that \\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca, cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,b)} returns \\axiom{[r,ca,cb]} such that \\axiom{r} is the resultant of \\axiom{a} and \\axiom{b} and \\axiom{r = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,b)} returns \\axiom{[g,cb]} such that \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,b)} returns \\axiom{[g,ca]} such that \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca, cb]} such that \\axiom{g} is a \\spad{gcd} of \\axiom{a} and \\axiom{b} in \\axiom{R^(-1) \\spad{P}} and \\axiom{g = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,b)} returns \\axiom{resultant(a,b)} if \\axiom{a} and \\axiom{b} has no non-trivial \\spad{gcd} in \\axiom{R^(-1) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,b)} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{b} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,b)} returns \\axiom{q} if \\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]} such that \\axiom{c^n * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]} where \\axiom{n + \\spad{g} = max(0, degree(b) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,b)} returns \\axiom{r} if \\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]}. This lazy pseudo-remainder is computed by means of the fmecg from NewSparseUnivariatePolynomial operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,b)} returns \\axiom{[r,c,n]} such that \\axiom{r} is reduced w.r.t. \\axiom{b} and \\axiom{b} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{c} is \\axiom{leadingCoefficient(b)} and \\axiom{n} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,b)} returns \\axiom{r} such that \\axiom{r} is reduced w.r.t. \\axiom{b} and \\axiom{b} divides \\axiom{a \\spad{-r}} where \\axiom{b} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(p1,e,r,p2)} returns \\axiom{p1 - \\spad{r} * x**e * \\spad{p2}} where \\axiom{x} is \\axiom{monomial(1,1)}"))) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4598 |has| |#1| (-368)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-784 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 -412) (QUOTE (-571)))))) -(-784 R E V P) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572)))))) +(-785 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 select(ts,v) is normalized w.r.t. every polynomial in collectUnder(ts,v). A polynomial \\spad{p} is said normalized w.r.t. a non-constant polynomial \\spad{q} if \\spad{p} is constant or degree(p,mdeg(q)) = 0 and init(p) is normalized w.r.t. \\spad{q.} One of the important features of normalized triangular sets is that they are regular sets."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-785 S) +(-786 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, \\spad{n)}} returns a real approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{x} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x,} or \"failed\" if \\axiom{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{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{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{x} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x,} or \"failed\" if \\axiom{x} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{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{x} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{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{x} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{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{x} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x,} or \"failed\" if \\axiom{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{x} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{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{x} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, \\spad{n)}} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places, or \"failed\" if \\axiom{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{x} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{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, \\spad{n)}} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x.}"))) NIL -((|HasCategory| |#1| (QUOTE (-561))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-173)))) -(-786) +((|HasCategory| |#1| (QUOTE (-562))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-174)))) +(-787) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers, to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s.}")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n.}")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s.}")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n.}"))) NIL NIL -(-787) +(-788) ((|constructor| (NIL "\\axiomType{NumericalIntegrationCategory} is the \\axiom{category} for describing the set of Numerical Integration \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{numericalIntegration}.")) (|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far."))) NIL NIL -(-788) +(-789) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables:\\br \\tab{5}dy/dx = f(y,x)\\tab{5}y is an n-vector\\br All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments:\\br \\spad{n,} the number of dependent variables;\\br \\spad{x1,} the initial point;\\br \\spad{h,} the step size;\\br \\spad{y,} a vector of initial conditions of length n\\br which upon exit contains the solution at \\spad{x1 + h};\\br \\blankline \\spad{derivs}, a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx}, a vector which contains the derivative information. \\blankline In order of increasing complexity:\\br \\tab{5}\\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to\\br \\tab{5}\\spad{x1 + \\spad{h}} and return the values in y.\\br \\blankline \\tab{5}\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as\\br \\tab{5}\\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch\\br \\tab{5}arrays \\spad{t1-t4} of size n.\\br \\blankline \\tab{5}Starting with \\spad{y} at \\spad{x1,} \\spad{rk4f(y,n,x1,x2,ns,derivs)}\\br \\tab{5}uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta\\br \\tab{5}integrator to advance the solution vector to \\spad{x2} and return\\br \\tab{5}the values in \\spad{y.} Argument \\spad{x2,} is the final point, and\\br \\tab{5}\\spad{ns}, the number of steps to take. \\blankline \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps}, the step is taken and the result is returned. If the error is not within \\spad{eps}, the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input, an trial step size must be given and upon return, an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as\\br \\tab{5}\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}\\br and this is compared against \\spad{eps}. If this is greater than \\spad{eps}, the step size is reduced accordingly to\\br \\tab{5}\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}\\br If the error criterion is satisfied, then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be\\br \\tab{5}\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(-1/5)}\\br Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by W.Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling published by Cambridge University Press. \\blankline Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)}, \\spad{eps} is the required accuracy, \\spad{yscal} is the scaling vector for the difference in solutions. On input, \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output, \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n.} \\blankline \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2,} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as\\br \\tab{5}\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}\\br where \\spad{y(i)} is the solution at location \\spad{x,} \\spad{dydx} is the ordinary differential equation's right hand side, \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. \\blankline The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point, \\spad{eps} is local truncation, \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use.")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation dy/dx = f(y,x) of \\spad{n} variables, where \\spad{y} is an n-vector. Starting with \\spad{y} at \\spad{x1,} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y.} For details, see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation dy/dx = f(y,x) of \\spad{n} variables, where \\spad{y} is an n-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details, see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation dy/dx = f(y,x) of \\spad{n} variables, where \\spad{y} is an n-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details, see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation dy/dx = f(y,x) of \\spad{n} variables, where \\spad{y} is an n-vector using a 4-th order Runge-Kutta method. For details, see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1-t4} of size \\spad{n.} For details, see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation dy/dx = f(y,x) of \\spad{n} variables, where \\spad{y} is an n-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + \\spad{h},} \\spad{n} is the number of dependent variables, \\spad{x1} is the initial point, \\spad{h} is the step size, and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details, see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-789) +(-790) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions), fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns, which contains value Float: estimate of the integral error Float: estimate of the error in the computation totalpts Integer: total number of function evaluations success Boolean: if the integral was computed within the user specified error criterion To produce this estimate, each routine generates an internal sequence of sub-estimates, denoted by S(i), depending on the routine, to which the various convergence criteria are applied. The user must supply a relative accuracy, \\spad{eps_r}, and an absolute accuracy, \\spad{eps_a}. Convergence is obtained when either\\br \\tab{5}\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}\\br \\tab{5}or \\spad{ABS(S(i) - S(i-1)) < eps_a} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: closed: romberg, simpson, trapezoidal open: rombergo, simpsono, trapezoidalo adaptive closed: aromberg, asimpson, atrapezoidal \\blankline The S(i) for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\blankline The S(i) for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\blankline The S(i) for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}-th level, this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the 2*(i+1) power only. \\blankline The three families come in a closed version, where the formulas include the endpoints, an open version where the formulas do not include the endpoints and an adaptive version, where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\blankline Each routine takes as arguments:\\br \\spad{f} integrand\\br a starting point\\br \\spad{b} ending point\\br eps_r relative error\\br eps_a absolute error\\br nmin refinement level when to start checking for convergence \\spad{(>} 1)\\br nmax maximum level of refinement\\br \\blankline The adaptive routines take as an additional parameter, nint, the number of independent intervals to apply a closed family integrator of the same name. \\blankline")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{fn} over the closed interval \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{fn} over the closed interval \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}, and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}, and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b}, with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs}, with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}, and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral, the estimate of the error in the computation, the total number of function evaluations, and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-790 |Curve|) +(-791 |Curve|) ((|constructor| (NIL "Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c.}"))) NIL NIL -(-791) +(-792) ((|constructor| (NIL "Ordered sets which are also abelian groups, such that the addition preserves the ordering."))) NIL NIL -(-792) +(-793) ((|constructor| (NIL "Ordered sets which are also abelian monoids, such that the addition preserves the ordering."))) NIL NIL -(-793) +(-794) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a sup operation added. The purpose of the sup operator in this domain is to act as a supremum with respect to the partial order imposed by `-`, rather than with respect to the total \\spad{$>$} order (since that is \"max\"). \\blankline Axioms\\br \\tab{5}sup(a,b)-a \\~~= \"failed\"\\br \\tab{5}sup(a,b)-b \\~~= \"failed\"\\br \\tab{5}x-a \\~~= \"failed\" and \\spad{x-b} \\~~= \"failed\" \\spad{=>} \\spad{x} \\spad{>=} sup(a,b)\\br")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-794) +(-795) ((|constructor| (NIL "Ordered sets which are also abelian semigroups, such that the addition preserves the ordering.\\br \\blankline Axiom\\br \\tab{5} \\spad{x} < \\spad{y} \\spad{=>} \\spad{x+z} < \\spad{y+z}"))) NIL NIL -(-795) +(-796) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids, such that the addition preserves the ordering."))) NIL NIL -(-796 S R) +(-797 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions, and eight-dimensional non-associative algebra, doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0, and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational, \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion, equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion, equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion o.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion o.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion o.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion o.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion o.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion o.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion o.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion o.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts i,j,k,E,I,J,K of octonian o."))) NIL -((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-373)))) -(-797 R) +((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-374)))) +(-798 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions, and eight-dimensional non-associative algebra, doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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,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 o.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion o.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion o.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion o.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion o.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion o.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion o.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion o.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts i,j,k,E,I,J,K of octonian o."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-798 -1831 R OS S) +(-799 -1841 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion u."))) NIL NIL -(-799 R) +(-800 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring, an eight-dimensional non-associative algebra, doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is octon which takes 8 arguments: the real part, the \\spad{i} imaginary part, the \\spad{j} imaginary part, the \\spad{k} imaginary part, (as with quaternions) and in addition the imaginary parts E, I, \\spad{J,} \\spad{K.}")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation \\spad{O} = \\spad{Q} + QE."))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -282) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (-1831 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (-1831 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))))) -(-800) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -283) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1006 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-1006 |#1|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (-1841 (|HasCategory| (-1006 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (-1841 (|HasCategory| (-1006 |#1|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))))) +(-801) ((|constructor| (NIL "\\axiomType{OrdinaryDifferentialEquationsSolverCategory} is the \\axiom{category} for describing the set of ODE solver \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{ODEsolve}.")) (|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far."))) NIL NIL -(-801 R -3280 L) +(-802 R -3313 L) ((|constructor| (NIL "Solution of linear ordinary differential equations, constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, \\spad{g,} \\spad{x)}} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op \\spad{y} = \\spad{g},} and the \\spad{yi}'s form a basis for the solutions of \\spad{op \\spad{y} = 0}."))) NIL NIL -(-802 R -3280) +(-803 R -3313) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, \\spad{y,} \\spad{x} = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = \\spad{y0,} y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, \\spad{y,} \\spad{x} = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = \\spad{y0,} y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, \\spad{y,} \\spad{x)}} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary, a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned, only the solutions which were found; If the equation is of the form {dy/dx = f(x,y)}, a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = \\spad{c}} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, \\spad{y,} \\spad{x)}} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary, a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned, only the solutions which were found; If the equation is of the form {dy/dx = f(x,y)}, a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = \\spad{c}} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], \\spad{x)}} returns either \"failed\" or, if the equations form a fist order linear system, a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], \\spad{x)}} returns either \"failed\" or, if the equations form a fist order linear system, a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, \\spad{x)}} returns a basis for the solutions of \\spad{D \\spad{y} = \\spad{m} \\spad{y}.} \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, \\spad{v,} \\spad{x)}} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D \\spad{y} = \\spad{m} \\spad{y} + \\spad{v}} are \\spad{v_p + \\spad{c_1} \\spad{v_1} + \\spad{...} + \\spad{c_m} v_m} where the \\spad{c_i's} are constants, and the \\spad{v_i's} form a basis for the solutions of \\spad{D \\spad{y} = \\spad{m} \\spad{y}.} \\spad{x} is the dependent variable."))) NIL NIL -(-803) +(-804) ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k.}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l.}")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-804 R -3280) +(-805 R -3313) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x.}")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, \\spad{x)}} returns e^{the integral of \\spad{f} with respect to \\spad{x}.}")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, \\spad{x)}} returns the integral of \\spad{f} with respect to \\spad{x.}"))) NIL NIL -(-805) +(-806) ((|constructor| (NIL "\\axiomType{AnnaOrdinaryDifferentialEquationPackage} is a \\axiom{package} of functions for the \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} with \\axiom{measure}, and \\axiom{solve}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{prob}. \\blankline It calls each \\axiom{domain} listed in \\axiom{R} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{prob}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations, \\axiom{f}, \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n] from \\axiom{xStart} to \\axiom{xEnd} with the initial values for y[1]..y[n] (\\axiom{yInitial}) to an absolute error requirement \\axiom{epsabs} and relative error \\axiom{epsrel}. The values of y[1]..y[n] will be output for the values of \\spad{x} in \\axiom{intVals}. The calculation will stop if the function G(x,y[1],..,y[n]) evaluates to zero before \\spad{x} = xEnd. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations, \\axiom{f}, \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n] from \\axiom{xStart} to \\axiom{xEnd} with the initial values for y[1]..y[n] (\\axiom{yInitial}) to a tolerance \\axiom{tol}. The values of y[1]..y[n] will be output for the values of \\spad{x} in \\axiom{intVals}. The calculation will stop if the function G(x,y[1],..,y[n]) evaluates to zero before \\spad{x} = xEnd. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations, \\axiom{f}, \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n] from \\axiom{xStart} to \\axiom{xEnd} with the initial values for y[1]..y[n] (\\axiom{yInitial}) to a tolerance \\axiom{tol}. The values of y[1]..y[n] will be output for the values of \\spad{x} in \\axiom{intVals}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations, \\axiom{f}, \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n] from \\axiom{xStart} to \\axiom{xEnd} with the initial values for y[1]..y[n] (\\axiom{yInitial}) to a tolerance \\axiom{tol}. The calculation will stop if the function G(x,y[1],..,y[n]) evaluates to zero before \\spad{x} = xEnd. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations, \\axiom{f}, \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n] from \\axiom{xStart} to \\axiom{xEnd} with the initial values for y[1]..y[n] (\\axiom{yInitial}) to a tolerance \\axiom{tol}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n], together with a starting value for \\spad{x} and y[1]..y[n] (called the initial conditions) and a final value of \\spad{x.} A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n], together with starting values for \\spad{x} and y[1]..y[n] (called the initial conditions), a final value of \\spad{x,} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{R} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives y[1]'..y[n]' defined in terms of x,y[1]..y[n], together with starting values for \\spad{x} and y[1]..y[n] (called the initial conditions), a final value of \\spad{x,} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate, \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-806 -3280 UP UPUP R) +(-807 -3313 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation, pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, \\spad{g)}} returns \\spad{[\"failed\", []]} if the equation \\spad{op \\spad{y} = \\spad{g}} has no solution in \\spad{R}. Otherwise, it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-807 -3280 UP L LQ) +(-808 -3313 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear ordinary differential equations, in the transcendental case. The derivation to use is given by the parameter \\spad{L}.")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op \\spad{y} = \\spad{c1} \\spad{g1} + \\spad{...} + \\spad{cm} \\spad{gm}} and \\spad{op0 \\spad{y} = \\spad{c1} \\spad{h1} + \\spad{...} + \\spad{cm} \\spad{hm}} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, \\spad{p)}} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p}, and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op}, and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, \\spad{p)}} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p}, and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op}, and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op \\spad{y} = \\spad{c1} \\spad{g1} + \\spad{...} + \\spad{cm} \\spad{gm}} is of the form \\spad{p/d} for some polynomial \\spad{p.}") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, \\spad{g)}} returns a polynomial \\spad{d} such that any rational solution of \\spad{op \\spad{y} = \\spad{g}} is of the form \\spad{p/d} for some polynomial \\spad{p,} and \"failed\", if the equation has no rational solution."))) NIL NIL -(-808) +(-809) ((|constructor| (NIL "\\axiomType{NumericalODEProblem} is a \\axiom{domain} for the representation of Numerical ODE problems for use by ANNA. \\blankline The representation is of type: \\blankline \\axiomType{Record}(xinit:\\axiomType{DoubleFloat},\\br xend:\\axiomType{DoubleFloat},\\br fn:\\axiomType{Vector Expression DoubleFloat},\\br yinit:\\axiomType{List DoubleFloat},intvals:\\axiomType{List DoubleFloat},\\br g:\\axiomType{Expression DoubleFloat},abserr:\\axiomType{DoubleFloat},\\br relerr:\\axiomType{DoubleFloat}) \\blankline")) (|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-809 -3280 UP L LQ) +(-810 -3313 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations, primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], \\spad{...} ,{} [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the fi's (up to the constant coefficient), in which case the equation for \\spad{z=y e^{-int \\spad{p}}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], \\spad{...} ,{} [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the pi's (up to the constant coefficient), in which case the equation for \\spad{z=y e^{-int \\spad{p}}} is \\spad{Li \\spad{z} =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], \\spad{...} ,{} [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op \\spad{y} = 0} must be one of the ai's in which case the equation for \\spad{z = \\spad{y} e^{-int ai}} is \\spad{Li \\spad{z} = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F}, whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], \\spad{...} ,{} [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op \\spad{y} = 0} must have degree \\spad{mj} for some \\spad{j,} and its leading coefficient is then a zero of \\spad{pj.} In addition,\\spad{m1>m2> \\spad{...} >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op \\spad{y} = 0} is of the form \\spad{p/d + q'/q + \\spad{r}} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r.} Also, \\spad{deg(p) < deg(d)} and {gcd(d,q) = 1}."))) NIL NIL -(-810 -3280 UP) +(-811 -3313 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear ordinary differential equations, in the rational case.")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], \\spad{M]}} such that any rational solution of \\spad{op \\spad{y} = \\spad{c1} \\spad{g1} + \\spad{...} + \\spad{cm} \\spad{gm}} is of the form \\spad{d1 \\spad{h1} + \\spad{...} + \\spad{dq} \\spad{hq}} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, \\spad{g)}} returns \\spad{[\"failed\", []]} if the equation \\spad{op \\spad{y} = \\spad{g}} has no rational solution. Otherwise, it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the yi's form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], \\spad{M]}} such that any rational solution of \\spad{op \\spad{y} = \\spad{c1} \\spad{g1} + \\spad{...} + \\spad{cm} \\spad{gm}} is of the form \\spad{d1 \\spad{h1} + \\spad{...} + \\spad{dq} \\spad{hq}} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, \\spad{g)}} returns \\spad{[\"failed\", []]} if the equation \\spad{op \\spad{y} = \\spad{g}} has no rational solution. Otherwise, it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the yi's form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-811 -3280 L UP A LO) +(-812 -3313 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, \\spad{g)}} returns \\spad{[m, \\spad{v]}} such that any solution in \\spad{A} of \\spad{op \\spad{z} = \\spad{g}} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A}, and the \\spad{z_i's} satisfy the differential system \\spad{M.z = \\spad{v}.}"))) NIL NIL -(-812 -3280 UP) +(-813 -3313 UP) ((|constructor| (NIL "In-field solution of Riccati equations, rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1,L1], [p2,L2], \\spad{...} ,{} [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op \\spad{y} = 0} must be one of the pi's (up to the constant coefficient), in which case the equation for \\spad{z = \\spad{y} e^{-int \\spad{p}}} is \\spad{Li \\spad{z} = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op \\spad{y} = 0} must be one of the fi's (up to the constant coefficient), in which case the equation for \\spad{z = \\spad{y} e^{-int ai}} is \\spad{Li \\spad{z} = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP}, not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op \\spad{y} = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-813 -3280 LO) +(-814 -3313 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, \\spad{v,} solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m \\spad{x} = \\spad{v}} are \\spad{v_p + \\spad{c_1} \\spad{v_1} + \\spad{...} + \\spad{c_m} v_m} where the \\spad{c_i's} are constants, and the \\spad{v_i's} form a basis for the solutions of \\spad{m \\spad{x} = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, \\spad{v,} solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D \\spad{x} = \\spad{m} \\spad{x} + \\spad{v}} are \\spad{v_p + \\spad{c_1} \\spad{v_1} + \\spad{...} + \\spad{c_m} v_m} where the \\spad{c_i's} are constants, and the \\spad{v_i's} form a basis for the solutions of \\spad{D \\spad{x} = \\spad{m} \\spad{x}.} Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, \\spad{v)}} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 \\spad{x} = v_0} is equivalent to \\spad{m \\spad{x} = \\spad{v}.}") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A \\spad{z},} the first order linear system \\spad{D \\spad{y} = \\spad{M} \\spad{y} + \\spad{v}} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i \\spad{z_j} = h_i}."))) NIL NIL -(-814 -3280 LODO) +(-815 -3313 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, \\spad{g,} [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op \\spad{y} = \\spad{g}} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(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, \\spad{g,} [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op \\spad{y} = \\spad{g}} is \\spad{f1 int(u1) + \\spad{...} + \\spad{fm} int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-818 (-1169)) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-818 (-1169)) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-818 (-1169)) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-818 (-1169)) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-818 (-1169)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-817 |Kernels| R |var|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-819 (-1170)) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-819 (-1170)) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-819 (-1170)) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-819 (-1170)) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-819 (-1170)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-818 |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."))) -(((-4602 "*") |has| |#2| (-367)) (-4593 |has| |#2| (-367)) (-4598 |has| |#2| (-367)) (-4592 |has| |#2| (-367)) (-4597 . T) (-4595 . T) (-4594 . T)) -((|HasCategory| |#2| (QUOTE (-367)))) -(-818 S) +(((-4604 "*") |has| |#2| (-368)) (-4595 |has| |#2| (-368)) (-4600 |has| |#2| (-368)) (-4594 |has| |#2| (-368)) (-4599 . T) (-4597 . T) (-4596 . T)) +((|HasCategory| |#2| (QUOTE (-368)))) +(-819 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}(u), \\spadfun{variable}(u))."))) NIL NIL -(-819 S) +(-820 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si \\spad{**} ni])} where the si's are in \\spad{S,} and the ni's are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < \\spad{y}} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} w.r.t. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\indented{1}{\\spad{varList(x)} returns the list of variables of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} varList \\spad{m1}")) (|length| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{length(x)} returns the length of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} length \\spad{m1}")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\indented{1}{\\spad{factors(a1\\^e1,...,an\\^en)} returns} \\indented{1}{\\spad{[[a1, e1],...,[an, en]]}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} factors \\spad{m1}")) (|nthFactor| ((|#1| $ (|Integer|)) "\\indented{1}{\\spad{nthFactor(x, \\spad{n)}} returns the factor of the \\spad{n-th}} \\indented{1}{monomial of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} nthFactor(m1,2)")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\indented{1}{\\spad{nthExpon(x, \\spad{n)}} returns the exponent of the} \\indented{1}{\\spad{n-th} monomial of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} nthExpon(m1,2)")) (|size| (((|NonNegativeInteger|) $) "\\indented{1}{\\spad{size(x)} returns the number of monomials in \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} size(m1,2)")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\indented{1}{\\spad{overlap(x, \\spad{y)}} returns \\spad{[l, \\spad{m,} \\spad{r]}} such that} \\indented{1}{\\spad{x = \\spad{l} * \\spad{m}} and \\spad{y = \\spad{m} * \\spad{r}} hold and such that} \\indented{1}{\\spad{l} and \\spad{r} have no overlap,} \\indented{1}{that is \\spad{overlap(l, \\spad{r)} = \\spad{[l,} 1, r]}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(x*y)$OFMONOID(Symbol) \\spad{X} overlap(m1,m2)")) (|divide| (((|Union| (|Record| (|:| |lm| (|Union| $ "failed")) (|:| |rm| (|Union| $ "failed"))) "failed") $ $) "\\indented{1}{\\spad{divide(x,y)} returns the left and right exact quotients of} \\indented{1}{\\spad{x} by \\spad{y}, that is \\spad{[l,r]} such that \\spad{x = l*y*r}.} \\indented{1}{\"failed\" is returned iff \\spad{x} is not of the form \\spad{l * \\spad{y} * r}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(x*y)$OFMONOID(Symbol) \\spad{X} divide(m1,m2)")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\indented{1}{\\spad{rquo(x, \\spad{s)}} returns the exact right quotient} \\indented{1}{of \\spad{x} by \\spad{s}.} \\blankline \\spad{X} m1:=(x*y)$OFMONOID(Symbol) \\spad{X} div(m1,y)") (((|Union| $ "failed") $ $) "\\indented{1}{\\spad{rquo(x, \\spad{y)}} returns the exact right quotient of \\spad{x}} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = \\spad{q} * y},} \\indented{1}{\"failed\" if \\spad{x} is not of the form \\spad{q * y}.} \\blankline \\spad{X} m1:=(q*y^3)$OFMONOID(Symbol) \\spad{X} m2:=(y^2)$OFMONOID(Symbol) \\spad{X} lquo(m1,m2)")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\indented{1}{\\spad{lquo(x, \\spad{s)}} returns the exact left quotient of \\spad{x}} \\indented{1}{by \\spad{s}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} lquo(m1,x)") (((|Union| $ "failed") $ $) "\\indented{1}{\\spad{lquo(x, \\spad{y)}} returns the exact left quotient of \\spad{x}} \\indented{2}{by \\spad{y} that is \\spad{q} such that \\spad{x = \\spad{y} * q},} \\indented{1}{\"failed\" if \\spad{x} is not of the form \\spad{y * q}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(x*y)$OFMONOID(Symbol) \\spad{X} lquo(m1,m2)")) (|hcrf| (($ $ $) "\\indented{1}{\\spad{hcrf(x, \\spad{y)}} returns the highest common right} \\indented{1}{factor of \\spad{x} and \\spad{y},} \\indented{1}{that is the largest \\spad{d} such that \\spad{x = a \\spad{d}}} \\indented{1}{and \\spad{y = \\spad{b} d}.} \\blankline \\spad{X} m1:=(x*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(y*z)$OFMONOID(Symbol) \\spad{X} hcrf(m1,m2)")) (|hclf| (($ $ $) "\\indented{1}{\\spad{hclf(x, \\spad{y)}} returns the highest common left factor} \\indented{1}{of \\spad{x} and \\spad{y},} \\indented{1}{that is the largest \\spad{d} such that \\spad{x = \\spad{d} a}} \\indented{1}{and \\spad{y = \\spad{d} b}.} \\blankline \\spad{X} m1:=(x*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(x*y)$OFMONOID(Symbol) \\spad{X} hclf(m1,m2)")) (|lexico| (((|Boolean|) $ $) "\\indented{1}{\\spad{lexico(x,y)} returns \\spad{true}} \\indented{1}{iff \\spad{x} is smaller than \\spad{y}} \\indented{1}{w.r.t. the pure lexicographical ordering induced by \\spad{S}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} m2:=(x*y)$OFMONOID(Symbol) \\spad{X} lexico(m1,m2) \\spad{X} lexico(m2,m1)")) (|mirror| (($ $) "\\indented{1}{\\spad{mirror(x)} returns the reversed word of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} mirror \\spad{m1}")) (|rest| (($ $) "\\indented{1}{\\spad{rest(x)} returns \\spad{x} except the first letter.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} rest \\spad{m1}")) (|first| ((|#1| $) "\\indented{1}{\\spad{first(x)} returns the first letter of \\spad{x}.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} first \\spad{m1}")) (** (($ |#1| (|NonNegativeInteger|)) "\\indented{1}{\\spad{s**n} returns the product of \\spad{s} by itself \\spad{n} times.} \\blankline \\spad{X} m1:=(y**3)$OFMONOID(Symbol)")) (* (($ $ |#1|) "\\indented{1}{\\spad{x*s} returns the product of \\spad{x} by \\spad{s} on the right.} \\blankline \\spad{X} m1:=(y**3)$OFMONOID(Symbol) \\spad{X} m1*x") (($ |#1| $) "\\indented{1}{\\spad{s*x} returns the product of \\spad{x} by \\spad{s} on the left.} \\blankline \\spad{X} m1:=(x*y*y*z)$OFMONOID(Symbol) \\spad{X} \\spad{x*m1}"))) NIL NIL -(-820) +(-821) ((|constructor| (NIL "The category of ordered commutative integral domains, where ordering and the arithmetic operations are compatible"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-821) +(-822) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}s.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) NIL NIL -(-822) +(-823) ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files, strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{dev}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{dev}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{dev}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{dev}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{dev}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{dev}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{dev}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{dev}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{dev}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{dev}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{dev}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{dev}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{dev}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{dev}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{dev}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{dev}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{dev}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{dev}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{dev}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{dev}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,cd,s)} writes the symbol \\axiom{s} from \\spad{CD} \\axiom{cd} to \\axiom{dev}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,i)} writes the string \\axiom{i} to \\axiom{dev}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,i)} writes the variable \\axiom{i} to \\axiom{dev}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,i)} writes the float \\axiom{i} to \\axiom{dev}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,i)} writes the integer \\axiom{i} to \\axiom{dev}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{dev}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{dev}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{dev}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{dev}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{dev}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{dev}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{dev}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{dev}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{dev}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{dev}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{dev}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{dev}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{dev}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{dev}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{dev} to \\axiom{enc}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{dev}, flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,mode)} opens the string \\axiom{s} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,mode,enc)} opens file \\axiom{f} for reading or writing OpenMath objects (depending on \\axiom{mode} which can be \"r\", \\spad{\"w\"} or \"a\" for read, write and append respectively), in the encoding \\axiom{enc}."))) NIL NIL -(-823) +(-824) ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device, the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL -(-824) +(-825) ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors, unknown \\spad{CD} or symbol errors, and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{u} is one of \\axiom{OMParseError}, \\axiom{OMReadError}, \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol}, otherwise it raises a runtime error."))) NIL NIL -(-825) +(-826) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error u.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-826 R) +(-827 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-827 P R) +(-828 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P.} That is, as sets \\spad{P = \\spad{$}} but \\spad{a * \\spad{b}} in \\spad{$} is equal to \\spad{b * a} in \\spad{P.}")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\spad{$.}")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P.}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-226)))) -(-828) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-227)))) +(-829) ((|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{u} to the OpenMath device \\axiom{dev} as a complete OpenMath object; OMwrite(dev, u, false) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{u} to the OpenMath device \\axiom{dev} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{u} as a complete OpenMath object; OMwrite(u, false) returns the OpenMath \\spad{XML} encoding of \\axiom{u} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{u} as a complete OpenMath object."))) NIL NIL -(-829) +(-830) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{s} from \\spad{CD} \\axiom{cd}, \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{cd}, \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{cd}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{f} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{f} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{dev} and passes it to AXIOM."))) NIL NIL -(-830 S) +(-831 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate u."))) -((-4600 . T) (-4590 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4592 . T) (-4603 . T) (-3389 . T)) NIL -(-831) +(-832) ((|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{portnum}. The parameter \\axiom{timeout} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{u} on \\axiom{c} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{c} and returns the appropriate AXIOM object."))) NIL NIL -(-832 R S) +(-833 R S) ((|constructor| (NIL "Lifting of maps to one-point completions.")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, \\spad{r,} i)} lifts \\spad{f} and applies it to \\spad{r,} assuming that f(infinity) = i.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, \\spad{r)}} lifts \\spad{f} and applies it to \\spad{r,} assuming that f(infinity) = infinity."))) NIL NIL -(-833 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."))) -((-4597 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-553))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-21))) (-1831 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845))))) (-834 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."))) +((-4599 |has| |#1| (-846))) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-554))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-21))) (-1841 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846))))) +(-835 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151)))) -(-835) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151)))) +(-836) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations), \\spad{\"k\"} (constructors), \\spad{\"d\"} (domains), \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) NIL NIL -(-836) +(-837) ((|constructor| (NIL "\\axiomType{NumericalOptimizationCategory} is the \\axiom{category} for describing the set of Numerical Optimization \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{optimize}.")) (|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far."))) NIL NIL -(-837) +(-838) ((|constructor| (NIL "\\axiomType{AnnaNumericalOptimizationPackage} is a \\axiom{package} of functions for the \\axiomType{NumericalOptimizationCategory} with \\axiom{measure} and \\axiom{optimize}.")) (|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions, \\axiom{lf}, of one or more variables without constraints. \\blankline The parameter \\axiom{start} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(lf,start) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{prob}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,start)} is a top level ANNA function to minimize a set of functions, \\axiom{lf}, of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{start} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,start)} is a top level ANNA function to minimize a function, \\axiom{f}, of one or more variables without constraints. \\blankline The parameter \\axiom{start} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,upper)} is a top level ANNA function to minimize a function, \\axiom{f}, of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{lower} and \\axiom{upper}. \\blankline The parameter \\axiom{start} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,cons,upper)} is a top level ANNA function to minimize a function, \\axiom{f}, of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{cons} would be an empty list and the bounds on those variables defined in \\axiom{lower} and \\axiom{upper}, or a mixture of simple, linear and non-linear constraints, where \\axiom{cons} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{upper} and \\axiom{lower}. \\blankline The parameter \\axiom{start} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{prob}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{prob}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{routines} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{prob} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{R} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{prob} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) NIL NIL -(-838) +(-839) ((|constructor| (NIL "\\axiomType{NumericalOptimizationProblem} is a \\axiom{domain} for the representation of Numerical Optimization problems for use by ANNA. \\blankline The representation is a Union of two record types - one for otimization of a single function of one or more variables: \\blankline \\axiomType{Record}(\\br fn:\\axiomType{Expression DoubleFloat},\\br init:\\axiomType{List DoubleFloat},\\br lb:\\axiomType{List OrderedCompletion DoubleFloat},\\br cf:\\axiomType{List Expression DoubleFloat},\\br ub:\\axiomType{List OrderedCompletion DoubleFloat}) \\blankline and one for least-squares problems \\spadignore{i.e.} optimization of a set of observations of a data set: \\blankline \\axiomType{Record}(lfn:\\axiomType{List Expression DoubleFloat},\\br init:\\axiomType{List DoubleFloat}).")) (|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-839 R S) +(-840 R S) ((|constructor| (NIL "Lifting of maps to ordered completions.")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, \\spad{r,} \\spad{p,} \\spad{m)}} lifts \\spad{f} and applies it to \\spad{r,} assuming that f(plusInfinity) = \\spad{p} and that f(minusInfinity) = \\spad{m.}") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, \\spad{r)}} lifts \\spad{f} and applies it to \\spad{r,} assuming that f(plusInfinity) = plusInfinity and that f(minusInfinity) = minusInfinity."))) NIL NIL -(-840 R) +(-841 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."))) -((-4597 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-553))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-21))) (-1831 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845))))) -(-841) +((-4599 |has| |#1| (-846))) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-554))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-21))) (-1841 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-846))))) +(-842) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-842 -3020 S) +(-843 -3465 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 -(-843) +(-844) ((|constructor| (NIL "Ordered sets which are also monoids, such that multiplication preserves the ordering. \\blankline Axioms\\br \\tab{5}\\spad{x < \\spad{y} \\spad{=>} \\spad{x*z} < y*z}\\br \\tab{5}\\spad{x < \\spad{y} \\spad{=>} \\spad{z*x} < z*y}"))) NIL NIL -(-844 S) +(-845 S) ((|constructor| (NIL "Ordered sets which are also rings, that is, domains where the ring operations are compatible with the ordering. \\blankline Axiom\\br \\tab{5}\\spad{0} ab< ac}")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x.}")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive, \\spad{-1} if \\spad{x} is negative, 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-845) +(-846) ((|constructor| (NIL "Ordered sets which are also rings, that is, domains where the ring operations are compatible with the ordering. \\blankline Axiom\\br \\tab{5}\\spad{0} ab< ac}")) (|abs| (($ $) "\\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."))) -((-4597 . T)) +((-4599 . T)) NIL -(-846 S) +(-847 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 \\spad{>=} \\spad{y}} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > \\spad{y}} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < \\spad{y}} is a strict total ordering on the elements of the set."))) NIL NIL -(-847) +(-848) ((|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 \\spad{>=} \\spad{y}} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > \\spad{y}} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < \\spad{y}} is a strict total ordering on the elements of the set."))) NIL NIL -(-848 S R) +(-849 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) \\spad{x} + \\delta a}. This category is an evolution of the types MonogenicLinearOperator, OppositeMonogenicLinearOperator, and NonCommutativeOperatorDivision")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = \\spad{c} * a + \\spad{d} * \\spad{b} = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\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") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q}, if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * \\spad{c} + \\spad{b} * \\spad{d} = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\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") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q}, if it exists, \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * \\spad{l0}} for some a in \\spad{R,} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l.}")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{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''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{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''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a, returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, \\spad{c,} \\spad{m)}} returns \\spad{p(m)} where the action is given by \\spad{x \\spad{m} = \\spad{c} sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l.}")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator, \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\spad{^=} 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) -(-849 R) +((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174)))) +(-850 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) \\spad{x} + \\delta a}. This category is an evolution of the types MonogenicLinearOperator, OppositeMonogenicLinearOperator, and NonCommutativeOperatorDivision")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = \\spad{c} * a + \\spad{d} * \\spad{b} = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\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") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q}, if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * \\spad{c} + \\spad{b} * \\spad{d} = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\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") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q}, if it exists, \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * \\spad{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 = \\spad{q*b} + \\spad{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''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{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''.")) (|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, \\spad{c,} \\spad{m)}} returns \\spad{p(m)} where the action is given by \\spad{x \\spad{m} = \\spad{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), \\spad{i} = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\spad{^=} 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), \\spad{i} = 0..n)}.}"))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-850 R C) +(-851 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, \\spad{b,} sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, \\spad{b,} sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{r}} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, \\spad{b,} sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{q*b} + \\spad{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{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, \\spad{b,} sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = \\spad{b*q} + \\spad{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{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, \\spad{c,} \\spad{m,} sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x \\spad{m} = \\spad{c} sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, \\spad{q,} sigma, delta)} returns \\spad{p * \\spad{q}.} \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL -((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) -(-851 R |sigma| -2410) +((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) +(-852 R |sigma| -4363) ((|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) \\spad{x} + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, \\spad{x)}} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-367)))) -(-852 |x| R |sigma| -2410) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-368)))) +(-853 |x| R |sigma| -4363) ((|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) \\spad{x} + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-367)))) -(-853 R) +((-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-368)))) +(-854 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, \\spad{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!, \\spad{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!, \\spad{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, \\spad{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, \\spad{n} = 0..)}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571)))))) -(-854) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572)))))) +(-855) ((|constructor| (NIL "A domain used in order to take the free R-module on the Integers I. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-855) +(-856) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX, or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not \\spad{f}} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or \\spad{g}} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and \\spad{g}} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo \\spad{g}} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem \\spad{g}} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div \\spad{g}} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f \\spad{**} \\spad{g}} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / \\spad{g}} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * \\spad{g}} creates the equivalent infix form.")) (- (($ $) "\\spad{- \\spad{f}} creates the equivalent prefix form.") (($ $ $) "\\spad{f - \\spad{g}} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + \\spad{g}} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f \\spad{>=} \\spad{g}} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f \\spad{<=} \\spad{g}} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > \\spad{g}} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < \\spad{g}} creates the equivalent infix form.")) (^= (($ $ $) "\\spad{f \\spad{^=} \\spad{g}} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = \\spad{g}} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile, \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and upperlimit.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a lowerlimit.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and upperlimit.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a lowerlimit.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital pi.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and upperlimit.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a lowerlimit.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n.}")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n.}")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n.}")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n.}")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m.}")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f,} \\spadignore{e.g.} \\spad{f'}, \\spad{f''}, \\spad{f'''}, \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f \\spad{->} \\spad{g}.}")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f \\spad{:=} \\spad{g}.}")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g.}")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g.}")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f.}") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f.}")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g.}")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n.}")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l.}")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator, and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a op.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, \\spad{b)}} creates a form which prints as: a \\spad{op} \\spad{b.}") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the n-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l.}")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the n-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l.}")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list u.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g.}")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list u.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g.}")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n.}")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n.}")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n.}")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space, \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n.}")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n.}")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf.}") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s.}") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s.}") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n.}")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s.}")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form u."))) NIL NIL -(-856) +(-857) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream, as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream, as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream, as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream, as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-857 |VariableList|) +(-858 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-858 R |vl| |wl| |wtlevel|) +(-859 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(R) into Weighted form, applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(R), ignoring weights"))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) -(-859) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) +(-860) ((|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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-860 |downLevel|) +(-861 |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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-865) (QUOTE (-151))) (|HasCategory| (-865) (QUOTE (-149))) (|HasCategory| (-865) (QUOTE (-373))) (|HasCategory| (-412 (-571)) (QUOTE (-151))) (|HasCategory| (-412 (-571)) (QUOTE (-149))) (|HasCategory| (-412 (-571)) (QUOTE (-373))) (-1831 (|HasCategory| (-412 (-571)) (QUOTE (-149))) (|HasCategory| (-412 (-571)) (QUOTE (-373))) (|HasCategory| (-865) (QUOTE (-149))) (|HasCategory| (-865) (QUOTE (-373)))) (-1831 (|HasCategory| (-412 (-571)) (QUOTE (-373))) (|HasCategory| (-865) (QUOTE (-373))))) -(-861) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-866) (QUOTE (-151))) (|HasCategory| (-866) (QUOTE (-149))) (|HasCategory| (-866) (QUOTE (-374))) (|HasCategory| (-413 (-572)) (QUOTE (-151))) (|HasCategory| (-413 (-572)) (QUOTE (-149))) (|HasCategory| (-413 (-572)) (QUOTE (-374))) (-1841 (|HasCategory| (-413 (-572)) (QUOTE (-149))) (|HasCategory| (-413 (-572)) (QUOTE (-374))) (|HasCategory| (-866) (QUOTE (-149))) (|HasCategory| (-866) (QUOTE (-374)))) (-1841 (|HasCategory| (-413 (-572)) (QUOTE (-374))) (|HasCategory| (-866) (QUOTE (-374))))) +(-862) ((|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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-862 K) +(-863 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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-373)))) -(-863) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-374)))) +(-864) ((|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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,n2). Any algebraic operations defined for several elements are only defined if all of the concerned elements are coming from a set of related tower 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)."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-864) +(-865) ((|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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-865) +(-866) ((|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} : K_0, K_1, ..., K_i...,K_n) where \\spad{K_0} = \\spad{K} and for \\spad{i} =1,2,...,n, K_i is an extension of K_{i-1} of degree > 1 and defined by an irreducible polynomial p(Z) in K_{i-1}. Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) and (T_2: K_02, K_12,...,K_i2,...,K_n2) are said to be related if \\spad{T_1} \\spad{<=} \\spad{T_2} (or \\spad{T_1} \\spad{>=} T_2), that is if \\spad{K_i1} = \\spad{K_i2} for \\spad{i=1,2,...,n1} (or i=1,2,...,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."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-412 (-571)) (QUOTE (-151))) (|HasCategory| (-412 (-571)) (QUOTE (-149))) (|HasCategory| (-412 (-571)) (QUOTE (-373))) (-1831 (|HasCategory| (-412 (-571)) (QUOTE (-149))) (|HasCategory| (-412 (-571)) (QUOTE (-373))))) -(-866 R PS UP) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-413 (-572)) (QUOTE (-151))) (|HasCategory| (-413 (-572)) (QUOTE (-149))) (|HasCategory| (-413 (-572)) (QUOTE (-374))) (-1841 (|HasCategory| (-413 (-572)) (QUOTE (-149))) (|HasCategory| (-413 (-572)) (QUOTE (-374))))) +(-867 R PS UP) ((|constructor| (NIL "This package computes reliable Pad&ea. approximants using a generalized Viskovatov continued fraction algorithm.")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant), \\spad{dd} (denominator degree of approximant), \\spad{ns} (numerator series of function), and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant), \\spad{dd} (denominator degree of approximant), \\spad{ns} (numerator series of function), and \\spad{ds} (denominator series of function)."))) NIL NIL -(-867 R |x| |pt|) +(-868 R |x| |pt|) ((|constructor| (NIL "This package computes reliable Pad&ea. approximants using a generalized Viskovatov continued fraction algorithm.")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant), \\spad{dd} (denominator degree of approximant), \\spad{ns} (numerator series of function), and \\spad{ds} (denominator series of function)."))) NIL NIL -(-868 |p|) +(-869 |p|) ((|constructor| (NIL "This is the category of stream-based representations of the 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 = \\spad{x} (mod p^n)} when \\spad{n} is positive, and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b,} where \\spad{x = a + \\spad{b} \\spad{p}.}")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a, where \\spad{x = a + \\spad{b} \\spad{p}.}")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p.}")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|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 p-adic digits of \\spad{x.}"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-869 |p|) +(-870 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} p-adic numbers are represented as sum(i = 0.., a[i] * p^i), where the a[i] lie in 0,1,...,(p - 1)."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-870 |p|) +(-871 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(i = k.., a[i] * p^i) where the a[i] lie in 0,1,...,(p - 1)."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-869 |#1|) (QUOTE (-909))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| (-869 |#1|) (QUOTE (-149))) (|HasCategory| (-869 |#1|) (QUOTE (-151))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-869 |#1|) (QUOTE (-1027))) (|HasCategory| (-869 |#1|) (QUOTE (-820))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-869 |#1|) (QUOTE (-1143))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| (-869 |#1|) (QUOTE (-226))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -526) (QUOTE (-1169)) (LIST (QUOTE -869) (|devaluate| |#1|)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -304) (LIST (QUOTE -869) (|devaluate| |#1|)))) (|HasCategory| (-869 |#1|) (LIST (QUOTE -282) (LIST (QUOTE -869) (|devaluate| |#1|)) (LIST (QUOTE -869) (|devaluate| |#1|)))) (|HasCategory| (-869 |#1|) (QUOTE (-302))) (|HasCategory| (-869 |#1|) (QUOTE (-553))) (|HasCategory| (-869 |#1|) (QUOTE (-847))) (-1831 (|HasCategory| (-869 |#1|) (QUOTE (-820))) (|HasCategory| (-869 |#1|) (QUOTE (-847)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-869 |#1|) (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-869 |#1|) (QUOTE (-909)))) (|HasCategory| (-869 |#1|) (QUOTE (-149))))) -(-871 |p| PADIC) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-870 |#1|) (QUOTE (-910))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-870 |#1|) (QUOTE (-149))) (|HasCategory| (-870 |#1|) (QUOTE (-151))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-870 |#1|) (QUOTE (-1028))) (|HasCategory| (-870 |#1|) (QUOTE (-821))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-870 |#1|) (QUOTE (-1144))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-870 |#1|) (QUOTE (-227))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -527) (QUOTE (-1170)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -305) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -283) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-303))) (|HasCategory| (-870 |#1|) (QUOTE (-554))) (|HasCategory| (-870 |#1|) (QUOTE (-848))) (-1841 (|HasCategory| (-870 |#1|) (QUOTE (-821))) (|HasCategory| (-870 |#1|) (QUOTE (-848)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-870 |#1|) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-870 |#1|) (QUOTE (-910)))) (|HasCategory| (-870 |#1|) (QUOTE (-149))))) +(-872 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp.}")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the p-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the p-adic rational \\spad{x}. A p-adic rational is represented by \\spad{(1)} an exponent and \\spad{(2)} a p-adic integer which may have leading zero digits. When the p-adic integer has a leading zero digit, a 'leading zero' is removed from the p-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the 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 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 = \\spad{x} (mod p^n)}."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-226))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -282) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-847))) (-1831 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-847)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-149))))) -(-872 K |symb| BLMET) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -283) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-303))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-848))) (-1841 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-848)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-149))))) +(-873 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 L-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the L-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(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 L-Polynomial of the curve in constant field extension of degree \\spad{d.}") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the L-Polynomial of the curve.")) (|adjunctionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial defined by setCurve.")) (|intersectionDivisor| (((|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{intersectionDivisor(pol)} compute the intersection divisor of the form \\spad{pol} with the curve. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{evalIfCan(f,pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl.}") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl.}") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{eval(f,pl)} evaluate \\spad{f} at the place \\spad{pl.}")) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) (|NonNegativeInteger|)) "\\spad{interpolateForms(d,n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d.}")) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| (((|NeitherSparseOrDensePowerSeries| (|PseudoAlgebraicClosureOfFiniteField| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{parametrize(f,pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl.}")) (|singularPoints| (((|List| (|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|desingTree| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |#1| |#2| |#3|)))) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{theCurve returns} the specified polynomial for the package.")) (|rationalPlaces| (((|List| (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|))) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| (((|ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |#1|) (|PlacesOverPseudoAlgebraicClosureOfFiniteField| |#1|)) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl.}"))) NIL -((|HasCategory| (-862 |#1|) (QUOTE (-373)))) -(-873 K |symb| BLMET) +((|HasCategory| (-863 |#1|) (QUOTE (-374)))) +(-874 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 L-Polynomial") (((|UnivariateTaylorSeriesCZero| (|Integer|) |t|)) "Returns the Zeta function of the curve. Calculated by using the L-Polynomial")) (|numberPlacesDegExtDeg| (((|Integer|) (|PositiveInteger|) (|PositiveInteger|)) "numberRatPlacesExtDegExtDeg(d, \\spad{n)} returns the number of places of degree \\spad{d} in the constant field extension of degree \\spad{n}")) (|numberRatPlacesExtDeg| (((|Integer|) (|PositiveInteger|)) "\\spad{numberRatPlacesExtDeg(n)} returns the number of rational places in the constant field extenstion of degree \\spad{n}")) (|numberOfPlacesOfDegree| (((|Integer|) (|PositiveInteger|)) "returns the number of places of the given degree")) (|placesOfDegree| (((|List| (|Places| |#1|)) (|PositiveInteger|)) "\\spad{placesOfDegree(d)} returns all places of degree \\spad{d} of the curve.")) (|classNumber| (((|Integer|)) "Returns the class number of the curve.")) (|LPolynomial| (((|SparseUnivariatePolynomial| (|Integer|)) (|PositiveInteger|)) "\\spad{LPolynomial(d)} returns the L-Polynomial of the curve in constant field extension of degree \\spad{d.}") (((|SparseUnivariatePolynomial| (|Integer|))) "Returns the L-Polynomial of the curve.")) (|adjunctionDivisor| (((|Divisor| (|Places| |#1|))) "\\spad{adjunctionDivisor computes} the adjunction divisor of the plane curve given by the polynomial set with the function setCurve.")) (|intersectionDivisor| (((|Divisor| (|Places| |#1|)) (|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{intersectionDivisor(pol)} compute the intersection divisor (the Cartier divisor) of the form \\spad{pol} with the curve. If some intersection points lie in an extension of the ground field, an error message is issued specifying the extension degree needed to find all the intersection points. (If \\spad{pol} is not homogeneous an error message is issued).")) (|evalIfCan| (((|Union| |#1| "failed") (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) "\\spad{evalIfCan(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{evalIfCan(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl} (returns \"failed\" if it is a pole).") (((|Union| |#1| "failed") (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{evalIfCan(f,pl)} evaluate \\spad{f} at the place \\spad{pl} (returns \"failed\" if it is a pole).")) (|eval| ((|#1| (|Fraction| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Places| |#1|)) "\\spad{eval(u,pl)} evaluate the function \\spad{u} at the place \\spad{pl.}") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{eval(f,g,pl)} evaluate the function \\spad{f/g} at the place \\spad{pl.}") ((|#1| (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{eval(f,pl)} evaluate \\spad{f} at the place \\spad{pl.}")) (|interpolateForms| (((|List| (|DistributedMultivariatePolynomial| |#2| |#1|)) (|Divisor| (|Places| |#1|)) (|NonNegativeInteger|)) "\\spad{interpolateForms(d,n)} returns a basis of the interpolate forms of degree \\spad{n} of the divisor \\spad{d.}")) (|lBasis| (((|Record| (|:| |num| (|List| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|:| |den| (|DistributedMultivariatePolynomial| |#2| |#1|))) (|Divisor| (|Places| |#1|))) "\\spad{lBasis computes} a basis associated to the specified divisor")) (|parametrize| (((|NeitherSparseOrDensePowerSeries| |#1|) (|DistributedMultivariatePolynomial| |#2| |#1|) (|Places| |#1|)) "\\spad{parametrize(f,pl)} returns a local parametrization of \\spad{f} at the place \\spad{pl.}")) (|singularPoints| (((|List| (|ProjectivePlane| |#1|))) "rationalPoints() returns the singular points of the curve defined by the polynomial given to the package. If the singular points lie in an extension of the specified ground field an error message is issued specifying the extension degree needed to find all singular points.")) (|desingTree| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) "\\spad{desingTree returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package.")) (|desingTreeWoFullParam| (((|List| (|DesingTree| (|InfClsPt| |#1| |#2| |#3|)))) "\\spad{desingTreeWoFullParam returns} the desingularisation trees at all singular points of the curve defined by the polynomial given to the package. The local parametrizations are not computed.")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus returns} the genus of the curve defined by the polynomial given to the package.")) (|theCurve| (((|DistributedMultivariatePolynomial| |#2| |#1|)) "\\spad{theCurve returns} the specified polynomial for the package.")) (|rationalPlaces| (((|List| (|Places| |#1|))) "\\spad{rationalPlaces returns} all the rational places of the curve defined by the polynomial given to the package.")) (|pointDominateBy| (((|ProjectivePlane| |#1|) (|Places| |#1|)) "\\spad{pointDominateBy(pl)} returns the projective point dominated by the place \\spad{pl.}"))) NIL -((|HasCategory| |#1| (QUOTE (-373)))) -(-874) +((|HasCategory| |#1| (QUOTE (-374)))) +(-875) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c.}")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p.}")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p.}")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue, \\spad{c,} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue, \\spad{c,} above bright, but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue, \\spad{c,} above dim, but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue, \\spad{c,} above dark, but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) NIL NIL -(-875) +(-876) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf}, a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-876 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) +(-877 K |symb| |PolyRing| E |ProjPt| PCS |Plc|) ((|constructor| (NIL "The following is part of the PAFF package")) (|parametrize| ((|#6| |#3| |#7| (|Integer|)) "\\spad{parametrize(f,pl,n)} returns t**n * parametrize(f,p).") ((|#6| |#3| |#3| |#7|) "\\spad{parametrize(f,g,pl)} returns the local parametrization of the rational function \\spad{f/g} at the place \\spad{pl.} Note that local parametrization of the place must have first been compute and set. For simple point on a curve, this done with \\spad{pointToPlace}. The local parametrization places corresponding to a leaf in a desingularization tree are compute at the moment of their \"creation\". (See package \\spad{DesingTreePackage}.") ((|#6| |#3| |#7|) "\\spad{parametrize(f,pl)} returns the local parametrization of the polynomial function \\spad{f} at the place \\spad{pl.} Note that local parametrization of the place must have first been compute and set. For simple point on a curve, this done with \\spad{pointToPlace}. The local parametrization places corresponding to a leaf in a desingularization tree are compute at the moment of their \"creation\". (See package \\spad{DesingTreePackage}."))) NIL NIL -(-877 CF1 CF2) +(-878 CF1 CF2) ((|constructor| (NIL "This package has no description")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-878 |ComponentFunction|) +(-879 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to i. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-879 CF1 CF2) +(-880 CF1 CF2) ((|constructor| (NIL "This package has no description")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-880 |ComponentFunction|) +(-881 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to i. This indicates what the function for the coordinate component, i, of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1}, \\spad{c2}, and \\spad{c3}."))) NIL NIL -(-881 CF1 CF2) +(-882 CF1 CF2) ((|constructor| (NIL "This package has no description")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-882 |ComponentFunction|) +(-883 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to i. This indicates what the function for the coordinate component, i, of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1}, \\spad{c2}, and \\spad{c3}."))) NIL NIL -(-883) +(-884) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions, and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,\\spad{l1} 1's,\\spad{l2} 2's,...,\\spad{ln} n's.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and l2.} \\indented{1}{For example,the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2}, 2 \\spad{3}'s, and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(l,u) on to all \\indented{1}{members \\spad{u} of \\spad{st,} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2,} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and l2.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions lp.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt.}")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l.}}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n.}") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,l,n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l.}}"))) NIL NIL -(-884 R) +(-885 R) ((|constructor| (NIL "Category of sets that can be converted to useful patterns An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-885 R S L) +(-886 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match, or a pair of PatternMatchResult, one for atoms (elements of the list), and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [r1,r2].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-886 S) +(-887 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S.}")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression expr. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially, res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-887 |Base| |Subject| |Pat|) +(-888 |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 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 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 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 -1043) (QUOTE (-1169)))) (-12 (-2931 (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169))))) (-2931 (|HasCategory| |#2| (QUOTE (-1053))))) (-12 (|HasCategory| |#2| (QUOTE (-1053))) (-2931 (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169))))))) -(-888 R A B) +((|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170)))) (-12 (-2959 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170))))) (-2959 (|HasCategory| |#2| (QUOTE (-1054))))) (-12 (|HasCategory| |#2| (QUOTE (-1054))) (-2959 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170))))))) +(-889 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 [(v1,f(a1)),...,(vn,f(an))]."))) NIL NIL -(-889 R S) +(-890 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match, or a list of matches of the form (var, expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, \\spad{p)}} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p,} \\spad{false} if they don'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 (v1,e1),...,(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, \\spad{r,} val)} adds the match (var, expr) in \\spad{r,} provided that \\spad{expr} satisfies the predicates attached to 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| $) "\\spad{insertMatch(var, expr, \\spad{r)}} adds the match (var, expr) in \\spad{r,} without checking predicates or previous matches for var.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, \\spad{r)}} adds the match (var, expr) in \\spad{r,} provided that \\spad{expr} satisfies the predicates attached to var, and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, \\spad{r)}} returns the expression that \\spad{var} matches in the result \\spad{r,} and \"failed\" if \\spad{var} is not matched in \\spad{r.}")) (|union| (($ $ $) "\\spad{union(a, \\spad{b)}} makes the set-union of two match results.")) (|new| (($) "\\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 -(-890 R -1544) +(-891 R -1557) ((|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, \\spad{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], \\spad{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, \\spad{p)}} returns f(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], \\spad{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 \\spad{...} and \\spad{fn} to the copy, which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, \\spad{f)}} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy, which is returned."))) NIL NIL -(-891 R S) +(-892 R S) ((|constructor| (NIL "Lifts maps to patterns")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, \\spad{p)}} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S.}"))) NIL NIL -(-892 R) +(-893 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, \\spad{b]}} and a is optional, and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p.}")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p.} Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, \\spad{v)}} adds \\spad{v} to the list of \"bad values\" for \\spad{p.} Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], \\spad{f]}} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], \\spad{f)}} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, \\spad{c?,} o?, m?)} creates a pattern variable \\spad{x,} which is constant if \\spad{c? = true}, optional if \\spad{o? = true}, and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and \\spad{...} and \\spad{pn} to the copy, which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and \\spad{...} and \\spad{pn} to \\spad{p.}")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and \\spad{...} and \\spad{pn.}")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s.}")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R).}")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p.}")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p.}")) (/ (($ $ $) "\\spad{a / \\spad{b}} returns the pattern \\spad{a / \\spad{b}.}")) (** (($ $ $) "\\spad{a \\spad{**} \\spad{b}} returns the pattern \\spad{a \\spad{**} \\spad{b}.}") (($ $ (|NonNegativeInteger|)) "\\spad{a \\spad{**} \\spad{n}} returns the pattern \\spad{a \\spad{**} \\spad{n}.}")) (* (($ $ $) "\\spad{a * \\spad{b}} returns the pattern \\spad{a * \\spad{b}.}")) (+ (($ $ $) "\\spad{a + \\spad{b}} returns the pattern \\spad{a + \\spad{b}.}")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, \\spad{b]}} if \\spad{p = a \\spad{**} \\spad{b},} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]}, \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, \\spad{b]}} if \\spad{p = a / \\spad{b},} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, \\spad{n]}} if \\spad{n > 0} and \\spad{p = \\spad{q} \\spad{**} \\spad{n},} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)}, and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)}, and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = \\spad{a1} * \\spad{...} * an}, and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = \\spad{a1} + \\spad{...} + an},} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-893 |VarSet|) +(-894 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C.} Reutenauer (Oxford science publications).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|listOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{listOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, \\spad{l2,} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln}, where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-894 UP R) +(-895 UP R) ((|constructor| (NIL "Polynomial composition and decomposition functions\\br If \\spad{f} = \\spad{g} \\spad{o} \\spad{h} then g=leftFactor(f,h) and h=rightFactor(f,g)")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-895) +(-896) ((|constructor| (NIL "\\axiomType{PartialDifferentialEquationsSolverCategory} is the \\axiom{category} for describing the set of PDE solver \\axiom{domains} with \\axiomFun{measure} and \\axiomFun{PDEsolve}.")) (|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter, labelled \\axiom{sofar}, which would contain the best compatibility found so far."))) NIL NIL -(-896 UP -3280) +(-897 UP -3313) ((|constructor| (NIL "Polynomial composition and decomposition functions\\br If \\spad{f} = \\spad{g} \\spad{o} \\spad{h} then g=leftFactor(f,h) and h=rightFactor(f,g)")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL -(-897) +(-898) ((|constructor| (NIL "AnnaPartialDifferentialEquationPackage is an uncompleted package for the interface to NAG PDE routines. It has been realised that a new approach to solving PDEs will need to be created.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{prob}. \\blankline It calls each \\axiom{domain} listed in \\axiom{R} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{prob}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{pde}), a grid (\\axiom{xmin}, \\axiom{ymin}, \\axiom{xmax}, \\axiom{ymax}, \\axiom{ngx}, \\axiom{ngy}) and the boundary values (\\axiom{bounds}). A default value for tolerance is used. There is also a parameter (\\axiom{st}) which should contain the value \"elliptic\" if the PDE is known to be elliptic, or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment, only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{pde}), a grid (\\axiom{xmin}, \\axiom{ymin}, \\axiom{xmax}, \\axiom{ymax}, \\axiom{ngx}, \\axiom{ngy}), the boundary values (\\axiom{bounds}) and a tolerance requirement (\\axiom{tol}). There is also a parameter (\\axiom{st}) which should contain the value \"elliptic\" if the PDE is known to be elliptic, or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment, only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment, only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment, only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-898) +(-899) ((|constructor| (NIL "\\axiomType{NumericalPDEProblem} is a \\axiom{domain} for the representation of Numerical PDE problems for use by ANNA. \\blankline The representation is of type: \\blankline \\axiomType{Record}(pde:\\axiomType{List Expression DoubleFloat}, \\spad{\\br} constraints:\\axiomType{List PDEC}, \\spad{\\br} f:\\axiomType{List List Expression DoubleFloat},\\br st:\\axiomType{String},\\br tol:\\axiomType{DoubleFloat}) \\blankline where \\axiomType{PDEC} is of type: \\blankline \\axiomType{Record}(start:\\axiomType{DoubleFloat}, \\spad{\\br} finish:\\axiomType{DoubleFloat},\\br grid:\\axiomType{NonNegativeInteger},\\br boundaryType:\\axiomType{Integer},\\br dStart:\\axiomType{Matrix DoubleFloat}, \\spad{\\br} dFinish:\\axiomType{Matrix DoubleFloat})")) (|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} is not documented")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} is not documented") (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} is not documented"))) NIL NIL -(-899 A S) +(-900 A S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S.} \\blankline Axioms\\br \\tab{5}\\spad{differentiate(x+y,e)=differentiate(x,e)+differentiate(y,e)}\\br \\tab{5}\\spad{differentiate(x*y,e)=x*differentiate(y,e)+differentiate(x,e)*y}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives, that is, \\spad{D(...D(x, \\spad{s1,} n1)..., \\spad{sn,} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x, \\spad{s,} \\spad{n)}} computes multiple partial derivatives, that is, \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s.}") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives, that is, \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#2|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v.}")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives, that is, \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x, \\spad{s,} \\spad{n)}} computes multiple partial derivatives, that is, \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s.}") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives, that is, \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v.}"))) NIL NIL -(-900 S) +(-901 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S.} \\blankline Axioms\\br \\tab{5}\\spad{differentiate(x+y,e)=differentiate(x,e)+differentiate(y,e)}\\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, that is, \\spad{D(...D(x, \\spad{s1,} n1)..., \\spad{sn,} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, \\spad{s,} \\spad{n)}} computes multiple partial derivatives, that is, \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s.}") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives, that is, \\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, that is, \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x, \\spad{s,} \\spad{n)}} computes multiple partial derivatives, that is, \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s.}") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives, that is, \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v.}"))) -((-4597 . T)) +((-4599 . T)) NIL -(-901 S) +(-902 S) ((|constructor| (NIL "A PendantTree(S) is either a leaf? and is an \\spad{S} or has a left and a right both PendantTree(S)'s")) (|coerce| (((|Tree| |#1|) $) "\\indented{1}{coerce(x) is not documented} \\blankline \\spad{X} t1:=ptree([1,2,3]) \\spad{X} t2:=ptree(t1,ptree([1,2,3])) \\spad{X} t2::Tree List PositiveInteger")) (|ptree| (($ $ $) "\\indented{1}{ptree(x,y) is not documented} \\blankline \\spad{X} t1:=ptree([1,2,3]) \\spad{X} ptree(t1,ptree([1,2,3]))") (($ |#1|) "\\indented{1}{ptree(s) is a leaf? pendant tree} \\blankline \\spad{X} t1:=ptree([1,2,3])"))) NIL -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-902 |n| R) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-903 |n| R) ((|constructor| (NIL "Permanent implements the functions permanent, the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x.} The permanent is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the determinant. The formula used is by H.J. Ryser, improved by [Nijenhuis and Wilf, \\spad{Ch.} 19]. Note that permanent(x) choose one of three algorithms, depending on the underlying ring \\spad{R} and on \\spad{n,} the number of rows (and columns) of x:\\br if 2 has an inverse in \\spad{R} we can use the algorithm of [Nijenhuis and Wilf, ch.19,p.158]; if 2 has no inverse, some modifications are necessary:\\br if \\spad{n} > 6 and \\spad{R} is an integral domain with characteristic different from 2 (the algorithm works if and only 2 is not a zero-divisor of \\spad{R} and characteristic()$R \\spad{^=} 2, but how to check that for any given \\spad{R} \\spad{?),} the local function \\spad{permanent2} is called;\\br else, the local function \\spad{permanent3} is called (works for all commutative rings \\spad{R).}"))) NIL NIL -(-903 S) +(-904 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment for subgroups of bijections of a set (that is, permutations)")) (< (((|Boolean|) $ $) "\\spad{p < \\spad{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,} that is, 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 ls.i to ls.i+1, indices modulo the length of the list, then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle \\spad{ls,} that is, a list with not repetitions to a permutation, which maps ls.i to ls.i+1, indices modulo the length of the list. Error: if repetitions occur."))) -((-4597 . T)) +((-4599 . T)) NIL -(-904 S) +(-905 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 Axiom 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: \\spad{(1)} with a small integer you get shorter words, but the routine takes longer than the standard routine for longer words. \\spad{(2)} be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). \\spad{(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(gp,0,1). Notes: \\spad{(1)} be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) \\spad{(2)} users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 \\spad{<=} gp2} returns \\spad{true} if and only if \\spad{gp1} is a subgroup of gp2. Note: because of a bug in the parser you have to call this function explicitly by \\spad{gp1} <=$(PERMGRP \\spad{S)} gp2.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if \\spad{gp1} is a proper subgroup of 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 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(gp)=random(gp,20).") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group \\spad{gp.}")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group \\spad{gp.}")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group \\spad{gp.}")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations \\spad{ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group \\spad{gp.}"))) NIL NIL -(-905 S) +(-906 S) ((|constructor| (NIL "Permutation(S) implements the group of all bijections on a set \\spad{S,} which move only a finite number of points. A permutation is considered as a map from \\spad{S} into \\spad{S.} In particular multiplication is defined as composition of maps:\\br \\spad{pi1} * \\spad{pi2} = \\spad{pi1} \\spad{o} pi2.\\br The internal representation of permuatations are two lists of equal length representing preimages and images.")) (|coerceImages| (($ (|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,...,n]. Note: {coerceImages(ls)=coercePreimagesImages([1,...,n],ls)}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\indented{1}{fixedPoints(p) returns the points fixed by the permutation \\spad{p.}} \\spad{X} \\spad{p} \\spad{:=} coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$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(p) is \\spad{-1.}")) (|even?| (((|Boolean|) $) "\\indented{1}{even?(p) returns \\spad{true} if and only if \\spad{p} is an even permutation,} \\indented{1}{\\spadignore{i.e.} sign(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(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(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 ls.i to ls.i+1, indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles \\spad{lls} to a permutation, each cycle being a list with no repetitions, is coerced to the permutation, which maps ls.i to ls.i+1, indices modulo the length of the list, then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\indented{1}{coercePreimagesImages(lls) coerces the representation 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, i.e \\spad{p} maps (rep.preimage).k to (rep.image).k for all indices \\spad{k.} Elements of \\spad{S} not in (rep.preimage).k are fixed points, and these are the only fixed points of the permutation."))) -((-4597 . T)) -((|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-847))))) -(-906 R E |VarSet| S) +((-4599 . T)) +((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-848))))) +(-907 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(R,E,VarSet,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 = \\spad{p} / prod pi}, a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists, then \"failed\" is returned."))) NIL NIL -(-907 R S) +(-908 R S) ((|constructor| (NIL "PolynomialFactorizationByRecursionUnivariate \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain, \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S,} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p.} This functions performs the recursion step for factorSquareFreePolynomial, as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p.} This function performs the recursion step for factorPolynomial, as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = \\spad{p} / prod pi}, a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists, then \"failed\" is returned."))) NIL NIL -(-908 S) +(-909 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields, it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}-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}-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], \\spad{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 ai's exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q.}")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p.}")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p.}"))) NIL ((|HasCategory| |#1| (QUOTE (-149)))) -(-909) +(-910) ((|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}-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}-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], \\spad{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 ai'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.}"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-910 |p|) +(-911 |p|) ((|constructor| (NIL "PrimeField(p) implements the field with \\spad{p} elements if \\spad{p} is a prime number."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| $ (QUOTE (-151))) (|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-373)))) -(-911 R0 -3280 UP UPUP R) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| $ (QUOTE (-151))) (|HasCategory| $ (QUOTE (-149))) (|HasCategory| $ (QUOTE (-374)))) +(-912 R0 -3313 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-912 UP UPUP R) +(-913 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-913 R |PolyRing| E -3020) +(-914 R |PolyRing| E -3465) ((|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, x->x+a, y->y+b, z->z+c") ((|#2| |#2| (|List| |#1|) (|Integer|)) "\\spad{translate(pol,[a,b,c],3)} apply to \\spad{pol} the linear change of coordinates, x->x+a, y->y+b, z->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 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 pol."))) NIL NIL -(-914 UP UPUP) +(-915 UP UPUP) ((|constructor| (NIL "Utilities for PFOQ and PFO")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime \\spad{n}} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-915 R) +(-916 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'' form has only one fractional term per prime in the denominator, while the ``p-adic'' form expands each numerator p-adically via the prime \\spad{p} in the denominator. For computational efficiency, the compact form is used, though the 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| $) "\\indented{1}{wholePart(p) extracts the whole part of the partial fraction} \\indented{1}{\\spad{p}.} \\blankline \\spad{X} a:=(74/13)::PFR(INT) \\spad{X} wholePart(a)")) (|partialFraction| (($ |#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(q) expands the fraction 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} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\indented{1}{numberOfFractionalTerms(p) computes the number of fractional} \\indented{1}{terms in \\spad{p}. This returns 0 if there is no fractional} \\indented{1}{part.} \\blankline \\spad{X} a:=partialFraction(1,factorial 10) \\spad{X} b:=padicFraction(a) \\spad{X} numberOfFractionalTerms(b)")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\indented{1}{nthFractionalTerm(p,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(b,3)")) (|firstNumer| ((|#1| $) "\\indented{1}{firstNumer(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|) $) "\\indented{1}{firstDenom(p) extracts the denominator of the first fractional} \\indented{1}{term. This returns 1 if there is no fractional part (use} \\indented{1}{wholePart from PartialFraction to get the whole part).} \\blankline \\spad{X} a:=partialFraction(1,factorial 10) \\spad{X} firstDenom(a)")) (|compactFraction| (($ $) "\\indented{1}{compactFraction(p) normalizes the partial fraction \\spad{p}} \\indented{1}{to the compact representation. In this form, the partial} \\indented{1}{fraction has only one fractional term per prime in the} \\indented{1}{denominator.} \\blankline \\spad{X} a:=partialFraction(1,factorial 10) \\spad{X} b:=padicFraction(a) \\spad{X} compactFraction(b)")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\indented{1}{coerce(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|) $) "\\indented{1}{coerce(p) sums up the components of the partial fraction and} \\indented{1}{returns a single fraction.} \\blankline \\spad{X} a:=(13/74)::PFR(INT) \\spad{X} a::FRAC(INT)"))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-916 R) +(-917 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials, and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{partialFraction(rf, var) returns the partial fraction decomposition} \\indented{1}{of the rational function \\spad{rf} with respect to the variable var.} \\blankline \\spad{X} a:=x+1/(y+1) \\spad{X} partialFraction(a,y)$PFRPAC(INT)"))) NIL NIL -(-917 E OV R P) +(-918 E OV R P) ((|constructor| (NIL "This package computes multivariate polynomial gcd's using a hensel lifting strategy. The contraint on the coefficient domain is imposed by the lifting strategy. It is assumed that the coefficient domain has the property that almost all specializations preserve the degree of the gcd.")) (|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive \\spad{lp}} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp.}") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q.}") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q.}")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp.}") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q.}") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp.}") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q.}"))) NIL NIL -(-918) +(-919) ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric, alternating, dihedral, cyclic, direct products of cyclic, which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore, Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition lambda.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups Sn1,...,Snk.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6, 1 \\spad{<=} \\spad{j} \\spad{<=} 8. The faces of Rubik's Cube are labelled in the obvious way Front, Right, Up, Down, Left, Back and numbered from 1 to 6 in this given ordering, the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces, represented as a two digit integer ij where \\spad{i} is the numer of theface \\spad{(1} to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators, which represent a 90 degree turns of the faces, or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6, 1 \\spad{<=} \\spad{j} <=8. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,...,100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list li. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,...,24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list li. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,...,23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list li. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,...,22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list li. Note that duplicates in the list will be removed. Error: if \\spad{li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,...,12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list li. Note that duplicates in the list will be removed Error: if \\spad{li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,...,11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list li. Note that duplicates in the list will be removed. error, if \\spad{li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of i1,...,ik. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,...,N.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers i1,...,ik. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,...,n.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order ni.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list li, generators are in general the n-2-cycle (li.3,...,li.n) and the 3-cycle (li.1,li.2,li.3), if \\spad{n} is odd and product of the 2-cycle (li.1,li.2) with n-2-cycle (li.3,...,li.n) and the 3-cycle (li.1,li.2,li.3), if \\spad{n} is even. Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group An acting on the integers 1,...,n, generators are in general the n-2-cycle (3,...,n) and the 3-cycle (1,2,3) if \\spad{n} is odd and the product of the 2-cycle (1,2) with n-2-cycle (3,...,n) and the 3-cycle (1,2,3) if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list li, generators are the cycle given by \\spad{li} and the 2-cycle (li.1,li.2). Note that duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group \\spad{Sn} acting on the integers 1,...,n, generators are the n-cycle (1,...,n) and the 2-cycle (1,2)."))) NIL NIL -(-919 -3280) +(-920 -3313) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} This package is an interface package to the groebner basis package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain, but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv.}")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv.}"))) NIL NIL -(-920 R) +(-921 R) ((|constructor| (NIL "Provides a coercion from the symbolic fractions in \\%pi with integer coefficients to any Expression type.")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(R)."))) NIL NIL -(-921) +(-922) ((|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 fi.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-922) +(-923) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for positive integers.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b.}"))) -(((-4602 "*") . T)) +(((-4604 "*") . T)) NIL -(-923 -3280 P) +(-924 -3313 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-924 |xx| -3280) +(-925 |xx| -3313) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL -(-925 K PCS) +(-926 K PCS) ((|constructor| (NIL "This is part of the PAFF package, related to projective space.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates if the places correspnd to a simple point")) (|setFoundPlacesToEmpty| (((|List| $)) "\\spad{setFoundPlacesToEmpty()} does what it says. (this should not be used)!!!")) (|foundPlaces| (((|List| $)) "\\spad{foundPlaces()} returns the list of all \"created\" places up to now.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(pl)} test if the place \\spad{pl} correspond to a leaf of a desingularisation tree.")) (|setDegree!| (((|Void|) $ (|PositiveInteger|)) "\\spad{setDegree!(pl,ls)} set the degree.")) (|setParam!| (((|Void|) $ (|List| |#2|)) "\\spad{setParam!(pl,ls)} set the local parametrization of \\spad{pl} to \\spad{ls.}")) (|localParam| (((|List| |#2|) $) "\\spad{localParam(pl)} returns the local parametrization associated to the place \\spad{pl.}"))) NIL NIL -(-926 K) +(-927 K) ((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-927 K) +(-928 K) ((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-928 K PCS) +(-929 K PCS) ((|constructor| (NIL "The following is part of the PAFF package"))) NIL NIL -(-929 R |Var| |Expon| GR) +(-930 R |Var| |Expon| GR) ((|constructor| (NIL "This package completely solves a parametric linear system of equations by decomposing the set of all parametric values for which the linear system is consistent into a union of quasi-algebraic sets (which need not be irredundant, but most of the time is). Each quasi-algebraic set is described by a list of polynomials that vanish on the set, and a list of polynomials that vanish at no point of the set. For each quasi-algebraic set, the solution of the linear system is given, as a particular solution and a basis of the homogeneous system. \\blankline The parametric linear system should be given in matrix form, with a coefficient matrix and a right hand side vector. The entries of the coefficient matrix and right hand side vector should be polynomials in the parametric variables, over a Euclidean domain of characteristic zero. \\blankline If the system is homogeneous, the right hand side need not be given. The right hand side can also be replaced by an indeterminate vector, in which case, the conditions required for consistency will also be given. \\blankline The package has other facilities for saving results to external files, as well as solving the system for a specified minimum rank. Altogether there are 12 mode maps for psolve, as explained below.")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, \\spad{w,} \\spad{p,} \\spad{r,} \\spad{rm,} \\spad{m)}} returns a regime, a list of polynomials specifying the consistency conditions, a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant y.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm.} The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants, and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous, or the right hand side is arbitrary, or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl;} otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of k-subsets of \\spad{{1,} ..., \\spad{n}.}")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p.}")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (s.mat) \\spad{z} = s.vec for the variables given by the column indices of s.cols in terms of the other variables and the right hand side s.vec by assuming that the rank is s.rank, that the system is consistent, with the linearly independent equations indexed by the given row indices s.rows; the coefficients in s.mat involving parameters are treated as polynomials. B1solve(s) returns a particular solution to the system and a basis of the homogeneous system (s.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, \\spad{l)}} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, \\spad{w,} \\spad{r,} \\spad{s,} \\spad{m)}} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r;} depending on the mode \\spad{m} chosen, it writes the output to a file given by the string \\spad{s.}")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w,} writes the results to a file named \\spad{s,} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-930 S) +(-931 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)}, \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-931) +(-932) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example, floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(false) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(false) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to i.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to i.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to i.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed, one list for each curve in the plot \\spad{p.}")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p.}")) (|refine| (($ $) "\\spad{refine(x)} is not documented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} is not documented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} is not documented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = f(t), \\spad{y} = g(t), \\spad{z} = h(t)} as \\spad{t} ranges over {/em[a,b]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} is not documented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = f(t), \\spad{y} = g(t), \\spad{z} = h(t)} as \\spad{t} ranges over {/em[a,b]}."))) NIL NIL -(-932) +(-933) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} is not documented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} is not documented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} is not documented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t)*cos(t)}, \\spad{y = f(t)*sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t)*cos(t)}, \\spad{y = f(t)*sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t \\spad{+->} (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; x-range of \\spad{[c,d]} and y-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t \\spad{+->} (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} is not documented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; x-range of \\spad{[c,d]} and y-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)}, \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},..., \\spad{y = fm(x)} on the interval \\spad{a..b}; y-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},..., \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; y-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\indented{1}{plot(f,a..b) plots the function \\spad{f(x)}} \\indented{1}{on the interval \\spad{[a,b]}.} \\blankline \\spad{X} fp:=(t:DFLOAT):DFLOAT \\spad{+->} sin(t) \\spad{X} plot(fp,-1.0..1.0)$PLOT"))) NIL NIL -(-933) +(-934) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-934 K |PolyRing| E -3020 |ProjPt|) +(-935 K |PolyRing| E -3465 |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 -(-935 R -3280) +(-936 R -3313) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching.")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists, multiple(x) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity \\spad{(0} in a sum, 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x, \\spad{s)}} makes the assertion \\spad{s} about \\spad{x.} Error: if \\spad{x} is not a symbol."))) NIL NIL -(-936) +(-937) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching.")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists, multiple(x) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity \\spad{(0} in a sum, 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x, \\spad{s)}} makes the assertion \\spad{s} about \\spad{x.}"))) NIL NIL -(-937 S A B) +(-938 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression expr; res contains the variables of \\spad{pat} which are already matched and their matches. Note that this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by g(a) = f(a::B)."))) NIL NIL -(-938 S R -3280) +(-939 S R -3313) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression expr; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-939 I) +(-940 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n;} res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-940 S E) +(-941 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-941 S R L) +(-942 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l;} res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-942 S E V R P) +(-943 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p;} res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p.} \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -886) (|devaluate| |#1|)))) -(-943 R -3280 -1544) +((|HasCategory| |#3| (LIST (QUOTE -887) (|devaluate| |#1|)))) +(-944 R -3313 -1557) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching.")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, \\spad{f2,} ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and \\spad{...} 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 -(-944 -1544) +(-945 -1557) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching.")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, \\spad{f2,} ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and \\spad{...} 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 -(-945 S R Q) +(-946 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient a/b; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-946 S) +(-947 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression expr; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-947 S R P) +(-948 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P.}")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects lsubj, allowing for commutativity; \\spad{op} is the operator such that op(lpat) should match op(lsubj) at the end, \\spad{r} contains the previous matches, and match is a pattern-matching function on \\spad{P.}"))) NIL NIL -(-948) +(-949) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note that Legendre polynomials, denoted \\spad{P[n](x)}, are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note that Laguerre polynomials, denoted \\spad{L[n](x)}, are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note that Hermite polynomials, denoted \\spad{H[n](x)}, are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k.} Note that fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for \\spad{k} in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note that Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = \\spad{n} E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note that \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note that Chebyshev polynomials of the second kind, denoted \\spad{U[n](x)}, computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note that Chebyshev polynomials of the first kind, denoted \\spad{T[n](x)}, computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = \\spad{n} B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-949 R) +(-950 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-950 |lv| R) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1009))) (|HasCategory| |#1| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-951 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-951 |TheField| |ThePols|) +(-952 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(l,s1,sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn.")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(l)} is the number of sign variations in the list of numbers \\spad{l,} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(p)} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(p) = sylvesterSequence(p,p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(p,q)} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-845)))) -(-952 R S) +((|HasCategory| |#1| (QUOTE (-846)))) +(-953 R S) ((|constructor| (NIL "This package takes a mapping between coefficient rings, and lifts it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, \\spad{p)}} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p.}"))) NIL NIL -(-953 |x| R) +(-954 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, \\spad{x)}} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))}, ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-954 S R E |VarSet|) +(-955 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, \\spad{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 = \\spad{a1} \\spad{...} an} and \\spad{n \\spad{>=} 2}, and, for each 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") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = \\spad{m1} + \\spad{...} + \\spad{mn}} and \\spad{n \\spad{>=} 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|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, \\spad{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 \\spad{**} 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 (-909))) (|HasAttribute| |#2| (QUOTE -4598)) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-847)))) -(-955 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-910))) (|HasAttribute| |#2| (QUOTE -4600)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#4| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#4| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#4| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-848)))) +(-956 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, \\spad{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 = \\spad{a1} \\spad{...} an} and \\spad{n \\spad{>=} 2}, and, for each 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") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = \\spad{m1} + \\spad{...} + \\spad{mn}} and \\spad{n \\spad{>=} 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|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, \\spad{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 \\spad{**} 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.}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-956 E V R P -3280) +(-957 E V R P -3313) ((|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, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0}, \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, \\spad{n]}} if \\spad{p = x**n} and \\spad{n \\spad{<>} 0}, \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = \\spad{a1} \\spad{...} an} and \\spad{n > 1}, \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [m1,...,mn] if \\spad{p = \\spad{m1} + \\spad{...} + \\spad{mn}} and \\spad{n > 1}, \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, \\spad{v)}} applies both the numerator and denominator of \\spad{f} to \\spad{v.}")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, \\spad{x,} \\spad{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, \\spad{v)}} returns \\spad{f} viewed as a univariate rational function in \\spad{v.}")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f,} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f.}"))) NIL NIL -(-957 E |Vars| R P S) +(-958 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function, which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S,} maps polynomials into \\spad{S.} \\spad{S} is assumed to support \\spad{+}, \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, \\spad{p)}} takes a varmap, a mapping from the variables of polynomial \\spad{p} into \\spad{S,} coefmap, a mapping from coefficients of \\spad{p} into \\spad{S,} and \\spad{p,} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-958 R) +(-959 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.}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1169) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-959 E V R P -3280) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-960 E V R P -3313) ((|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, \\spad{n)}} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = \\spad{c} * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, \\spad{n)}} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = \\spad{c} * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, \\spad{n)}} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = \\spad{c} * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL -((|HasCategory| |#3| (QUOTE (-456)))) -(-960) +((|HasCategory| |#3| (QUOTE (-457)))) +(-961) ((|constructor| (NIL "This is a low-level package which implements operations on vectors treated as univariate modular polynomials. Most operations takes modulus as parameter. Modulus is machine sized prime which should be small enough to avoid overflow in intermediate calculations.")) (|resultant| (((|Integer|) (|U32Vector|) (|U32Vector|) (|Integer|)) "\\spad{resultant(v1, \\spad{v2,} \\spad{p)}} computes resultant of \\spad{v1} and \\spad{v2} modulo \\spad{p.}")) (|extendedgcd| (((|List| (|U32Vector|)) (|U32Vector|) (|U32Vector|) (|Integer|)) "extended_gcd(v1, \\spad{v2,} \\spad{p)} gives \\spad{[g,} \\spad{c1,} \\spad{c2]} such that \\spad{g} is \\spad{gcd(v1, \\spad{v2,} p)}, \\spad{g = \\spad{c1*v1} + c2*v2} and degree(c1) < max(degree(v2) - degree(g), 0) and degree(c2) < max(degree(v1) - degree(g), 1)")) (|degree| (((|Integer|) (|U32Vector|)) "\\spad{degree(v)} is degree of \\spad{v} treated as polynomial")) (|lcm| (((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{lcm(a, lo, hi, \\spad{p)}} computes \\spad{lcm} of elements a(lo), a(lo+1), ..., a(hi).")) (|gcd| (((|U32Vector|) (|PrimitiveArray| (|U32Vector|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{gcd(a, lo, hi, \\spad{p)}} computes \\spad{gcd} of elements a(lo), a(lo+1), ..., a(hi).") (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) "\\spad{gcd(v1, \\spad{v2,} \\spad{p)}} computes monic \\spad{gcd} of \\spad{v1} and \\spad{v2} modulo \\spad{p.}")) (|tomodpa| (((|U32Vector|) (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "to_mod_pa(s, \\spad{p)} reduces coefficients of polynomial \\spad{s} modulo prime \\spad{p} and converts the result to vector")) (|vectorcombination| (((|Void|) (|U32Vector|) (|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "vector_combination(v1, \\spad{c1,} \\spad{v2,} \\spad{c2,} \\spad{n,} delta, \\spad{p)} replaces first \\spad{n} + 1 entires of \\spad{v1} by corresponding entries of \\spad{c1*v1+c2*x^delta*v2} mod \\spad{p.}")) (|remainder!| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|)) "Polynomial remainder")) (|divide!| (((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) "Polynomial division.")) (|differentiate| (((|U32Vector|) (|U32Vector|) (|NonNegativeInteger|) (|Integer|)) "Polynomial differentiation.") (((|U32Vector|) (|U32Vector|) (|Integer|)) "Polynomial differentiation.")) (|pow| (((|U32Vector|) (|U32Vector|) (|PositiveInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{pow(u, \\spad{n,} \\spad{d,} \\spad{p)}} returns u^n truncated after degree \\spad{d,} except if n=1, in which case \\spad{u} itself is returned")) (|truncatedmuladd| (((|Void|) (|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) "truncated_mul_add(x, \\spad{y,} \\spad{z,} \\spad{d,} \\spad{p)} adds to \\spad{z} the produce x*y truncated after degree \\spad{d}")) (|truncatedmultiplication| (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) "truncated_multiplication(x, \\spad{y,} \\spad{d,} \\spad{p)} computes x*y truncated after degree \\spad{d}")) (|mul| (((|U32Vector|) (|U32Vector|) (|U32Vector|) (|Integer|)) "Polynomial multiplication.")) (|mulbyscalar| (((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) "mul_by_scalar(v, deg, \\spad{c,} \\spad{p)} treats \\spad{v} as coefficients of polynomial of degree deg and multiplies in place this polynomial by scalar \\spad{c}")) (|mulbybinomial| (((|Void|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) "mul_by_binomial(v, deg, \\spad{pt,} \\spad{p)} treats \\spad{v} as coefficients of polynomial of degree deg and multiplies in place this polynomial by binomial \\spad{(x} + pt). Highest coefficient of product is ignored.") (((|Void|) (|U32Vector|) (|Integer|) (|Integer|)) "mul_by_binomial(v, \\spad{pt,} \\spad{p)} treats \\spad{v} a polynomial and multiplies in place this polynomial by binomial \\spad{(x} + pt). Highest coefficient of product is ignored.")) (|vectoraddmul| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "vector_add_mul(v1, \\spad{v2,} \\spad{m,} \\spad{n,} \\spad{c,} \\spad{p)} sets v1(m), ..., v1(n) to corresponding extries in \\spad{v1} + \\spad{c*v2} modulo \\spad{p.}")) (|evalat| (((|Integer|) (|U32Vector|) (|Integer|) (|Integer|) (|Integer|)) "\\indented{1}{eval_at(v, deg, \\spad{pt,} \\spad{p)} treats \\spad{v} as coefficients of} \\indented{1}{polynomial of degree deg and evaluates the} \\indented{1}{polynomial at point \\spad{pt} modulo \\spad{p}} \\blankline \\spad{X} a:=new(3,1)$U32VEC \\spad{X} \\spad{a.1:=2} \\spad{X} eval_at(a,2,3,1024) \\spad{X} eval_at(a,2,2,8) \\spad{X} eval_at(a,2,3,10)")) (|copyslice| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|) (|Integer|)) "copy_first(v1, \\spad{v2,} \\spad{m,} \\spad{n)} copies the slice of \\spad{v2} starting at \\spad{m} elements and having \\spad{n} elements into corresponding positions in \\spad{v1.}")) (|copyfirst| (((|Void|) (|U32Vector|) (|U32Vector|) (|Integer|)) "copy_first(v1, \\spad{v2,} \\spad{n)} copies first \\spad{n} elements of \\spad{v2} into \\spad{n} first positions in \\spad{v1.}"))) NIL NIL -(-961) +(-962) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J.} Williamson} Date Created: 11 January 1990 Date Last Updated: 15 June 1990 Description:")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the y-coordinates of the points on the curve \\spad{c.}")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the x-coordinates of the points on the curve \\spad{c.}")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points, representing the branches of the curve \\spad{c.}"))) NIL NIL -(-962 R L) +(-963 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, \\spad{m)}} returns the matrix A such that \\spad{A \\spad{w} = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of op. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), \\spad{m}.}"))) NIL NIL -(-963 A B) +(-964 A B) ((|constructor| (NIL "This package provides tools for operating on primitive arrays with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\indented{1}{map(f,a) applies function \\spad{f} to each member of primitive array} \\indented{1}{\\spad{a} resulting in a new primitive array over a} \\indented{1}{possibly different underlying domain.} \\blankline \\spad{X} T1:=PrimitiveArrayFunctions2(Integer,Integer) \\spad{X} map(x+->x+2,[i for \\spad{i} in 1..10])$T1")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\indented{1}{reduce(f,a,r) applies function \\spad{f} to each} \\indented{1}{successive element of the} \\indented{1}{primitive array \\spad{a} and an accumulant initialized to \\spad{r.}} \\indented{1}{For example, \\spad{reduce(_+$Integer,[1,2,3],0)}} \\indented{1}{does \\spad{3+(2+(1+0))}. Note that third argument \\spad{r}} \\indented{1}{may be regarded as the identity element for the function \\spad{f.}} \\blankline \\spad{X} T1:=PrimitiveArrayFunctions2(Integer,Integer) \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} reduce(adder,[i for \\spad{i} in 1..10],0)$T1")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\indented{1}{scan(f,a,r) successively applies} \\indented{1}{\\spad{reduce(f,x,r)} to more and more leading sub-arrays} \\indented{1}{x of primitive array \\spad{a}.} \\indented{1}{More precisely, if \\spad{a} is \\spad{[a1,a2,...]}, then} \\indented{1}{\\spad{scan(f,a,r)} returns} \\indented{1}{\\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.} \\blankline \\spad{X} T1:=PrimitiveArrayFunctions2(Integer,Integer) \\spad{X} adder(a:Integer,b:Integer):Integer \\spad{==} a+b \\spad{X} scan(adder,[i for \\spad{i} in 1..10],0)$T1"))) NIL NIL -(-964 S) +(-965 S) ((|constructor| (NIL "This provides a fast array type with no bound checking on elt's. Minimum index is 0 in this type, cannot be changed"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-965) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-966) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, \\spad{x} = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b.}") (($ $ (|Symbol|)) "\\spad{integral(f, \\spad{x)}} returns the formal integral of \\spad{f} \\spad{dx.}"))) NIL NIL -(-966 -3280) +(-967 -3313) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], \\spad{q]}} such that then \\spad{k(a1,...,an) = k(a)}, where \\spad{a = \\spad{a1} \\spad{c1} + \\spad{...} + an cn}, \\spad{ai = qi(a)}, and \\spad{q(a) = 0}. The pi's are the defining polynomials for the ai's. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], \\spad{q]}} such that then \\spad{k(a1,...,an) = k(a)}, where \\spad{a = \\spad{a1} \\spad{c1} + \\spad{...} + an cn}, \\spad{ai = qi(a)}, and \\spad{q(a) = 0}. The pi's are the defining polynomials for the ai's. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, \\spad{p2,} a2)} returns \\spad{[c1, \\spad{c2,} \\spad{q]}} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = \\spad{c1} \\spad{a1} + \\spad{c2} a2, and q(a) = 0}. The pi's are the defining polynomials for the ai's. The \\spad{p2} may involve a1, but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-967 I) +(-968 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime}, \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a \\spad{<=} \\spad{p} \\spad{<=} \\spad{b}}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? \\spad{n}} returns false, \\spad{n} is proven composite. If \\spad{prime? \\spad{n}} returns true, prime? may be in error however, the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al), below 10**12 and 10**13 due to results of Pinch, and below 341550071728321 due to a result of Jaeschke. Specifically, this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n,} that is \\spad{O( (log \\spad{n)**3} \\spad{)},} for n<10**20. beyond that, the algorithm is quartic, \\spad{O( (log \\spad{n)**4} \\spad{)}.} Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes, such as [Jaeschke, 1991] 1377161253229053 * 413148375987157, which the original algorithm regards as prime"))) NIL NIL -(-968) +(-969) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-969 K |symb| |PolyRing| E |ProjPt|) +(-970 K |symb| |PolyRing| E |ProjPt|) ((|constructor| (NIL "The following is part of the PAFF package")) (|rationalPoints| (((|List| |#5|) |#3| (|PositiveInteger|)) "\\axiom{rationalPoints(f,d)} returns all points on the curve \\axiom{f} in the extension of the ground field of degree \\axiom{d}. For \\axiom{d > 1} this only works if \\axiom{K} is a \\axiomType{LocallyAlgebraicallyClosedField}")) (|algebraicSet| (((|List| |#5|) (|List| |#3|)) "\\spad{algebraicSet returns} the algebraic set if finite (dimension 0).")) (|singularPoints| (((|List| |#5|) |#3|) "\\spad{singularPoints retourne} les points singulier")) (|singularPointsWithRestriction| (((|List| |#5|) |#3| (|List| |#3|)) "return the singular points that anhilate"))) NIL NIL -(-970 R E) +(-971 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}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-138)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598))) -(-971 A B) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-138)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600))) +(-972 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,b) computes the product of two functions} \\blankline \\spad{X} f:=(x:INT):INT \\spad{+->} 3*x \\spad{X} g:=(x:INT):INT \\spad{+->} \\spad{x^3} \\spad{X} h(x:INT):Product(INT,INT) \\spad{==} makeprod(f \\spad{x,} \\spad{g} \\spad{x)} \\spad{X} h(3)"))) -((-4597 -12 (|has| |#2| (-481)) (|has| |#1| (-481)))) -((-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-481)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847)))))) -(-972 K) +((-4599 -12 (|has| |#2| (-482)) (|has| |#1| (-482)))) +((-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-482)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-482)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-138))) (|HasCategory| |#2| (QUOTE (-138)))) (-12 (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-482)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794))))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-848)))))) +(-973 K) ((|constructor| (NIL "This is part of the PAFF package, related to projective space."))) NIL NIL -(-973 K) +(-974 K) ((|constructor| (NIL "This is part of the PAFF package, related to projective space."))) NIL NIL -(-974 -3020 K) +(-975 -3465 K) ((|constructor| (NIL "This is part of the PAFF package, related to projective space."))) NIL NIL -(-975 S) +(-976 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.}"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-976 R |polR|) +(-977 R |polR|) ((|constructor| (NIL "This package contains some functions: discriminant, resultant, subResultantGcd, chainSubResultants, degreeSubResultant, lastSubResultant, resultantEuclidean, subResultantGcdEuclidean, semiSubResultantGcdEuclidean1, semiSubResultantGcdEuclidean2\\br These procedures come from improvements of the subresultants algorithm.")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(P,Q)} returns the semi-extended resultant of \\axiom{P} and \\axiom{Q} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(P,Q)} returns the extended resultant of \\axiom{P} and \\axiom{Q} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(P,Q)} returns the resultant of \\axiom{P} and \\axiom{Q} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(P, \\spad{Q,} \\spad{Z,} \\spad{s)}} returns the subresultant \\axiom{S_{e-1}} where \\axiom{P ~ S_d, \\spad{Q} = S_{d-1}, \\spad{Z} = S_e, \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(F, \\spad{x,} \\spad{y,} \\spad{n)}} computes \\axiom{(x/y)**(n-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(x, \\spad{y,} \\spad{n)}} computes \\axiom{x**n/y**(n-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(F,G)} computes quotient and rest of the exact euclidean division of \\axiom{F} by \\axiom{G}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(P,Q)} computes the pseudoDivide of \\axiom{P} by \\axiom{Q}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{v exquo \\spad{r}} computes the exact quotient of \\axiom{v} by \\axiom{r}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{r * \\spad{v}} computes the product of \\axiom{r} and \\axiom{v}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(P, \\spad{Q)}} returns the \\spad{gcd} of \\axiom{P} and \\axiom{Q}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(P,Q)} returns the \"reduce resultant\" and carries out the equality \\axiom{...P + coef2*Q = resultantReduit(P,Q)}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(P,Q)} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(P,Q)}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(P,Q)} returns the \"reduce resultant\" of \\axiom{P} and \\axiom{Q}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(P,Q)} returns the list of degrees of non zero subresultants of \\axiom{P} and \\axiom{Q}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(P, \\spad{Q)}} computes the list of non zero subresultants of \\axiom{P} and \\axiom{Q}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(P)} carries out the equality \\axiom{...P + \\spad{coef2} * D(P) = discriminant(P)}. Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(P)} carries out the equality \\axiom{coef1 * \\spad{P} + \\spad{coef2} * D(P) = discriminant(P)}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(P, \\spad{Q)}} returns the discriminant of \\axiom{P} and \\axiom{Q}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(P,Q)} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(P,Q)} where the degree (not the indice) of the subresultant \\axiom{S_i(P,Q)} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(P,Q)} carries out the equality \\axiom{...P + coef2*Q = \\spad{+/-} S_i(P,Q)} where the degree (not the indice) of the subresultant \\axiom{S_i(P,Q)} is the smaller as possible. Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(P,Q)} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(P,Q)} where the degree (not the indice) of the subresultant \\axiom{S_i(P,Q)} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(P, \\spad{Q)}} returns the \\spad{gcd} of two primitive polynomials \\axiom{P} and \\axiom{Q}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(P, \\spad{Q)}} computes the last non zero subresultant \\axiom{S} and carries out the equality \\axiom{...P + coef2*Q = \\spad{S}.} Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(P, \\spad{Q)}} computes the last non zero subresultant \\axiom{S} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}.}")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(P, \\spad{Q)}} computes the last non zero subresultant of \\axiom{P} and \\axiom{Q}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(P, \\spad{Q,} i)} returns a subresultant \\axiom{S} of degree \\axiom{d} and carries out the equality \\axiom{...P + coef2*Q = S_i}. Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(P, \\spad{Q,} i)} returns a subresultant \\axiom{S} of degree \\axiom{d} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(P, \\spad{Q,} \\spad{d)}} computes a subresultant of degree \\axiom{d}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(P, \\spad{Q,} i)} returns the subresultant \\axiom{S_i(P,Q)} and carries out the equality \\axiom{...P + coef2*Q = S_i(P,Q)} Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(P, \\spad{Q,} i)} returns the subresultant \\axiom{S_i(P,Q)} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(P,Q)}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(P, \\spad{Q,} i)} returns the subresultant of indice \\axiom{i}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(P,Q)} carries out the equality \\axiom{coef1.P + ? \\spad{Q} = resultant(P,Q)}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(P,Q)} carries out the equality \\axiom{...P + coef2*Q = resultant(P,Q)}. Warning. \\axiom{degree(P) \\spad{>=} degree(Q)}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(P,Q)} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(P,Q)}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(P, \\spad{Q)}} returns the resultant of \\axiom{P} and \\axiom{Q}"))) NIL -((|HasCategory| |#1| (QUOTE (-456)))) -(-977 K) +((|HasCategory| |#1| (QUOTE (-457)))) +(-978 K) ((|constructor| (NIL "This is part of the PAFF package, related to projective space.")) (|pointValue| (((|List| |#1|) $) "\\spad{pointValue returns} the coordinates of the point or of the point of origin that represent an infinitly close point")) (|setelt| ((|#1| $ (|Integer|) |#1|) "\\spad{setelt sets} the value of a specified coordinates")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt returns} the value of a specified coordinates")) (|list| (((|List| |#1|) $) "\\spad{list returns} the list of the coordinates")) (|lastNonNull| (((|Integer|) $) "\\spad{lastNonNull returns} the integer corresponding to the last non null coordinates.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(p)} test if the point is rational according to the characteristic of the ground field.") (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{rational?(p,n)} test if the point is rational according to \\spad{n.}")) (|removeConjugate| (((|List| $) (|List| $)) "\\spad{removeConjugate(lp)} returns removeConjugate(lp,n) where \\spad{n} is the characteristic of the ground field.") (((|List| $) (|List| $) (|NonNegativeInteger|)) "\\spad{removeConjugate(lp,n)} returns a list of points such that no points in the list is the conjugate (according to \\spad{n)} of another point.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns conjugate(p,n) where \\spad{n} is the characteristic of the ground field.") (($ $ (|NonNegativeInteger|)) "\\spad{conjugate(p,n)} returns p**n, that is all the coordinates of \\spad{p} to the power of \\spad{n}")) (|orbit| (((|List| $) $ (|NonNegativeInteger|)) "\\spad{orbit(p,n)} returns the orbit of the point \\spad{p} according to \\spad{n,} that is orbit(p,n) = \\spad{\\{} \\spad{p,} p**n, p**(n**2), p**(n**3), ..... \\spad{\\}}") (((|List| $) $) "\\spad{orbit(p)} returns the orbit of the point \\spad{p} according to the characteristic of \\spad{K,} that is, for \\spad{q=} char \\spad{K,} orbit(p) = \\spad{\\{} \\spad{p,} p**q, p**(q**2), p**(q**3), ..... \\spad{\\}}")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce a} list of \\spad{K} to a projective point.") (((|List| |#1|) $) "\\spad{coerce a} a projective point list of \\spad{K}")) (|projectivePoint| (($ (|List| |#1|)) "\\spad{projectivePoint creates} a projective point from a list")) (|homogenize| (($ $) "\\spad{homogenize(pt)} the point according to the coordinate which is the last non null.") (($ $ (|Integer|)) "\\spad{homogenize the} point according to the coordinate specified by the integer"))) NIL NIL -(-978) +(-979) ((|constructor| (NIL "Domain for partitions of positive integers Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus, \\spad{(5 2 2 1)} will represent \\spad{s5 * \\spad{s2**2} * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 \\spad{a2**n2} ...)} returns \\spad{n1! * \\spad{a1**n1} * \\spad{n2!} * \\spad{a2**n2} * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(li)} returns a list of 2-element lists. For each 2-element list, the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in li. There is a 2-element list for each value occurring in \\spad{l.}")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-979 S |Coef| |Expon| |Var|) +(-980 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note that this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f.}")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * \\spad{x1**n1} * \\spad{..} * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-980 |Coef| |Expon| |Var|) +(-981 |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 * \\spad{x1**n1} * \\spad{..} * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-981) +(-982) ((|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 z-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the z-coordinates of the points on the curve \\spad{c.}")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the y-coordinates of the points on the curve \\spad{c.}")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the x-coordinates of the points on the curve \\spad{c.}")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points, representing the branches of the curve \\spad{c.}"))) NIL NIL -(-982 S R E |VarSet| P) +(-983 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore, for \\spad{R} being an integral domain, a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) \\spad{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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set, \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases w.r.t. \\axiom{cs} and \\axiom{(lp,cs)} and \\axiom{(lr,cs)} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}.}")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases w.r.t. \\axiom{cs} and \\axiom{(lp,cs)} and \\axiom{(lr,cs)} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}.}")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,ps)} returns \\axiom{[c,b,r]} such that \\axiom{b} is fully reduced in the sense of Groebner bases w.r.t. \\axiom{ps}, \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore, if \\axiom{R} is a gcd-domain, \\axiom{b} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,ps)} returns \\axiom{[b,r]} such that the leading monomial of \\axiom{b} is reduced in the sense of Groebner bases w.r.t. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains \\indented{1}{some non null element lying in the base ring \\axiom{R}.}")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(ps1,ps2)} returns \\spad{true} iff it can proved that \\axiom{ps1} and \\axiom{ps2} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(ps1,ps2)} returns \\spad{true} iff it can proved that all polynomials in \\axiom{ps1} lie in the ideal generated by \\axiom{ps2} in \\axiom{\\axiom{(R)^(-1) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{p,q}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(v,ps)} returns \\axiom{us,vs,ws} such that \\axiom{us} is \\axiom{collectUnder(ps,v)}, \\axiom{vs} is \\axiom{collect(ps,v)} and \\axiom{ws} is \\axiom{collectUpper(ps,v)}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{v}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{v} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{v}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(v,ps)} returns \\spad{true} iff \\axiom{v} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable, if any, else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists, otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists, otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-561)))) -(-983 R E |VarSet| P) +((|HasCategory| |#2| (QUOTE (-562)))) +(-984 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) \\spad{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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set, \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases w.r.t. \\axiom{cs} and \\axiom{(lp,cs)} and \\axiom{(lr,cs)} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}.}")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases w.r.t. \\axiom{cs} and \\axiom{(lp,cs)} and \\axiom{(lr,cs)} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}.}")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,ps)} returns \\axiom{[c,b,r]} such that \\axiom{b} is fully reduced in the sense of Groebner bases w.r.t. \\axiom{ps}, \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore, if \\axiom{R} is a gcd-domain, \\axiom{b} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,ps)} returns \\axiom{[b,r]} such that the leading monomial of \\axiom{b} is reduced in the sense of Groebner bases w.r.t. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains \\indented{1}{some non null element lying in the base ring \\axiom{R}.}")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(ps1,ps2)} returns \\spad{true} iff it can proved that \\axiom{ps1} and \\axiom{ps2} generate the same ideal in \\axiom{(R)^(-1) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(ps1,ps2)} returns \\spad{true} iff it can proved that all polynomials in \\axiom{ps1} lie in the ideal generated by \\axiom{ps2} in \\axiom{\\axiom{(R)^(-1) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{p,q}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(v,ps)} returns \\axiom{us,vs,ws} such that \\axiom{us} is \\axiom{collectUnder(ps,v)}, \\axiom{vs} is \\axiom{collect(ps,v)} and \\axiom{ws} is \\axiom{collectUpper(ps,v)}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{v}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{v} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,v)} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{v}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(v,ps)} returns \\spad{true} iff \\axiom{v} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable, if any, else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists, otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists, otherwise \\axiom{\"failed\"} is returned."))) -((-4600 . T) (-3348 . T)) +((-4602 . T) (-3389 . T)) NIL -(-984 R E V P) +(-985 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(lp,lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [p1,...,pn]} and \\axiom{lf = [f1,...,fm]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0}, and the \\axiom{fi} are irreducible over \\axiom{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{R}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [p1,...,pn]} and \\axiom{lf = [f1,...,fm]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0}, and the \\axiom{fi} are irreducible over \\axiom{R} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{p} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{f} in \\axiom{lf}. Moreover, squares over \\axiom{R} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{f} in \\axiom{lf}. Moreover, squares over \\axiom{R} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{f} in \\axiom{lf}. Moreover, squares over \\axiom{R} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{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(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(p)} returns the square-free factors of \\axiom{p} over \\axiom{R}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,redOp?,redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(-1) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover, \\axiom{lq} is computed by reducing \\axiom{lp} w.r.t. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,pred?,redOp?,redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set w.r.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 w.r.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(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{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(p,lf)} returns the same as removeRoughlyRedundantFactorsInPols([p],lf,true)")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,lf,opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,lf)} if \\axiom{opt} is \\axiom{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(lp,lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{p} of \\axiom{lp} any occurence of a polynomial \\axiom{f} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,nbps} where \\axiom{bps} is a list of the bivariate polynomials, and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(p)} returns \\spad{true} iff \\axiom{p} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,nlps} where \\axiom{lps} is a list of the linear polynomials in \\spad{lp,} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(p)} returns \\spad{true} iff \\axiom{p} does not lie in the base ring \\axiom{R} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(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?(p)} returns \\spad{true} iff \\axiom{p} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{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?,ps)} returns \\axiom{gps,bps} where \\axiom{gps} is a list of the polynomial \\axiom{p} in \\axiom{ps} such that \\axiom{pred?(p)} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,ps)} returns \\axiom{gps,bps} where \\axiom{gps} is a list of the polynomial \\axiom{p} in \\axiom{ps} such that \\axiom{pred?(p)} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,ps)} returns \\axiom{gps,bps} where \\axiom{gps} is a list of the polynomial \\axiom{p} in \\axiom{ps} such that \\axiom{pred?(p)} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,lp)} returns \\spad{true} iff for every \\axiom{p} in \\axiom{lp} the remainder of \\axiom{p} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(p,q)} returns the same as \\axiom{removeRedundantFactors(p,q)} but does assume that neither \\axiom{p} nor \\axiom{q} lie in the base ring \\axiom{R} and assumes that \\axiom{infRittWu?(p,q)} holds. Moreover, if \\axiom{R} is gcd-domain, then \\axiom{p} and \\axiom{q} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(p)$P for \\spad{p} in lp]} if \\axiom{R} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,lq,remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,lq)),lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,q)} returns the same as \\axiom{removeRedundantFactors(cons(q,lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(p,q)} returns the same as \\axiom{removeRedundantFactors([p,q])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [p1,...,pn]} and \\axiom{lq = [q1,...,qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes, and the product of degrees of the \\axiom{qi} is not greater than the one of the \\axiom{pj}, and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular, polynomials lying in the base ring \\axiom{R} are removed. Moreover, \\axiom{lq} is sorted w.r.t \\axiom{infRittWu?}. Furthermore, if \\spad{R} is gcd-domain, the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-302)))) (|HasCategory| |#1| (QUOTE (-456)))) -(-985 K) +((-12 (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-303)))) (|HasCategory| |#1| (QUOTE (-457)))) +(-986 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, \\spad{v)}} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A \\spad{y}.} \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-986 |VarSet| E RC P) +(-987 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p.} Each factor has no repeated roots, and the factors are pairwise relatively prime."))) NIL NIL -(-987 R) +(-988 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.}"))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-988 R1 R2) +(-989 R1 R2) ((|constructor| (NIL "This package has no description")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-989 R) +(-990 R) ((|constructor| (NIL "This package has no description")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point, \\spad{pt,} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically, shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point, \\spad{pt,} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically, hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point, \\spad{pt,} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically, color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point, \\spad{pt,} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-990 K) +(-991 K) ((|constructor| (NIL "A package which provides partial transcendental functions, for example, functions which return an answer or \"failed\" This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(z) if possible, and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(z) if possible, and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(z) if possible, and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(z) if possible, and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(z) if possible, and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(z) if possible, and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(z) if possible, and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(z) if possible, and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(z) if possible, and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(z) if possible, and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(z) if possible, and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(z) if possible, and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(z) if possible, and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(z) if possible, and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(z) if possible, and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(z) if possible, and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(z) if possible, and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(z) if possible, and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(z) if possible, and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(z) if possible, and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(z) if possible, and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(z) if possible, and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(z) if possible, and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(z) if possible, and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(z) if possible, and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(z) if possible, and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible, and \"failed\" otherwise."))) NIL NIL -(-991 R E OV PPR) +(-992 R E OV PPR) ((|constructor| (NIL "This package has no description")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-992 K R UP -3280) +(-993 K R UP -3313) ((|constructor| (NIL "In this package \\spad{K} is a finite field, \\spad{R} is a ring of univariate polynomials over \\spad{K,} and \\spad{F} is a monogenic algebra over \\spad{R.} We require that \\spad{F} is monogenic, \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))}, because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F.} \\spad{F} is a framed algebra with R-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{j} = 1..n)}, \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly, the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F.} \\spad{F} is a framed algebra with R-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{j} = 1..n)}, \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly, the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}."))) NIL NIL -(-993 |vl| |nv|) +(-994 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set, defined as the common zeros of a given list of polynomials (the defining polynomials for equations), and a principal Zariski open set, defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet}, where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals, it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer}, and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis, and the defining polynomial for the inequation reduced with respect to the basis, using using groebner basis of radical ideals"))) NIL NIL -(-994 R |Var| |Expon| |Dpoly|) +(-995 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets, which is the intersection of a Zariski closed set, defined as the common zeros of a given list of polynomials (the defining polynomials for equations), and a principal Zariski open set, defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone, while the second, \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis, and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only, as it is inefficient compared to the other two, as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods, please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L.} While this may be obtained using the usual normal form algorithm, there is no canonical form for \\spad{q.} \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis, and the defining polynomial for the inequation reduced with respect to the basis, using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis, and the defining polynomial for the inequation reduced with respect to the basis, using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation, that is, the Zariski open part of \\spad{s.}")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations, that is, for the Zariski closed part of \\spad{s.}")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points, and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s,} but asserts the following: if \\spad{t} is true, then \\spad{s} is empty, if \\spad{t} is false, then \\spad{s} is non-empty, and if \\spad{t} = \"failed\", then no assertion is made (that is, \"don't know\"). Note: for internal use only, with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty, \\spad{false} if it is not, and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl,} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-302))))) -(-995 R E V P TS) +((-12 (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-303))))) +(-996 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets.")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,ts,lineq,b1,b2,b3,b4,b5)} is an internal subroutine, exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,lts,b1,b2)} is an internal subroutine, exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine, exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,lpwt2)} is an internal subroutine, exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,us)} returns \\spad{true} iff internalSubQuasiComponent? returs true.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{b} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(lp1,lp2)} is an internal subroutine, exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(lp1,lp2)} is an internal subroutine, exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(lp1,lp2)} returns \\spad{true} iff \\axiom{lp1} is a sub-set of \\axiom{lp2} assuming that these lists are sorted increasingly w.r.t. infRittWu? from RecursivePolynomialCategory.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(lp1,lp2)} returns \\spad{true} iff \\axiom{lp1} is a sub-set of \\axiom{lp2}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty, or \\axiom{ts} has less elements than \\axiom{us}, or some variable is algebraic w.r.t. \\axiom{us} and is not w.r.t. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} w.r.t supDimElseRittWu?")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} w.r.t. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine, exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(s1,s2,s3)} is an internal subroutine, exported only for developement."))) NIL NIL -(-996) +(-997) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{q}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{q}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-997 A B R S) +(-998 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of frac."))) NIL NIL -(-998 A S) +(-999 A S) ((|constructor| (NIL "QuotientField(S) is the category of fractions of an Integral Domain \\spad{S.}")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x.}")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x.}")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x.} \\spad{x} = wholePart(x) + fractionPart(x)")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\spad{%.}")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\spad{%.}")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x.}")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x.}")) (/ (($ |#2| |#2|) "\\spad{d1 / \\spad{d2}} returns the fraction \\spad{d1} divided by \\spad{d2.}"))) NIL -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-1143)))) -(-999 S) +((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-303))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1144)))) +(-1000 S) ((|constructor| (NIL "QuotientField(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(x) + fractionPart(x)")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\spad{%.}")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\spad{%.}")) (|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 / \\spad{d2}} returns the fraction \\spad{d1} divided by \\spad{d2.}"))) -((-3348 . T) (-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3389 . T) (-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1000 |n| K) +(-1001 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v,} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf.}")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric, square matrix \\spad{m.}"))) NIL NIL -(-1001 S) +(-1002 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note that \\axiom{length(q) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! \\spad{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!(q)).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! \\spad{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."))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-1002 S R) +(-1003 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 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 true, the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it true} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number, and {\\it false} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-286)))) -(-1003 R) +((|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-287)))) +(-1004 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 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 true, the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it true} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number, and {\\it 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}."))) -((-4593 |has| |#1| (-286)) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 |has| |#1| (-287)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1004 QR R QS S) +(-1005 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(f,u) maps \\spad{f} onto the component parts of the quaternion u.} \\indented{1}{to convert an expression in Quaterion(R) to Quaternion(S)} \\blankline \\spad{X} f(a:FRAC(INT)):COMPLEX(FRAC(INT)) \\spad{==} a::COMPLEX(FRAC(INT)) \\spad{X} q:=quatern(2/11,-8,3/4,1) \\spad{X} map(f,q)"))) NIL NIL -(-1005 R) +(-1006 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."))) -((-4593 |has| |#1| (-286)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-286))) (-1831 (|HasCategory| |#1| (QUOTE (-286))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -282) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-553))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))))) -(-1006 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(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} every?(x+->(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|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\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([x,y,...,z]) creates a queue with first (top)} \\indented{1}{element \\spad{x,} second element y,...,and last (bottom) element \\spad{z.}} \\blankline \\spad{E} e:Queue INT:= queue [1,2,3,4,5]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) +((-4595 |has| |#1| (-287)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-287))) (-1841 (|HasCategory| |#1| (QUOTE (-287))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -283) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-554))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))))) (-1007 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(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} every?(x+->(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|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:Queue INT:= queue [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\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! 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T)) +((|HasCategory| (-413 |#2|) (QUOTE (-149))) (|HasCategory| (-413 |#2|) (QUOTE (-151))) (|HasCategory| (-413 |#2|) (QUOTE (-353))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (-1841 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-353)))) (|HasCategory| (-413 |#2|) (QUOTE (-374))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-374))) (-1841 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-1841 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-413 |#2|) (QUOTE (-353))))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-227))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-1841 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-227))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-353))))) +(-1011 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) 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T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-572) (QUOTE (-910))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-1170)))) (|HasCategory| (-572) (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-151))) (|HasCategory| (-572) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-572) (QUOTE (-1028))) (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1144))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| (-572) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-227))) (|HasCategory| (-572) (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| (-572) (LIST (QUOTE -527) (QUOTE (-1170)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -305) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -283) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-303))) (|HasCategory| (-572) (QUOTE (-554))) (|HasCategory| (-572) (QUOTE (-848))) (-1841 (|HasCategory| (-572) (QUOTE (-821))) (|HasCategory| (-572) (QUOTE (-848)))) (|HasCategory| (-572) (LIST (QUOTE -634) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| (-572) (QUOTE (-910)))) (|HasCategory| (-572) (QUOTE (-149))))) +(-1012) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b.}"))) NIL NIL -(-1012) +(-1013) ((|constructor| (NIL "Random number generators. All random numbers used in the system should originate from the same generator. This package is intended to be the source.")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n.}")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n.}") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-1013 RP) +(-1014 RP) ((|constructor| (NIL "Factorization of extended polynomials with rational coefficients. This package implements factorization of extended polynomials whose coefficients are rational numbers. It does this by taking the \\spad{lcm} of the coefficients of the polynomial and creating a polynomial with integer coefficients. The algorithm in \\spadtype{GaloisGroupFactorizer} is then used to factor the integer polynomial. The result is normalized with respect to the original \\spad{lcm} of the denominators.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-1014 S) +(-1015 S) ((|constructor| (NIL "Rational number testing and retraction functions.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number, \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number, \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-1015 A S) +(-1016 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,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{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 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 u.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate u."))) NIL -((|HasAttribute| |#1| (QUOTE -4601)) (|HasCategory| |#2| (QUOTE (-1097)))) -(-1016 S) +((|HasAttribute| |#1| (QUOTE -4603)) (|HasCategory| |#2| (QUOTE (-1098)))) +(-1017 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,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{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 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 u.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate u."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1017 S) +(-1018 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common access functions for all real closed fields. provides computations with generic real roots of polynomials")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(n,p)} gives an approximation of \\axiom{n} that has precision \\axiom{p}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(x,name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(x,name)} changes the way \\axiom{x} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(x,n)} is \\axiom{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,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,n,name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(x)} is the expression of \\axiom{x} in terms of \\axiom{SparseUnivariatePolynomial($)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(x)} is the defining polynomial for the main algebraic quantity of \\axiom{x}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(x)} is the main algebraic quantity name of \\axiom{x}"))) NIL NIL -(-1018) +(-1019) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common access functions for all real closed fields. provides computations with generic real roots of polynomials")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(n,p)} gives an approximation of \\axiom{n} that has precision \\axiom{p}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(x,name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(x,name)} changes the way \\axiom{x} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(x)} is \\axiom{x \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(x,n)} is \\axiom{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,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,n,name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(x)} is the expression of \\axiom{x} in terms of \\axiom{SparseUnivariatePolynomial($)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(x)} is the defining polynomial for the main algebraic quantity of \\axiom{x}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(x)} is the main algebraic quantity name of \\axiom{x}"))) -((-4593 . T) (-4598 . T) (-4592 . T) (-4595 . T) (-4594 . T) ((-4602 "*") . T) (-4597 . T)) +((-4595 . T) (-4600 . T) (-4594 . T) (-4597 . T) (-4596 . T) ((-4604 "*") . T) (-4599 . T)) NIL -(-1019 R -3280) +(-1020 R -3313) ((|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, \\spad{f,} \\spad{g,} \\spad{x,} lim, ext)} returns \\spad{[y, \\spad{h,} \\spad{b]}} such that \\spad{dy/dx + \\spad{n} df/dx \\spad{y} = \\spad{h}} and \\spad{b \\spad{:=} \\spad{h} = \\spad{g}.} The equation \\spad{dy/dx + \\spad{n} df/dx \\spad{y} = \\spad{g}} has no solution if \\spad{h \\~~= \\spad{g}} (y is a partial solution in that case). Notes: \\spad{lim} is a limited integration function, and ext is an extended integration function."))) NIL NIL -(-1020 R -3280) +(-1021 R -3313) ((|constructor| (NIL "Risch differential equation, elementary case.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, \\spad{f,} g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - \\spad{n} df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist, \"failed\" otherwise. \\spad{lim} is a limited integration function, \\spad{ext} is an extended integration function."))) NIL NIL -(-1021 -3280 UP) +(-1022 -3313 UP) ((|constructor| (NIL "Risch differential equation, transcendental case.")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, \\spad{B,} \\spad{C,} \\spad{n,} \\spad{D)}} returns either: 1. \\spad{[Q, \\spad{b]}} such that \\spad{degree(Q) \\spad{<=} \\spad{n}} and \\indented{3}{\\spad{a \\spad{Q'+} \\spad{B} \\spad{Q} = \\spad{C}} if \\spad{b = true}, \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, \\spad{C1,} \\spad{m,} \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A \\spad{Q'} + \\spad{BQ} = \\spad{C}} must be of the form} \\indented{3}{\\spad{Q = \\alpha \\spad{H} + \\beta} where \\spad{degree(H) \\spad{<=} \\spad{m}} and} \\indented{3}{H satisfies \\spad{H' + \\spad{B1} \\spad{H} = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, \\spad{g)}} returns a \\spad{[y, \\spad{b]}} such that \\spad{y' + fy = \\spad{g}} if \\spad{b = true}, \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, \\spad{B,} \\spad{C,} \\spad{T]}} such that \\spad{y' + \\spad{f} \\spad{y} = \\spad{g}} has a solution if and only if \\spad{y = \\spad{Q} / \\spad{T},} where \\spad{Q} satisfies \\spad{A \\spad{Q'} + \\spad{B} \\spad{Q} = \\spad{C}} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1022 -3280 UP) +(-1023 -3313 UP) ((|constructor| (NIL "Risch differential equation system, transcendental case.")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, \\spad{g1,} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), \\spad{(f,} 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist, \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, \\spad{B,} \\spad{H,} \\spad{C1,} \\spad{C2,} \\spad{T]}} such that \\spad{(y1', y2') + ((0, -f), \\spad{(f,} 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = \\spad{Q1} / \\spad{T,} \\spad{y2} = \\spad{Q2} / \\spad{T},} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), \\spad{(B,} \\spad{H))} (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL -(-1023 S) +(-1024 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1024 F1 UP UPUP R F2) +(-1025 F1 UP UPUP R F2) ((|constructor| (NIL "Finds the order of a divisor over a finite field")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-1025 |Pol|) +(-1026 |Pol|) ((|constructor| (NIL "This package provides functions for finding the real zeros of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals isolist.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval int.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of pol; the operation returns an isolating interval which is contained within range, or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record int.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial pol.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial pol."))) NIL NIL -(-1026 |Pol|) +(-1027 |Pol|) ((|constructor| (NIL "This package provides functions for finding the real zeros of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals, expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of pol, and returns an isolating interval which is contained within range, or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record int.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial pol.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial pol."))) NIL NIL -(-1027) +(-1028) ((|constructor| (NIL "The category of real numeric domains, that is, convertible to floats."))) NIL NIL -(-1028) +(-1029) ((|constructor| (NIL "This package provides numerical solutions of systems of polynomial equations for use in ACPLOT")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\indented{1}{realSolve(lp,lv,eps) = compute the list of the real} \\indented{1}{solutions of the list \\spad{lp} of polynomials with integer} \\indented{1}{coefficients with respect to the variables in lv,} \\indented{1}{with precision eps.} \\blankline \\spad{X} \\spad{p1} \\spad{:=} x**2*y*z + \\spad{y*z} \\spad{X} \\spad{p2} \\spad{:=} x**2*y**2*z + \\spad{x} + \\spad{z} \\spad{X} \\spad{p3} \\spad{:=} \\spad{x**2*y**2*z**2} + \\spad{z} + 1 \\spad{X} \\spad{lp} \\spad{:=} [p1, \\spad{p2,} \\spad{p3]} \\spad{X} realSolve(lp,[x,y,z],0.01)")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\indented{1}{solve(p,eps) finds the real zeroes of a univariate} \\indented{1}{integer polynomial \\spad{p} with precision eps.} \\blankline \\spad{X} \\spad{p} \\spad{:=} 4*x^3 - 3*x^2 + 2*x - 4 \\spad{X} solve(p,0.01)$REALSOLV") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\indented{1}{solve(p,eps) finds the real zeroes of a} \\indented{1}{univariate rational polynomial \\spad{p} with precision eps.} \\blankline \\spad{X} \\spad{p} \\spad{:=} 4*x^3 - 3*x^2 + 2*x - 4 \\spad{X} solve(p::POLY(FRAC(INT)),0.01)$REALSOLV"))) NIL NIL -(-1029 |TheField|) +(-1030 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(n,p)} gives a relative approximation of \\axiom{n} that has precision \\axiom{p}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(x)} is the main algebraic quantity of \\axiom{x} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-4593 . T) (-4598 . T) (-4592 . T) (-4595 . T) (-4594 . T) ((-4602 "*") . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-412 (-571)) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-412 (-571)) (LIST (QUOTE -1043) (QUOTE (-571)))) (-1831 (|HasCategory| (-412 (-571)) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))))) -(-1030 R -3280) +((-4595 . T) (-4600 . T) (-4594 . T) (-4597 . T) (-4596 . T) ((-4604 "*") . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-413 (-572)) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-413 (-572)) (LIST (QUOTE -1044) (QUOTE (-572)))) (-1841 (|HasCategory| (-413 (-572)) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))))) +(-1031 R -3313) ((|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 \\spad{f},} if \\spad{f} represents the coefficient of a recurrence or ADE, returns the operator representing the solution")) (|getEq| ((|#2| |#2|) "\\spad{getEq \\spad{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, \\spad{x,} \\spad{n,} eq, values)} creates an expression that stands for the coefficient of \\spad{x^n} in the Taylor expansion of f(x), where f(x) is given by the functional equation eq. However, for technical reasons the variable \\spad{x} has to be replaced by a \\spad{dummy} variable \\spad{dummy} in eq. The argument values specifies the first few Taylor coefficients.")) (|evalRec| ((|#2| (|BasicOperator|) (|Symbol|) |#2| |#2| |#2| (|List| |#2|)) "\\spad{evalRec(u, dummy, \\spad{n,} \\spad{n0,} eq, values)} creates an expression that stands for u(n0), where u(n) is given by the equation eq. However, for technical reasons the variable \\spad{n} has to be replaced by a \\spad{dummy} variable \\spad{dummy} in eq. The argument values specifies the initial values of the recurrence u(0), u(1),... For the moment we don't allow recursions that contain \\spad{u} inside of another operator."))) NIL -((|HasCategory| |#1| (QUOTE (-1053)))) -(-1031 -3280 L) +((|HasCategory| |#1| (QUOTE (-1054)))) +(-1032 -3313 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 \\spad{z} = 0}, \\spad{y = \\spad{gk} \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op \\spad{y} = 0}. Each \\spad{fi} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, \\spad{s)}} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 \\spad{z} = 0}, \\spad{y = \\spad{s} \\int \\spad{z}} is a solution of \\spad{op \\spad{y} = 0}. \\spad{s} must satisfy \\spad{op \\spad{s} = 0}."))) NIL NIL -(-1032 S) +(-1033 S) ((|constructor| (NIL "\\spadtype{Reference} is for making a changeable instance of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m.}")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n.}")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n.}"))) NIL -((|HasCategory| |#1| (QUOTE (-1097)))) -(-1033 R E V P) +((|HasCategory| |#1| (QUOTE (-1098)))) +(-1034 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(lp,b1,b2)} is an internal subroutine, exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,b1,b2,b3)} is an internal subroutine, exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,b1,b2.b3,b4)} is an internal subroutine, exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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(p,ts,b1,b2,b3,b4,b5)} is an internal subroutine, exported only for developement."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1097))) (-12 (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-373)))) -(-1034 R) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#4| (QUOTE (-1098))) (-12 (|HasCategory| |#4| (LIST (QUOTE -305) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-374)))) +(-1035 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,pi1(i)),...,(deltai,pik(i))] if the permutations pi1,...,pik are in list notation and are permuting {1,2,...,n}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices [(deltai,pi1(i)),...,(deltai,pik(i))] (Kronecker delta) for the permutations pi1,...,pik of {1,2,...,n}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix (deltai,pi(i)) (Kronecker delta) if the permutation \\spad{pi} is in list notation and permutes {1,2,...,n}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix (deltai,pi(i)) (Kronecker delta) for a permutation \\spad{pi} of {1,2,...,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 \\spad{{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 \\spad{{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 m-by-m square matrix in the list \\spad{la} the irreducible, polynomial representation of the general linear group \\spad{GLm} which corresponds to the partition (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 n-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the m-by-m square matrix a the irreducible, polynomial representation of the general linear group \\spad{GLm} which corresponds to the partition (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 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 x[i,j] (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each m-by-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 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 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 n-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4602 "*")))) -(-1035 R) +((|HasAttribute| |#1| (QUOTE (-4604 "*")))) +(-1036 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 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)/(q-1) of them. We first reduce \\spad{n} modulo this number, then find the largest \\spad{i} such that +/[q**i for \\spad{i} in 0..i-1] \\spad{<=} \\spad{n.} Subtracting this sum of powers from \\spad{n} results in an 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(aG,true,numberOfTries,7). Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls meatAxe(aG,false,6,7), only using Parker's fingerprints, if randomElemnts is false. If it is true, it calls meatAxe(aG,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(aG,false,25,7) returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra, say \\spad{A}, of the algebra of all square matrices of dimension \\spad{n.} \\spad{V} \\spad{R} is an A-module in the usual way. meatAxe(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's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker'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(aG,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's irreducibility test can be used either to prove irreducibility or to find the splitting. If \\spad{randomElements} is false, the first 6 tries use Parker'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 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(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?(aG,25). Note that the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton'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?(aG0,aG1,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?(aG0,aG1,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 \\spad{!)} 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 aG0.i * \\spad{TM} = \\spad{TM} * aG1.i for all 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(lm,v) calculates a matrix whose non-zero column vectors are the R-Basis of Av achieved in the way as described in section 6 of \\spad{R.} A. Parker'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(lm,v) generates the R-Basis of Av as described in section 6 of \\spad{R.} A. Parker'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 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 -((|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-302)))) -(-1036 S) +((|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-303)))) +(-1037 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, \\spad{r)}} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1037) +(-1038) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse \\spad{b)}} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible, the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse \\spad{b)}} is diagonal, or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m;} when possible, the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(s) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c;} when possible, values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m;} when possible, values are expressed in terms of radicals."))) NIL NIL -(-1038 S) +(-1039 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-1039 S) +(-1040 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example, it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1040 -3280 |Expon| |VarSet| |FPol| |LFPol|) +(-1041 -3313 |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"))) -(((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1041) +(-1042) ((|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.}"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -4279) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097)))) (|HasCategory| (-1169) (QUOTE (-847))) (|HasCategory| (-57) (QUOTE (-1097))) (-1831 (|HasCategory| (-57) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -304) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1097))))) -(-1042 A S) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -4320) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098)))) (|HasCategory| (-1170) (QUOTE (-848))) (|HasCategory| (-57) (QUOTE (-1098))) (-1841 (|HasCategory| (-57) (QUOTE (-1098))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -305) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1098))))) +(-1043 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elements if 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 \\spad{%.}"))) NIL NIL -(-1043 S) +(-1044 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elements if A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S.}")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S.}")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\spad{%.}"))) NIL NIL -(-1044 Q R) +(-1045 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv.} The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1045) +(-1046) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1046 UP) +(-1047 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p.}"))) NIL NIL -(-1047 R) +(-1048 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r.}"))) NIL NIL -(-1048 R) +(-1049 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R.}")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, \\spad{[v1} = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel, \\spadignore{i.e.} vi's appearing inside the gi's are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, \\spad{v} = \\spad{g)}} returns \\spad{f} with \\spad{v} replaced by \\spad{g.} Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel, \\spadignore{i.e.} vi's appearing inside the gi's are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, \\spad{v,} \\spad{g)}} returns \\spad{f} with \\spad{v} replaced by \\spad{g.}")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, \\spad{v)}} applies both the numerator and denominator of \\spad{f} to \\spad{v.}")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, \\spad{v)}} returns \\spad{f} viewed as a univariate rational function in \\spad{v.}")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f,} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f.}"))) NIL NIL -(-1049 K) +(-1050 K) ((|constructor| (NIL "This pacackage finds all the roots of a polynomial. If the constant field is not large enough then it returns the list of found zeros and the degree of the extension need to find the other roots missing. If the return degree is 1 then all the roots have been found. If 0 is return for the extension degree then there are an infinite number of zeros, that is you ask for the zeroes of 0. In the case of infinite field a list of all found zeros is kept and for each other call of a function that finds zeroes, a check is made on that list; this is to keep a kind of \"canonical\" representation of the elements.")) (|setFoundZeroes| (((|List| |#1|) (|List| |#1|)) "\\spad{setFoundZeroes sets} the list of foundZeroes to the given one.")) (|foundZeroes| (((|List| |#1|)) "\\spad{foundZeroes returns} the list of already found zeros by the functions distinguishedRootsOf and distinguishedCommonRootsOf.")) (|distinguishedCommonRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|List| (|SparseUnivariatePolynomial| |#1|)) |#1|) "\\spad{distinguishedCommonRootsOf returns} the common zeros of a list of polynomial. It returns a record as in distinguishedRootsOf. If 0 is returned as extension degree then there are an infinite number of common zeros (in this case, the polynomial 0 was given in the list of input polynomials).")) (|distinguishedRootsOf| (((|Record| (|:| |zeros| (|List| |#1|)) (|:| |extDegree| (|Integer|))) (|SparseUnivariatePolynomial| |#1|) |#1|) "\\spad{distinguishedRootsOf returns} a record consisting of a list of zeros of the input polynomial followed by the smallest extension degree needed to find all the zeros. If \\spad{K} has \\spad{PseudoAlgebraicClosureOfFiniteFieldCategory} or \\spad{PseudoAlgebraicClosureOfRationalNumberCategory} then a root is created for each irreducible factor, and only these roots are returns and not their conjugate."))) NIL NIL -(-1050 R |ls|) +(-1051 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a 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."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-780 |#1| (-857 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-780 |#1| (-857 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-780 |#1| (-857 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -780) (|devaluate| |#1|) (LIST (QUOTE -857) (|devaluate| |#2|))))) (|HasCategory| (-780 |#1| (-857 |#2|)) (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-857 |#2|) (QUOTE (-373)))) -(-1051) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-781 |#1| (-858 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-781 |#1| (-858 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-781 |#1| (-858 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -781) (|devaluate| |#1|) (LIST (QUOTE -858) (|devaluate| |#2|))))) (|HasCategory| (-781 |#1| (-858 |#2|)) (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| (-858 |#2|) (QUOTE (-374)))) +(-1052) ((|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}{l + \\spad{u0} + \\spad{w*u1} + \\spad{w**2*u2} +...+ \\spad{w**(n-1)*u-1} + w**n*m} where \\indented{4}{s = a..b} \\indented{4}{l = min(a,b)} \\indented{4}{m = abs(b-a) + 1} \\indented{4}{w**n < \\spad{m} < w**(n+1)} \\indented{4}{u0,...,un-1\\space{2}are uniform on\\space{2}0..w-1} \\indented{4}{m\\space{12}is\\space{2}uniform on\\space{2}0..(m quo w**n)-1}"))) NIL NIL -(-1052 S) +(-1053 S) ((|constructor| (NIL "The category of rings with unity, always associative, but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note that \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring, or zero if no such \\spad{n} exists."))) NIL NIL -(-1053) +(-1054) ((|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."))) -((-4597 . T)) +((-4599 . T)) NIL -(-1054 |xx| -3280) +(-1055 |xx| -3313) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1055 S |m| |n| R |Row| |Col|) +(-1056 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be R-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m.}")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m.} This is the dimension of the null space of the matrix \\spad{m.}")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m.}")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m.}")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r.} Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r,} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c,} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i}, \\spad{j.}") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b,} where \\spad{b(i,j) = a(i,j)} for all i, \\spad{j.}")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m.} Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m.} Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m.} Note that there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m,} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column, and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m.} Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m.}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m.}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m.}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m.}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m.}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m.}")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric. That is, \\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 (that is, \\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 (that is, all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (that is, if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix, where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL -((|HasCategory| |#4| (QUOTE (-302))) (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (QUOTE (-561))) (|HasCategory| |#4| (QUOTE (-173)))) -(-1056 |m| |n| R |Row| |Col|) +((|HasCategory| |#4| (QUOTE (-303))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (QUOTE (-562))) (|HasCategory| |#4| (QUOTE (-174)))) +(-1057 |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 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 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. That is, \\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 (that is, \\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 (that is, all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (that is, if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|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"))) -((-4600 . T) (-3348 . T) (-4595 . T) (-4594 . T)) +((-4602 . T) (-3389 . T) (-4597 . T) (-4596 . T)) NIL -(-1057 |m| |n| R) +(-1058 |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}."))) -((-4600 . T) (-4595 . T) (-4594 . T)) -((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (QUOTE (-302))) (|HasCategory| |#3| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-173))) (-1831 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-173)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-367)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -304) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1097)))))) -(-1058 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4602 . T) (-4597 . T) (-4596 . T)) +((|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1098))) (|HasCategory| |#3| (QUOTE (-303))) (|HasCategory| |#3| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-174))) (-1841 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -305) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-1098)))))) +(-1059 |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{i} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-1059 R) +(-1060 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplication by elements of the rng. \\blankline Axioms\\br \\tab{5}\\spad{x*(a*b) = (x*a)*b}\\br \\tab{5}\\spad{x*(a+b) = (x*a)+(x*b)}\\br \\tab{5}\\spad{(x+y)*x = (x*a)+(y*a)}")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r.}"))) NIL NIL -(-1060) +(-1061) ((|constructor| (NIL "The category of associative rings, not necessarily commutative, and not necessarily with a 1. This is a combination of an abelian group and a semigroup, with multiplication distributing over addition. \\blankline Axioms\\br \\tab{5}\\spad{ x*(y+z) = x*y + x*z}\\br \\tab{5}\\spad{ (x+y)*z = \\spad{x*z} + \\spad{y*z} } \\blankline Conditional attributes\\br \\tab{5}noZeroDivisors\\tab{5}\\spad{ ab = 0 \\spad{=>} \\spad{a=0} or b=0}"))) NIL NIL -(-1061 S) +(-1062 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs \\spad{x}} returns the absolute value of \\spad{x.}")) (|round| (($ $) "\\spad{round \\spad{x}} computes the integer closest to \\spad{x.}")) (|truncate| (($ $) "\\spad{truncate \\spad{x}} returns the integer between \\spad{x} and 0 closest to \\spad{x.}")) (|fractionPart| (($ $) "\\spad{fractionPart \\spad{x}} returns the fractional part of \\spad{x.}")) (|wholePart| (((|Integer|) $) "\\spad{wholePart \\spad{x}} returns the integer part of \\spad{x.}")) (|floor| (($ $) "\\spad{floor \\spad{x}} returns the largest integer \\spad{<= \\spad{x}.}")) (|ceiling| (($ $) "\\spad{ceiling \\spad{x}} returns the small integer \\spad{>= \\spad{x}.}")) (|norm| (($ $) "\\spad{norm \\spad{x}} returns the same as absolute value."))) NIL NIL -(-1062) +(-1063) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs \\spad{x}} returns the absolute value of \\spad{x.}")) (|round| (($ $) "\\spad{round \\spad{x}} computes the integer closest to \\spad{x.}")) (|truncate| (($ $) "\\spad{truncate \\spad{x}} returns the integer between \\spad{x} and 0 closest to \\spad{x.}")) (|fractionPart| (($ $) "\\spad{fractionPart \\spad{x}} returns the fractional part of \\spad{x.}")) (|wholePart| (((|Integer|) $) "\\spad{wholePart \\spad{x}} returns the integer part of \\spad{x.}")) (|floor| (($ $) "\\spad{floor \\spad{x}} returns the largest integer \\spad{<= \\spad{x}.}")) (|ceiling| (($ $) "\\spad{ceiling \\spad{x}} returns the small integer \\spad{>= \\spad{x}.}")) (|norm| (($ $) "\\spad{norm \\spad{x}} returns the same as absolute value."))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1063 |TheField| |ThePolDom|) +(-1064 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,c,p) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(p,r)} is \\spad{false} if \\axiom{p.r} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1064) +(-1065) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting integers to roman numerals.")) (|roman| (($ (|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."))) -((-4588 . T) (-4592 . T) (-4587 . T) (-4598 . T) (-4599 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4590 . T) (-4594 . T) (-4589 . T) (-4600 . T) (-4601 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1065) +(-1066) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -4279) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097)))) (|HasCategory| (-1169) (QUOTE (-847))) (|HasCategory| (-57) (QUOTE (-1097))) (-1831 (|HasCategory| (-57) (QUOTE (-1097))) (|HasCategory| (-2 (|:| -4080 (-1169)) (|:| -4279 (-57))) (QUOTE (-1097)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -304) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1097))))) -(-1066 S R E V) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -4320) (QUOTE (-57)))))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098)))) (|HasCategory| (-1170) (QUOTE (-848))) (|HasCategory| (-57) (QUOTE (-1098))) (-1841 (|HasCategory| (-57) (QUOTE (-1098))) (|HasCategory| (-2 (|:| -4111 (-1170)) (|:| -4320 (-57))) (QUOTE (-1098)))) (-12 (|HasCategory| (-57) (LIST (QUOTE -305) (QUOTE (-57)))) (|HasCategory| (-57) (QUOTE (-1098))))) +(-1067 S R E V) ((|constructor| (NIL "\\indented{1}{Author: Marc Moreno Maza} Date Created: 04/22/1994 Date Last Updated: 14/12/1998 Description:")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(p)} returns the square free part of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(p)} returns the primitive part of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|mainContent| (($ $) "\\axiom{mainContent(p)} returns the content of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(p)} replaces \\axiom{p} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(r,p)} returns the \\spad{gcd} of \\axiom{r} and the content of \\axiom{p}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(p,q,z,s)} is the multivariate version of the operation \\spad{next_sousResultant2} from PseudoRemainderSequence from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(p,a,b,n)} returns \\axiom{(a**(n-1) * \\spad{p)} exquo b**(n-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,b,n)} returns \\axiom{a**n exquo b**(n-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,b)} returns the last non-zero subresultant of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,b)}, where \\axiom{a} and \\axiom{b} are not contant polynomials with the same main variable, returns the subresultant chain of \\axiom{a} and \\axiom{b}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,b)} computes the resultant of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,b)} returns \\axiom{[g,cb]} if \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca,cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,b)} returns \\axiom{[g,ca]} if \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca,cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[ca,cb,r]} such that \\axiom{r} is \\axiom{subResultantGcd(a,b)} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,b)} computes a \\spad{gcd} of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{R}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,b)} replaces \\axiom{a} by \\axiom{exactQuotient(a,b)}") (($ $ |#2|) "\\axiom{exactQuotient!(p,r)} replaces \\axiom{p} by \\axiom{exactQuotient(p,r)}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,b)} computes the exact quotient of \\axiom{a} by \\axiom{b}, which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(p,r)} computes the exact quotient of \\axiom{p} by \\axiom{r}, which is assumed to be a divisor of \\axiom{p}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(p)} replaces \\axiom{p} by \\axiom{primPartElseUnitCanonical(p)}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(p)} returns \\axiom{primitivePart(p)} if \\axiom{R} is a gcd-domain, otherwise \\axiom{unitCanonical(p)}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}, otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,b)} returns a polynomial \\axiom{r} such that \\axiom{initiallyReduced?(r,b)} holds and there exists an integer \\axiom{e} such that \\axiom{init(b)^e a - \\spad{r}} is zero modulo \\axiom{b}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,b)} returns a polynomial \\axiom{r} such that \\axiom{headReduced?(r,b)} holds and there exists an integer \\axiom{e} such that \\axiom{init(b)^e a - \\spad{r}} is zero modulo \\axiom{b}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,b)} returns \\axiom{[p,q,n]} where \\axiom{p / q**n} represents the residue class of \\axiom{a} modulo \\axiom{b} and \\axiom{p} is reduced w.r.t. \\axiom{b} and \\axiom{q} is \\axiom{init(b)}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,b)} computes \\axiom{a mod \\spad{b},} if \\axiom{b} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,b)} computes \\axiom{[pquo(a,b),prem(a,b)]}, both polynomials viewed as univariate polynomials in the main variable of \\axiom{b}, if \\axiom{b} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,b,v)} returns \\axiom{[c,g,q,r]} such that \\axiom{r = lazyPrem(a,b,v)}, \\axiom{(c**g)*r = prem(a,b,v)} and \\axiom{q} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]} such that \\axiom{[c,g,r] = lazyPremWithDefault(a,b)} and \\axiom{q} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,b,v)} returns \\axiom{[c,g,r]} such that \\axiom{r = lazyPrem(a,b,v)} and \\axiom{(c**g)*r = prem(a,b,v)}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,b)} returns \\axiom{[c,g,r]} such that \\axiom{r = lazyPrem(a,b)} and \\axiom{(c**g)*r = prem(a,b)}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,b,v)} returns the polynomial \\axiom{q} such that \\axiom{lazyPseudoDivide(a,b,v)} returns \\axiom{[c,g,q,r]}.") (($ $ $) "\\axiom{lazyPquo(a,b)} returns the polynomial \\axiom{q} such that \\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,b,v)} returns the polynomial \\axiom{r} reduced w.r.t. \\axiom{b} viewed as univariate polynomials in the variable \\axiom{v} such that \\axiom{b} divides \\axiom{init(b)^e a - \\spad{r}} where \\axiom{e} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,b)} returns the polynomial \\axiom{r} reduced w.r.t. \\axiom{b} and such that \\axiom{b} divides \\axiom{init(b)^e a - \\spad{r}} where \\axiom{e} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,b,v)} computes the pseudo-quotient of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in \\axiom{v}.") (($ $ $) "\\axiom{pquo(a,b)} computes the pseudo-quotient of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in the main variable of \\axiom{b}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,b,v)} computes the pseudo-remainder of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in \\axiom{v}.") (($ $ $) "\\axiom{prem(a,b)} computes the pseudo-remainder of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in the main variable of \\axiom{b}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(q,lp)} returns \\spad{true} iff \\axiom{normalized?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,b)} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero w.r.t. the main variable of \\axiom{b}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(q,lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,b)} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced w.r.t \\axiom{b}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(q,lp)} returns \\spad{true} iff \\axiom{headReduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,b)} returns \\spad{true} iff \\axiom{degree(head(a),mvar(b)) < mdeg(b)}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(q,lp)} returns \\spad{true} iff \\axiom{reduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,b)} returns \\spad{true} iff \\axiom{degree(a,mvar(b)) < mdeg(b)}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,b)} returns \\spad{true} if \\axiom{a} is greater than \\axiom{b} w.r.t. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,b)} returns \\spad{true} if \\axiom{a} is less than \\axiom{b} w.r.t. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,b)} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{b} have same rank w.r.t. Ritt and Wu Wen Tsun ordering using the refinement of Lazard, otherwise returns \\axiom{infRittWu?(a,b)}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns [1], otherwise returns the list of the monomials of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns [p], otherwise returns the list of the coefficients of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{1}, otherwise, the monomial of \\axiom{p} with lowest degree, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{1}, otherwise, \\axiom{mvar(p)} raised to the power \\axiom{mdeg(p)}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(p)} returns \\spad{false} if \\axiom{p} belongs to \\axiom{R}, otherwise returns \\spad{true} iff the initial of \\axiom{p} lies in the base ring \\axiom{R}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(p)} returns \\spad{false} if \\axiom{p} belongs to \\axiom{R}, otherwise returns \\spad{true} iff \\axiom{p} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(p,v)} returns the reductum of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in \\axiom{v}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(p,v)} returns the leading coefficient of \\axiom{p}, where \\axiom{p} is viewed as A univariate polynomial in \\axiom{v}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns the last term of \\axiom{iteratedInitials(p)}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(p)} returns \\axiom{[]} if \\axiom{p} belongs to \\axiom{R}, otherwise returns the list of the iterated initials of \\axiom{p}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(p)} returns \\axiom{0} if \\axiom{p} belongs to \\axiom{R}, otherwise returns tail(p), if \\axiom{tail(p)} belongs to \\axiom{R} or \\axiom{mvar(tail(p)) < mvar(p)}, otherwise returns \\axiom{deepestTail(tail(p))}.")) (|tail| (($ $) "\\axiom{tail(p)} returns its reductum, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(p)} returns \\axiom{p} if \\axiom{p} belongs to \\axiom{R}, otherwise returns its leading term (monomial in the AXIOM sense), where \\axiom{p} is viewed as a univariate polynomial \\indented{1}{in its main variable.}")) (|init| (($ $) "\\axiom{init(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns its leading coefficient, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(p)} returns an error if \\axiom{p} is \\axiom{0}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{0}, otherwise, returns the degree of \\axiom{p} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns its main variable \\spad{w.} \\spad{r.} \\spad{t.} to the total ordering on the elements in \\axiom{V}."))) NIL -((|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -43) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -999) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-1169))))) -(-1067 R E V) +((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -43) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1000) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-1170))))) +(-1068 R E V) ((|constructor| (NIL "\\indented{1}{Author: Marc Moreno Maza} Date Created: 04/22/1994 Date Last Updated: 14/12/1998 Description:")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(p)} returns the square free part of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(p)} returns the primitive part of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|mainContent| (($ $) "\\axiom{mainContent(p)} returns the content of \\axiom{p} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{R}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(p)} replaces \\axiom{p} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(r,p)} returns the \\spad{gcd} of \\axiom{r} and the content of \\axiom{p}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(p,q,z,s)} is the multivariate version of the operation \\spad{next_sousResultant2} from PseudoRemainderSequence from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(p,a,b,n)} returns \\axiom{(a**(n-1) * \\spad{p)} exquo b**(n-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,b,n)} returns \\axiom{a**n exquo b**(n-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,b)} returns the last non-zero subresultant of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,b)}, where \\axiom{a} and \\axiom{b} are not contant polynomials with the same main variable, returns the subresultant chain of \\axiom{a} and \\axiom{b}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,b)} computes the resultant of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,b)} returns \\axiom{[g,cb]} if \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca,cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,b)} returns \\axiom{[g,ca]} if \\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[g,ca,cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,b)} returns \\axiom{[ca,cb,r]} such that \\axiom{r} is \\axiom{subResultantGcd(a,b)} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,b)} computes a \\spad{gcd} of \\axiom{a} and \\axiom{b} where \\axiom{a} and \\axiom{b} are assumed to have the same main variable \\axiom{v} and are viewed as univariate polynomials in \\axiom{v} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{R}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,b)} replaces \\axiom{a} by \\axiom{exactQuotient(a,b)}") (($ $ |#1|) "\\axiom{exactQuotient!(p,r)} replaces \\axiom{p} by \\axiom{exactQuotient(p,r)}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,b)} computes the exact quotient of \\axiom{a} by \\axiom{b}, which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(p,r)} computes the exact quotient of \\axiom{p} by \\axiom{r}, which is assumed to be a divisor of \\axiom{p}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(p)} replaces \\axiom{p} by \\axiom{primPartElseUnitCanonical(p)}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(p)} returns \\axiom{primitivePart(p)} if \\axiom{R} is a gcd-domain, otherwise \\axiom{unitCanonical(p)}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}, otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(p)} returns the same as \\axiom{retract(p)}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(p)} returns \\axiom{p} as an element of the current domain if \\axiom{retractIfCan(p)} does not return \"failed\", otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(p)} returns \\axiom{p} as an element of the current domain if all its variables belong to \\axiom{V}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,b)} returns a polynomial \\axiom{r} such that \\axiom{initiallyReduced?(r,b)} holds and there exists an integer \\axiom{e} such that \\axiom{init(b)^e a - \\spad{r}} is zero modulo \\axiom{b}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,b)} returns a polynomial \\axiom{r} such that \\axiom{headReduced?(r,b)} holds and there exists an integer \\axiom{e} such that \\axiom{init(b)^e a - \\spad{r}} is zero modulo \\axiom{b}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,b)} returns \\axiom{[p,q,n]} where \\axiom{p / q**n} represents the residue class of \\axiom{a} modulo \\axiom{b} and \\axiom{p} is reduced w.r.t. \\axiom{b} and \\axiom{q} is \\axiom{init(b)}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,b)} computes \\axiom{a mod \\spad{b},} if \\axiom{b} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,b)} computes \\axiom{[pquo(a,b),prem(a,b)]}, both polynomials viewed as univariate polynomials in the main variable of \\axiom{b}, if \\axiom{b} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,b,v)} returns \\axiom{[c,g,q,r]} such that \\axiom{r = lazyPrem(a,b,v)}, \\axiom{(c**g)*r = prem(a,b,v)} and \\axiom{q} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]} such that \\axiom{[c,g,r] = lazyPremWithDefault(a,b)} and \\axiom{q} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,b,v)} returns \\axiom{[c,g,r]} such that \\axiom{r = lazyPrem(a,b,v)} and \\axiom{(c**g)*r = prem(a,b,v)}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,b)} returns \\axiom{[c,g,r]} such that \\axiom{r = lazyPrem(a,b)} and \\axiom{(c**g)*r = prem(a,b)}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,b,v)} returns the polynomial \\axiom{q} such that \\axiom{lazyPseudoDivide(a,b,v)} returns \\axiom{[c,g,q,r]}.") (($ $ $) "\\axiom{lazyPquo(a,b)} returns the polynomial \\axiom{q} such that \\axiom{lazyPseudoDivide(a,b)} returns \\axiom{[c,g,q,r]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,b,v)} returns the polynomial \\axiom{r} reduced w.r.t. \\axiom{b} viewed as univariate polynomials in the variable \\axiom{v} such that \\axiom{b} divides \\axiom{init(b)^e a - \\spad{r}} where \\axiom{e} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,b)} returns the polynomial \\axiom{r} reduced w.r.t. \\axiom{b} and such that \\axiom{b} divides \\axiom{init(b)^e a - \\spad{r}} where \\axiom{e} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,b,v)} computes the pseudo-quotient of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in \\axiom{v}.") (($ $ $) "\\axiom{pquo(a,b)} computes the pseudo-quotient of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in the main variable of \\axiom{b}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,b,v)} computes the pseudo-remainder of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in \\axiom{v}.") (($ $ $) "\\axiom{prem(a,b)} computes the pseudo-remainder of \\axiom{a} by \\axiom{b}, both viewed as univariate polynomials in the main variable of \\axiom{b}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(q,lp)} returns \\spad{true} iff \\axiom{normalized?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,b)} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero w.r.t. the main variable of \\axiom{b}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(q,lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,b)} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced w.r.t \\axiom{b}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(q,lp)} returns \\spad{true} iff \\axiom{headReduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,b)} returns \\spad{true} iff \\axiom{degree(head(a),mvar(b)) < mdeg(b)}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(q,lp)} returns \\spad{true} iff \\axiom{reduced?(q,p)} holds for every \\axiom{p} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,b)} returns \\spad{true} iff \\axiom{degree(a,mvar(b)) < mdeg(b)}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,b)} returns \\spad{true} if \\axiom{a} is greater than \\axiom{b} w.r.t. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,b)} returns \\spad{true} if \\axiom{a} is less than \\axiom{b} w.r.t. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,b)} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{b} have same rank w.r.t. Ritt and Wu Wen Tsun ordering using the refinement of Lazard, otherwise returns \\axiom{infRittWu?(a,b)}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns [1], otherwise returns the list of the monomials of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns [p], otherwise returns the list of the coefficients of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{1}, otherwise, the monomial of \\axiom{p} with lowest degree, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(p)} returns an error if \\axiom{p} is \\axiom{O}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{1}, otherwise, \\axiom{mvar(p)} raised to the power \\axiom{mdeg(p)}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(p)} returns \\spad{false} if \\axiom{p} belongs to \\axiom{R}, otherwise returns \\spad{true} iff the initial of \\axiom{p} lies in the base ring \\axiom{R}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(p)} returns \\spad{false} if \\axiom{p} belongs to \\axiom{R}, otherwise returns \\spad{true} iff \\axiom{p} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(p,v)} returns the reductum of \\axiom{p}, where \\axiom{p} is viewed as a univariate polynomial in \\axiom{v}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(p,v)} returns the leading coefficient of \\axiom{p}, where \\axiom{p} is viewed as A univariate polynomial in \\axiom{v}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns the last term of \\axiom{iteratedInitials(p)}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(p)} returns \\axiom{[]} if \\axiom{p} belongs to \\axiom{R}, otherwise returns the list of the iterated initials of \\axiom{p}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(p)} returns \\axiom{0} if \\axiom{p} belongs to \\axiom{R}, otherwise returns tail(p), if \\axiom{tail(p)} belongs to \\axiom{R} or \\axiom{mvar(tail(p)) < mvar(p)}, otherwise returns \\axiom{deepestTail(tail(p))}.")) (|tail| (($ $) "\\axiom{tail(p)} returns its reductum, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(p)} returns \\axiom{p} if \\axiom{p} belongs to \\axiom{R}, otherwise returns its leading term (monomial in the AXIOM sense), where \\axiom{p} is viewed as a univariate polynomial \\indented{1}{in its main variable.}")) (|init| (($ $) "\\axiom{init(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns its leading coefficient, where \\axiom{p} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(p)} returns an error if \\axiom{p} is \\axiom{0}, otherwise, if \\axiom{p} belongs to \\axiom{R} returns \\axiom{0}, otherwise, returns the degree of \\axiom{p} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(p)} returns an error if \\axiom{p} belongs to \\axiom{R}, otherwise returns its main variable \\spad{w.} \\spad{r.} \\spad{t.} to the total ordering on the elements in \\axiom{V}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-1068 S |TheField| |ThePols|) +(-1069 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common access functions for all real roots of polynomials")) (|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,n)} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure, assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1069 |TheField| |ThePols|) +(-1070 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common access functions for all real roots of polynomials")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,root,prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,root,prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,n)} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure, assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1070 R E V P TS) +(-1071 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu, Wang or Lazard methods). This algorithm is valid for any type of regular set. It does not care about the way a polynomial is added in an regular set, or how two quasi-components are compared (by an inclusion-test), or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(R,E,V,P,TS) and \\axiomType{RSETGCD}(R,E,V,P,TS). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call directly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus, the operations of this package are not documented."))) NIL NIL -(-1071 S R E V P) +(-1072 S R E V P) ((|constructor| (NIL "The category of regular triangular sets, introduced under the name regular chains in \\spad{[1]} (and other papers). In \\spad{[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,...,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,...,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(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (w.r.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 false. This category provides operations related to both kinds of splits, the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the RegularTriangularSet constructor for more explanations about decompositions by means of regular triangular sets.")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is false, it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or, in other words, a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for \\spad{ts} in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? \\spad{lp}} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first \\spad{lp,} extend(rest \\spad{lp,} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for \\spad{ts} in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself, if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest \\spad{lp,} internalAugment(first \\spad{lp,} ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for \\spad{ts} in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp}, \\spad{augment(p,ts)} if \\spad{lp = [p]}, otherwise \\spad{augment(first \\spad{lp,} augment(rest \\spad{lp,} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for \\spad{ts} in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set, say \\spad{ts+p}, is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself, if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for \\spad{ts} in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial w.r.t. \\spad{lpwt.i.tower}, this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower}, for every \\spad{i}. Moreover, the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts}, then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} w.r.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} w.r.t. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials w.r.t. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same main variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} w.r.t. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{I} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic w.r.t. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic w.r.t. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic w.r.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(ts,v) and \\spad{ts_v_-} is collectUnder from TriangularSetCategory(ts,v).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic w.r.t. \\spad{ts}."))) NIL NIL -(-1072 R E V P) +(-1073 R E V P) ((|constructor| (NIL "The category of regular triangular sets, introduced under the name regular chains in \\spad{[1]} (and other papers). In \\spad{[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,...,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,...,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(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (w.r.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 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 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 \\spad{ts} in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? \\spad{lp}} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first \\spad{lp,} extend(rest \\spad{lp,} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for \\spad{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|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest \\spad{lp,} internalAugment(first \\spad{lp,} ts))}") (($ |#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 \\spad{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 \\spad{lp,} augment(rest \\spad{lp,} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for \\spad{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 \\spad{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 w.r.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} w.r.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} w.r.t. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials w.r.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} w.r.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{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 w.r.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 w.r.t. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic w.r.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(ts,v) and \\spad{ts_v_-} is collectUnder from TriangularSetCategory(ts,v).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic w.r.t. \\spad{ts}."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1073 R E V P TS) +(-1074 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(p,ts)} has the same specifications as squareFreePart from RegularTriangularSetCategory.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(p1,p2,ts)} has the same specifications as invertibleSet from RegularTriangularSetCategory.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(p1,p2,ts)} has the same specifications as invertible? from RegularTriangularSetCategory.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(p1,p2,ts)} has the same specifications as invertible? from RegularTriangularSetCategory.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(p1,p2,ts)} has the same specifications as lastSubResultant from RegularTriangularSetCategory.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(p1,p2,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,v,flag)} is an internal subroutine, exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(p1,p2,ts,inv?,break?)} is an internal subroutine, exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(p1,p2,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!(s1,s2,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!(s1,s2,s3)} is an internal subroutine, exported only for developement."))) NIL NIL -(-1074 |f|) +(-1075 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1075 |Base| R -3280) +(-1076 |Base| R -3313) ((|constructor| (NIL "Rules for the pattern matcher")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted, that is they are not evaluated during any rewrite, but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or r(f, \\spad{n)} applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r.}")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r.}")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r.}")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], \\spad{f)}} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, \\spad{g,} [f1,...,fn])} creates the rewrite rule \\spad{f \\spad{==} eval(eval(g, \\spad{g} is \\spad{f),} [f1,...,fn])}, that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g;} The symbols f1,...,fn are the operators that are considered quoted, that is they are not evaluated during any rewrite, but just applied formally to their arguments.") (($ |#3| |#3|) "\\indented{1}{rule(f, \\spad{g)} creates the rewrite rule: \\spad{f \\spad{==} eval(g, \\spad{g} is f)},} \\indented{1}{with left-hand side \\spad{f} and right-hand side \\spad{g.}} \\blankline \\spad{X} logrule \\spad{:=} rule log(x) + log(y) \\spad{==} log(x*y) \\spad{X} \\spad{f} \\spad{:=} log(sin(x)) + log(x) \\spad{X} logrule \\spad{f}"))) NIL NIL -(-1076 |Base| R -3280) +(-1077 |Base| R -3313) ((|constructor| (NIL "Sets of rules for the pattern matcher. A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or r(f, \\spad{n)} applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r.}")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL -(-1077 R |ls|) +(-1078 R |ls|) ((|constructor| (NIL "A package for computing the rational univariate representation of a zero-dimensional algebraic variety given by a regular triangular set. This package is essentially an interface for the \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover, if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls}, called the coordinate of \\spad{c}, and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover, a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient w.r.t. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1078 UP SAE UPA) +(-1079 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p.}"))) NIL NIL -(-1079 R UP M) +(-1080 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."))) -((-4593 |has| |#1| (-367)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-352))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-352)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-367)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-352))))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (QUOTE (-367)))) (-1831 (-12 (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-352))))) -(-1080 UP SAE UPA) +((-4595 |has| |#1| (-368)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-353))))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-368)))) (-1841 (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-353))))) +(-1081 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p.}"))) NIL NIL -(-1081) +(-1082) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1082 S) +(-1083 S) ((|constructor| (NIL "A sorted cache of a cachable set \\spad{S} is a dynamic structure that keeps the elements of \\spad{S} sorted and assigns an integer to each element of \\spad{S} once it is in the cache. This way, equality and ordering on \\spad{S} are tested directly on the integers associated with the elements of \\spad{S,} once they have been entered in the cache.")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, \\spad{f)}} enters \\spad{x} in the cache, calling \\spad{f(x, \\spad{y)}} to determine whether \\spad{x < \\spad{y} (f(x,y) < 0), \\spad{x} = \\spad{y} (f(x,y) = 0)}, or \\spad{x > \\spad{y} (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, \\spad{f)}} enters \\spad{x} in the cache, calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y.} It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1083 R) +(-1084 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},...,\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra, \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note, that the it is not checked, whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt,} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls.} The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt,} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls.} The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1084 R) +(-1085 R) ((|constructor| (NIL "A basic implementation of StochasticDifferential(R) using the associated domain BasicStochasticDifferential in the underlying representation as sparse multivariate polynomials. The domain is a module over Expression(R), and is a ring without identity (AXIOM term is \"Rng\"). Note that separate instances, for example using R=Integer and R=Float, have different hidden structure (multiplication and drift tables).")) (|uncorrelated?| (((|Boolean|) (|List| (|List| $))) "\\spad{uncorrelated?(ll)} checks whether its argument is a list of lists of stochastic differentials of zero inter-list quadratic co-variation.") (((|Boolean|) (|List| $) (|List| $)) "\\spad{uncorrelated?(l1,l2)} checks whether its two arguments are lists of stochastic differentials of zero inter-list quadratic co-variation.") (((|Boolean|) $ $) "\\spad{uncorrelated?(dx,dy)} checks whether its two arguments have zero quadratic co-variation.")) (|statusIto| (((|OutputForm|)) "\\indented{1}{statusIto() displays the current state of \\axiom{setBSD},} \\indented{1}{\\axiom{tableDrift}, and \\axiom{tableQuadVar}. Question} \\indented{1}{marks are printed instead of undefined entries} \\blankline \\spad{X} dt:=introduce!(t,dt) \\spad{X} dX:=introduce!(X,dX) \\spad{X} dY:=introduce!(Y,dY) \\spad{X} copyBSD() \\spad{X} copyIto() \\spad{X} copyhQuadVar() \\spad{X} statusIto()")) (^ (($ $ (|PositiveInteger|)) "\\spad{dx^n} is \\spad{dx} multiplied by itself \\spad{n} times.")) (** (($ $ (|PositiveInteger|)) "\\spad{dx**n} is \\spad{dx} multiplied by itself \\spad{n} times.")) (/ (($ $ (|Expression| |#1|)) "\\spad{dx/y} divides the stochastic differential \\spad{dx} by the previsible function \\spad{y.}")) (|copyQuadVar| (((|Table| $ $)) "\\spad{copyQuadVar returns} private multiplication table of basic stochastic differentials for inspection")) (|copyDrift| (((|Table| $ $)) "\\spad{copyDrift returns} private table of drifts of basic stochastic differentials for inspection")) (|equation| (((|Union| (|Equation| $) "failed") |#1| $) "\\spad{equation(0,dx)} allows \\spad{LHS} of Equation \\% to be zero") (((|Union| (|Equation| $) "failed") $ |#1|) "\\spad{equation(dx,0)} allows \\spad{RHS} of Equation \\% to be zero")) (|listSD| (((|List| (|BasicStochasticDifferential|)) $) "\\spad{listSD(dx)} returns a list of all \\axiom{BSD} involved in the generation of \\axiom{dx} as a module element")) (|coefficient| (((|Expression| |#1|) $ (|BasicStochasticDifferential|)) "\\spad{coefficient(sd,dX)} returns the coefficient of \\axiom{dX} in the stochastic differential \\axiom{sd}")) (|freeOf?| (((|Boolean|) $ (|BasicStochasticDifferential|)) "\\spad{freeOf?(sd,dX)} checks whether \\axiom{dX} occurs in \\axiom{sd} as a module element")) (|drift| (($ $) "\\spad{drift(dx)} returns the drift of \\axiom{dx}")) (|alterDrift!| (((|Union| $ "failed") (|BasicStochasticDifferential|) $) "\\spad{alterDrift! adds} drift formula for a stochastic differential to a private table. Failure occurs if \\indented{1}{(a) first arguments is not basic} \\indented{1}{(b) second argument is not exactly of first degree}")) (|alterQuadVar!| (((|Union| $ "failed") (|BasicStochasticDifferential|) (|BasicStochasticDifferential|) $) "\\spad{alterQuadVar! adds} multiplication formula for a pair of stochastic differentials to a private table. Failure occurs if \\indented{1}{(a) either of first or second arguments is not basic} \\indented{1}{(b) third argument is not exactly of first degree}"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-1085 R) +(-1086 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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1086 (-1169)) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1086 (-1169)) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1086 (-1169)) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1086 (-1169)) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1086 (-1169)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-1086 S) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1087 (-1170)) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1087 (-1170)) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1087 (-1170)) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1087 (-1170)) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1087 (-1170)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-1087 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}(u), \\spadfun{order}(u))."))) NIL NIL -(-1087 R S) +(-1088 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s,} applying \\spad{f} to each value. For example, if \\spad{s = l..h by \\spad{k},} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed, where \\spad{lN \\spad{<=} \\spad{h} < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-845)))) -(-1088 R S) +((|HasCategory| |#1| (QUOTE (-846)))) +(-1089 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}s.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1089 S) +(-1090 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used, for example, by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example, if \\spad{segb} is \\spad{v=a..b}, then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example, if \\spad{segb} is \\spad{v=a..b}, then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1097)))) -(-1090 S) +((|HasCategory| |#1| (QUOTE (-1098)))) +(-1091 S) ((|constructor| (NIL "This category provides operations on ranges, or segments as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n}, where \\spad{s} is a segment in which every \\spad{n}-th element is used. Note that \\spad{incr(l..h by \\spad{n)} = \\spad{n}.}")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s.} Note that \\spad{high(l..h) = \\spad{h}.}")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s.} Note that \\spad{low(l..h) = \\spad{l}.}")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s.} Note that \\spad{hi(l..h) = \\spad{h}.}")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s.} Note that \\spad{lo(l..h) = \\spad{l}.}")) (BY (($ $ (|Integer|)) "\\spad{s by \\spad{n}} creates a new segment in which only every \\spad{n}-th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1091 S) +(-1092 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1097)))) -(-1092 S L) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1098)))) +(-1093 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by \\spad{k)}} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment, that is, \\spad{[f(l), f(l+k), ..., f(lN)]}, where \\spad{lN \\spad{<=} \\spad{h} < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by \\spad{k)}} creates value of type \\spad{L} with elements \\spad{l, l+k, \\spad{...} \\spad{lN}} where \\spad{lN \\spad{<=} \\spad{h} < lN+k}. For example, \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by \\spad{k}} is replaced with \\spad{l, l+k, \\spad{...} lN}, where \\spad{lN \\spad{<=} \\spad{h} < lN+k}. For example, \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1093 A S) +(-1094 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both, the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x,} \\axiom{union(x,u)} returns a copy of u.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x,} \\axiom{union(u,x)} returns a copy of 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|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v.} Note that equivalent to \\axiom{reduce(and,{member?(x,v) for \\spad{x} in u},true,false)}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common, \\axiom{symmetricDifference(u,v)} returns a copy of u. Note that \\axiom{symmetricDifference(u,v) = \\indented{1}{union(difference(u,v),difference(v,u))}}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x,} a copy of \\spad{u} is returned. Note that \\axiom{difference(s, \\spad{x)} = difference(s, {x})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v.} If \\spad{u} and \\spad{v} have no elements in common, \\axiom{difference(u,v)} returns a copy of u. Note that equivalent to the notation (not currently supported) \\axiom{{x for \\spad{x} in \\spad{u} | not member?(x,v)}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v.} Note that equivalent to the notation (not currently supported) \\spad{{x} for \\spad{x} in \\spad{u} | member?(x,v)}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items x,y,...,z.") (($) "\\spad{set()}$D creates an empty set aggregate of type \\spad{D.}")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items x,y,...,z. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}$D (otherwise written {}$D) creates an empty set aggregate of type \\spad{D.} This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < \\spad{t}} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t.}"))) NIL NIL -(-1094 S) +(-1095 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both, the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x,} \\axiom{union(x,u)} returns a copy of u.") (($ $ |#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(u,x)} returns a copy of 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|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v.} Note that equivalent to \\axiom{reduce(and,{member?(x,v) for \\spad{x} in u},true,false)}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common, \\axiom{symmetricDifference(u,v)} returns a copy of u. Note that \\axiom{symmetricDifference(u,v) = \\indented{1}{union(difference(u,v),difference(v,u))}}")) (|difference| (($ $ |#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(s, \\spad{x)} = difference(s, {x})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v.} If \\spad{u} and \\spad{v} have no elements in common, \\axiom{difference(u,v)} returns a copy of u. Note that equivalent to the notation (not currently supported) \\axiom{{x for \\spad{x} in \\spad{u} | not member?(x,v)}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v.} Note that equivalent to the notation (not currently supported) \\spad{{x} for \\spad{x} in \\spad{u} | member?(x,v)}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items x,y,...,z.") (($) "\\spad{set()}$D creates an empty set aggregate of type \\spad{D.}")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items x,y,...,z. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}$D (otherwise written {}$D) creates an empty set aggregate of type \\spad{D.} This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < \\spad{t}} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t.}"))) -((-4590 . T) (-3348 . T)) +((-4592 . T) (-3389 . T)) NIL -(-1095) +(-1096) ((|constructor| (NIL "This is part of the PAFF package, related to projective space."))) NIL NIL -(-1096 S) +(-1097 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes\\br \\tab{5}canonical\\tab{5}data structure equality is the same as \\spadop{=}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s.}")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s.}"))) NIL NIL -(-1097) +(-1098) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes\\br \\tab{5}canonical\\tab{5}data structure equality is the same as \\spadop{=}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s.}")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s.}"))) NIL NIL -(-1098 |m| |n|) +(-1099 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S.}")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, \\spad{s)}} returns \\spad{true} is \\spad{p} is in \\spad{s,} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {a_1,...,a_m}. Error if {a_1,...,a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p,} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S,} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1099 S) +(-1100 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 = \\spad{m}} and \\spad{\\#t = \\spad{n},} the complexity of\\br \\tab{5}\\spad{s = \\spad{t}} is \\spad{O(min(n,m))}\\br \\tab{5}\\spad{s < \\spad{t}} is \\spad{O(max(n,m))}\\br \\tab{5}\\spad{union(s,t)}, \\spad{intersect(s,t)}, \\spad{minus(s,t)},\\br \\tab{10 \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}\\br \\tab{5}\\spad{member(x,t)} is \\spad{O(n log n)}\\br \\tab{5}\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}"))) -((-4600 . T) (-4590 . T) (-4601 . T)) -((|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-847))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-1100 |Str| |Sym| |Int| |Flt| |Expr|) +((-4602 . T) (-4592 . T) (-4603 . T)) +((|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (QUOTE (-848))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-1101 |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{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n.}")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|convert| (($ |#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 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 Flt; Error: if \\spad{s} is not an atom that also belongs to 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 Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,...,an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to 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 Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list, possibly \\spad{().}")) (|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 S-expression \\spad{().}")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, \\spad{t)}} is \\spad{true} if EQ(s,t) is \\spad{true} in Lisp."))) NIL NIL -(-1101) +(-1102) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1102 |Str| |Sym| |Int| |Flt| |Expr|) +(-1103 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1103 R FS) +(-1104 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(f,type)} provides a simple model of some FORTRAN subprograms, making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{f}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name, the type and the \\spad{body} of the program."))) NIL NIL -(-1104 R E V P TS) +(-1105 R E V P TS) ((|constructor| (NIL "A internal package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets.")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,ts,lineq,b1,b2,b3,b4,b5)} is an internal subroutine, exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,lts,b1,b2)} is an internal subroutine, exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine, exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,lpwt2)} is an internal subroutine, exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,us)} returns \\spad{true} iff internalSubQuasiComponent?(ts,us) from QuasiComponentPackage returns true.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{b} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(lp1,lp2)} is an internal subroutine, exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(lp1,lp2)} is an internal subroutine, exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(lp1,lp2)} returns \\spad{true} iff \\axiom{lp1} is a sub-set of \\axiom{lp2} assuming that these lists are sorted increasingly w.r.t. infRittWu? from RecursivePolynomialCategory.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(lp1,lp2)} returns \\spad{true} iff \\axiom{lp1} is a sub-set of \\axiom{lp2}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty, or \\axiom{ts} has less elements than \\axiom{us}, or some variable is algebraic w.r.t. \\axiom{us} and is not w.r.t. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} w.r.t supDimElseRittWu from QuasiComponentPackage.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} w.r.t. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine, exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(s1,s2,s3)} is an internal subroutine, exported only for developement."))) NIL NIL -(-1105 R E V P TS) +(-1106 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}."))) NIL NIL -(-1106 R E V P) +(-1107 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(p,mvar(p)) w.r.t. collectUnder(ts,mvar(p)) has degree zero w.r.t. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1107) +(-1108) ((|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 m-subset of the set 0,1,...,(n-1) in the lexicographic order considered as a decreasing map from 0,...,(m-1) into 0,...,(n-1). See S.G. Williamson: Theorem 1.60. Error: if not \\spad{(0} \\spad{<=} \\spad{m} \\spad{<=} \\spad{n} and 0 < = \\spad{k} < \\spad{(n} choose m)).")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: 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 gamma. the first partition is achieved by part=[]. Also, \\spad{[]} 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 gamma. The first partition is achieved by part=[]. Also, \\spad{[]} 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 true. If \\spad{constructNotFirst} is 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 lambda. Notes: see listYoungTableaus. The entries are from 0,...,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 lambda. Notes: the functions nextLatticePermutation and makeYoungTableau are used. The entries are from 0,...,n-1.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums 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 alpha). For such a matrix \\spad{C,} inverseColeman(alpha,beta,C) calculates the lexicographical smallest \\spad{pi} in the corresponding double coset. Note that the resulting permutation \\spad{pi} of {1,2,...,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,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums 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 alpha). For a representing element \\spad{pi} of such a double coset, coleman(alpha,beta,pi) generates the Coleman-matrix corresponding to alpha, beta, pi. Note that The permutation \\spad{pi} of {1,2,...,n} has to be given in list form. Note that the inverse of this map is inverseColeman (if \\spad{pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1108 S) +(-1109 S) ((|constructor| (NIL "the class of all multiplicative semigroups, that is, a set with an associative operation \\spadop{*}. \\blankline Axioms\\br \\tab{5}\\spad{associative(\"*\":(\\%,\\%)->\\%)}\\tab{5}\\spad{(x*y)*z = x*(y*z)} \\blankline Conditional attributes\\br \\tab{5}\\spad{commutative(\"*\":(\\%,\\%)->\\%)}\\tab{5}\\spad{x*y = y*x}")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times, exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times, exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y.}"))) NIL NIL -(-1109) +(-1110) ((|constructor| (NIL "the class of all multiplicative semigroups, that is, a set with an associative operation \\spadop{*}. \\blankline Axioms\\br \\tab{5}\\spad{associative(\"*\":(\\%,\\%)->\\%)}\\tab{5}\\spad{(x*y)*z = x*(y*z)} \\blankline Conditional attributes\\br \\tab{5}\\spad{commutative(\"*\":(\\%,\\%)->\\%)}\\tab{5}\\spad{x*y = y*x}")) (^ (($ $ (|PositiveInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times, exponentiation.")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times, exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y.}"))) NIL NIL -(-1110 |dimtot| |dim1| S) +(-1111 |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}."))) -((-4594 |has| |#3| (-1053)) (-4595 |has| |#3| (-1053)) (-4597 |has| |#3| (-6 -4597)) ((-4602 "*") |has| |#3| (-173)) (-4600 . T)) -((|HasCategory| |#3| (QUOTE (-1097))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1053))) (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (QUOTE (-845))) (-1831 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (QUOTE (-845)))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-173))) (-1831 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1053)))) (-1831 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (-1831 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-1053)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#3| (QUOTE (-226))) (-1831 (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-226))) 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real roots \\spad{p} has, counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with p2<0. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1.}")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL -((|HasCategory| |#1| (QUOTE (-456)))) -(-1112 R -3280) +((|HasCategory| |#1| (QUOTE (-457)))) +(-1113 R -3313) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, \\spad{x,} a, \\spad{s)}} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\", or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, \\spad{x,} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a}, from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1113 R) +(-1114 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, \\spad{x,} a, \\spad{s)}} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"}, or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, \\spad{x,} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a}, from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign \\spad{f}} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1114) +(-1115) ((|constructor| (NIL "Package to allow simplify to be called on AlgebraicNumbers by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1115) +(-1116) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical or of the single integers \\spad{n} and \\spad{m.}")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical and of the single integers \\spad{n} and \\spad{m.}")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical not of the single integer \\spad{n.}")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical xor of the single integers \\spad{n} and \\spad{m.}")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical or of the single integers \\spad{n} and \\spad{m.}")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical and of the single integers \\spad{n} and \\spad{m.}")) (~ (($ $) "\\spad{~ \\spad{n}} returns the bit-by-bit logical not of the single integer \\spad{n.}")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical not of the single integer \\spad{n.}")) (|min| (($) "\\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."))) -((-4588 . T) (-4592 . T) (-4587 . T) (-4598 . T) (-4599 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4590 . T) (-4594 . T) (-4589 . T) (-4600 . T) (-4601 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1116 S) +(-1117 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s.} \\indented{1}{Note that \\axiom{depth(s) = \\#s}.} \\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} depth a")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s;} \\spad{s} remains unchanged. \\indented{1}{Note that Use \\axiom{pop!(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| $) "\\spad{pop!(s)} returns the top element \\spad{x,} destructively removing \\spad{x} from \\spad{s.} \\indented{1}{Note that Use \\axiom{top(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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s,} that is, destructively changing \\spad{s} \\indented{1}{so as to have a new first (top) element \\spad{x.}} \\indented{1}{Afterwards, pop!(s) produces \\spad{x} and pop!(s) produces the original \\spad{s.}} \\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} push! a \\spad{X} a"))) -((-4600 . T) (-4601 . T) (-3348 . T)) +((-4602 . T) (-4603 . T) (-3389 . T)) NIL -(-1117 S |ndim| R |Row| |Col|) +(-1118 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 * \\spad{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 * \\spad{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 n-by-n matrix with \\spad{r's} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4602 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) -(-1118 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-368))) (|HasAttribute| |#3| (QUOTE (-4604 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +(-1119 |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 * \\spad{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 * \\spad{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 n-by-n matrix with \\spad{r's} on the diagonal and zeroes elsewhere."))) -((-3348 . T) (-4600 . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-3389 . T) (-4602 . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1119 R |Row| |Col| M) +(-1120 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 = \\spad{B}.}")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m.}")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m.}"))) NIL NIL -(-1120 R |VarSet|) +(-1121 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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-1121 |Coef| |Var| SMP) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-1122 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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, \\spad{n)}} gives the terms of total degree \\spad{n.}} \\blankline \\spad{X} xts:=x::TaylorSeries Fraction Integer \\spad{X} t1:=sin(xts) \\spad{X} coefficient(t1,3)"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-561))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1122 R E V P) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-562))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368)))) +(-1123 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."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1123 UP -3280) +(-1124 UP -3313) ((|constructor| (NIL "This package factors the formulas out of the general solve code, allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL -(-1124 R) +(-1125 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R.}")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x,} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} contractSolve(b,x)") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x.} The result contains new symbols for common subexpressions in order to reduce the size of the output. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} contractSolve(b=0,x)")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols lvar. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1) \\spad{X} radicalRoots([b,c],[x,y])") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} radicalRoots(b,x)")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in leq. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1) \\spad{X} radicalSolve([b=0,c=0])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols lvar. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1) \\spad{X} radicalSolve([b=0,c=0],[x,y])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0, where \\spad{lrf} is a system of univariate rational functions. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1) \\spad{X} radicalSolve([b,c])") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols lvar, \\indented{1}{where \\spad{lrf} is a list of rational functions.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} c:Fraction(Polynomial(Integer)):=(y^2+4)/(y+1) \\spad{X} radicalSolve([b,c],[x,y])") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in eq. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(b=0)") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x.} \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(b=0,x)") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0, where \\spad{rf} is a univariate rational function. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(b)") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x,} where \\spad{rf} is a rational function. \\blankline \\spad{X} b:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) \\spad{X} radicalSolve(b,x)"))) NIL NIL -(-1125 R) +(-1126 R) ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} are given and \\spad{func1} = func3(func2) . If there is no solution then function \\spad{func1} will be returned. An example would be \\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and \\spad{func2:=2*X ::EXPR INT} convert them via univariate to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X} of type FRAC SUP EXPR INT")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, \\spad{n)}} returns \\spad{vect(1) + vect(2)*var + \\spad{...} + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = func3(func2) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1126 R) +(-1127 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(R). This means expressions involving transcendental, exponential, logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules, it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\spad{-2 \\spad{tan(x/2)**4} \\spad{-2} \\spad{tan(x/2)**3} \\spad{-4} \\spad{tan(x/2)**2} \\spad{+2} tan(x/2) \\spad{-2}} by using the function normalize and then to \\spad{-2 \\spad{tan(x)**2} + tan(x) \\spad{-2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\spad{sqrt(sin(x))+1} .")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\indented{1}{solve(expr,x) finds the solutions of the equation expr = 0} \\indented{1}{with respect to the symbol \\spad{x} where expr is a function} \\indented{1}{of type Expression(R).} \\blankline \\spad{X} solve(1/2*v*v*cos(theta+phi)*cos(theta+phi)+g*l*cos(phi)=g*l,phi) \\spad{X} definingPolynomial \\spad{%phi0} \\spad{X} definingPolynomial \\spad{%phi1}") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(R) with respect to the symbol \\spad{x.}") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(R) with respect to the unique symbol \\spad{x} appearing in eq.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(R) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1127 S A) +(-1128 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-847)))) -(-1128 R) +((|HasCategory| |#1| (QUOTE (-848)))) +(-1129 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points, curves, polygons, constructs and the subspaces containing them."))) NIL NIL -(-1129 R) +(-1130 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points, curves, polygons, constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace}, \\spad{s.}")) (|check| (($ $) "\\spad{check(s)} returns lllpt, list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s.}")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace}, \\spad{s,} in the form of a 3D object record containing information on the number of points, curves, polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a list of subspace component properties, and if so, returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a list of curves which are lists of the subspace component properties of the curves, and if so, returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a list of components, which are lists of curves, which are lists of points, and if so, returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a list of components, which are lists of curves, which are lists of indices to points, and if so, returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace}, \\spad{s,} contains; these points are used by reference, that is, the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component, a mesh comprising a list of curves which are lists of points, or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a single surface component defined by a list curves which contain lists of points, and if so, returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves, \\spad{p0} through \\spad{pn,} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is, the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists, \\spad{p0} through \\spad{pn,} of points, and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s, LLLR, close1, close2)} where \\spad{LLLR} is of the form [[[r10]...,[r1m]],[[r20]...,[r2m]],...,[[rn0]...,[rnm]]], adds a surface component to the \\spadtype{ThreeSpace} \\spad{s,} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (that is, the last point of the list is to be connected to the first point); if \\spad{close2} is true, this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s, LLP, close1, close2)} where \\spad{LLP} is of the form [[p0],[p1],...,[pn]] adds a surface component to the \\spadtype{ThreeSpace}, which is defined over a list of curves, in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed, that is, the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end, that is, the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s, LLLR, [props], prop)} where \\spad{LLLR} is of the form: [[[r10]...,[r1m]],[[r20]...,[r2m]],...,[[rn0]...,[rnm]]], adds a surface component to the \\spadtype{ThreeSpace} \\spad{s,} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list, and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component, defined over a list curves which contains lists of points, to the \\spadtype{ThreeSpace} \\spad{s;} props is a list which contains the subspace component properties for each surface parameter, and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component, or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a single polygon component defined by a list of points, and if so, returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points, \\spad{p0} through \\spad{pn,} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn}, which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s,} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points, \\spad{p0} throught \\spad{pn,} to the \\spadtype{ThreeSpace} \\spad{s.}")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component, that is, the first element of the curve is also the last element, or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a single closed curve component defined by a list of points in which the first point is also the last point, all of which are from the domain \\spad{PointDomain(m,R)} and if so, returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp.}") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn}, which are lists of elements from the domain \\spad{PointDomain(m,R)}, where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points, in which the last element of the list of points contains a copy of the first element list, lr0. The closed curve is added to the \\spadtype{ThreeSpace}, \\spad{s.}") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again, to the \\spadtype{ThreeSpace} \\spad{s.}")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace}, \\spad{s,} is a curve, that is, has one component, a list of list of points, and returns \\spad{true} if it is, or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a single curve defined by a list of points and if so, returns the curve, that is, list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn}, and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,R)}, where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points, to the \\spadtype{ThreeSpace} \\spad{s.}") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn}, to the \\spadtype{ThreeSpace} \\spad{s.}")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace}, \\spad{s,} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace}, \\spad{s,} is composed of only a single point and if so, returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component, the point \\spad{p.}") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace}, \\spad{s,} at the index given by i.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace}, \\spad{s,} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point, \\spad{p,} specified as a list from \\spad{List(R)}, to the \\spadtype{ThreeSpace}, \\spad{s,} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace}, \\spad{s,} to that of point \\spad{p.} This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace}, \\spad{s,} and returns the index, to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s.}")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s,} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s.} If \\spad{s} has no composites defined (composites need to be explicitly created), the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s,} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s.} If \\spad{s} has no components defined, the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list, grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents, or composites, in the \\spadtype{ThreeSpace}, \\spad{s;} Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and, outside of the requirement that no component can belong to more than one composite at a time, the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace}, \\spad{s,} such as points, curves, polygons, and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s.}") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point, curve, mesh components and any combination."))) NIL NIL -(-1130) +(-1131) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN, Tex and Script Formula Formatter output from programs.")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l)} output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l)} output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l)} output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1131) +(-1132) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)}, (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x.}"))) NIL NIL -(-1132 V C) +(-1133 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value, that is the current expression to evaluate. The second one is its condition, that is the hypothesis under which the value has to be evaluated. The last one is its status, that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(n1,n2,o2)} returns \\spad{true} iff \\axiom{value(n1) = value(n2)} and \\axiom{o2(condition(n1),condition(n2))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(n1,n2,o1,o2)} returns \\spad{true} iff \\axiom{o1(value(n1),value(n2))} or \\axiom{value(n1) = value(n2)} and \\axiom{o2(condition(n1),condition(n2))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(n)} replaces \\spad{n} by \\axiom{empty()$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(n,b)} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty, else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(n,t)} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty, else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(n,v)} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty, else an error is produced.")) (|copy| (($ $) "\\axiom{copy(n)} returns a copy of \\spad{n.}")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(v,lt)} returns the same as \\axiom{[construct(v,t) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,vt.tower) for \\spad{vt} in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(v,t)} returns the same as \\axiom{construct(v,t,false)}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(v,t,b)} returns the non-empty node with value \\spad{v,} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(n)} returns the status of the node \\spad{n.}")) (|condition| ((|#2| $) "\\axiom{condition(n)} returns the condition of the node \\spad{n.}")) (|value| ((|#1| $) "\\axiom{value(n)} returns the value of the node \\spad{n.}")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(n)} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()$V,empty()$C,false]$\\%}"))) NIL NIL -(-1133 V C) +(-1134 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{true}. Thus, if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{true}, then \\axiom{status(value(d))} is \\axiom{true} for any subtree \\axiom{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!(l,a,ls,sub?)} returns \\axiom{a} where the children list of \\axiom{l} has been set to \\axiom{[[s]$% for \\spad{s} in \\spad{ls} | not subNodeOf?(s,a,sub?)]}. Thus, if \\axiom{l} is not a node of \\axiom{a}, this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(l,a,ls)} returns \\axiom{a} where the children list of \\axiom{l} has been set to \\axiom{[[s]$% for \\spad{s} in \\spad{ls} | not nodeOf?(s,a)]}. Thus, if \\axiom{l} is not a node of \\axiom{a}, this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(s,a)} replaces a by remove(s,a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(s,a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{b} such that \\axiom{value(b)} and \\axiom{s} have the same value, condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(s,a,sub?)} returns \\spad{true} iff for some node \\axiom{n} in \\axiom{a} we have \\axiom{s = \\spad{n}} or \\axiom{status(n)} and \\axiom{subNode?(s,n,sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(s,a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{s}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(s),condition(s)]$VT for \\spad{s} in 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(v1,t,v2,lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[v,t]$S} and with children list given by \\axiom{[[[v,t]$S]$% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(v,t,ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[v,t]$S} and with children list given by \\axiom{[[s]$% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(v,t,la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[v,t]$S} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(s)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{s} and no children. Thus, if the status of \\axiom{s} is false, \\axiom{[s]} represents the starting point of the evaluation \\axiom{value(s)} under the hypothesis \\axiom{condition(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."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1097))) (-12 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -304) (LIST (QUOTE -1132) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1097))))) -(-1134 |ndim| R) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1098))) (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -305) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1098))))) +(-1135 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices, where the number of rows \\spad{(=} 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.}"))) -((-4597 . T) (-4589 |has| |#2| (-6 (-4602 "*"))) (-4600 . T) (-4594 . T) (-4595 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226))) (|HasAttribute| |#2| (QUOTE (-4602 "*"))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-302))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-367))) (-1831 (|HasAttribute| |#2| (QUOTE (-4602 "*"))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-226)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-226)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097))))) (|HasCategory| |#2| (QUOTE (-173)))) -(-1135 S) +((-4599 . T) (-4591 |has| |#2| (-6 (-4604 "*"))) (-4602 . T) (-4596 . T) (-4597 . T)) +((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4604 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (QUOTE (-303))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-368))) (-1841 (|HasAttribute| |#2| (QUOTE (-4604 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098))))) (|HasCategory| |#2| (QUOTE (-174)))) +(-1136 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 \\spad{\",} char \" \\spad{\")}} 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 \\spad{\",} char \" \\spad{\")}} returns \\axiom{\"abc \\spad{\"}.}")) (|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 \\spad{\",} char \" \\spad{\")}} 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{j \\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{j \\spad{>=} i} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{s(i..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{p} matches subject \\axiom{s} where \\axiom{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\",\"*\")} 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 i. Note that \\axiom{substring?(s,t,0) = prefix?(s,t)}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t.} Note that \\axiom{suffix?(s,t) \\spad{==} \\indented{1}{reduce(and,[s.i = t.(n - \\spad{m} + i) for \\spad{i} in 0..maxIndex s])}} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t.} Note that \\axiom{prefix?(s,t) \\spad{==} \\indented{2}{reduce(and,[s.i = t.i for \\spad{i} in 0..maxIndex s])}.}")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1136) +(-1137) ((|constructor| (NIL "A string aggregate is a category for strings, that is, one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t.} It is provided to allow juxtaposition of strings to work as concatenation. For example, \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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 \\spad{\",} char \" \\spad{\")}} 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 \\spad{\",} char \" \\spad{\")}} returns \\axiom{\"abc \\spad{\"}.}")) (|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 \\spad{\",} char \" \\spad{\")}} 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{j \\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{j \\spad{>=} i} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{s(i..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{p} matches subject \\axiom{s} where \\axiom{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\",\"*\")} 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 i. Note that \\axiom{substring?(s,t,0) = prefix?(s,t)}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t.} Note that \\axiom{suffix?(s,t) \\spad{==} \\indented{1}{reduce(and,[s.i = t.(n - \\spad{m} + i) for \\spad{i} in 0..maxIndex s])}} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t.} Note that \\axiom{prefix?(s,t) \\spad{==} \\indented{2}{reduce(and,[s.i = t.i for \\spad{i} in 0..maxIndex s])}.}")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1137 R E V P TS) +(-1138 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's algorithm) or in the sense of the regular zeros (like in Wu, Wang or Lazard- Moreno methods). This algorithm is valid for any 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 directly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus, the operations of this package are not documented."))) NIL NIL -(-1138 R E V P) +(-1139 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(lp,b1,b2)} is an internal subroutine, exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,b1,b2,b3)} is an internal subroutine, exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,b1,b2.b3,b4)} is an internal subroutine, exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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(p,ts,b1,b2,b3,b4,b5)} is an internal subroutine, exported only for developement."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1097))) (-12 (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-373)))) -(-1139 S) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#4| (QUOTE (-1098))) (-12 (|HasCategory| |#4| (LIST (QUOTE -305) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-374)))) +(-1140 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(x+->(x>2),a)")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} any?(x+->(x=4),a)")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} every?(x+->(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|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} map!(x+->x+10,a) \\spad{X} a")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} map(x+->x+10,a) \\spad{X} a")) (|eq?| (((|Boolean|) $ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} b:=copy a \\spad{X} eq?(a,b)")) (|copy| (($ $) "\\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5] \\spad{X} copy a")) (|sample| (($) "\\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([x,y,...,z]) creates a stack with first (top)} \\indented{1}{element \\spad{x,} second element y,...,and last element \\spad{z.}} \\blankline \\spad{X} a:Stack INT:= stack [1,2,3,4,5]"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-1140 A S) +((-4602 . T) (-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-1141 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?(s) = not explictlyFinite?(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?(s) = not possiblyInfinite?(s)}."))) NIL NIL -(-1141 S) +(-1142 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?(s) = not explictlyFinite?(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?(s) = not possiblyInfinite?(s)}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1142 |Key| |Ent| |dent|) +(-1143 |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."))) -((-4601 . T)) -((|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1097))) (-12 (|HasCategory| |#2| (LIST (QUOTE -304) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1097)))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097)))) (-1831 (|HasCategory| (-2 (|:| -4080 |#1|) (|:| -4279 |#2|)) (QUOTE (-1097))) (|HasCategory| |#2| (QUOTE (-1097))))) -(-1143) +((-4603 . T)) +((|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-1098))) (-12 (|HasCategory| |#2| (LIST (QUOTE -305) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1098)))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098)))) (-1841 (|HasCategory| (-2 (|:| -4111 |#1|) (|:| -4320 |#2|)) (QUOTE (-1098))) (|HasCategory| |#2| (QUOTE (-1098))))) +(-1144) ((|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\\br \\tab{5}infinite\\tab{5}repeated nextItem's are never \"failed\".")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item, or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1144 |Coef|) +(-1145 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1145 R) +(-1146 R) ((|constructor| (NIL "This package has no description")) (|tensorMap| (((|Stream| |#1|) (|Stream| |#1|) (|Mapping| (|List| |#1|) |#1|)) "\\spad{tensorMap([s1, \\spad{s2,} ...], \\spad{f)}} returns the stream consisting of all elements of f(s1) followed by all elements of f(s2) and so on."))) NIL NIL -(-1146 S) +(-1147 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\indented{1}{concat(u) returns the left-to-right concatentation of the} \\indented{1}{streams in u. Note that \\spad{concat(u) = reduce(concat,u)}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 10..] \\spad{X} n:=[j for \\spad{j} in 1.. | prime? \\spad{j]} \\spad{X} p:=[m,n]::Stream(Stream(PositiveInteger)) \\spad{X} concat(p)"))) NIL NIL -(-1147 A B) +(-1148 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\indented{1}{reduce(b,f,u), where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},} \\indented{1}{returns the value \\spad{r(n)} computed as follows:} \\indented{1}{\\spad{r0 = f(x0,b),} \\indented{1}{r1 = f(x1,r0),...,} \\indented{1}{r(n) = f(xn,r(n-1))}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..300]::Stream(Integer) \\spad{X} f(i:Integer,j:Integer):Integer==i+j \\spad{X} reduce(1,f,m)")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\indented{1}{scan(b,h,[x0,x1,x2,...]) returns \\spad{[y0,y1,y2,...]}, where} \\indented{1}{\\spad{y0 = h(x0,b)},} \\indented{1}{\\spad{y1 = h(x1,y0)},\\spad{...}} \\indented{1}{\\spad{yn = h(xn,y(n-1))}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..]::Stream(Integer) \\spad{X} f(i:Integer,j:Integer):Integer==i+j \\spad{X} scan(1,f,m)")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\indented{1}{map(f,s) returns a stream whose elements are the function \\spad{f} applied} \\indented{1}{to the corresponding elements of \\spad{s.}} \\indented{1}{Note that \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} \\spad{f(i:PositiveInteger):PositiveInteger==i**2} \\spad{X} map(f,m)"))) NIL NIL -(-1148 A B C) +(-1149 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\indented{1}{map(f,st1,st2) returns the stream whose elements are the} \\indented{1}{function \\spad{f} applied to the corresponding elements of \\spad{st1} and st2.} \\indented{1}{\\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}.} \\blankline \\spad{S} \\spad{X} m:=[i for \\spad{i} in 1..]::Stream(Integer) \\spad{X} n:=[i for \\spad{i} in 1..]::Stream(Integer) \\spad{X} f(i:Integer,j:Integer):Integer \\spad{==} i+j \\spad{X} map(f,m,n)"))) NIL NIL -(-1149 S) +(-1150 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|) $) "\\indented{1}{filterUntil(p,s) returns \\spad{[x0,x1,...,x(n)]} where} \\indented{1}{\\spad{s = [x0,x1,x2,..]} and} \\indented{1}{n is the smallest index such that \\spad{p(xn) = true}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} f(x:PositiveInteger):Boolean \\spad{==} \\spad{x} < 5 \\spad{X} filterUntil(f,m)")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\indented{1}{filterWhile(p,s) returns \\spad{[x0,x1,...,x(n-1)]} where} \\indented{1}{\\spad{s = [x0,x1,x2,..]} and} \\indented{1}{n is the smallest index such that \\spad{p(xn) = false}.} \\blankline \\spad{X} m:=[i for \\spad{i} in 1..] \\spad{X} f(x:PositiveInteger):Boolean \\spad{==} \\spad{x} < 5 \\spad{X} filterWhile(f,m)")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\indented{1}{generate(f,x) creates an infinite stream whose first element is} \\indented{1}{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} f(x:Integer):Integer \\spad{==} \\spad{x+10} \\spad{X} generate(f,10)") (($ (|Mapping| |#1|)) "\\indented{1}{generate(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} f():Integer \\spad{==} 1 \\spad{X} generate(f)")) (|setrest!| (($ $ (|Integer|) $) "\\indented{1}{setrest!(x,n,y) sets rest(x,n) to \\spad{y.} The function will expand} \\indented{1}{cycles if necessary.} \\blankline \\spad{X} p:=[i for \\spad{i} in 1..] \\spad{X} q:=[i for \\spad{i} in 9..] \\spad{X} setrest!(p,4,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(s) creates an output form which displays all} \\indented{1}{computed elements.} \\blankline \\spad{X} 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|) $) "\\indented{1}{output(n,st) computes and displays the first \\spad{n} entries} \\indented{1}{of st.} \\blankline \\spad{X} m:=[1,2,3] \\spad{X} n:=repeating(m) \\spad{X} output(5,n)")) (|cons| (($ |#1| $) "\\indented{1}{cons(a,s) returns a stream whose \\spad{first} is \\spad{a}} \\indented{1}{and whose \\spad{rest} is \\spad{s.}} \\indented{1}{Note: \\spad{cons(a,s) = concat(a,s)}.} \\blankline \\spad{X} m:=[1,2,3] \\spad{X} n:=repeating(m) \\spad{X} cons(4,n)")) (|delay| (($ (|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(n,st) determines if st is periodic within \\spad{n.}} \\blankline \\spad{X} m:=[1,2,3] \\spad{X} n:=repeating(m) \\spad{X} findCycle(3,n) \\spad{X} findCycle(2,n)")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\indented{1}{repeating?(l,s) returns \\spad{true} if a stream \\spad{s} is periodic} \\indented{1}{with period \\spad{l,} and \\spad{false} otherwise.} \\blankline \\spad{X} m:=[1,2,3] \\spad{X} n:=repeating(m) \\spad{X} repeating?(m,n)")) (|repeating| (($ (|List| |#1|)) "\\indented{1}{repeating(l) is a repeating stream whose period is the list \\spad{l.}} \\blankline \\spad{X} m:=repeating([-1,0,1,2,3])")) (|coerce| (($ (|List| |#1|)) "\\indented{1}{coerce(l) converts a list \\spad{l} to a stream.} \\blankline \\spad{X} m:=[1,2,3,4,5,6,7,8,9,10,11,12] \\spad{X} coerce(m)@Stream(Integer) \\spad{X} m::Stream(Integer)")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4601 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-571) (QUOTE (-847)))) -(-1150) +((-4603 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-572) (QUOTE (-848)))) +(-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1151) +(-1152) ((|constructor| (NIL "This is the domain of character strings. Strings are 1 based."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-148) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-148) (QUOTE (-847))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-148) (QUOTE (-1097))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-847)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -304) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1097)))))) -(-1152 |Entry|) +((-4603 . T) (-4602 . T)) +((|HasCategory| (-148) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-148) (QUOTE (-848))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| (-148) (QUOTE (-1098))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-848)))) (-12 (|HasCategory| (-148) (LIST (QUOTE -305) (QUOTE (-148)))) (|HasCategory| (-148) (QUOTE (-1098)))))) +(-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (QUOTE (-1097))) (-12 (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (LIST (QUOTE -304) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4080) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -4279) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (QUOTE (-1097)))) (|HasCategory| (-1151) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097))) (-1831 (|HasCategory| (-2 (|:| -4080 (-1151)) (|:| -4279 |#1|)) (QUOTE (-1097))) (|HasCategory| |#1| (QUOTE (-1097)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) -(-1153 A) +((-4602 . T) (-4603 . T)) +((|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (QUOTE (-1098))) (-12 (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (LIST (QUOTE -305) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4111) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -4320) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (QUOTE (-1098)))) (|HasCategory| (-1152) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098))) (-1841 (|HasCategory| (-2 (|:| -4111 (-1152)) (|:| -4320 |#1|)) (QUOTE (-1098))) (|HasCategory| |#1| (QUOTE (-1098)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-1154 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 \\spad{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 + \\spad{d))} + f(x**(a + 2 \\spad{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 f(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 \\spad{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 [r,r+1,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 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 / \\spad{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 * \\spad{r}} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * \\spad{r} = \\spad{[a0} * \\spad{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,...] = \\spad{[r} * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * \\spad{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 + \\spad{j} = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = \\spad{[-} a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - \\spad{b}} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = \\spad{[a0} - \\spad{b0,a1} - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + \\spad{b}} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = \\spad{[a0} + \\spad{b0,a1} + b1,..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571)))))) -(-1154 |Coef|) +((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572)))))) +(-1155 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring, where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st.}")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st.}")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st.}")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st.}")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st.}")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st.}")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st.}")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st.}")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st.}")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st.}")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st.}")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st.}")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st.}")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st.}")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st.}")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st.}")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st.}")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st.}")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st.}")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st.}")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st.}")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st.}")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st.}")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st.}")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 \\spad{**} st2} computes the power of a power series \\spad{st1} by another power series st2.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st.}"))) NIL NIL -(-1155 |Coef|) +(-1156 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series, where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st.}")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st.}")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st.}")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st.}")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st.}")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st.}")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st.}")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st.}")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st.}")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st.}")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st.}")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st.}")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st.}")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st.}")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st.}")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st.}")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st.}")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st.}")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st.}")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st.}")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st.}")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st.}")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st.}")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st.}")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st.}")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st.}")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 \\spad{**} st2} computes the power of a power series \\spad{st1} by another power series st2.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st.}"))) NIL NIL -(-1156 R UP) +(-1157 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one.")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, \\spad{q)}} reduces the coefficient of \\spad{p} modulo \\spad{q,} takes the primitive part of the result, and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, \\spad{q)}} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q.} In particular, \\spad{p0 = resultant(p, q)}."))) NIL -((|HasCategory| |#1| (QUOTE (-302)))) -(-1157 |n| R) +((|HasCategory| |#1| (QUOTE (-303)))) +(-1158 |n| R) ((|constructor| (NIL "This domain is not documented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s.}")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s.} If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s.}")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s.}")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s.} If the property is closed, \\spad{True} is returned, otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s.}")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s.}")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace, \\spad{s,} along the path dictated by the list of non negative integers, li, which points to the component which has been traversed to. The subspace, \\spad{s,} is returned, where \\spad{s} is now the subspace pointed to by li.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace, \\spad{s,} to be that of \\spad{p,} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component whose property is being defined. The subspace, \\spad{s,} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace, \\spad{s,} to be closed if \\spad{b} is true, or open if \\spad{b} is false. The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component whose closed property is to be set. The subspace, \\spad{s,} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location, ind, by replacing it with the point, \\spad{p} in the 3 dimensional subspace, \\spad{s.} An error message occurs if \\spad{s} is empty, otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace, \\spad{s,} with the 4 dimensional point indicated by the index location, i. The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty, otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace, \\spad{s,} with the 4 dimensional point, \\spad{p.} The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty, otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point, \\spad{p,} to the 3 dimensional subspace, \\spad{s.} \\spad{s2} point to the end of the subspace \\spad{s.} \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point, \\spad{p,} to the 3 dimensional subspace, \\spad{s.} The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point, \\spad{p,} to the 3 dimensional subspace, \\spad{s,} and returns the new total number of points in \\spad{s.}") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location, i, to the 3 dimensional subspace, \\spad{s.} The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1}, then a specific lowest level component is being referenced. If it is less than \\spad{n - 1}, then some higher level component \\spad{(0} indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point, \\spad{p,} to the 3 dimensional subspace, \\spad{s.} The list of non negative integers, li, dictates the path to follow, or, to look at it another way, points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1}, then a specific lowest level component is being referenced. If it is less than \\spad{n - 1}, then some higher level component \\spad{(0} indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace}, \\spad{s,} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces, \\spad{ls,} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} is not documented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} is not documented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} is not documented")) (|children| (((|List| $) $) "\\spad{children(x)} is not documented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} is not documented")) (|birth| (($ $) "\\spad{birth(x)} is not documented")) (|subspace| (($) "\\spad{subspace()} is not documented")) (|new| (($) "\\spad{new()} is not documented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} is not documented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} is not documented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} is not documented"))) NIL NIL -(-1158 S1 S2) +(-1159 S1 S2) ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form \\spad{s:t}"))) NIL NIL -(-1159 |Coef| |var| |cen|) +(-1160 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4602 "*") -1831 (-3997 (|has| |#1| (-367)) (|has| (-1167 |#1| |#2| |#3|) (-820))) (|has| |#1| (-173)) (-3997 (|has| |#1| (-367)) (|has| (-1167 |#1| |#2| |#3|) (-909)))) (-4593 -1831 (-3997 (|has| |#1| (-367)) (|has| (-1167 |#1| |#2| |#3|) (-820))) (|has| |#1| (-561)) (-3997 (|has| |#1| (-367)) (|has| (-1167 |#1| |#2| |#3|) (-909)))) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . 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(|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\indented{1}{sum(f(n), \\spad{n} = a..b) returns \\spad{f(a) + f(a+1) + \\spad{...} f(b)}.} \\blankline \\spad{X} sum(i::Fraction(Polynomial(Integer)),i=1..n)") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\indented{1}{sum(f(n), \\spad{n} = a..b) returns \\spad{f(a) + f(a+1) + \\spad{...} f(b)}.} \\blankline \\spad{X} sum(i,i=1..n)") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\indented{1}{sum(a(n), \\spad{n)} returns \\spad{A} which} \\indented{1}{is the indefinite sum of \\spad{a} with respect to} \\indented{1}{upward difference on \\spad{n}, \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.} \\blankline \\spad{X} sum(i::Fraction(Polynomial(Integer)),i::Symbol)") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\indented{1}{sum(a(n), \\spad{n)} returns \\spad{A} which} \\indented{1}{is the indefinite sum of \\spad{a} with respect to} \\indented{1}{upward difference on \\spad{n}, \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.} \\blankline \\spad{X} sum(i::Polynomial(Integer),variable(i=1..n))"))) NIL NIL -(-1162 R S) +(-1163 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S.} Note that the mapping is assumed to send zero to zero, since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1163 R) +(-1164 R) ((|constructor| (NIL "This domain has no description"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4596 |has| |#1| (-367)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . 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T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-1190))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) +(-1165 E OV R P) ((|constructor| (NIL "SupFractionFactorize contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R.} Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R.}"))) NIL NIL -(-1165 R) +(-1166 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.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{x} : \\spad{p1} - \\spad{r} * x**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4596 |has| |#1| (-367)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (-1831 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| |#1| (QUOTE (-226))) (|HasAttribute| |#1| (QUOTE -4598)) (|HasCategory| |#1| (QUOTE (-456))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-456))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-149))))) -(-1166 |Coef| |var| |cen|) -((|constructor| (NIL "Sparse Puiseux series in one variable \\spadtype{SparseUnivariatePuiseuxSeries} 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{SparseUnivariatePuiseuxSeries(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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|))))) (|HasCategory| (-412 (-571)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4598 |has| |#1| (-368)) (-4600 |has| |#1| (-6 -4600)) (-4597 . 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T)) +((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1144))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (-1841 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4600)) (|HasCategory| |#1| (QUOTE (-457))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-149))))) (-1167 |Coef| |var| |cen|) +((|constructor| (NIL "Sparse Puiseux series in one variable \\spadtype{SparseUnivariatePuiseuxSeries} 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{SparseUnivariatePuiseuxSeries(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."))) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasCategory| (-413 (-572)) (QUOTE (-1110))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1168 |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,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}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasCategory| (-768) (QUOTE (-1109))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1168) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasCategory| (-769) (QUOTE (-1110))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1169) ((|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| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and \\spad{y}.}")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = \\spad{y}.}")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or \\spad{y}.}")) (GE (($ (|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!(x,y)} stores the item whose key is \\axiom{x} and whose entry is \\axiom{y}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(x)} searches the item whose key is \\axiom{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!(x)} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(x,y)} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{x} is displayed. If an item is stored then \\axiom{y} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1182) +(-1183) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input, and removes comments, and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input, by parsing and interpreting it."))) NIL NIL -(-1183 S) +(-1184 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1184) +(-1185) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue, a tex part and an epilogue. The functions \\spadfun{prologue}, \\spadfun{tex} and \\spadfun{epilogue} extract these parts, respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!}, \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example, the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'', respectively, so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to strings.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to strings.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to strings.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t.}")) (|new| (($) "\\spad{new()} create a new, empty object. Use \\spadfun{setPrologue!}, \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t.}")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t.}")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{width}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and type. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1185) +(-1186) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output, then this test is always true.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f,} if possible. If \\spad{f} is not readable or if it is positioned at the end of file, then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f,} if possible. If \\spad{f} is not readable or if it is positioned at the end of file, then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f.}")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f.} An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f.} The value of \\spad{s} is returned."))) NIL NIL -(-1186 R) +(-1187 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1187) +(-1188) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point, curve, mesh components and any combination."))) NIL NIL -(-1188 S) +(-1189 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant pi."))) NIL NIL -(-1189) +(-1190) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant pi."))) NIL NIL -(-1190 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(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?(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?(t1,t2)")) (|cyclicEntries| (((|List| $) $) "\\indented{1}{cyclicEntries(t) returns a list of top-level cycles in tree \\spad{t.}} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} cyclicEntries \\spad{t1}")) (|cyclicCopy| (($ $) "\\indented{1}{cyclicCopy(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|) $) "\\indented{1}{cyclic?(t) tests if \\spad{t} is a cyclic tree.} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} cyclic? \\spad{t1}")) (|tree| (($ |#1|) "\\indented{1}{tree(nd) creates a tree with value \\spad{nd,} and no children} \\blankline \\spad{X} tree 6") (($ (|List| |#1|)) "\\indented{1}{tree(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(nd,ls) creates a tree with value \\spad{nd,} and children ls.} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} tree(5,[t1])"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097))))) (-1191 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(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?(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?(t1,t2)")) (|cyclicEntries| (((|List| $) $) "\\indented{1}{cyclicEntries(t) returns a list of top-level cycles in tree \\spad{t.}} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} cyclicEntries \\spad{t1}")) (|cyclicCopy| (($ $) "\\indented{1}{cyclicCopy(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|) $) "\\indented{1}{cyclic?(t) tests if \\spad{t} is a cyclic tree.} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} cyclic? \\spad{t1}")) (|tree| (($ |#1|) "\\indented{1}{tree(nd) creates a tree with value \\spad{nd,} and no children} \\blankline \\spad{X} tree 6") (($ (|List| |#1|)) "\\indented{1}{tree(ls) creates a tree from a list of elements of \\spad{s.}} \\blankline \\spad{X} tree [1,2,3,4]") (($ |#1| (|List| $)) "\\indented{1}{tree(nd,ls) creates a tree with value \\spad{nd,} and children ls.} \\blankline \\spad{X} t1:=tree [1,2,3,4] \\spad{X} tree(5,[t1])"))) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098))))) +(-1192 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x.}")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x.}")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x.}")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x.}")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x.}")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x.}"))) NIL NIL -(-1192) +(-1193) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x.}")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x.}")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x.}")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x.}")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x.}")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x.}"))) NIL NIL -(-1193 R -3280) +(-1194 R -3313) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms, and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real \\spad{f,} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real \\spad{f}.}")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, \\spad{x)}} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, \\spad{x)}} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-1194 R |Row| |Col| M) +(-1195 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(B) also has entries in \\spad{R,} we return \\spad{d} * inv(B). Thus, it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M,} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = \\spad{d} * inv(B)} has entries in \\spad{R.}")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M,} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = \\spad{d} * inv(B)} has entries in \\spad{R.}"))) NIL NIL -(-1195 R -3280) +(-1196 R -3313) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(x)*sin(y)} by \\spad{(cos(x-y)-cos(x+y))/2}, \\axiom{cos(x)*cos(y)} by \\spad{(cos(x-y)+cos(x+y))/2}, and \\axiom{sin(x)*cos(y)} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2}, and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2}, and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2}, and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2}, and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)}, and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)}, every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,\\spad{cos}, \\spad{sinh}, \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh}, \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs, \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -886) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -886) (|devaluate| |#1|))))) -(-1196 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -613) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -887) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -887) (|devaluate| |#1|))))) +(-1197 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{R} be an integral domain and \\axiom{V} a finite ordered set of variables, say \\axiom{X1 < \\spad{X2} < \\spad{...} < Xn}. A set \\axiom{S} of polynomials in \\axiom{R[X1,X2,...,Xn]} is triangular if no elements of \\axiom{S} lies in \\axiom{R}, and if two distinct elements of \\axiom{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 \\spad{[1]} for more details. A polynomial \\axiom{P} is reduced w.r.t a non-constant polynomial \\axiom{Q} if the degree of \\axiom{P} in the main variable of \\axiom{Q} is less than the main degree of \\axiom{Q}. A polynomial \\axiom{P} is reduced w.r.t a triangular set \\axiom{T} if it is reduced w.r.t. every polynomial of \\axiom{T}.")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$V} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,p)} returns a triangular set which encodes the simple extension by \\axiom{p} of the extension of the base field defined by \\axiom{ts}, according to the properties of triangular sets of the current category. If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,p)} returns a triangular set which encodes the simple extension by \\axiom{p} of the extension of the base field defined by \\axiom{ts}, according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,v)} returns the polynomial of \\axiom{ts} with \\axiom{v} as main variable, if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(v,ts)} returns \\spad{true} iff \\axiom{v} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty, otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty, otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty, otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[ts1,qs1],...,[tsn,qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(p,ts)} returns the same as \\axiom{remainder(p,collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{R}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(p,ts)} returns \\axiom{0} if \\axiom{p} reduces to \\axiom{0} by pseudo-division w.r.t \\axiom{ts} otherwise returns a polynomial \\axiom{q} computed from \\axiom{p} by removing any coefficient in \\axiom{p} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{initiallyReduced?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{headReduce?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{stronglyReduced?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,ts,redOp,redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(p,ts,redOp,redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover, for every polynomial \\axiom{q} in \\axiom{lq} and every polynomial \\axiom{t} in \\axiom{ts} \\axiom{redOp?(q,t)} holds and there exists a polynomial \\axiom{p} in the ideal generated by \\axiom{lp} and a product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{p} and \\axiom{q} we have \\axiom{redOp?(redOp(p,q),q)} and there exists an integer \\axiom{e} and a polynomial \\axiom{f} such that \\axiom{init(q)^e*p = \\spad{f*q} + redOp(p,q)}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(p,ts,redOp,redOp?)} returns a polynomial \\axiom{r} such that \\axiom{redOp?(r,p)} holds for every \\axiom{p} of \\axiom{ts} and there exists some product \\axiom{h} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{p} and \\axiom{q} we have \\axiom{redOp?(redOp(p,q),q)} and there exists an integer \\axiom{e} and a polynomial \\axiom{f} such that \\axiom{init(q)^e*p = \\spad{f*q} + redOp(p,q)}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced w.r.t to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{p} of \\axiom{ts}. \\axiom{p} and all its iterated initials are reduced w.r.t. to the other elements of \\axiom{ts} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(p,ts)} returns \\spad{true} iff \\axiom{p} and all its iterated initials are reduced w.r.t. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{ts} is reduced w.r.t to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(p,ts)} returns \\spad{true} iff the head of \\axiom{p} is reduced w.r.t. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced w.r.t to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(p,ts)} returns \\spad{true} iff \\axiom{p} is reduced w.r.t. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(p,ts,redOp?)} returns \\spad{true} iff \\axiom{p} is reduced w.r.t.in the sense of the operation \\axiom{redOp?}, that is if for every \\axiom{t} in \\axiom{ts} \\axiom{redOp?(p,t)} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{p} in \\axiom{ts} we have \\axiom{normalized?(p,us)} where \\axiom{us} is \\axiom{collectUnder(ts,mvar(p))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(p,ts)} returns \\spad{true} iff \\axiom{p} and all its iterated initials have degree zero w.r.t. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,pred?,redOp?)} returns the same as \\axiom{basicSet(qs,redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,redOp?)} returns \\axiom{[bs,ts]} where \\axiom{concat(bs,ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} w.r.t the reduction-test \\axiom{redOp?}, if no non-zero constant polynomial lie in \\axiom{ps}, otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(ts1,ts2)} returns \\spad{true} iff \\axiom{ts2} has higher rank than \\axiom{ts1} in Wu Wen Tsun sense."))) NIL -((|HasCategory| |#4| (QUOTE (-373)))) -(-1197 R E V P) +((|HasCategory| |#4| (QUOTE (-374)))) +(-1198 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{R} be an integral domain and \\axiom{V} a finite ordered set of variables, say \\axiom{X1 < \\spad{X2} < \\spad{...} < Xn}. A set \\axiom{S} of polynomials in \\axiom{R[X1,X2,...,Xn]} is triangular if no elements of \\axiom{S} lies in \\axiom{R}, and if two distinct elements of \\axiom{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 \\spad{[1]} for more details. A polynomial \\axiom{P} is reduced w.r.t a non-constant polynomial \\axiom{Q} if the degree of \\axiom{P} in the main variable of \\axiom{Q} is less than the main degree of \\axiom{Q}. A polynomial \\axiom{P} is reduced w.r.t a triangular set \\axiom{T} if it is reduced w.r.t. every polynomial of \\axiom{T}.")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$V} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,p)} returns a triangular set which encodes the simple extension by \\axiom{p} of the extension of the base field defined by \\axiom{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(ts,p)} returns a triangular set which encodes the simple extension by \\axiom{p} of the extension of the base field defined by \\axiom{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(ts,v)} returns the polynomial of \\axiom{ts} with \\axiom{v} as main variable, if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(v,ts)} returns \\spad{true} iff \\axiom{v} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty, otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty, otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty, otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[ts1,qs1],...,[tsn,qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(p,ts)} returns the same as \\axiom{remainder(p,collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{R}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(p,ts)} returns \\axiom{0} if \\axiom{p} reduces to \\axiom{0} by pseudo-division w.r.t \\axiom{ts} otherwise returns a polynomial \\axiom{q} computed from \\axiom{p} by removing any coefficient in \\axiom{p} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{initiallyReduced?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{headReduce?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(p,ts)} returns a polynomial \\axiom{r} such that \\axiom{stronglyReduced?(r,ts)} holds and there exists some product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,ts,redOp,redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(p,ts,redOp,redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover, for every polynomial \\axiom{q} in \\axiom{lq} and every polynomial \\axiom{t} in \\axiom{ts} \\axiom{redOp?(q,t)} holds and there exists a polynomial \\axiom{p} in the ideal generated by \\axiom{lp} and a product \\axiom{h} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{p} and \\axiom{q} we have \\axiom{redOp?(redOp(p,q),q)} and there exists an integer \\axiom{e} and a polynomial \\axiom{f} such that \\axiom{init(q)^e*p = \\spad{f*q} + redOp(p,q)}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(p,ts,redOp,redOp?)} returns a polynomial \\axiom{r} such that \\axiom{redOp?(r,p)} holds for every \\axiom{p} of \\axiom{ts} and there exists some product \\axiom{h} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{p} and \\axiom{q} we have \\axiom{redOp?(redOp(p,q),q)} and there exists an integer \\axiom{e} and a polynomial \\axiom{f} such that \\axiom{init(q)^e*p = \\spad{f*q} + redOp(p,q)}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced w.r.t to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{p} of \\axiom{ts}. \\axiom{p} and all its iterated initials are reduced w.r.t. to the other elements of \\axiom{ts} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(p,ts)} returns \\spad{true} iff \\axiom{p} and all its iterated initials are reduced w.r.t. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{ts} is reduced w.r.t to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(p,ts)} returns \\spad{true} iff the head of \\axiom{p} is reduced w.r.t. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced w.r.t to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(p,ts)} returns \\spad{true} iff \\axiom{p} is reduced w.r.t. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(p,ts,redOp?)} returns \\spad{true} iff \\axiom{p} is reduced w.r.t.in the sense of the operation \\axiom{redOp?}, that is if for every \\axiom{t} in \\axiom{ts} \\axiom{redOp?(p,t)} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{p} in \\axiom{ts} we have \\axiom{normalized?(p,us)} where \\axiom{us} is \\axiom{collectUnder(ts,mvar(p))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(p,ts)} returns \\spad{true} iff \\axiom{p} and all its iterated initials have degree zero w.r.t. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,pred?,redOp?)} returns the same as \\axiom{basicSet(qs,redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,redOp?)} returns \\axiom{[bs,ts]} where \\axiom{concat(bs,ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} w.r.t the reduction-test \\axiom{redOp?}, if no non-zero constant polynomial lie in \\axiom{ps}, otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(ts1,ts2)} returns \\spad{true} iff \\axiom{ts2} has higher rank than \\axiom{ts1} in Wu Wen Tsun sense."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1198 |Coef|) +(-1199 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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, \\spad{n)}} gives the terms of total degree \\spad{n.}"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-561))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1199 |Curve|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-151))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-562))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368)))) +(-1200 |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 true, or if \\spad{b} is false, \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points, or the 'loops', of the given tube plot \\spad{t.}")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t.}"))) NIL NIL -(-1200) +(-1201) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r,} around the center point indicated by the point \\spad{p,} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n,} and the binormal vector given by the point(vector) \\spad{b,} and a list of lists, lls, which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n,} in the form \\spad{[[cos(n-1) a,sin(n-1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note that \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note that \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates, and keeping the color of the first point \\spad{p.} The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates, and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - \\spad{q}} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q}, using the color, or fourth coordinate, of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + \\spad{q}} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q}, using the color, or fourth coordinate, of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * \\spad{p}} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s,} preserving the color, or fourth coordinate, of \\spad{p.}")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1}, \\spad{x2}, \\spad{x3}, and also a fourth coordinate, \\spad{c,} which is generally used to specify the color of the point."))) NIL NIL -(-1201 S) +(-1202 S) ((|constructor| (NIL "This domain is used to interface with the interpreter's notion of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\indented{1}{length(x) returns the number of elements in tuple \\spad{x}} \\blankline \\spad{X} t1:PrimitiveArray(Integer):= \\spad{[i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(t1)$Tuple(Integer) \\spad{X} length(t2)")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\indented{1}{select(x,n) returns the \\spad{n}-th element of tuple \\spad{x.}} \\indented{1}{tuples are 0-based} \\blankline \\spad{X} t1:PrimitiveArray(Integer):= \\spad{[i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(t1)$Tuple(Integer) \\spad{X} select(t2,3)")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\indented{1}{coerce(a) makes a tuple from primitive array a} \\blankline \\spad{X} t1:PrimitiveArray(Integer):= \\spad{[i} for \\spad{i} in 1..10] \\spad{X} t2:=coerce(t1)$Tuple(Integer)"))) NIL -((|HasCategory| |#1| (QUOTE (-1097)))) -(-1202 -3280) +((|HasCategory| |#1| (QUOTE (-1098)))) +(-1203 -3313) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p,} a sparse univariate polynomial (sup) over a sup over \\spad{F.} Also, \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p).}")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p,} a sparse univariate polynomial (sup) over a sup over \\spad{F.}")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p,} a sparse univariate polynomial (sup) over a sup over \\spad{F.}"))) NIL NIL -(-1203) +(-1204) ((|constructor| (NIL "The fundamental Type."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1204) -((|constructor| (NIL "This is a low-level domain which implements matrices (two dimensional arrays) of 16-bit integers. Indexing is 0 based, there is no bound checking (unless provided by lower level).")) (|qnew| (($ (|Integer|) (|Integer|)) "\\indented{1}{qnew(n, \\spad{m)} creates a new \\spad{n} by \\spad{m} matrix of zeros.} \\blankline \\spad{X} qnew(3,4)$U16Matrix()"))) -((-4600 . T) (-4601 . T)) -((|HasCategory| (-571) (QUOTE (-1097))) (-12 (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-302))) (|HasCategory| (-571) (QUOTE (-561))) (|HasAttribute| (-571) (QUOTE (-4602 "*"))) (|HasCategory| (-571) (QUOTE (-173))) (|HasCategory| (-571) (QUOTE (-367)))) (-1205) -((|constructor| (NIL "\\indented{2}{fill!(x, \\spad{s)} modifies a vector \\spad{x} so every element has value \\spad{s}} \\blankline \\spad{X} t1:=new(10,7)$U16Vector \\spad{X} fill!(t1,9)"))) -((-4601 . T) (-4600 . T)) -((|HasCategory| (-571) (QUOTE (-1097))) (|HasCategory| (-571) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| (-571) (QUOTE (-847))) (-1831 (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| (-571) (QUOTE (-1097)))) (-12 (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-847)))) (-12 (|HasCategory| (-571) (LIST (QUOTE -304) (QUOTE (-571)))) (|HasCategory| (-571) (QUOTE (-1097)))))) +((|constructor| (NIL "This is a low-level domain which implements matrices (two dimensional arrays) of 16-bit integers. Indexing is 0 based, there is no bound checking (unless provided by lower level).")) (|qnew| (($ (|Integer|) (|Integer|)) "\\indented{1}{qnew(n, \\spad{m)} creates a new \\spad{n} by \\spad{m} matrix of zeros.} \\blankline \\spad{X} qnew(3,4)$U16Matrix()"))) +((-4602 . T) (-4603 . 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(|largest| ((|#1| (|List| |#1|)) "\\spad{largest \\spad{l}} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S.}") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn.}")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, \\spad{b,} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder, and returns \\spad{fn(a, \\spad{b)}} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, \\spad{b)}} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < \\spad{b2} < \\spad{...} < \\spad{bm} < \\spad{a1} < \\spad{a2} < \\spad{...} < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < \\spad{c} < ai}\\space{2}for \\spad{c} not among the ai's and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the ai's,bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < \\spad{a2} < \\spad{...} < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for \\spad{i} = 1..n} and \\spad{b} not among the ai's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, \\spad{c)}} if neither is among the ai's.}"))) NIL -((|HasCategory| |#1| (QUOTE (-847)))) -(-1211) +((|HasCategory| |#1| (QUOTE (-848)))) +(-1212) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials, fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > \\spad{b2} > \\spad{...} > \\spad{bm} \\spad{>}} other variables \\spad{> \\spad{a1} > \\spad{a2} > \\spad{...} > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > \\spad{a2} > \\spad{...} > an > other variables}."))) NIL NIL -(-1212 S) +(-1213 S) ((|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."))) NIL NIL -(-1213) +(-1214) ((|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."))) -((-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1214 |Coef|) +(-1215 |Coef|) ((|constructor| (NIL "This package has no description"))) NIL NIL -(-1215 |Coef|) +(-1216 |Coef|) ((|constructor| (NIL "This domain has no description"))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasCategory| (-768) (QUOTE (-1109))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1216 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasCategory| (-769) (QUOTE (-1110))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1217 |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 -(-1217 |Coef|) +(-1218 |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 \\spad{<=} \\spad{d} \\spad{<=} 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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1218 S |Coef| UTS) +(-1219 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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series, if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by \\spad{(1)} an exponent and \\spad{(2)} a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient, the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by \\spad{(1)} an exponent and \\spad{(2)} a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient, the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note that \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)}, where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)}, which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL -((|HasCategory| |#2| (QUOTE (-367)))) -(-1219 |Coef| UTS) +((|HasCategory| |#2| (QUOTE (-368)))) +(-1220 |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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series, if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by \\spad{(1)} an exponent and \\spad{(2)} a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient, the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by \\spad{(1)} an exponent and \\spad{(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)}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-3348 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-3389 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1220 |Coef| UTS) +(-1221 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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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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(|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s,} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of seg."))) NIL -((|HasCategory| |#1| (QUOTE (-845)))) -(-1224 S) +((|HasCategory| |#1| (QUOTE (-846)))) +(-1225 S) ((|constructor| (NIL "This domain provides segments which may be half open. That is, ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\spad{%.}")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment, that is, one with no upper bound."))) NIL -((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1097)))) -(-1225 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1098)))) +(-1226 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(x,R) to \\spadtype{UnivariatePolynomial}(y,S). Note that the mapping is assumed to send zero to zero, since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1226 R Q UP) +(-1227 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, \\spad{d]}} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q.}")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q.}")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q.}"))) NIL NIL -(-1227 R UP) +(-1228 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition \\spad{([} \\spad{f1,} ..., \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} \\spad{...} \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor \\spad{(g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h)} of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor \\spad{(h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h)} of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor \\spad{(h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h)} of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1228 R UP) +(-1229 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1229 R U) +(-1230 R U) ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath, but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) NIL NIL -(-1230 |x| R) +(-1231 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented. Note that if the coefficient ring is a field, then this domain forms a euclidean domain.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{x} : \\spad{p1} - \\spad{r} * x**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) -(((-4602 "*") |has| |#2| (-173)) (-4593 |has| |#2| (-561)) (-4596 |has| |#2| (-367)) (-4598 |has| |#2| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-384))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-571))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-384)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -892) (QUOTE (-571)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-544))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-571)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1169)))) (-1831 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| |#2| (QUOTE (-226))) (|HasAttribute| |#2| (QUOTE -4598)) (|HasCategory| |#2| (QUOTE (-456))) (-1831 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-909)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (-1831 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-149))))) -(-1231 R PR S PS) +(((-4604 "*") |has| |#2| (-174)) (-4595 |has| |#2| (-562)) (-4598 |has| |#2| (-368)) (-4600 |has| |#2| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-385)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-385))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -887) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-572))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-385)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -613) (LIST (QUOTE -893) (QUOTE (-572)))))) (-12 (|HasCategory| (-1082) (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-545))))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-151))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (-1841 (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE -4600)) (|HasCategory| |#2| (QUOTE (-457))) (-1841 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-910)))) (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (-1841 (-12 (|HasCategory| $ (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-149))))) +(-1232 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, \\spad{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 NIL -(-1232 S R) +(-1233 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R.} No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(b)")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, \\spad{q)}} returns \\spad{[a, \\spad{b]}} such that polynomial \\spad{p = a \\spad{b}} and \\spad{a} is relatively prime to \\spad{q.}")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, \\spad{q,} r]}, when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1) = \\spad{c} * \\spad{p}} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r,} the quotient when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1)} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, \\spad{q)}} returns \\spad{h} if \\spad{f} = h(q), and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, \\spad{q)}} returns \\spad{h} if \\spad{p = h(q)}, and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\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, \\spad{q)}} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r.}") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b.}")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q.}")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p.}")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, \\spad{d,} x')} extends the R-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x',} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r,} for polynomials \\spad{p} and \\spad{q,} returns the remainder when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1)} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|shiftLeft| (($ $ (|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't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n,} or \"failed\" if some exponent is not exactly divisible by \\spad{n.}")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n.}")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note that converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, \\spad{n)}} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = \\spad{a0} + a1*x + \\spad{...} + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-456))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1143)))) -(-1233 R) +((|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1144)))) +(-1234 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(b)")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, \\spad{q)}} returns \\spad{[a, \\spad{b]}} such that polynomial \\spad{p = a \\spad{b}} and \\spad{a} is relatively prime to \\spad{q.}")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, \\spad{q,} r]}, when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1) = \\spad{c} * \\spad{p}} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r,} the quotient when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1)} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, \\spad{q)}} returns \\spad{h} if \\spad{f} = h(q), and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, \\spad{q)}} returns \\spad{h} if \\spad{p = h(q)}, and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\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, \\spad{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|) $) "\\spad{differentiate(p, \\spad{d,} x')} extends the R-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x',} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r,} for polynomials \\spad{p} and \\spad{q,} returns the remainder when \\spad{p' \\spad{:=} p*lc(q)**(deg \\spad{p} - deg \\spad{q} + 1)} is pseudo right-divided by \\spad{q,} \\spadignore{i.e.} \\spad{p' = \\spad{s} \\spad{q} + \\spad{r}.}")) (|shiftLeft| (($ $ (|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'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, \\spad{n)}} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = \\spad{a0} + a1*x + \\spad{...} + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4596 |has| |#1| (-367)) (-4598 |has| |#1| (-6 -4598)) (-4595 . T) (-4594 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4598 |has| |#1| (-368)) (-4600 |has| |#1| (-6 -4600)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-1234 S |Coef| |Expon|) +(-1235 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 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= \\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 -900) (QUOTE (-1169)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3942) (LIST (|devaluate| |#2|) (QUOTE (-1169)))))) -(-1235 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1110))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3972) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +(-1236 |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 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= \\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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms, where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1236 RC P) +(-1237 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings, \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero, the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic, then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case, the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function, exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p,} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p.} Each factor has no repeated roots, and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q.}"))) NIL NIL -(-1237 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1238 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1238 |Coef|) +(-1239 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1239 S |Coef| ULS) +(-1240 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]}, where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible, \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)}, which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1240 |Coef| ULS) +(-1241 |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)}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1241 |Coef| ULS) +(-1242 |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)}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|))))) (|HasCategory| (-412 (-571)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1242 |Coef| |var| |cen|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasCategory| (-413 (-572)) (QUOTE (-1110))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1243 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable")) (|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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4598 |has| |#1| (-367)) (-4592 |has| |#1| (-367)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571))) (|devaluate| |#1|))))) (|HasCategory| (-412 (-571)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-1831 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1243 R FE |var| |cen|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4600 |has| |#1| (-368)) (-4594 |has| |#1| (-368)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasCategory| (-413 (-572)) (QUOTE (-1110))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-1841 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1244 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 g(x) is a univariate Puiseux series and f(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 \\spad{->} 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 \\spad{->} cen+,f(var))}."))) -(((-4602 "*") |has| (-1242 |#2| |#3| |#4|) (-173)) (-4593 |has| (-1242 |#2| |#3| |#4|) (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-151))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-173))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1043) (QUOTE (-571)))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-456))) (-1831 (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1043) (LIST (QUOTE -412) (QUOTE (-571)))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-561)))) -(-1244 A S) +(((-4604 "*") |has| (-1243 |#2| |#3| |#4|) (-174)) (-4595 |has| (-1243 |#2| |#3| |#4|) (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| (-1243 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-151))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-174))) (|HasCategory| (-1243 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-1243 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-572)))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-457))) (-1841 (|HasCategory| (-1243 |#2| |#3| |#4|) (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| (-1243 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -413) (QUOTE (-572)))))) (|HasCategory| (-1243 |#2| |#3| |#4|) (QUOTE (-562)))) +(-1245 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{v = rest(u,n)} and \\axiom{w = first(u,n)}, returning \\axiom{v}. Note that afterwards \\axiom{rest(u,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{u.last \\spad{:=} \\spad{b})} is equivalent to \\axiom{setlast!(u,v)}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{u.rest \\spad{:=} \\spad{v})} is equivalent to \\axiom{setrest!(u,v)}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{u.first \\spad{:=} \\spad{x})} is equivalent to \\axiom{setfirst!(u,x)}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x.}")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry, or nil if none exists. For example, if \\axiom{w = concat(u,v)} is the cyclic list where \\spad{v} is the head of the cycle, \\axiom{cycleSplit!(w)} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to u, and returning \\spad{v.}")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of u. Note that \\axiom{concat!(a,x) = setlast!(a,[x])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of u. Note that \\axiom{concat!(u,v) = setlast_!(u,v)}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle, or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate u, or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate u, or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of u. Note that \\axiom{third(u) = first(rest(rest(u)))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of u. Note that \\axiom{second(u) = first(rest(u))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of u. Note that if \\spad{u} is \\axiom{shallowlyMutable}, \\axiom{setrest(tail(u),v) = concat(u,v)}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{n \\spad{>=} 0}) nodes of u. Note that \\axiom{last(u,n)} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of u. Note that for lists, \\axiom{last(u)=u . (maxIndex u)=u . \\spad{(#} \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{n}th \\spad{(n} \\spad{>=} 0) node of u. Note that \\axiom{rest(u,0) = u}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently, the next node of u).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{u . last}) is equivalent to last u.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{u.rest}) is equivalent to \\axiom{rest u}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{u . first}) is equivalent to first u.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{n \\spad{>=} 0}) elements of u.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently, the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of u. Note that if \\axiom{v = concat(x,u)} then \\axiom{x = first \\spad{v}} and \\axiom{u = rest \\spad{v}.}") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v.} Note that \\axiom{v = rest(w,\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4601))) -(-1245 S) +((|HasAttribute| |#1| (QUOTE -4603))) +(-1246 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models, though not precisely, a linked list possibly with a single cycle. A node with one children models a non-empty list, with the \\spadfun{value} of the list designating the head, or \\spadfun{first}, of the list, and the child designating the tail, or \\spadfun{rest}, of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates, they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{v = rest(u,n)} and \\axiom{w = first(u,n)}, returning \\axiom{v}. Note that afterwards \\axiom{rest(u,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{u.last \\spad{:=} \\spad{b})} is equivalent to \\axiom{setlast!(u,v)}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{u.rest \\spad{:=} \\spad{v})} is equivalent to \\axiom{setrest!(u,v)}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{u.first \\spad{:=} \\spad{x})} is equivalent to \\axiom{setfirst!(u,x)}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x.}")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry, or nil if none exists. For example, if \\axiom{w = concat(u,v)} is the cyclic list where \\spad{v} is the head of the cycle, \\axiom{cycleSplit!(w)} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to u, and returning \\spad{v.}")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of u. Note that \\axiom{concat!(a,x) = setlast!(a,[x])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of u. Note that \\axiom{concat!(u,v) = setlast_!(u,v)}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle, or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate u, or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate u, or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of u. Note that \\axiom{third(u) = first(rest(rest(u)))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of u. Note that \\axiom{second(u) = first(rest(u))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of u. Note that if \\spad{u} is \\axiom{shallowlyMutable}, \\axiom{setrest(tail(u),v) = concat(u,v)}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{n \\spad{>=} 0}) nodes of u. Note that \\axiom{last(u,n)} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of u. Note that for lists, \\axiom{last(u)=u . (maxIndex u)=u . \\spad{(#} \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{n}th \\spad{(n} \\spad{>=} 0) node of u. Note that \\axiom{rest(u,0) = u}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently, the next node of u).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{u . last}) is equivalent to last u.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{u.rest}) is equivalent to \\axiom{rest u}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{u . first}) is equivalent to first u.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{n \\spad{>=} 0}) elements of u.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently, the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of u. Note that if \\axiom{v = concat(x,u)} then \\axiom{x = first \\spad{v}} and \\axiom{u = rest \\spad{v}.}") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v.} Note that \\axiom{v = rest(w,\\#a)}."))) -((-3348 . T)) +((-3389 . T)) NIL -(-1246 |Coef1| |Coef2| UTS1 UTS2) +(-1247 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. This package allows one to apply a function to the coefficients of a univariate Taylor series.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1247 S |Coef|) +(-1248 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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) \\spad{**} 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 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= \\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 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns \\spad{a1 + \\spad{a2} \\spad{x} + \\spad{a3} \\spad{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|) $) "\\spad{coefficients(a0 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{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 (-571)))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-1189))) (|HasSignature| |#2| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3403) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1169))))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#2| (QUOTE (-367)))) -(-1248 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasSignature| |#2| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2774) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-368)))) +(-1249 |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) \\spad{**} 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 \\spad{<=} \\spad{d} \\spad{<=} k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= \\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 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns \\spad{a1 + \\spad{a2} \\spad{x} + \\spad{a3} \\spad{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|) $) "\\spad{coefficients(a0 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{x**2} + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + \\spad{a1} \\spad{x} + \\spad{a2} \\spad{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."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1249 |Coef| |var| |cen|) +(-1250 |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,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|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)}, and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = \\spad{x}.} Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + \\spad{d))} + \\indented{1}{f(x^(a + 2 \\spad{d))} + \\spad{...} \\spad{}.} \\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}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasCategory| (-768) (QUOTE (-1109))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1250 |Coef| UTS) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasCategory| (-769) (QUOTE (-1110))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1251 |Coef| UTS) ((|constructor| (NIL "Taylor series solutions of explicit ODE'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..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..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) = \\spad{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) = \\spad{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 NIL -(-1251 -3280 UP L UTS) +(-1252 -3313 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series ODE solver when presented with linear ODEs.")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op \\spad{y} = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, \\spad{n)}} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL -((|HasCategory| |#1| (QUOTE (-561)))) -(-1252 -3280 UTSF UTSSUPF) +((|HasCategory| |#1| (QUOTE (-562)))) +(-1253 -3313 UTSF UTSSUPF) ((|constructor| (NIL "This package has no description"))) NIL NIL -(-1253 |Coef| |var|) +(-1254 |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|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)}, and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = \\spad{x}.} Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + \\spad{d))} + \\indented{1}{f(x^(a + 2 \\spad{d))} + \\spad{...} \\spad{}.} \\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}."))) -(((-4602 "*") |has| |#1| (-173)) (-4593 |has| |#1| (-561)) (-4594 . T) (-4595 . T) (-4597 . T)) -((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-1831 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasCategory| (-768) (QUOTE (-1109))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3942) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasCategory| |#1| (QUOTE (-367))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-571)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1189)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasSignature| |#1| (LIST (QUOTE -3403) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -3424) (LIST (LIST (QUOTE -637) (QUOTE (-1169))) (|devaluate| |#1|))))))) -(-1254 |sym|) +(((-4604 "*") |has| |#1| (-174)) (-4595 |has| |#1| (-562)) (-4596 . T) (-4597 . T) (-4599 . T)) +((|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-1841 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-151))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-769)) (|devaluate| |#1|))))) (|HasCategory| (-769) (QUOTE (-1110))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-769))))) (|HasSignature| |#1| (LIST (QUOTE -3972) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasCategory| |#1| (QUOTE (-368))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -43) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2774) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3456) (LIST (LIST (QUOTE -638) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(-1255 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1255 S R) +(-1256 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects, that is, finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(v,v)), that is, the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(v,v)), that is, the magnitude")) (|cross| (($ $ $) "\\spad{cross(u,v)} constructs the cross product of \\spad{u} and \\spad{v.} Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (i,j)'th element is u(i)*v(j).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y.} Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * \\spad{r}} multiplies each component of the vector \\spad{y} by the element \\spad{r.}") (($ |#2| $) "\\spad{r * \\spad{y}} multiplies the element \\spad{r} times each component of the vector \\spad{y.}") (($ (|Integer|) $) "\\spad{n * \\spad{y}} multiplies each component of the vector \\spad{y} by the integer \\spad{n.}")) (- (($ $ $) "\\spad{x - \\spad{y}} returns the component-wise difference of the vectors \\spad{x} and \\spad{y.} Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x.}")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n.}")) (+ (($ $ $) "\\spad{x + \\spad{y}} returns the component-wise sum of the vectors \\spad{x} and \\spad{y.} Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1256 R) +((|HasCategory| |#2| (QUOTE (-1009))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1257 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects, that is, 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(v,v)), that is, the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(v,v)), that is, the magnitude")) (|cross| (($ $ $) "\\spad{cross(u,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 (i,j)'th element is u(i)*v(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 * \\spad{r}} multiplies each component of the vector \\spad{y} by the element \\spad{r.}") (($ |#1| $) "\\spad{r * \\spad{y}} multiplies the element \\spad{r} times each component of the vector \\spad{y.}") (($ (|Integer|) $) "\\spad{n * \\spad{y}} multiplies each component of the vector \\spad{y} by the integer \\spad{n.}")) (- (($ $ $) "\\spad{x - \\spad{y}} returns the component-wise difference of the vectors \\spad{x} and \\spad{y.} Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x.}")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n.}")) (+ (($ $ $) "\\spad{x + \\spad{y}} returns the component-wise sum of the vectors \\spad{x} and \\spad{y.} Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4601 . T) (-4600 . T) (-3348 . T)) +((-4603 . T) (-4602 . T) (-3389 . T)) NIL -(-1257 A B) +(-1258 A B) ((|constructor| (NIL "This package provides operations which all take as arguments vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B.} The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B.}")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, \\spad{v)}} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, \\spad{v)}} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function func. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function func, increasing initial subsequences of the vector vec, and the element ident."))) NIL NIL -(-1258 R) +(-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#1| (QUOTE (-1097))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-847))) (-1831 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1097)))) (|HasCategory| (-571) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))) (-1831 (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-847)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -304) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1097)))))) -(-1259) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#1| (QUOTE (-1098))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#1| (QUOTE (-848))) (-1841 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-1098)))) (|HasCategory| (-572) (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1009))) (|HasCategory| |#1| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))) (-1841 (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-848)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -305) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-1098)))))) +(-1260) ((|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 x-coordinate direction from the center of the viewport, and by \\spad{dy} in the 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 x-coordinate direction and by the factor \\spad{sy} in the 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,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{gi} of domain \\spadtype{GraphImage}. The contents of viewport, \\spad{v,} will contain \\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 box, 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'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(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph, \\spad{gi}, of domain \\spadtype{GraphImage}, and whose options field is set to be the list of options, \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport, \\spad{v,} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v.}")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system, some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface, how to default to graphs, etc."))) NIL NIL -(-1260) +(-1261) ((|constructor| (NIL "ThreeDimensionalViewport creates viewports to display graphs")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, and creates a directory indicated by \\spad{s,} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf.}") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, and creates a directory indicated by \\spad{s,} which contains the graph data file for \\spad{v} and an optional file type \\spad{f.}") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, and creates a directory indicated by \\spad{s,} which contains the graph data file for \\spad{v.}")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2}, for the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to i, for the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x,} \\spad{y,} and \\spad{z} and displays the graph for the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\", or displays the graph without clipping implemented if \\spad{s} is \"off\", for the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h,} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d,} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\", or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy}, for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the x-coordinate axis to \\spad{sx}, the y-coordinate axis to \\spad{sy} and the z-coordinate axis to \\spad{sz} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s,} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v.}") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s.} If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"}, \\spad{\"solid\"} or \\spad{\"opaque\"}, \\spad{\"smooth\"}, and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set, for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline, for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, if \\spad{s} is \"on\", or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the x-axis to be \\spad{rotx} radians, sets the rotation about the y-axis to be \\spad{roty} radians, and sets the rotation about the z-axis to be \\spad{rotz} radians, for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v.}") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees, the latitudinal view angle to \\spad{phi} degrees, the scale factor to \\spad{s}, the horizontal viewport offset to \\spad{dx}, and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v.}") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles, the zoom factor, the x,y and \\spad{z} scales, and the \\spad{x} and \\spad{y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport, \\spad{v.} This function is useful in the situation where the user has created a viewport, proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians, the latitudinal view angle to \\spad{phi} radians, the scale factor to \\spad{s}, the horizontal viewport offset to \\spad{dx}, and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v.}")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, to the window coordinate \\spad{x,} \\spad{y,} and sets the dimensions of the window to that of \\spad{width}, \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v.}")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window, \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, with a width of \\spad{w} and a height of \\spad{h,} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport, \\spad{v,} which is of domain \\spadtype{ThreeDimensionalViewport}, with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x,} \\spad{y.}")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport, \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list, \\spad{lopt}, which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport, \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v.}")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport, \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}, and places the data point, \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}, in the subspace \\spad{sp}, which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v,} which is of the domain \\spadtype{ThreeDimensionalViewport}, as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space, \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp}, and whose draw options are indicated by the list \\spad{lopt}, which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space, \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp}, and whose title is given by \\spad{s.}") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport, \\spad{v,} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v.}")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s.}") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p.}") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t.}") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1261) +(-1262) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r.}")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to i.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} x=0..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} x=0..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} x=0..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} x=0..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing, such as BITMAP, POSTSCRIPT, etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l;} a viewalone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewalone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h.}") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{x} and \\spad{y} position of a viewport window unless overriden explicityly, newly created viewports will have the \\spad{x} and \\spad{y} coordinates \\spad{x,} \\spad{y.}") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{x} and \\spad{y} position of a viewport window unless overriden explicityly, newly created viewports will have this \\spad{x} and \\spad{y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to i.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p.}") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p.}") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p.}") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p.}") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1262) +(-1263) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage}, gi, into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points, \\spad{p0} throught \\spad{pn,} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points, \\spad{p0} throught \\spad{pn,} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor}, the line color is specified by \\spad{lineColor}, and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points, \\spad{p0} throught \\spad{pn,} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn.}") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points, \\spad{p0} throught \\spad{pn,} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor}, the graph line color is specified by \\spad{lineColor}, and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1263) +(-1264) ((|constructor| (NIL "This type is used when no value is needed, \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void, it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1264 A S) +(-1265 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y.}"))) NIL NIL -(-1265 S) +(-1266 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.}"))) -((-4595 . T) (-4594 . T)) +((-4597 . T) (-4596 . T)) NIL -(-1266 R) +(-1267 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(v,p) where \\spad{v} is a variable, and \\spad{p} is a TaylorSeries(R) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,s>0, is a list of TaylorSeries coefficients A[i] of the equivalent polynomial A = A[0] + A[1]*v + \\spad{A[2]*v**2} + \\spad{...} + A[s-1]*v**(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 \\spad{n}} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest \\spad{n}} is used internally."))) NIL NIL -(-1267 K R UP -3280) +(-1268 K R UP -3313) ((|constructor| (NIL "In this package \\spad{K} is a finite field, \\spad{R} is a ring of univariate polynomials over \\spad{K,} and \\spad{F} is a framed algebra over \\spad{R.} The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F,} where \\spad{F} is a framed algebra with R-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F,} where \\spad{F} is a framed algebra with R-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * \\spad{wj,} \\spad{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{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, \\spad{i} = 1..n, \\spad{j} = 1..n)}, then \\spad{wi = sum(bij * \\spad{vj,} \\spad{j} = 1..n)}."))) NIL NIL -(-1268 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1269 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 \"P\", ignoring weights"))) -((-4595 |has| |#1| (-173)) (-4594 |has| |#1| (-173)) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1269 R E V P) +((-4597 |has| |#1| (-174)) (-4596 |has| |#1| (-174)) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) +(-1270 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 w.r.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(ps)} returns the same as \\axiom{characteristicSerie(ps,initiallyReduced?,initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,redOp?,redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,redOp?,redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,initiallyReduced?,initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,redOp?,redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense w.r.t the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials w.r.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(p,q),q)} holds for every polynomials \\axiom{p,q} and there exists an integer \\axiom{e} and a polynomial \\axiom{f} such that we have \\axiom{init(q)^e*p = \\spad{f*q} + redOp(p,q)}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,initiallyReduced?,initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,redOp?,redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense w.r.t the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}), if no non-zero constant polynomials appear during the computatioms, else \\axiom{\"failed\"} is returned. In the former case, \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm, \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-4601 . T) (-4600 . T)) -((|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1097))) (-12 (|HasCategory| |#4| (LIST (QUOTE -304) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1097)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-373)))) -(-1270 R) +((-4603 . T) (-4602 . T)) +((|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-545)))) (|HasCategory| |#4| (QUOTE (-1098))) (-12 (|HasCategory| |#4| (LIST (QUOTE -305) (|devaluate| |#4|))) (|HasCategory| |#4| (QUOTE (-1098)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#3| (QUOTE (-374)))) +(-1271 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}."))) -((-4594 . T) (-4595 . T) (-4597 . T)) +((-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1271 |vl| R) +(-1272 |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."))) -((-4597 . T) (-4593 |has| |#2| (-6 -4593)) (-4595 . T) (-4594 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4593))) -(-1272 R |VarSet| XPOLY) +((-4599 . T) (-4595 |has| |#2| (-6 -4595)) (-4597 . T) (-4596 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4595))) +(-1273 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,b,n)} returns log(exp(a)*exp(b)) truncated at order \\axiom{n}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(p, \\spad{n)}} returns the logarithm of \\axiom{p} truncated at order \\axiom{n}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(p, \\spad{n)}} returns the exponential of \\axiom{p} truncated at order \\axiom{n}."))) NIL NIL -(-1273 |vl| R) +(-1274 |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 * \\spad{r}} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * \\spad{x}} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4593 |has| |#2| (-6 -4593)) (-4595 . T) (-4594 . T) (-4597 . T)) +((-4595 |has| |#2| (-6 -4595)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-1274 S -3280) +(-1275 S -3313) ((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()$F.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a \\spad{**} \\spad{q}} where \\spad{q} is the \\spad{size()$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension, 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic, and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F,} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F.}")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F.}")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F.}"))) NIL -((|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151)))) -(-1275 -3280) +((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-151)))) +(-1276 -3313) ((|constructor| (NIL "ExtensionField \\spad{F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()$F.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a \\spad{**} \\spad{q}} where \\spad{q} is the \\spad{size()$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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F.}"))) -((-4592 . T) (-4598 . T) (-4593 . T) ((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +((-4594 . T) (-4600 . T) (-4595 . T) ((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL -(-1276 |VarSet| R) +(-1277 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations.")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(p,n)} returns the logarithm of \\axiom{p} (truncated up to order \\axiom{n}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(p,n)} returns the exponential of \\axiom{p} (truncated up to order \\axiom{n}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,b,n)} returns \\axiom{a*b} (truncated up to order \\axiom{n}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(p)} return \\axiom{p} if \\axiom{p} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(p)} returns \\axiom{p} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(p)} returns \\axiom{p} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(p)} returns \\axiom{p}."))) -((-4593 |has| |#2| (-6 -4593)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -712) (LIST (QUOTE -412) (QUOTE (-571))))) (|HasAttribute| |#2| (QUOTE -4593))) -(-1277 |vl| R) +((-4595 |has| |#2| (-6 -4595)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -413) (QUOTE (-572))))) (|HasAttribute| |#2| (QUOTE -4595))) +(-1278 |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 variables.")) (|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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4593 |has| |#2| (-6 -4593)) (-4595 . T) (-4594 . T) (-4597 . T)) +((-4595 |has| |#2| (-6 -4595)) (-4597 . T) (-4596 . T) (-4599 . T)) NIL -(-1278 R) +(-1279 R) ((|constructor| (NIL "This type supports multivariate polynomials whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However, coefficients and variables commute."))) -((-4593 |has| |#1| (-6 -4593)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4593))) -(-1279 R E) +((-4595 |has| |#1| (-6 -4595)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4595))) +(-1280 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring), and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used, for instance, by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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|) $) "\\spad{# \\spad{p}} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4597 . T) (-4598 |has| |#1| (-6 -4598)) (-4593 |has| |#1| (-6 -4593)) (-4595 . T) (-4594 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4597)) (|HasAttribute| |#1| (QUOTE -4598)) (|HasAttribute| |#1| (QUOTE -4593))) -(-1280 |VarSet| R) +((-4599 . T) (-4600 |has| |#1| (-6 -4600)) (-4595 |has| |#1| (-6 -4595)) (-4597 . T) (-4596 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4599)) (|HasAttribute| |#1| (QUOTE -4600)) (|HasAttribute| |#1| (QUOTE -4595))) +(-1281 |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."))) -((-4593 |has| |#2| (-6 -4593)) (-4595 . T) (-4594 . T) (-4597 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4593))) -(-1281 A) +((-4595 |has| |#2| (-6 -4595)) (-4597 . T) (-4596 . T) (-4599 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4595))) +(-1282 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g,} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f.}"))) NIL NIL -(-1282 R |ls| |ls2|) +(-1283 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING. The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see \\spadtype{LexTriangularPackage} package constructor). For that purpose, the operations univariateSolve, realSolve and positiveSolve admit an optional argument.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover, each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts}, which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING. \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover, if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(lp,false)). Otherwise, the triangular decomposition is computed directly from the input system by using the zeroSetSplit from \\spadtype{RegularChain}. WARNING. For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed w.r.t. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover, if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(lp,false)). Otherwise, the triangular decomposition is computed directly from the input system by using the zeroSetSplit from \\spadtype{RegularChain}. WARNING. For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed w.r.t. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING. For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed w.r.t. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover, if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See rur from RationalUnivariateRepresentationPackage(lp,true). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(lp,false)). Otherwise, the triangular decomposition is computed directly from the input system by using the zeroSetSplit from RegularChain") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See rur from RationalUnivariateRepresentationPackage(lp,true).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{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{lp} needs to generate a zero-dimensional ideal. If \\axiom{lp} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (w.r.t. Zarisky topology). Moreover, if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See zeroSetSplit from RegularTriangularSetCategory(lp,true,info?). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see zeroSetSplit from LexTriangularPackage(lp,false)). Otherwise, the triangular decomposition is computed directly from the input system by using the zeroSetSplit from RegularChain"))) NIL NIL -(-1283 R) +(-1284 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + \\spad{...} + cn*vn = u}, \"failed\" if no such rational numbers ci's exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + \\spad{...} + cn*vn = 0} and not all the ci's are 0, \"failed\" if the vi's are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the vi's are linearly dependent over the integers, \\spad{false} otherwise."))) NIL NIL -(-1284 |p|) +(-1285 |p|) ((|constructor| (NIL "IntegerMod(n) creates the ring of integers reduced modulo the integer \\spad{n.}"))) -(((-4602 "*") . T) (-4594 . T) (-4595 . T) (-4597 . T)) +(((-4604 "*") . T) (-4596 . T) (-4597 . T) (-4599 . T)) NIL NIL NIL @@ -5088,4 +5092,4 @@ NIL NIL NIL NIL -((-1289 NIL 2388706 2388711 2388716 2388721) (-3 NIL 2388686 2388691 2388696 2388701) (-2 NIL 2388666 2388671 2388676 2388681) (-1 NIL 2388646 2388651 2388656 2388661) (0 NIL 2388626 2388631 2388636 2388641) (-1284 "bookvol10.3.pamphlet" 2388443 2388456 2388564 2388621) (-1283 "bookvol10.4.pamphlet" 2387563 2387574 2388433 2388438) (-1282 "bookvol10.4.pamphlet" 2378179 2378201 2387553 2387558) (-1281 "bookvol10.4.pamphlet" 2377676 2377687 2378169 2378174) (-1280 "bookvol10.3.pamphlet" 2376911 2376931 2377532 2377601) (-1279 "bookvol10.3.pamphlet" 2374644 2374657 2376629 2376728) (-1278 "bookvol10.3.pamphlet" 2374216 2374227 2374500 2374569) (-1277 "bookvol10.2.pamphlet" 2373534 2373550 2374142 2374211) (-1276 "bookvol10.3.pamphlet" 2372199 2372219 2373314 2373383) (-1275 "bookvol10.2.pamphlet" 2370663 2370678 2372101 2372194) (-1274 NIL 2369107 2369124 2370547 2370552) (-1273 "bookvol10.2.pamphlet" 2366142 2366158 2369033 2369102) (-1272 "bookvol10.4.pamphlet" 2365541 2365567 2366132 2366137) (-1271 "bookvol10.3.pamphlet" 2365172 2365188 2365397 2365466) (-1270 "bookvol10.2.pamphlet" 2364871 2364882 2365128 2365167) (-1269 "bookvol10.3.pamphlet" 2361539 2361556 2364573 2364600) (-1268 "bookvol10.3.pamphlet" 2360569 2360613 2361397 2361464) (-1267 "bookvol10.4.pamphlet" 2358144 2358166 2360559 2360564) (-1266 "bookvol10.4.pamphlet" 2356408 2356419 2358134 2358139) (-1265 "bookvol10.2.pamphlet" 2356081 2356092 2356376 2356403) (-1264 NIL 2355774 2355787 2356071 2356076) (-1263 "bookvol10.3.pamphlet" 2355368 2355377 2355764 2355769) (-1262 "bookvol10.4.pamphlet" 2353084 2353093 2355358 2355363) (-1261 "bookvol10.4.pamphlet" 2348344 2348353 2353074 2353079) (-1260 "bookvol10.3.pamphlet" 2332560 2332569 2348334 2348339) (-1259 "bookvol10.3.pamphlet" 2320751 2320760 2332550 2332555) (-1258 "bookvol10.3.pamphlet" 2319648 2319659 2319899 2319926) (-1257 "bookvol10.4.pamphlet" 2318322 2318335 2319638 2319643) (-1256 "bookvol10.2.pamphlet" 2316322 2316333 2318278 2318317) (-1255 NIL 2314141 2314154 2316099 2316104) (-1254 "bookvol10.3.pamphlet" 2313921 2313936 2314131 2314136) (-1253 "bookvol10.3.pamphlet" 2309097 2309119 2312388 2312485) (-1252 "bookvol10.4.pamphlet" 2309000 2309028 2309087 2309092) (-1251 "bookvol10.4.pamphlet" 2308294 2308318 2308956 2308961) (-1250 "bookvol10.4.pamphlet" 2306484 2306504 2308284 2308289) (-1249 "bookvol10.3.pamphlet" 2301283 2301311 2304951 2305048) (-1248 "bookvol10.2.pamphlet" 2298600 2298616 2301181 2301278) (-1247 NIL 2295561 2295579 2298144 2298149) (-1246 "bookvol10.4.pamphlet" 2295186 2295221 2295551 2295556) (-1245 "bookvol10.2.pamphlet" 2290470 2290481 2295166 2295181) (-1244 NIL 2285728 2285741 2290426 2290431) (-1243 "bookvol10.3.pamphlet" 2283395 2283421 2284809 2284942) (-1242 "bookvol10.3.pamphlet" 2280946 2280974 2281527 2281676) (-1241 "bookvol10.3.pamphlet" 2278707 2278727 2279078 2279227) (-1240 "bookvol10.2.pamphlet" 2277177 2277197 2278553 2278702) (-1239 NIL 2275789 2275811 2277167 2277172) (-1238 "bookvol10.2.pamphlet" 2274380 2274396 2275635 2275784) (-1237 "bookvol10.4.pamphlet" 2273923 2273976 2274370 2274375) (-1236 "bookvol10.4.pamphlet" 2272351 2272365 2273913 2273918) (-1235 "bookvol10.2.pamphlet" 2269921 2269945 2272249 2272346) (-1234 NIL 2267197 2267223 2269527 2269532) (-1233 "bookvol10.2.pamphlet" 2262049 2262060 2267039 2267192) (-1232 NIL 2256793 2256806 2261785 2261790) (-1231 "bookvol10.4.pamphlet" 2256258 2256277 2256783 2256788) (-1230 "bookvol10.3.pamphlet" 2253217 2253232 2253808 2253961) (-1229 "bookvol10.4.pamphlet" 2252151 2252164 2253207 2253212) (-1228 "bookvol10.4.pamphlet" 2251716 2251730 2252141 2252146) (-1227 "bookvol10.4.pamphlet" 2249957 2249971 2251706 2251711) (-1226 "bookvol10.4.pamphlet" 2249158 2249174 2249947 2249952) (-1225 "bookvol10.4.pamphlet" 2248560 2248581 2249148 2249153) (-1224 "bookvol10.3.pamphlet" 2247913 2247924 2248479 2248484) (-1223 "bookvol10.4.pamphlet" 2247420 2247433 2247869 2247874) (-1222 "bookvol10.4.pamphlet" 2246543 2246555 2247410 2247415) (-1221 "bookvol10.3.pamphlet" 2237215 2237243 2238188 2238617) (-1220 "bookvol10.3.pamphlet" 2231256 2231276 2231624 2231773) (-1219 "bookvol10.2.pamphlet" 2228849 2228869 2231076 2231251) (-1218 NIL 2226576 2226598 2228805 2228810) (-1217 "bookvol10.2.pamphlet" 2224786 2224802 2226422 2226571) (-1216 "bookvol10.4.pamphlet" 2224330 2224383 2224776 2224781) (-1215 "bookvol10.3.pamphlet" 2222723 2222739 2222797 2222894) (-1214 "bookvol10.4.pamphlet" 2222638 2222654 2222713 2222718) (-1213 "bookvol10.2.pamphlet" 2221707 2221716 2222564 2222633) (-1212 NIL 2220838 2220849 2221697 2221702) (-1211 "bookvol10.4.pamphlet" 2219649 2219658 2220828 2220833) (-1210 "bookvol10.4.pamphlet" 2217175 2217186 2219605 2219610) (-1209 "bookvol10.3.pamphlet" 2216406 2216415 2216609 2216636) (-1208 "bookvol10.3.pamphlet" 2215651 2215660 2216038 2216065) (-1207 "bookvol10.3.pamphlet" 2214881 2214890 2215085 2215112) (-1206 "bookvol10.3.pamphlet" 2214124 2214133 2214513 2214540) (-1205 "bookvol10.3.pamphlet" 2213354 2213363 2213558 2213585) (-1204 "bookvol10.3.pamphlet" 2212597 2212606 2212986 2213013) (-1203 "bookvol10.2.pamphlet" 2212519 2212528 2212577 2212592) (-1202 "bookvol10.4.pamphlet" 2211179 2211194 2212509 2212514) (-1201 "bookvol10.3.pamphlet" 2210188 2210199 2211134 2211139) (-1200 "bookvol10.4.pamphlet" 2207082 2207091 2210178 2210183) (-1199 "bookvol10.3.pamphlet" 2205772 2205789 2207072 2207077) (-1198 "bookvol10.3.pamphlet" 2204363 2204379 2205337 2205434) (-1197 "bookvol10.2.pamphlet" 2193919 2193936 2204319 2204358) (-1196 NIL 2183473 2183492 2193875 2193880) (-1195 "bookvol10.4.pamphlet" 2177929 2177946 2183179 2183184) (-1194 "bookvol10.4.pamphlet" 2176900 2176925 2177919 2177924) (-1193 "bookvol10.4.pamphlet" 2175397 2175414 2176890 2176895) (-1192 "bookvol10.2.pamphlet" 2174909 2174918 2175387 2175392) (-1191 NIL 2174419 2174430 2174899 2174904) (-1190 "bookvol10.3.pamphlet" 2172632 2172643 2174249 2174276) (-1189 "bookvol10.2.pamphlet" 2172479 2172488 2172622 2172627) (-1188 NIL 2172324 2172335 2172469 2172474) (-1187 "bookvol10.4.pamphlet" 2172002 2172011 2172314 2172319) (-1186 "bookvol10.4.pamphlet" 2171665 2171676 2171992 2171997) (-1185 "bookvol10.3.pamphlet" 2170244 2170253 2171655 2171660) (-1184 "bookvol10.3.pamphlet" 2167381 2167390 2170234 2170239) (-1183 "bookvol10.4.pamphlet" 2166937 2166948 2167371 2167376) (-1182 "bookvol10.4.pamphlet" 2166498 2166507 2166927 2166932) (-1181 "bookvol10.4.pamphlet" 2164689 2164712 2166488 2166493) (-1180 "bookvol10.2.pamphlet" 2163711 2163734 2164657 2164684) (-1179 NIL 2162753 2162778 2163701 2163706) (-1178 "bookvol10.4.pamphlet" 2162129 2162140 2162743 2162748) (-1177 "bookvol10.3.pamphlet" 2161102 2161125 2161372 2161399) (-1176 "bookvol10.3.pamphlet" 2160592 2160603 2161092 2161097) (-1175 "bookvol10.4.pamphlet" 2157510 2157521 2160582 2160587) (-1174 "bookvol10.4.pamphlet" 2154141 2154152 2157500 2157505) (-1173 "bookvol10.3.pamphlet" 2152238 2152247 2154131 2154136) (-1172 "bookvol10.3.pamphlet" 2148303 2148312 2152228 2152233) (-1171 "bookvol10.3.pamphlet" 2147310 2147321 2147392 2147519) (-1170 "bookvol10.4.pamphlet" 2146731 2146742 2147300 2147305) (-1169 "bookvol10.3.pamphlet" 2144193 2144202 2146721 2146726) (-1168 "bookvol10.3.pamphlet" 2140939 2140948 2144183 2144188) (-1167 "bookvol10.3.pamphlet" 2137970 2137998 2139406 2139503) (-1166 "bookvol10.3.pamphlet" 2135104 2135132 2136102 2136251) (-1165 "bookvol10.3.pamphlet" 2131799 2131810 2132654 2132807) (-1164 "bookvol10.4.pamphlet" 2130919 2130937 2131789 2131794) (-1163 "bookvol10.3.pamphlet" 2128363 2128374 2128432 2128585) (-1162 "bookvol10.4.pamphlet" 2127757 2127770 2128353 2128358) (-1161 "bookvol10.4.pamphlet" 2126359 2126370 2127747 2127752) (-1160 "bookvol10.4.pamphlet" 2126037 2126054 2126349 2126354) (-1159 "bookvol10.3.pamphlet" 2116696 2116724 2117682 2118111) (-1158 "bookvol10.3.pamphlet" 2116378 2116393 2116686 2116691) (-1157 "bookvol10.3.pamphlet" 2108733 2108748 2116368 2116373) (-1156 "bookvol10.4.pamphlet" 2107905 2107919 2108689 2108694) (-1155 "bookvol10.4.pamphlet" 2104006 2104022 2107895 2107900) (-1154 "bookvol10.4.pamphlet" 2100476 2100492 2103996 2104001) (-1153 "bookvol10.4.pamphlet" 2093048 2093059 2100357 2100362) (-1152 "bookvol10.3.pamphlet" 2092127 2092144 2092276 2092303) (-1151 "bookvol10.3.pamphlet" 2091510 2091519 2091608 2091635) (-1150 "bookvol10.2.pamphlet" 2091286 2091295 2091466 2091505) (-1149 "bookvol10.3.pamphlet" 2086874 2086885 2091034 2091049) (-1148 "bookvol10.4.pamphlet" 2086215 2086230 2086864 2086869) (-1147 "bookvol10.4.pamphlet" 2084788 2084801 2086205 2086210) (-1146 "bookvol10.4.pamphlet" 2084296 2084307 2084778 2084783) (-1145 "bookvol10.4.pamphlet" 2083981 2083992 2084286 2084291) (-1144 "bookvol10.4.pamphlet" 2082917 2082933 2083971 2083976) (-1143 "bookvol10.2.pamphlet" 2082143 2082152 2082907 2082912) (-1142 "bookvol10.3.pamphlet" 2081233 2081261 2081398 2081413) (-1141 "bookvol10.2.pamphlet" 2080332 2080343 2081213 2081228) (-1140 NIL 2079439 2079452 2080322 2080327) (-1139 "bookvol10.3.pamphlet" 2075476 2075487 2079269 2079296) (-1138 "bookvol10.3.pamphlet" 2073723 2073740 2075178 2075205) (-1137 "bookvol10.4.pamphlet" 2072489 2072509 2073713 2073718) (-1136 "bookvol10.2.pamphlet" 2067826 2067835 2072445 2072484) (-1135 NIL 2063195 2063206 2067816 2067821) (-1134 "bookvol10.3.pamphlet" 2060877 2060895 2061783 2061870) (-1133 "bookvol10.3.pamphlet" 2056384 2056397 2060628 2060655) (-1132 "bookvol10.3.pamphlet" 2053432 2053445 2056374 2056379) (-1131 "bookvol10.2.pamphlet" 2052243 2052252 2053422 2053427) (-1130 "bookvol10.4.pamphlet" 2050812 2050821 2052233 2052238) (-1129 "bookvol10.2.pamphlet" 2035202 2035213 2050802 2050807) (-1128 "bookvol10.3.pamphlet" 2034984 2034995 2035192 2035197) (-1127 "bookvol10.4.pamphlet" 2034533 2034546 2034940 2034945) (-1126 "bookvol10.4.pamphlet" 2032128 2032139 2034523 2034528) (-1125 "bookvol10.4.pamphlet" 2030717 2030728 2032118 2032123) (-1124 "bookvol10.4.pamphlet" 2025205 2025216 2030707 2030712) (-1123 "bookvol10.4.pamphlet" 2023669 2023687 2025195 2025200) (-1122 "bookvol10.2.pamphlet" 2023440 2023457 2023625 2023664) (-1121 "bookvol10.3.pamphlet" 2021594 2021620 2023005 2023102) (-1120 "bookvol10.3.pamphlet" 2019050 2019070 2019423 2019550) (-1119 "bookvol10.4.pamphlet" 2017887 2017912 2019040 2019045) (-1118 "bookvol10.2.pamphlet" 2015995 2016025 2017819 2017882) (-1117 NIL 2014047 2014079 2015873 2015878) (-1116 "bookvol10.2.pamphlet" 2012649 2012660 2014003 2014042) (-1115 "bookvol10.3.pamphlet" 2011012 2011021 2012515 2012644) (-1114 "bookvol10.4.pamphlet" 2010755 2010764 2011002 2011007) (-1113 "bookvol10.4.pamphlet" 2009845 2009856 2010745 2010750) (-1112 "bookvol10.4.pamphlet" 2009104 2009121 2009835 2009840) (-1111 "bookvol10.4.pamphlet" 2007068 2007083 2009060 2009065) (-1110 "bookvol10.3.pamphlet" 1998781 1998808 1999283 1999414) (-1109 "bookvol10.2.pamphlet" 1998093 1998102 1998771 1998776) (-1108 NIL 1997403 1997414 1998083 1998088) (-1107 "bookvol10.4.pamphlet" 1990915 1990924 1997393 1997398) (-1106 "bookvol10.2.pamphlet" 1990478 1990495 1990871 1990910) (-1105 "bookvol10.4.pamphlet" 1990177 1990197 1990468 1990473) (-1104 "bookvol10.4.pamphlet" 1986094 1986114 1990167 1990172) (-1103 "bookvol10.3.pamphlet" 1985555 1985569 1986084 1986089) (-1102 "bookvol10.3.pamphlet" 1985398 1985438 1985545 1985550) (-1101 "bookvol10.3.pamphlet" 1985290 1985299 1985388 1985393) (-1100 "bookvol10.2.pamphlet" 1982541 1982581 1985280 1985285) (-1099 "bookvol10.3.pamphlet" 1980905 1980916 1982018 1982057) (-1098 "bookvol10.3.pamphlet" 1979385 1979402 1980895 1980900) (-1097 "bookvol10.2.pamphlet" 1978875 1978884 1979375 1979380) (-1096 NIL 1978363 1978374 1978865 1978870) (-1095 "bookvol10.2.pamphlet" 1978254 1978263 1978353 1978358) (-1094 "bookvol10.2.pamphlet" 1975144 1975155 1978222 1978249) (-1093 NIL 1972054 1972067 1975134 1975139) (-1092 "bookvol10.2.pamphlet" 1971116 1971129 1972034 1972049) (-1091 "bookvol10.3.pamphlet" 1970929 1970940 1971035 1971040) (-1090 "bookvol10.2.pamphlet" 1969717 1969728 1970909 1970924) (-1089 "bookvol10.3.pamphlet" 1968803 1968814 1969672 1969677) (-1088 "bookvol10.4.pamphlet" 1968509 1968522 1968793 1968798) (-1087 "bookvol10.4.pamphlet" 1967928 1967941 1968465 1968470) (-1086 "bookvol10.3.pamphlet" 1967226 1967237 1967918 1967923) (-1085 "bookvol10.3.pamphlet" 1964630 1964641 1964907 1965034) (-1084 "bookvol10.3.pamphlet" 1961101 1961112 1964598 1964625) (-1083 "bookvol10.4.pamphlet" 1959204 1959215 1961091 1961096) (-1082 "bookvol10.4.pamphlet" 1958053 1958064 1959194 1959199) (-1081 "bookvol10.3.pamphlet" 1957925 1957934 1958043 1958048) (-1080 "bookvol10.4.pamphlet" 1957638 1957658 1957915 1957920) (-1079 "bookvol10.3.pamphlet" 1955767 1955783 1956424 1956559) (-1078 "bookvol10.4.pamphlet" 1955468 1955488 1955757 1955762) (-1077 "bookvol10.4.pamphlet" 1953204 1953220 1955458 1955463) (-1076 "bookvol10.3.pamphlet" 1952636 1952660 1953194 1953199) (-1075 "bookvol10.3.pamphlet" 1950818 1950842 1952626 1952631) (-1074 "bookvol10.3.pamphlet" 1950670 1950683 1950808 1950813) (-1073 "bookvol10.4.pamphlet" 1948040 1948060 1950660 1950665) (-1072 "bookvol10.2.pamphlet" 1938878 1938895 1947996 1948035) (-1071 NIL 1929748 1929767 1938868 1938873) (-1070 "bookvol10.4.pamphlet" 1928501 1928521 1929738 1929743) (-1069 "bookvol10.2.pamphlet" 1926907 1926937 1928491 1928496) (-1068 NIL 1925311 1925343 1926897 1926902) (-1067 "bookvol10.2.pamphlet" 1908553 1908568 1925179 1925306) (-1066 NIL 1891509 1891526 1908137 1908142) (-1065 "bookvol10.3.pamphlet" 1887994 1888003 1890738 1890765) (-1064 "bookvol10.3.pamphlet" 1887241 1887250 1887860 1887989) (-1063 "bookvol10.3.pamphlet" 1886375 1886407 1887231 1887236) (-1062 "bookvol10.2.pamphlet" 1885198 1885207 1886277 1886370) (-1061 NIL 1884107 1884118 1885188 1885193) (-1060 "bookvol10.2.pamphlet" 1883627 1883636 1884097 1884102) (-1059 "bookvol10.2.pamphlet" 1883142 1883153 1883617 1883622) (-1058 "bookvol10.4.pamphlet" 1882570 1882627 1883132 1883137) (-1057 "bookvol10.3.pamphlet" 1881305 1881324 1881793 1881832) (-1056 "bookvol10.2.pamphlet" 1876941 1876972 1881249 1881300) (-1055 NIL 1872479 1872512 1876789 1876794) (-1054 "bookvol10.4.pamphlet" 1872367 1872387 1872469 1872474) (-1053 "bookvol10.2.pamphlet" 1871726 1871735 1872347 1872362) (-1052 NIL 1871093 1871104 1871716 1871721) (-1051 "bookvol10.4.pamphlet" 1870121 1870130 1871083 1871088) (-1050 "bookvol10.3.pamphlet" 1868800 1868816 1869681 1869708) (-1049 "bookvol10.4.pamphlet" 1866850 1866861 1868790 1868795) (-1048 "bookvol10.4.pamphlet" 1864506 1864517 1866840 1866845) (-1047 "bookvol10.4.pamphlet" 1863968 1863979 1864496 1864501) (-1046 "bookvol10.4.pamphlet" 1863703 1863715 1863958 1863963) (-1045 "bookvol10.4.pamphlet" 1862699 1862708 1863693 1863698) (-1044 "bookvol10.4.pamphlet" 1862118 1862131 1862689 1862694) (-1043 "bookvol10.2.pamphlet" 1861460 1861471 1862108 1862113) (-1042 NIL 1860800 1860813 1861450 1861455) (-1041 "bookvol10.3.pamphlet" 1859444 1859453 1860029 1860056) (-1040 "bookvol10.3.pamphlet" 1858791 1858838 1859382 1859439) (-1039 "bookvol10.4.pamphlet" 1858117 1858128 1858781 1858786) (-1038 "bookvol10.4.pamphlet" 1857848 1857859 1858107 1858112) (-1037 "bookvol10.4.pamphlet" 1855404 1855413 1857838 1857843) (-1036 "bookvol10.4.pamphlet" 1855103 1855114 1855394 1855399) (-1035 "bookvol10.4.pamphlet" 1845123 1845134 1854945 1854950) (-1034 "bookvol10.4.pamphlet" 1839511 1839522 1845073 1845078) (-1033 "bookvol10.3.pamphlet" 1837806 1837823 1839213 1839240) (-1032 "bookvol10.3.pamphlet" 1837156 1837167 1837761 1837766) (-1031 "bookvol10.4.pamphlet" 1836286 1836303 1837146 1837151) (-1030 "bookvol10.4.pamphlet" 1834693 1834710 1836241 1836246) (-1029 "bookvol10.3.pamphlet" 1833526 1833546 1834180 1834273) (-1028 "bookvol10.4.pamphlet" 1832099 1832108 1833516 1833521) (-1027 "bookvol10.2.pamphlet" 1831983 1831992 1832089 1832094) (-1026 "bookvol10.4.pamphlet" 1829334 1829349 1831973 1831978) (-1025 "bookvol10.4.pamphlet" 1826243 1826258 1829324 1829329) (-1024 "bookvol10.4.pamphlet" 1825992 1826017 1826233 1826238) (-1023 "bookvol10.4.pamphlet" 1825559 1825570 1825982 1825987) (-1022 "bookvol10.4.pamphlet" 1824413 1824431 1825549 1825554) (-1021 "bookvol10.4.pamphlet" 1822378 1822396 1824403 1824408) (-1020 "bookvol10.4.pamphlet" 1821619 1821636 1822368 1822373) (-1019 "bookvol10.4.pamphlet" 1820675 1820692 1821609 1821614) (-1018 "bookvol10.2.pamphlet" 1818004 1818013 1820577 1820670) (-1017 NIL 1815419 1815430 1817994 1817999) (-1016 "bookvol10.2.pamphlet" 1813392 1813403 1815399 1815414) (-1015 NIL 1811302 1811315 1813311 1813316) (-1014 "bookvol10.4.pamphlet" 1810723 1810734 1811292 1811297) (-1013 "bookvol10.4.pamphlet" 1809907 1809919 1810713 1810718) (-1012 "bookvol10.4.pamphlet" 1809264 1809273 1809897 1809902) (-1011 "bookvol10.4.pamphlet" 1809020 1809029 1809254 1809259) (-1010 "bookvol10.3.pamphlet" 1805835 1805849 1807487 1807580) (-1009 "bookvol10.3.pamphlet" 1804264 1804301 1804367 1804523) (-1008 "bookvol10.2.pamphlet" 1803895 1803904 1804254 1804259) (-1007 NIL 1803524 1803535 1803885 1803890) (-1006 "bookvol10.3.pamphlet" 1799341 1799352 1803354 1803381) (-1005 "bookvol10.3.pamphlet" 1797971 1797982 1798265 1798330) (-1004 "bookvol10.4.pamphlet" 1797375 1797394 1797961 1797966) (-1003 "bookvol10.2.pamphlet" 1795581 1795592 1797305 1797370) (-1002 NIL 1793538 1793551 1795264 1795269) (-1001 "bookvol10.2.pamphlet" 1792351 1792362 1793494 1793533) (-1000 "bookvol10.3.pamphlet" 1791819 1791834 1792341 1792346) (-999 "bookvol10.2.pamphlet" 1790514 1790524 1791709 1791814) (-998 NIL 1788812 1788824 1790009 1790014) (-997 "bookvol10.4.pamphlet" 1788513 1788529 1788802 1788807) (-996 "bookvol10.3.pamphlet" 1788088 1788096 1788503 1788508) (-995 "bookvol10.4.pamphlet" 1784072 1784091 1788078 1788083) (-994 "bookvol10.3.pamphlet" 1780245 1780277 1783986 1783991) (-993 "bookvol10.4.pamphlet" 1778257 1778275 1780235 1780240) (-992 "bookvol10.4.pamphlet" 1775585 1775606 1778247 1778252) (-991 "bookvol10.4.pamphlet" 1774922 1774941 1775575 1775580) (-990 "bookvol10.2.pamphlet" 1771201 1771211 1774912 1774917) (-989 "bookvol10.4.pamphlet" 1768327 1768337 1771191 1771196) (-988 "bookvol10.4.pamphlet" 1768146 1768160 1768317 1768322) (-987 "bookvol10.2.pamphlet" 1767238 1767248 1768102 1768141) (-986 "bookvol10.4.pamphlet" 1766549 1766573 1767228 1767233) (-985 "bookvol10.4.pamphlet" 1765419 1765429 1766539 1766544) (-984 "bookvol10.4.pamphlet" 1752928 1752944 1765297 1765302) (-983 "bookvol10.2.pamphlet" 1747783 1747806 1752896 1752923) (-982 NIL 1742624 1742649 1747739 1747744) (-981 "bookvol10.2.pamphlet" 1741649 1741657 1742614 1742619) (-980 "bookvol10.2.pamphlet" 1740412 1740441 1741547 1741644) (-979 NIL 1739265 1739296 1740402 1740407) (-978 "bookvol10.3.pamphlet" 1738068 1738076 1739255 1739260) (-977 "bookvol10.2.pamphlet" 1735563 1735573 1738058 1738063) (-976 "bookvol10.4.pamphlet" 1727232 1727249 1735519 1735524) (-975 "bookvol10.2.pamphlet" 1726655 1726665 1727188 1727227) (-974 "bookvol10.3.pamphlet" 1726539 1726555 1726645 1726650) (-973 "bookvol10.3.pamphlet" 1726429 1726439 1726529 1726534) (-972 "bookvol10.3.pamphlet" 1726319 1726329 1726419 1726424) (-971 "bookvol10.3.pamphlet" 1723758 1723770 1724285 1724340) (-970 "bookvol10.3.pamphlet" 1722156 1722168 1722849 1722976) (-969 "bookvol10.4.pamphlet" 1721410 1721449 1722146 1722151) (-968 "bookvol10.4.pamphlet" 1721162 1721170 1721400 1721405) (-967 "bookvol10.4.pamphlet" 1719395 1719405 1721152 1721157) (-966 "bookvol10.4.pamphlet" 1717482 1717496 1719385 1719390) (-965 "bookvol10.2.pamphlet" 1717093 1717101 1717472 1717477) (-964 "bookvol10.3.pamphlet" 1716346 1716356 1716499 1716526) (-963 "bookvol10.4.pamphlet" 1714452 1714464 1716336 1716341) (-962 "bookvol10.4.pamphlet" 1713818 1713830 1714442 1714447) (-961 "bookvol10.2.pamphlet" 1713183 1713191 1713808 1713813) (-960 "bookvol10.4.pamphlet" 1707992 1708000 1713173 1713178) (-959 "bookvol10.4.pamphlet" 1706736 1706758 1707948 1707953) (-958 "bookvol10.3.pamphlet" 1704054 1704064 1704550 1704677) (-957 "bookvol10.4.pamphlet" 1703343 1703366 1704044 1704049) (-956 "bookvol10.4.pamphlet" 1701353 1701375 1703333 1703338) (-955 "bookvol10.2.pamphlet" 1694783 1694804 1701221 1701348) (-954 NIL 1687515 1687538 1693955 1693960) (-953 "bookvol10.4.pamphlet" 1686961 1686975 1687505 1687510) (-952 "bookvol10.4.pamphlet" 1686567 1686579 1686951 1686956) (-951 "bookvol10.4.pamphlet" 1685608 1685637 1686523 1686528) (-950 "bookvol10.4.pamphlet" 1684356 1684371 1685598 1685603) (-949 "bookvol10.3.pamphlet" 1683417 1683427 1683504 1683531) (-948 "bookvol10.4.pamphlet" 1680089 1680097 1683407 1683412) (-947 "bookvol10.4.pamphlet" 1678910 1678924 1680079 1680084) (-946 "bookvol10.4.pamphlet" 1678467 1678477 1678900 1678905) (-945 "bookvol10.4.pamphlet" 1678066 1678080 1678457 1678462) (-944 "bookvol10.4.pamphlet" 1677586 1677600 1678056 1678061) (-943 "bookvol10.4.pamphlet" 1677081 1677103 1677576 1677581) (-942 "bookvol10.4.pamphlet" 1676161 1676179 1677013 1677018) (-941 "bookvol10.4.pamphlet" 1675746 1675760 1676151 1676156) (-940 "bookvol10.4.pamphlet" 1675325 1675337 1675736 1675741) (-939 "bookvol10.4.pamphlet" 1674905 1674915 1675315 1675320) (-938 "bookvol10.4.pamphlet" 1674490 1674508 1674895 1674900) (-937 "bookvol10.4.pamphlet" 1673800 1673814 1674480 1674485) (-936 "bookvol10.4.pamphlet" 1672867 1672875 1673790 1673795) (-935 "bookvol10.4.pamphlet" 1671891 1671907 1672857 1672862) (-934 "bookvol10.4.pamphlet" 1670789 1670827 1671881 1671886) (-933 "bookvol10.4.pamphlet" 1670569 1670577 1670779 1670784) (-932 "bookvol10.3.pamphlet" 1665421 1665429 1670559 1670564) (-931 "bookvol10.3.pamphlet" 1662035 1662043 1665411 1665416) (-930 "bookvol10.4.pamphlet" 1661186 1661196 1662025 1662030) (-929 "bookvol10.4.pamphlet" 1647299 1647326 1661176 1661181) (-928 "bookvol10.3.pamphlet" 1647206 1647220 1647289 1647294) (-927 "bookvol10.3.pamphlet" 1647117 1647127 1647196 1647201) (-926 "bookvol10.3.pamphlet" 1647028 1647038 1647107 1647112) (-925 "bookvol10.2.pamphlet" 1646070 1646084 1647018 1647023) (-924 "bookvol10.4.pamphlet" 1645692 1645711 1646060 1646065) (-923 "bookvol10.4.pamphlet" 1645476 1645492 1645682 1645687) (-922 "bookvol10.3.pamphlet" 1645100 1645108 1645450 1645471) (-921 "bookvol10.2.pamphlet" 1644080 1644088 1645026 1645095) (-920 "bookvol10.4.pamphlet" 1643825 1643835 1644070 1644075) (-919 "bookvol10.4.pamphlet" 1642443 1642457 1643815 1643820) (-918 "bookvol10.4.pamphlet" 1634401 1634409 1642433 1642438) (-917 "bookvol10.4.pamphlet" 1632975 1632992 1634391 1634396) (-916 "bookvol10.4.pamphlet" 1632026 1632036 1632965 1632970) (-915 "bookvol10.3.pamphlet" 1627596 1627606 1631928 1632021) (-914 "bookvol10.4.pamphlet" 1626943 1626959 1627586 1627591) (-913 "bookvol10.4.pamphlet" 1625084 1625113 1626933 1626938) (-912 "bookvol10.4.pamphlet" 1624454 1624472 1625074 1625079) (-911 "bookvol10.4.pamphlet" 1623875 1623902 1624444 1624449) (-910 "bookvol10.3.pamphlet" 1623550 1623562 1623680 1623773) (-909 "bookvol10.2.pamphlet" 1621258 1621266 1623476 1623545) (-908 NIL 1618994 1619004 1621214 1621219) (-907 "bookvol10.4.pamphlet" 1616901 1616913 1618984 1618989) (-906 "bookvol10.4.pamphlet" 1614561 1614584 1616891 1616896) (-905 "bookvol10.3.pamphlet" 1609883 1609893 1614391 1614406) (-904 "bookvol10.3.pamphlet" 1604648 1604658 1609873 1609878) (-903 "bookvol10.2.pamphlet" 1603311 1603321 1604628 1604643) (-902 "bookvol10.4.pamphlet" 1602070 1602084 1603301 1603306) (-901 "bookvol10.3.pamphlet" 1601342 1601352 1601922 1601927) (-900 "bookvol10.2.pamphlet" 1599717 1599727 1601322 1601337) (-899 NIL 1598100 1598112 1599707 1599712) (-898 "bookvol10.3.pamphlet" 1596279 1596287 1598090 1598095) (-897 "bookvol10.4.pamphlet" 1590355 1590363 1596269 1596274) (-896 "bookvol10.4.pamphlet" 1589707 1589724 1590345 1590350) (-895 "bookvol10.2.pamphlet" 1587857 1587865 1589697 1589702) (-894 "bookvol10.4.pamphlet" 1587592 1587605 1587847 1587852) (-893 "bookvol10.3.pamphlet" 1586234 1586251 1587582 1587587) (-892 "bookvol10.3.pamphlet" 1580519 1580529 1586224 1586229) (-891 "bookvol10.4.pamphlet" 1580250 1580262 1580509 1580514) (-890 "bookvol10.4.pamphlet" 1578548 1578564 1580240 1580245) (-889 "bookvol10.3.pamphlet" 1576209 1576221 1578538 1578543) (-888 "bookvol10.4.pamphlet" 1575921 1575935 1576199 1576204) (-887 "bookvol10.4.pamphlet" 1574142 1574173 1575629 1575634) (-886 "bookvol10.2.pamphlet" 1573581 1573591 1574132 1574137) (-885 "bookvol10.3.pamphlet" 1572691 1572705 1573571 1573576) (-884 "bookvol10.2.pamphlet" 1572397 1572407 1572681 1572686) (-883 "bookvol10.4.pamphlet" 1569915 1569923 1572387 1572392) (-882 "bookvol10.3.pamphlet" 1569373 1569401 1569905 1569910) (-881 "bookvol10.4.pamphlet" 1569166 1569182 1569363 1569368) (-880 "bookvol10.3.pamphlet" 1568624 1568652 1569156 1569161) (-879 "bookvol10.4.pamphlet" 1568411 1568427 1568614 1568619) (-878 "bookvol10.3.pamphlet" 1567881 1567909 1568401 1568406) (-877 "bookvol10.4.pamphlet" 1567668 1567684 1567871 1567876) (-876 "bookvol10.4.pamphlet" 1566491 1566540 1567658 1567663) (-875 "bookvol10.4.pamphlet" 1565905 1565913 1566481 1566486) (-874 "bookvol10.3.pamphlet" 1564913 1564921 1565895 1565900) (-873 "bookvol10.4.pamphlet" 1559360 1559383 1564869 1564874) (-872 "bookvol10.4.pamphlet" 1553241 1553264 1559309 1559314) (-871 "bookvol10.3.pamphlet" 1550617 1550635 1551746 1551839) (-870 "bookvol10.3.pamphlet" 1548680 1548692 1548853 1548946) (-869 "bookvol10.3.pamphlet" 1548425 1548437 1548606 1548675) (-868 "bookvol10.2.pamphlet" 1546971 1546983 1548351 1548420) (-867 "bookvol10.4.pamphlet" 1545916 1545935 1546961 1546966) (-866 "bookvol10.4.pamphlet" 1544921 1544937 1545906 1545911) (-865 "bookvol10.3.pamphlet" 1543756 1543764 1544592 1544685) (-864 "bookvol10.2.pamphlet" 1542740 1542748 1543658 1543751) (-863 "bookvol10.2.pamphlet" 1541039 1541047 1542642 1542735) (-862 "bookvol10.3.pamphlet" 1539998 1540008 1540835 1540928) (-861 "bookvol10.2.pamphlet" 1538985 1538993 1539900 1539993) (-860 "bookvol10.3.pamphlet" 1537524 1537544 1538375 1538468) (-859 "bookvol10.2.pamphlet" 1536500 1536508 1537426 1537519) (-858 "bookvol10.3.pamphlet" 1535508 1535538 1536358 1536425) (-857 "bookvol10.3.pamphlet" 1535289 1535312 1535498 1535503) (-856 "bookvol10.4.pamphlet" 1534415 1534423 1535279 1535284) (-855 "bookvol10.3.pamphlet" 1523829 1523837 1534405 1534410) (-854 "bookvol10.3.pamphlet" 1523434 1523442 1523819 1523824) (-853 "bookvol10.4.pamphlet" 1521891 1521901 1523351 1523356) (-852 "bookvol10.3.pamphlet" 1521241 1521269 1521571 1521610) (-851 "bookvol10.3.pamphlet" 1520526 1520550 1520921 1520960) (-850 "bookvol10.4.pamphlet" 1518286 1518298 1520446 1520451) (-849 "bookvol10.2.pamphlet" 1512298 1512308 1518242 1518281) (-848 NIL 1506200 1506212 1512146 1512151) (-847 "bookvol10.2.pamphlet" 1505340 1505348 1506190 1506195) (-846 NIL 1504478 1504488 1505330 1505335) (-845 "bookvol10.2.pamphlet" 1503812 1503820 1504458 1504473) (-844 NIL 1503154 1503164 1503802 1503807) (-843 "bookvol10.2.pamphlet" 1502878 1502886 1503144 1503149) (-842 "bookvol10.4.pamphlet" 1502025 1502041 1502868 1502873) (-841 "bookvol10.2.pamphlet" 1501959 1501967 1502015 1502020) (-840 "bookvol10.3.pamphlet" 1500451 1500461 1501506 1501535) (-839 "bookvol10.4.pamphlet" 1499803 1499815 1500441 1500446) (-838 "bookvol10.3.pamphlet" 1497569 1497577 1499793 1499798) (-837 "bookvol10.4.pamphlet" 1490021 1490029 1497559 1497564) (-836 "bookvol10.2.pamphlet" 1487499 1487507 1490011 1490016) (-835 "bookvol10.4.pamphlet" 1487054 1487062 1487489 1487494) (-834 "bookvol10.3.pamphlet" 1486796 1486806 1486876 1486943) (-833 "bookvol10.3.pamphlet" 1485572 1485582 1486343 1486372) (-832 "bookvol10.4.pamphlet" 1485063 1485075 1485562 1485567) (-831 "bookvol10.4.pamphlet" 1484113 1484121 1485053 1485058) (-830 "bookvol10.2.pamphlet" 1483897 1483907 1484057 1484108) (-829 "bookvol10.4.pamphlet" 1482573 1482581 1483887 1483892) (-828 "bookvol10.2.pamphlet" 1481648 1481656 1482563 1482568) (-827 "bookvol10.3.pamphlet" 1481065 1481077 1481534 1481573) (-826 "bookvol10.4.pamphlet" 1480899 1480909 1481055 1481060) (-825 "bookvol10.3.pamphlet" 1480452 1480460 1480889 1480894) (-824 "bookvol10.3.pamphlet" 1479504 1479512 1480442 1480447) (-823 "bookvol10.3.pamphlet" 1478850 1478858 1479494 1479499) (-822 "bookvol10.3.pamphlet" 1473593 1473601 1478840 1478845) (-821 "bookvol10.3.pamphlet" 1473010 1473018 1473583 1473588) (-820 "bookvol10.2.pamphlet" 1472787 1472795 1472936 1473005) (-819 "bookvol10.3.pamphlet" 1466414 1466424 1472777 1472782) (-818 "bookvol10.3.pamphlet" 1465697 1465707 1466404 1466409) (-817 "bookvol10.3.pamphlet" 1465145 1465171 1465509 1465658) (-816 "bookvol10.3.pamphlet" 1462505 1462515 1462831 1462958) (-815 "bookvol10.3.pamphlet" 1454362 1454382 1454720 1454851) (-814 "bookvol10.4.pamphlet" 1452887 1452906 1454352 1454357) (-813 "bookvol10.4.pamphlet" 1450347 1450364 1452877 1452882) (-812 "bookvol10.4.pamphlet" 1446276 1446293 1450304 1450309) (-811 "bookvol10.4.pamphlet" 1445637 1445661 1446266 1446271) (-810 "bookvol10.4.pamphlet" 1443081 1443098 1445627 1445632) (-809 "bookvol10.4.pamphlet" 1440096 1440118 1443071 1443076) (-808 "bookvol10.3.pamphlet" 1438752 1438760 1440086 1440091) (-807 "bookvol10.4.pamphlet" 1436010 1436032 1438742 1438747) (-806 "bookvol10.4.pamphlet" 1435376 1435400 1436000 1436005) (-805 "bookvol10.4.pamphlet" 1423120 1423128 1435366 1435371) (-804 "bookvol10.4.pamphlet" 1422539 1422555 1423110 1423115) (-803 "bookvol10.3.pamphlet" 1419942 1419950 1422529 1422534) (-802 "bookvol10.4.pamphlet" 1415259 1415275 1419932 1419937) (-801 "bookvol10.4.pamphlet" 1414768 1414786 1415249 1415254) (-800 "bookvol10.2.pamphlet" 1413159 1413167 1414758 1414763) (-799 "bookvol10.3.pamphlet" 1411327 1411337 1412009 1412048) (-798 "bookvol10.4.pamphlet" 1410973 1410994 1411317 1411322) (-797 "bookvol10.2.pamphlet" 1408921 1408931 1410929 1410968) (-796 NIL 1406594 1406606 1408604 1408609) (-795 "bookvol10.2.pamphlet" 1406444 1406452 1406584 1406589) (-794 "bookvol10.2.pamphlet" 1406210 1406218 1406434 1406439) (-793 "bookvol10.2.pamphlet" 1405564 1405572 1406200 1406205) (-792 "bookvol10.2.pamphlet" 1405427 1405435 1405554 1405559) (-791 "bookvol10.2.pamphlet" 1405291 1405299 1405417 1405422) (-790 "bookvol10.4.pamphlet" 1405018 1405034 1405281 1405286) (-789 "bookvol10.4.pamphlet" 1393747 1393755 1405008 1405013) (-788 "bookvol10.4.pamphlet" 1385314 1385322 1393737 1393742) (-787 "bookvol10.2.pamphlet" 1382669 1382677 1385304 1385309) (-786 "bookvol10.4.pamphlet" 1381511 1381519 1382659 1382664) (-785 "bookvol10.4.pamphlet" 1373669 1373679 1381316 1381321) (-784 "bookvol10.2.pamphlet" 1373076 1373092 1373625 1373664) (-783 "bookvol10.4.pamphlet" 1372627 1372637 1372993 1372998) (-782 "bookvol10.3.pamphlet" 1366528 1366538 1370177 1370330) (-781 "bookvol10.4.pamphlet" 1365924 1365936 1366518 1366523) (-780 "bookvol10.3.pamphlet" 1362135 1362154 1362427 1362554) (-779 "bookvol10.3.pamphlet" 1360659 1360669 1360736 1360829) (-778 "bookvol10.4.pamphlet" 1359049 1359063 1360649 1360654) (-777 "bookvol10.4.pamphlet" 1358941 1358970 1359039 1359044) (-776 "bookvol10.4.pamphlet" 1358189 1358209 1358931 1358936) (-775 "bookvol10.3.pamphlet" 1358077 1358091 1358169 1358184) (-774 "bookvol10.4.pamphlet" 1357671 1357710 1358067 1358072) (-773 "bookvol10.4.pamphlet" 1356519 1356538 1357661 1357666) (-772 "bookvol10.4.pamphlet" 1356201 1356227 1356509 1356514) (-771 "bookvol10.3.pamphlet" 1355942 1355950 1356191 1356196) (-770 "bookvol10.4.pamphlet" 1355618 1355628 1355932 1355937) (-769 "bookvol10.4.pamphlet" 1355075 1355091 1355608 1355613) (-768 "bookvol10.3.pamphlet" 1353965 1353973 1355049 1355070) (-767 "bookvol10.4.pamphlet" 1352591 1352601 1353955 1353960) (-766 "bookvol10.3.pamphlet" 1350279 1350287 1352581 1352586) (-765 "bookvol10.4.pamphlet" 1347747 1347764 1350269 1350274) (-764 "bookvol10.4.pamphlet" 1347066 1347080 1347737 1347742) (-763 "bookvol10.4.pamphlet" 1345206 1345222 1347056 1347061) (-762 "bookvol10.4.pamphlet" 1344863 1344877 1345196 1345201) (-761 "bookvol10.4.pamphlet" 1343041 1343055 1344853 1344858) (-760 "bookvol10.2.pamphlet" 1342639 1342647 1343031 1343036) (-759 NIL 1342235 1342245 1342629 1342634) (-758 "bookvol10.2.pamphlet" 1341613 1341621 1342225 1342230) (-757 NIL 1340989 1340999 1341603 1341608) (-756 "bookvol10.4.pamphlet" 1340066 1340074 1340979 1340984) (-755 "bookvol10.4.pamphlet" 1330508 1330516 1340056 1340061) (-754 "bookvol10.4.pamphlet" 1329008 1329016 1330498 1330503) (-753 "bookvol10.4.pamphlet" 1323472 1323480 1328998 1329003) (-752 "bookvol10.4.pamphlet" 1317628 1317636 1323462 1323467) (-751 "bookvol10.4.pamphlet" 1313438 1313446 1317618 1317623) (-750 "bookvol10.4.pamphlet" 1307232 1307240 1313428 1313433) (-749 "bookvol10.4.pamphlet" 1297989 1297997 1307222 1307227) (-748 "bookvol10.4.pamphlet" 1294080 1294088 1297979 1297984) (-747 "bookvol10.4.pamphlet" 1292119 1292127 1294070 1294075) (-746 "bookvol10.4.pamphlet" 1284925 1284933 1292109 1292114) (-745 "bookvol10.4.pamphlet" 1279469 1279477 1284915 1284920) (-744 "bookvol10.4.pamphlet" 1275401 1275409 1279459 1279464) (-743 "bookvol10.4.pamphlet" 1273947 1273955 1275391 1275396) (-742 "bookvol10.4.pamphlet" 1273277 1273285 1273937 1273942) (-741 "bookvol10.2.pamphlet" 1272829 1272839 1273245 1273272) (-740 NIL 1272401 1272413 1272819 1272824) (-739 "bookvol10.3.pamphlet" 1269628 1269642 1269951 1270104) (-738 "bookvol10.3.pamphlet" 1267747 1267761 1267819 1268039) (-737 "bookvol10.4.pamphlet" 1264715 1264732 1267737 1267742) (-736 "bookvol10.4.pamphlet" 1264113 1264130 1264705 1264710) (-735 "bookvol10.2.pamphlet" 1262143 1262164 1264011 1264108) (-734 "bookvol10.4.pamphlet" 1261802 1261812 1262133 1262138) (-733 "bookvol10.4.pamphlet" 1261260 1261268 1261792 1261797) (-732 "bookvol10.3.pamphlet" 1259323 1259333 1261022 1261061) (-731 "bookvol10.2.pamphlet" 1259156 1259166 1259279 1259318) (-730 "bookvol10.3.pamphlet" 1256191 1256203 1258864 1258931) (-729 "bookvol10.4.pamphlet" 1255753 1255767 1256181 1256186) (-728 "bookvol10.4.pamphlet" 1255314 1255331 1255743 1255748) (-727 "bookvol10.4.pamphlet" 1253387 1253406 1255304 1255309) (-726 "bookvol10.3.pamphlet" 1250839 1250854 1251181 1251308) (-725 "bookvol10.4.pamphlet" 1250118 1250137 1250829 1250834) (-724 "bookvol10.4.pamphlet" 1249928 1249971 1250108 1250113) (-723 "bookvol10.4.pamphlet" 1249676 1249712 1249918 1249923) (-722 "bookvol10.4.pamphlet" 1248047 1248064 1249666 1249671) (-721 "bookvol10.2.pamphlet" 1246949 1246957 1248037 1248042) (-720 NIL 1245849 1245859 1246939 1246944) (-719 "bookvol10.2.pamphlet" 1244577 1244590 1245709 1245844) (-718 NIL 1243327 1243342 1244461 1244466) (-717 "bookvol10.2.pamphlet" 1241480 1241488 1243317 1243322) (-716 NIL 1239631 1239641 1241470 1241475) (-715 "bookvol10.2.pamphlet" 1238822 1238830 1239621 1239626) (-714 NIL 1238011 1238021 1238812 1238817) (-713 "bookvol10.3.pamphlet" 1236668 1236682 1237991 1238006) (-712 "bookvol10.2.pamphlet" 1236381 1236391 1236636 1236663) (-711 NIL 1236114 1236126 1236371 1236376) (-710 "bookvol10.3.pamphlet" 1235433 1235472 1236094 1236109) (-709 "bookvol10.3.pamphlet" 1234053 1234065 1235255 1235322) (-708 "bookvol10.3.pamphlet" 1233566 1233584 1234043 1234048) (-707 "bookvol10.3.pamphlet" 1230226 1230242 1231044 1231197) (-706 "bookvol10.3.pamphlet" 1229593 1229632 1230128 1230221) (-705 "bookvol10.3.pamphlet" 1228398 1228406 1229583 1229588) (-704 "bookvol10.4.pamphlet" 1228132 1228166 1228388 1228393) (-703 "bookvol10.2.pamphlet" 1226550 1226560 1228088 1228127) (-702 "bookvol10.4.pamphlet" 1225166 1225183 1226540 1226545) (-701 "bookvol10.4.pamphlet" 1224606 1224624 1225156 1225161) (-700 "bookvol10.4.pamphlet" 1224198 1224211 1224596 1224601) (-699 "bookvol10.4.pamphlet" 1223483 1223493 1224188 1224193) (-698 "bookvol10.4.pamphlet" 1222333 1222343 1223473 1223478) (-697 "bookvol10.3.pamphlet" 1222111 1222121 1222323 1222328) (-696 "bookvol10.4.pamphlet" 1221550 1221568 1222101 1222106) (-695 "bookvol10.3.pamphlet" 1220989 1220997 1221452 1221545) (-694 "bookvol10.4.pamphlet" 1219628 1219638 1220979 1220984) (-693 "bookvol10.3.pamphlet" 1218076 1218084 1219518 1219623) (-692 "bookvol10.4.pamphlet" 1217476 1217498 1218066 1218071) (-691 "bookvol10.4.pamphlet" 1215388 1215396 1217466 1217471) (-690 "bookvol10.4.pamphlet" 1213641 1213651 1215378 1215383) (-689 "bookvol10.2.pamphlet" 1212922 1212932 1213609 1213636) (-688 "bookvol10.3.pamphlet" 1208895 1208903 1209509 1209710) (-687 "bookvol10.4.pamphlet" 1208097 1208109 1208885 1208890) (-686 "bookvol10.4.pamphlet" 1205357 1205383 1208087 1208092) (-685 "bookvol10.4.pamphlet" 1202637 1202647 1205347 1205352) (-684 "bookvol10.3.pamphlet" 1201530 1201540 1202012 1202039) (-683 "bookvol10.4.pamphlet" 1198938 1198962 1201414 1201419) (-682 "bookvol10.2.pamphlet" 1185066 1185088 1198894 1198933) (-681 NIL 1171042 1171066 1184872 1184877) (-680 "bookvol10.4.pamphlet" 1170324 1170372 1171032 1171037) (-679 "bookvol10.4.pamphlet" 1169118 1169130 1170314 1170319) (-678 "bookvol10.4.pamphlet" 1167993 1168007 1169108 1169113) (-677 "bookvol10.4.pamphlet" 1167299 1167311 1167983 1167988) (-676 "bookvol10.4.pamphlet" 1166121 1166131 1167289 1167294) (-675 "bookvol10.4.pamphlet" 1165933 1165947 1166111 1166116) (-674 "bookvol10.4.pamphlet" 1165702 1165714 1165923 1165928) (-673 "bookvol10.4.pamphlet" 1165338 1165348 1165692 1165697) (-672 "bookvol10.4.pamphlet" 1161010 1161034 1165328 1165333) (-671 "bookvol10.3.pamphlet" 1159294 1159311 1161000 1161005) (-670 "bookvol10.2.pamphlet" 1157150 1157165 1159284 1159289) (-669 "bookvol10.3.pamphlet" 1155135 1155145 1156751 1156756) (-668 "bookvol10.2.pamphlet" 1150883 1150893 1155115 1155130) (-667 NIL 1146639 1146651 1150873 1150878) (-666 "bookvol10.3.pamphlet" 1143877 1143894 1146629 1146634) (-665 "bookvol10.3.pamphlet" 1142175 1142189 1142557 1142608) (-664 "bookvol10.4.pamphlet" 1141718 1141735 1142165 1142170) (-663 "bookvol10.4.pamphlet" 1140520 1140548 1141708 1141713) (-662 "bookvol10.4.pamphlet" 1138282 1138296 1140510 1140515) (-661 "bookvol10.2.pamphlet" 1137939 1137949 1138238 1138277) (-660 NIL 1137628 1137640 1137929 1137934) (-659 "bookvol10.3.pamphlet" 1136776 1136795 1137484 1137553) (-658 "bookvol10.4.pamphlet" 1136037 1136047 1136766 1136771) (-657 "bookvol10.4.pamphlet" 1134513 1134562 1136027 1136032) (-656 "bookvol10.4.pamphlet" 1133186 1133196 1134503 1134508) (-655 "bookvol10.3.pamphlet" 1132583 1132597 1133120 1133147) (-654 "bookvol10.2.pamphlet" 1132215 1132223 1132573 1132578) (-653 NIL 1131845 1131855 1132205 1132210) (-652 "bookvol10.4.pamphlet" 1130775 1130787 1131835 1131840) (-651 "bookvol10.3.pamphlet" 1130146 1130162 1130455 1130494) (-650 "bookvol10.4.pamphlet" 1129194 1129211 1130103 1130108) (-649 "bookvol10.2.pamphlet" 1127843 1127853 1129150 1129189) (-648 NIL 1126490 1126502 1127799 1127804) (-647 "bookvol10.3.pamphlet" 1125750 1125762 1126170 1126209) (-646 "bookvol10.3.pamphlet" 1125137 1125147 1125430 1125469) (-645 "bookvol10.4.pamphlet" 1123863 1123881 1125127 1125132) (-644 "bookvol10.2.pamphlet" 1122286 1122296 1123765 1123858) (-643 "bookvol10.2.pamphlet" 1118762 1118772 1122266 1122281) (-642 NIL 1115212 1115224 1118718 1118723) (-641 "bookvol10.3.pamphlet" 1111824 1111841 1115202 1115207) (-640 "bookvol10.2.pamphlet" 1111339 1111349 1111814 1111819) (-639 "bookvol10.3.pamphlet" 1110461 1110471 1111113 1111140) (-638 "bookvol10.4.pamphlet" 1109912 1109926 1110451 1110456) (-637 "bookvol10.3.pamphlet" 1107875 1107885 1109282 1109309) (-636 "bookvol10.4.pamphlet" 1107190 1107204 1107865 1107870) (-635 "bookvol10.4.pamphlet" 1105870 1105882 1107180 1107185) (-634 "bookvol10.4.pamphlet" 1102733 1102745 1105860 1105865) (-633 "bookvol10.2.pamphlet" 1102111 1102121 1102713 1102728) (-632 "bookvol10.4.pamphlet" 1100984 1100996 1102023 1102028) (-631 "bookvol10.4.pamphlet" 1098942 1098952 1100974 1100979) (-630 "bookvol10.4.pamphlet" 1097817 1097830 1098932 1098937) (-629 "bookvol10.3.pamphlet" 1095847 1095859 1097107 1097252) (-628 "bookvol10.2.pamphlet" 1095432 1095442 1095773 1095842) (-627 NIL 1095045 1095057 1095388 1095393) (-626 "bookvol10.3.pamphlet" 1093580 1093588 1094286 1094301) (-625 "bookvol10.4.pamphlet" 1090958 1090977 1093570 1093575) (-624 "bookvol10.4.pamphlet" 1089737 1089753 1090948 1090953) (-623 "bookvol10.2.pamphlet" 1088590 1088598 1089727 1089732) (-622 "bookvol10.4.pamphlet" 1084422 1084437 1088580 1088585) (-621 "bookvol10.3.pamphlet" 1082657 1082684 1084402 1084417) (-620 "bookvol10.4.pamphlet" 1081087 1081104 1082647 1082652) (-619 "bookvol10.4.pamphlet" 1080197 1080219 1081077 1081082) (-618 "bookvol10.3.pamphlet" 1078973 1078986 1079790 1079859) (-617 "bookvol10.4.pamphlet" 1078518 1078534 1078963 1078968) (-616 "bookvol10.3.pamphlet" 1077928 1077942 1078440 1078479) (-615 "bookvol10.2.pamphlet" 1077704 1077714 1077908 1077923) (-614 NIL 1077488 1077500 1077694 1077699) (-613 "bookvol10.4.pamphlet" 1076169 1076186 1077478 1077483) (-612 "bookvol10.2.pamphlet" 1075893 1075903 1076159 1076164) (-611 "bookvol10.2.pamphlet" 1075630 1075640 1075883 1075888) (-610 "bookvol10.3.pamphlet" 1074191 1074201 1075414 1075419) (-609 "bookvol10.4.pamphlet" 1073894 1073906 1074181 1074186) (-608 "bookvol10.2.pamphlet" 1073033 1073055 1073862 1073889) (-607 NIL 1072192 1072216 1073023 1073028) (-606 "bookvol10.3.pamphlet" 1070830 1070846 1071539 1071566) (-605 "bookvol10.3.pamphlet" 1068839 1068851 1070120 1070265) (-604 "bookvol10.2.pamphlet" 1067083 1067107 1068819 1068834) (-603 NIL 1065192 1065218 1066930 1066935) (-602 "bookvol10.3.pamphlet" 1064200 1064215 1064340 1064367) (-601 "bookvol10.3.pamphlet" 1063320 1063330 1064190 1064195) (-600 "bookvol10.4.pamphlet" 1062083 1062102 1063310 1063315) (-599 "bookvol10.4.pamphlet" 1061589 1061603 1062073 1062078) (-598 "bookvol10.4.pamphlet" 1061333 1061345 1061579 1061584) (-597 "bookvol10.3.pamphlet" 1059141 1059156 1061169 1061294) (-596 "bookvol10.3.pamphlet" 1051529 1051544 1058115 1058212) (-595 "bookvol10.4.pamphlet" 1050996 1051012 1051519 1051524) (-594 "bookvol10.3.pamphlet" 1050226 1050239 1050392 1050419) (-593 "bookvol10.4.pamphlet" 1049221 1049240 1050216 1050221) (-592 "bookvol10.4.pamphlet" 1047289 1047297 1049211 1049216) (-591 "bookvol10.4.pamphlet" 1045836 1045846 1047245 1047250) (-590 "bookvol10.4.pamphlet" 1045437 1045448 1045826 1045831) (-589 "bookvol10.4.pamphlet" 1043753 1043763 1045427 1045432) (-588 "bookvol10.3.pamphlet" 1041476 1041490 1043608 1043635) (-587 "bookvol10.4.pamphlet" 1040620 1040636 1041466 1041471) (-586 "bookvol10.4.pamphlet" 1039797 1039813 1040610 1040615) (-585 "bookvol10.4.pamphlet" 1039573 1039581 1039787 1039792) (-584 "bookvol10.3.pamphlet" 1039274 1039286 1039378 1039471) (-583 "bookvol10.3.pamphlet" 1039045 1039071 1039200 1039269) (-582 "bookvol10.4.pamphlet" 1038642 1038658 1039035 1039040) (-581 "bookvol10.4.pamphlet" 1031664 1031681 1038632 1038637) (-580 "bookvol10.4.pamphlet" 1029529 1029545 1031238 1031243) (-579 "bookvol10.4.pamphlet" 1028849 1028857 1029519 1029524) (-578 "bookvol10.3.pamphlet" 1028625 1028635 1028763 1028844) (-577 "bookvol10.4.pamphlet" 1026989 1027003 1028615 1028620) (-576 "bookvol10.4.pamphlet" 1026482 1026492 1026979 1026984) (-575 "bookvol10.4.pamphlet" 1025151 1025168 1026472 1026477) (-574 "bookvol10.4.pamphlet" 1023464 1023480 1024794 1024799) (-573 "bookvol10.4.pamphlet" 1021121 1021139 1023396 1023401) (-572 "bookvol10.4.pamphlet" 1011646 1011654 1021111 1021116) (-571 "bookvol10.3.pamphlet" 1011007 1011015 1011500 1011641) (-570 "bookvol10.4.pamphlet" 1010273 1010290 1010997 1011002) (-569 "bookvol10.4.pamphlet" 1009918 1009942 1010263 1010268) (-568 "bookvol10.4.pamphlet" 1006297 1006305 1009908 1009913) (-567 "bookvol10.4.pamphlet" 999455 999473 1006229 1006234) (-566 "bookvol10.3.pamphlet" 993453 993461 999445 999450) (-565 "bookvol10.4.pamphlet" 992605 992662 993443 993448) (-564 "bookvol10.4.pamphlet" 991691 991701 992595 992600) (-563 "bookvol10.4.pamphlet" 991559 991583 991681 991686) (-562 "bookvol10.4.pamphlet" 989917 989933 991549 991554) (-561 "bookvol10.2.pamphlet" 988569 988577 989843 989912) (-560 NIL 987283 987293 988559 988564) (-559 "bookvol10.4.pamphlet" 986429 986516 987273 987278) (-558 "bookvol10.2.pamphlet" 985050 985060 986343 986424) (-557 "bookvol10.4.pamphlet" 984581 984589 985040 985045) (-556 "bookvol10.4.pamphlet" 983739 983766 984571 984576) (-555 "bookvol10.4.pamphlet" 983215 983231 983729 983734) (-554 "bookvol10.3.pamphlet" 982295 982326 982458 982485) (-553 "bookvol10.2.pamphlet" 979629 979637 982197 982290) (-552 NIL 977049 977059 979619 979624) (-551 "bookvol10.4.pamphlet" 976497 976510 977039 977044) (-550 "bookvol10.4.pamphlet" 975593 975612 976487 976492) (-549 "bookvol10.4.pamphlet" 974681 974705 975583 975588) (-548 "bookvol10.4.pamphlet" 973687 973704 974671 974676) (-547 "bookvol10.4.pamphlet" 972844 972874 973677 973682) (-546 "bookvol10.4.pamphlet" 971189 971211 972834 972839) (-545 "bookvol10.4.pamphlet" 970269 970288 971179 971184) (-544 "bookvol10.3.pamphlet" 967190 967198 970259 970264) (-543 "bookvol10.4.pamphlet" 966835 966845 967180 967185) (-542 "bookvol10.4.pamphlet" 966423 966431 966825 966830) (-541 "bookvol10.3.pamphlet" 965840 965903 966413 966418) (-540 "bookvol10.3.pamphlet" 965282 965305 965830 965835) (-539 "bookvol10.2.pamphlet" 963935 963998 965272 965277) (-538 "bookvol10.4.pamphlet" 962479 962501 963925 963930) (-537 "bookvol10.3.pamphlet" 962385 962402 962469 962474) (-536 "bookvol10.4.pamphlet" 961802 961812 962375 962380) (-535 "bookvol10.4.pamphlet" 957696 957707 961792 961797) (-534 "bookvol10.3.pamphlet" 956828 956854 957340 957367) (-533 "bookvol10.4.pamphlet" 955920 955964 956784 956789) (-532 "bookvol10.4.pamphlet" 954533 954557 955876 955881) (-531 "bookvol10.3.pamphlet" 953420 953435 953939 953966) (-530 "bookvol10.3.pamphlet" 953145 953183 953250 953277) (-529 "bookvol10.3.pamphlet" 952575 952591 952826 952919) (-528 "bookvol10.3.pamphlet" 949808 949823 951981 952008) (-527 "bookvol10.3.pamphlet" 949646 949663 949764 949769) (-526 "bookvol10.2.pamphlet" 949043 949055 949636 949641) (-525 NIL 948438 948452 949033 949038) (-524 "bookvol10.3.pamphlet" 948251 948263 948428 948433) (-523 "bookvol10.3.pamphlet" 948024 948036 948241 948246) (-522 "bookvol10.3.pamphlet" 947759 947771 948014 948019) (-521 "bookvol10.2.pamphlet" 946697 946709 947749 947754) (-520 "bookvol10.3.pamphlet" 946457 946469 946687 946692) (-519 "bookvol10.3.pamphlet" 946219 946231 946447 946452) (-518 "bookvol10.4.pamphlet" 943491 943509 946209 946214) (-517 "bookvol10.3.pamphlet" 938571 938610 943426 943431) (-516 "bookvol10.3.pamphlet" 938028 938051 938561 938566) (-515 "bookvol10.4.pamphlet" 937261 937277 938018 938023) (-514 "bookvol10.3.pamphlet" 936544 936552 937251 937256) (-513 "bookvol10.4.pamphlet" 935187 935204 936534 936539) (-512 "bookvol10.3.pamphlet" 934469 934482 934881 934908) (-511 "bookvol10.4.pamphlet" 931396 931415 934459 934464) (-510 "bookvol10.4.pamphlet" 930306 930321 931386 931391) (-509 "bookvol10.3.pamphlet" 930037 930063 930136 930163) (-508 "bookvol10.3.pamphlet" 929350 929365 929443 929470) (-507 "bookvol10.3.pamphlet" 927573 927581 929166 929259) (-506 "bookvol10.4.pamphlet" 927130 927163 927563 927568) (-505 "bookvol10.2.pamphlet" 926508 926516 927120 927125) (-504 NIL 925884 925894 926498 926503) (-503 "bookvol10.3.pamphlet" 924736 924744 925874 925879) (-502 "bookvol10.2.pamphlet" 922530 922540 924716 924731) (-501 NIL 920165 920177 922353 922358) (-500 "bookvol10.3.pamphlet" 918034 918042 918632 918725) (-499 "bookvol10.4.pamphlet" 916986 916997 918024 918029) (-498 "bookvol10.3.pamphlet" 916618 916642 916976 916981) (-497 "bookvol10.3.pamphlet" 912755 912765 916448 916475) (-496 "bookvol10.3.pamphlet" 904610 904626 904970 905101) (-495 "bookvol10.3.pamphlet" 901805 901820 902404 902531) (-494 "bookvol10.4.pamphlet" 900401 900409 901795 901800) (-493 "bookvol10.3.pamphlet" 899435 899466 899644 899671) (-492 "bookvol10.3.pamphlet" 899046 899054 899337 899430) (-491 "bookvol10.4.pamphlet" 885143 885155 899036 899041) (-490 "bookvol10.4.pamphlet" 884888 884896 884988 884993) (-489 "bookvol10.4.pamphlet" 869185 869221 884758 884763) (-488 "bookvol10.4.pamphlet" 868946 868954 869044 869049) (-487 "bookvol10.4.pamphlet" 868767 868781 868880 868885) (-486 "bookvol10.4.pamphlet" 868644 868658 868757 868762) (-485 "bookvol10.4.pamphlet" 868477 868485 868577 868582) (-484 "bookvol10.3.pamphlet" 867693 867709 868179 868206) (-483 "bookvol10.3.pamphlet" 866776 866811 866948 866963) (-482 "bookvol10.3.pamphlet" 863949 863976 864908 865057) (-481 "bookvol10.2.pamphlet" 862927 862935 863929 863944) (-480 NIL 861913 861923 862917 862922) (-479 "bookvol10.4.pamphlet" 860504 860525 861903 861908) (-478 "bookvol10.2.pamphlet" 859144 859156 860494 860499) (-477 NIL 857782 857796 859134 859139) (-476 "bookvol10.3.pamphlet" 850821 850829 857772 857777) (-475 "bookvol10.4.pamphlet" 849216 849224 850811 850816) (-474 "bookvol10.4.pamphlet" 847757 847765 849206 849211) (-473 "bookvol10.2.pamphlet" 846960 846972 847747 847752) (-472 NIL 846161 846175 846950 846955) (-471 "bookvol10.3.pamphlet" 845687 845710 845899 845926) (-470 "bookvol10.4.pamphlet" 840461 840548 845643 845648) (-469 "bookvol10.4.pamphlet" 839730 839748 840451 840456) (-468 "bookvol10.3.pamphlet" 834023 834031 839720 839725) (-467 "bookvol10.3.pamphlet" 830438 830446 834013 834018) (-466 "bookvol10.3.pamphlet" 829555 829582 830406 830433) (-465 "bookvol10.4.pamphlet" 828727 828741 829545 829550) (-464 "bookvol10.4.pamphlet" 824540 824553 828717 828722) (-463 "bookvol10.4.pamphlet" 824144 824154 824530 824535) (-462 "bookvol10.4.pamphlet" 823794 823811 824134 824139) (-461 "bookvol10.4.pamphlet" 823261 823280 823784 823789) (-460 "bookvol10.4.pamphlet" 821743 821756 823251 823256) (-459 "bookvol10.4.pamphlet" 820208 820216 821733 821738) (-458 "bookvol10.3.pamphlet" 817249 817266 818002 818129) (-457 "bookvol10.3.pamphlet" 811220 811247 817043 817110) (-456 "bookvol10.2.pamphlet" 810174 810182 811146 811215) (-455 NIL 809190 809200 810164 810169) (-454 "bookvol10.4.pamphlet" 804737 804775 809146 809151) (-453 "bookvol10.4.pamphlet" 800835 800873 804727 804732) (-452 "bookvol10.4.pamphlet" 796300 796338 800825 800830) (-451 "bookvol10.4.pamphlet" 792953 792991 796290 796295) (-450 "bookvol10.4.pamphlet" 792276 792284 792943 792948) (-449 "bookvol10.4.pamphlet" 790602 790612 792232 792237) (-448 "bookvol10.4.pamphlet" 789069 789082 790592 790597) (-447 "bookvol10.4.pamphlet" 787274 787293 789059 789064) (-446 "bookvol10.4.pamphlet" 777712 777723 787264 787269) (-445 "bookvol10.2.pamphlet" 774655 774663 777692 777707) (-444 "bookvol10.2.pamphlet" 773699 773707 774635 774650) (-443 "bookvol10.3.pamphlet" 773548 773560 773689 773694) (-442 "bookvol10.3.pamphlet" 771780 771788 773538 773543) (-441 "bookvol10.3.pamphlet" 770951 770959 771770 771775) (-440 "bookvol10.4.pamphlet" 769997 770016 770887 770892) (-439 "bookvol10.3.pamphlet" 768141 768149 769987 769992) (-438 "bookvol10.4.pamphlet" 767565 767581 768131 768136) (-437 "bookvol10.4.pamphlet" 766425 766441 767522 767527) (-436 "bookvol10.4.pamphlet" 763712 763728 766415 766420) (-435 "bookvol10.2.pamphlet" 757622 757632 763475 763707) (-434 NIL 751322 751334 757177 757182) (-433 "bookvol10.4.pamphlet" 750938 750954 751312 751317) (-432 "bookvol10.3.pamphlet" 750266 750278 750758 750857) (-431 "bookvol10.4.pamphlet" 749530 749546 750256 750261) (-430 "bookvol10.2.pamphlet" 748707 748717 749474 749525) (-429 NIL 747858 747870 748627 748632) (-428 "bookvol10.4.pamphlet" 746601 746617 747848 747853) (-427 "bookvol10.4.pamphlet" 741092 741126 746591 746596) (-426 "bookvol10.4.pamphlet" 740704 740720 741082 741087) (-425 "bookvol10.4.pamphlet" 739867 739890 740694 740699) (-424 "bookvol10.4.pamphlet" 738867 738877 739857 739862) (-423 "bookvol10.3.pamphlet" 730843 730853 737891 737960) (-422 "bookvol10.2.pamphlet" 726026 726036 730785 730838) (-421 NIL 721221 721233 725982 725987) (-420 "bookvol10.4.pamphlet" 720669 720687 721211 721216) (-419 "bookvol10.3.pamphlet" 720079 720109 720600 720605) (-418 "bookvol10.3.pamphlet" 719312 719333 720059 720074) (-417 "bookvol10.4.pamphlet" 719050 719082 719302 719307) (-416 "bookvol10.2.pamphlet" 718724 718734 719040 719045) (-415 NIL 718264 718276 718582 718587) (-414 "bookvol10.2.pamphlet" 716670 716683 718220 718259) (-413 NIL 715108 715123 716660 716665) (-412 "bookvol10.3.pamphlet" 712225 712235 712610 712783) (-411 "bookvol10.4.pamphlet" 711838 711850 712215 712220) (-410 "bookvol10.4.pamphlet" 711196 711208 711828 711833) (-409 "bookvol10.2.pamphlet" 708145 708153 711086 711191) (-408 NIL 705122 705132 708065 708070) (-407 "bookvol10.2.pamphlet" 704176 704184 705024 705117) (-406 NIL 703316 703326 704166 704171) (-405 "bookvol10.2.pamphlet" 703068 703078 703296 703311) (-404 "bookvol10.3.pamphlet" 701818 701835 703058 703063) (-403 "bookvol10.3.pamphlet" 700303 700352 701808 701813) (-402 "bookvol10.4.pamphlet" 699252 699260 700293 700298) (-401 "bookvol10.2.pamphlet" 696342 696350 699232 699247) (-400 "bookvol10.2.pamphlet" 696045 696053 696322 696337) (-399 "bookvol10.3.pamphlet" 693439 693447 696035 696040) (-398 "bookvol10.4.pamphlet" 692918 692928 693429 693434) (-397 "bookvol10.4.pamphlet" 692699 692723 692908 692913) (-396 "bookvol10.4.pamphlet" 691900 691908 692689 692694) (-395 "bookvol10.3.pamphlet" 691322 691344 691868 691895) (-394 "bookvol10.2.pamphlet" 689666 689674 691312 691317) (-393 "bookvol10.3.pamphlet" 689558 689566 689656 689661) (-392 "bookvol10.2.pamphlet" 689356 689364 689484 689553) (-391 "bookvol10.3.pamphlet" 686126 686136 689312 689317) (-390 "bookvol10.3.pamphlet" 685829 685841 686060 686087) (-389 "bookvol10.2.pamphlet" 682779 682787 685809 685824) (-388 "bookvol10.2.pamphlet" 681823 681831 682759 682774) (-387 "bookvol10.2.pamphlet" 679517 679535 681791 681818) (-386 "bookvol10.3.pamphlet" 678979 678991 679451 679478) (-385 "bookvol10.4.pamphlet" 676787 676801 678969 678974) (-384 "bookvol10.3.pamphlet" 673692 673700 676653 676782) (-383 "bookvol10.4.pamphlet" 671158 671172 673682 673687) (-382 "bookvol10.2.pamphlet" 670860 670870 671138 671153) (-381 NIL 670516 670528 670796 670801) (-380 "bookvol10.4.pamphlet" 669772 669784 670506 670511) (-379 "bookvol10.2.pamphlet" 667839 667858 669698 669767) (-378 "bookvol10.2.pamphlet" 665045 665055 667807 667834) (-377 NIL 662164 662176 664928 664933) (-376 "bookvol10.4.pamphlet" 660885 660901 662154 662159) (-375 "bookvol10.2.pamphlet" 659006 659019 660841 660880) (-374 NIL 657053 657068 658890 658895) (-373 "bookvol10.2.pamphlet" 656048 656056 657043 657048) (-372 NIL 655041 655051 656038 656043) (-371 "bookvol10.2.pamphlet" 644390 644400 654983 655036) (-370 NIL 633751 633763 644346 644351) (-369 "bookvol10.3.pamphlet" 633338 633348 633741 633746) (-368 "bookvol10.2.pamphlet" 631785 631802 633328 633333) (-367 "bookvol10.2.pamphlet" 631123 631131 631687 631780) (-366 NIL 630547 630557 631113 631118) (-365 "bookvol10.3.pamphlet" 629088 629098 630527 630542) (-364 "bookvol10.4.pamphlet" 627995 628010 629078 629083) (-363 "bookvol10.3.pamphlet" 627424 627439 627711 627804) (-362 "bookvol10.4.pamphlet" 627297 627314 627414 627419) (-361 "bookvol10.4.pamphlet" 626800 626821 627287 627292) (-360 "bookvol10.4.pamphlet" 618199 618210 626790 626795) (-359 "bookvol10.4.pamphlet" 617281 617298 618189 618194) (-358 "bookvol10.3.pamphlet" 616777 616797 616997 617090) (-357 "bookvol10.3.pamphlet" 616245 616261 616458 616551) (-356 "bookvol10.3.pamphlet" 614795 614815 615961 616054) (-355 "bookvol10.3.pamphlet" 613331 613348 614511 614604) (-354 "bookvol10.3.pamphlet" 611872 611893 613012 613105) (-353 "bookvol10.4.pamphlet" 609242 609261 611862 611867) (-352 "bookvol10.2.pamphlet" 606840 606848 609144 609237) (-351 NIL 604524 604534 606830 606835) (-350 "bookvol10.4.pamphlet" 603317 603334 604514 604519) (-349 "bookvol10.4.pamphlet" 600792 600803 603307 603312) (-348 "bookvol10.4.pamphlet" 594914 594930 600782 600787) (-347 "bookvol10.4.pamphlet" 593589 593608 594904 594909) (-346 "bookvol10.4.pamphlet" 593008 593025 593579 593584) (-345 "bookvol10.4.pamphlet" 592929 592946 592998 593003) (-344 "bookvol10.3.pamphlet" 591810 591830 592645 592738) (-343 "bookvol10.3.pamphlet" 590725 590745 591526 591619) (-342 "bookvol10.3.pamphlet" 589552 589573 590406 590499) (-341 "bookvol10.2.pamphlet" 578357 578379 589391 589547) (-340 NIL 567241 567265 578277 578282) (-339 "bookvol10.4.pamphlet" 566980 567020 567231 567236) (-338 "bookvol10.3.pamphlet" 559656 559702 566736 566775) (-337 "bookvol10.2.pamphlet" 559366 559376 559646 559651) (-336 NIL 558861 558873 559143 559148) (-335 "bookvol10.3.pamphlet" 558312 558336 558851 558856) (-334 "bookvol10.2.pamphlet" 556324 556348 558302 558307) (-333 NIL 554334 554360 556314 556319) (-332 "bookvol10.4.pamphlet" 554080 554120 554324 554329) (-331 "bookvol10.4.pamphlet" 552641 552649 554070 554075) (-330 "bookvol10.3.pamphlet" 552172 552182 552631 552636) (-329 "bookvol10.3.pamphlet" 542137 542145 552162 552167) (-328 "bookvol10.2.pamphlet" 535414 535428 542039 542132) (-327 NIL 528743 528759 535370 535375) (-326 "bookvol10.3.pamphlet" 527171 527181 528149 528176) (-325 "bookvol10.2.pamphlet" 525313 525325 527069 527166) (-324 NIL 523439 523453 525197 525202) (-323 "bookvol10.4.pamphlet" 523013 523035 523429 523434) (-322 "bookvol10.3.pamphlet" 522670 522680 522967 522972) (-321 "bookvol10.2.pamphlet" 520853 520865 522660 522665) (-320 "bookvol10.3.pamphlet" 520467 520477 520749 520776) (-319 "bookvol10.4.pamphlet" 518679 518696 520457 520462) (-318 "bookvol10.4.pamphlet" 518561 518571 518669 518674) (-317 "bookvol10.4.pamphlet" 517755 517765 518551 518556) (-316 "bookvol10.4.pamphlet" 517637 517647 517745 517750) (-315 "bookvol10.3.pamphlet" 514474 514497 515769 515918) (-314 "bookvol10.4.pamphlet" 511942 511950 514464 514469) (-313 "bookvol10.4.pamphlet" 511844 511873 511932 511937) (-312 "bookvol10.4.pamphlet" 508588 508604 511834 511839) (-311 "bookvol10.3.pamphlet" 503855 503865 504577 504984) (-310 "bookvol10.4.pamphlet" 499945 499958 503845 503850) (-309 "bookvol10.4.pamphlet" 499715 499727 499935 499940) (-308 "bookvol10.3.pamphlet" 496649 496674 497287 497380) (-307 "bookvol10.4.pamphlet" 496502 496510 496639 496644) (-306 "bookvol10.3.pamphlet" 496173 496181 496492 496497) (-305 "bookvol10.4.pamphlet" 495667 495681 496163 496168) (-304 "bookvol10.2.pamphlet" 495231 495241 495657 495662) (-303 NIL 494793 494805 495221 495226) (-302 "bookvol10.2.pamphlet" 492365 492373 494719 494788) (-301 NIL 489999 490009 492355 492360) (-300 "bookvol10.4.pamphlet" 481857 481865 489989 489994) (-299 "bookvol10.4.pamphlet" 481452 481466 481847 481852) (-298 "bookvol10.4.pamphlet" 481137 481148 481442 481447) (-297 "bookvol10.2.pamphlet" 474084 474092 481127 481132) (-296 NIL 466937 466947 473982 473987) (-295 "bookvol10.4.pamphlet" 463746 463754 466927 466932) (-294 "bookvol10.4.pamphlet" 463487 463499 463736 463741) (-293 "bookvol10.4.pamphlet" 462994 463010 463477 463482) (-292 "bookvol10.4.pamphlet" 462552 462568 462984 462989) (-291 "bookvol10.4.pamphlet" 460028 460036 462542 462547) (-290 "bookvol10.3.pamphlet" 459062 459084 459271 459298) (-289 "bookvol10.3.pamphlet" 453988 453998 456735 456847) (-288 "bookvol10.4.pamphlet" 453706 453718 453978 453983) (-287 "bookvol10.4.pamphlet" 450060 450070 453696 453701) (-286 "bookvol10.2.pamphlet" 449604 449612 450004 450055) (-285 "bookvol10.3.pamphlet" 448800 448841 449530 449599) (-284 "bookvol10.2.pamphlet" 447256 447275 448790 448795) (-283 NIL 445676 445697 447212 447217) (-282 "bookvol10.2.pamphlet" 445208 445226 445666 445671) (-281 "bookvol10.4.pamphlet" 444597 444616 445198 445203) (-280 "bookvol10.2.pamphlet" 444294 444302 444587 444592) (-279 NIL 443989 443999 444284 444289) (-278 "bookvol10.2.pamphlet" 441905 441915 443957 443984) (-277 NIL 439770 439782 441824 441829) (-276 "bookvol10.3.pamphlet" 436545 436575 439726 439731) (-275 "bookvol10.3.pamphlet" 433381 433404 436501 436506) (-274 "bookvol10.4.pamphlet" 431378 431394 433371 433376) (-273 "bookvol10.4.pamphlet" 426154 426170 431368 431373) (-272 "bookvol10.3.pamphlet" 424468 424476 426144 426149) (-271 "bookvol10.3.pamphlet" 424006 424014 424458 424463) (-270 "bookvol10.3.pamphlet" 423585 423593 423996 424001) (-269 "bookvol10.3.pamphlet" 423167 423175 423575 423580) (-268 "bookvol10.3.pamphlet" 422705 422713 423157 423162) (-267 "bookvol10.3.pamphlet" 422243 422251 422695 422700) (-266 "bookvol10.3.pamphlet" 421781 421789 422233 422238) (-265 "bookvol10.3.pamphlet" 421319 421327 421771 421776) (-264 "bookvol10.4.pamphlet" 417061 417069 421309 421314) (-263 "bookvol10.2.pamphlet" 413810 413820 417051 417056) (-262 NIL 410557 410569 413800 413805) (-261 "bookvol10.4.pamphlet" 407642 407729 410547 410552) (-260 "bookvol10.3.pamphlet" 406848 406858 407472 407499) (-259 "bookvol10.2.pamphlet" 406442 406452 406804 406843) (-258 "bookvol10.3.pamphlet" 403885 403899 404178 404305) (-257 "bookvol10.3.pamphlet" 397648 397656 403875 403880) (-256 "bookvol10.4.pamphlet" 397319 397329 397638 397643) (-255 "bookvol10.4.pamphlet" 392278 392286 397309 397314) (-254 "bookvol10.4.pamphlet" 390519 390527 392268 392273) (-253 "bookvol10.4.pamphlet" 383427 383440 390509 390514) (-252 "bookvol10.4.pamphlet" 382690 382700 383417 383422) (-251 "bookvol10.4.pamphlet" 380115 380123 382680 382685) (-250 "bookvol10.4.pamphlet" 379662 379677 380105 380110) (-249 "bookvol10.4.pamphlet" 369102 369110 379652 379657) (-248 "bookvol10.2.pamphlet" 367312 367322 369058 369097) (-247 "bookvol10.2.pamphlet" 362709 362725 367180 367307) (-246 NIL 358192 358210 362665 362670) (-245 "bookvol10.3.pamphlet" 351567 351583 351689 351990) (-244 "bookvol10.3.pamphlet" 344939 344957 345064 345365) (-243 "bookvol10.3.pamphlet" 342180 342195 342733 342860) (-242 "bookvol10.4.pamphlet" 341520 341530 342170 342175) (-241 "bookvol10.3.pamphlet" 340235 340245 340926 340953) (-240 "bookvol10.2.pamphlet" 338682 338692 340215 340230) (-239 "bookvol10.2.pamphlet" 338123 338131 338626 338677) (-238 NIL 337608 337618 338113 338118) (-237 "bookvol10.3.pamphlet" 337461 337471 337540 337567) (-236 "bookvol10.2.pamphlet" 336226 336236 337429 337456) (-235 "bookvol10.4.pamphlet" 334440 334448 336216 336221) (-234 "bookvol10.3.pamphlet" 333720 333735 334276 334401) (-233 "bookvol10.3.pamphlet" 325310 325326 325935 326066) (-232 "bookvol10.4.pamphlet" 324171 324189 325300 325305) (-231 "bookvol10.2.pamphlet" 323102 323118 324023 324166) (-230 NIL 321774 321792 322697 322702) (-229 "bookvol10.4.pamphlet" 320619 320627 321764 321769) (-228 "bookvol10.2.pamphlet" 319699 319709 320587 320614) (-227 NIL 318765 318777 319655 319660) (-226 "bookvol10.2.pamphlet" 317886 317894 318745 318760) (-225 NIL 317015 317025 317876 317881) (-224 "bookvol10.2.pamphlet" 316166 316176 316995 317010) (-223 NIL 315234 315246 316065 316070) (-222 "bookvol10.2.pamphlet" 314854 314864 315202 315229) (-221 NIL 314494 314506 314844 314849) (-220 "bookvol10.3.pamphlet" 312776 312786 314138 314165) (-219 "bookvol10.3.pamphlet" 311514 311522 311900 311927) (-218 "bookvol10.4.pamphlet" 302708 302716 311504 311509) (-217 "bookvol10.3.pamphlet" 301925 301933 302340 302367) (-216 "bookvol10.3.pamphlet" 298310 298318 301815 301920) (-215 "bookvol10.4.pamphlet" 296545 296561 298300 298305) (-214 "bookvol10.3.pamphlet" 294503 294535 296525 296540) (-213 "bookvol10.3.pamphlet" 288693 288703 294333 294360) (-212 "bookvol10.4.pamphlet" 288308 288322 288683 288688) (-211 "bookvol10.4.pamphlet" 285773 285783 288298 288303) (-210 "bookvol10.4.pamphlet" 284253 284269 285763 285768) (-209 "bookvol10.3.pamphlet" 282134 282142 282720 282813) (-208 "bookvol10.4.pamphlet" 280011 280028 282124 282129) (-207 "bookvol10.4.pamphlet" 279619 279643 280001 280006) (-206 "bookvol10.3.pamphlet" 278272 278282 279609 279614) (-205 "bookvol10.3.pamphlet" 278100 278108 278262 278267) (-204 "bookvol10.3.pamphlet" 277920 277928 278090 278095) (-203 "bookvol10.4.pamphlet" 276865 276873 277910 277915) (-202 "bookvol10.3.pamphlet" 276329 276337 276855 276860) (-201 "bookvol10.3.pamphlet" 275809 275817 276319 276324) (-200 "bookvol10.3.pamphlet" 275301 275309 275799 275804) (-199 "bookvol10.3.pamphlet" 274793 274801 275291 275296) (-198 "bookvol10.4.pamphlet" 269738 269746 274783 274788) (-197 "bookvol10.4.pamphlet" 268061 268069 269728 269733) (-196 "bookvol10.3.pamphlet" 268038 268046 268051 268056) (-195 "bookvol10.3.pamphlet" 267562 267570 268028 268033) (-194 "bookvol10.3.pamphlet" 267086 267094 267552 267557) (-193 "bookvol10.3.pamphlet" 266556 266564 267076 267081) (-192 "bookvol10.3.pamphlet" 266051 266059 266546 266551) (-191 "bookvol10.3.pamphlet" 265533 265541 266041 266046) (-190 "bookvol10.3.pamphlet" 265029 265037 265523 265528) (-189 "bookvol10.3.pamphlet" 264541 264549 265019 265024) (-188 "bookvol10.3.pamphlet" 264083 264091 264531 264536) (-187 "bookvol10.3.pamphlet" 263613 263621 264073 264078) (-186 "bookvol10.3.pamphlet" 263138 263146 263603 263608) (-185 "bookvol10.4.pamphlet" 259245 259253 263128 263133) (-184 "bookvol10.4.pamphlet" 258749 258757 259235 259240) (-183 "bookvol10.4.pamphlet" 255560 255568 258739 258744) (-182 "bookvol10.4.pamphlet" 254945 254955 255550 255555) (-181 "bookvol10.4.pamphlet" 253413 253429 254935 254940) (-180 "bookvol10.4.pamphlet" 252202 252215 253403 253408) (-179 "bookvol10.4.pamphlet" 246217 246230 252192 252197) (-178 "bookvol10.4.pamphlet" 245374 245384 246207 246212) (-177 "bookvol10.4.pamphlet" 244886 244901 245299 245304) (-176 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216951 218095 218100) (-158 "bookvol10.4.pamphlet" 216277 216294 216933 216938) (-157 "bookvol10.4.pamphlet" 212397 212405 216267 216272) (-156 "bookvol10.3.pamphlet" 211112 211128 212353 212392) (-155 "bookvol10.2.pamphlet" 208132 208142 211092 211107) (-154 NIL 205033 205045 207995 208000) (-153 "bookvol10.4.pamphlet" 204372 204385 205023 205028) (-152 "bookvol10.4.pamphlet" 202342 202364 204362 204367) (-151 "bookvol10.2.pamphlet" 202257 202265 202322 202337) (-150 "bookvol10.4.pamphlet" 201771 201781 202247 202252) (-149 "bookvol10.2.pamphlet" 201524 201532 201751 201766) (-148 "bookvol10.3.pamphlet" 197885 197893 201514 201519) (-147 "bookvol10.2.pamphlet" 197058 197066 197875 197880) (-146 "bookvol10.3.pamphlet" 195365 195373 195996 196023) (-145 "bookvol10.3.pamphlet" 194497 194505 194921 194948) (-144 "bookvol10.4.pamphlet" 193737 193751 194487 194492) (-143 "bookvol10.3.pamphlet" 192148 192156 193206 193245) (-142 "bookvol10.3.pamphlet" 183327 183351 192138 192143) (-141 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2062134) (-1134 "bookvol10.3.pamphlet" 2056648 2056661 2060892 2060919) (-1133 "bookvol10.3.pamphlet" 2053696 2053709 2056638 2056643) (-1132 "bookvol10.2.pamphlet" 2052507 2052516 2053686 2053691) (-1131 "bookvol10.4.pamphlet" 2051076 2051085 2052497 2052502) (-1130 "bookvol10.2.pamphlet" 2035466 2035477 2051066 2051071) (-1129 "bookvol10.3.pamphlet" 2035248 2035259 2035456 2035461) (-1128 "bookvol10.4.pamphlet" 2034797 2034810 2035204 2035209) (-1127 "bookvol10.4.pamphlet" 2032392 2032403 2034787 2034792) (-1126 "bookvol10.4.pamphlet" 2030981 2030992 2032382 2032387) (-1125 "bookvol10.4.pamphlet" 2025469 2025480 2030971 2030976) (-1124 "bookvol10.4.pamphlet" 2023933 2023951 2025459 2025464) (-1123 "bookvol10.2.pamphlet" 2023704 2023721 2023889 2023928) (-1122 "bookvol10.3.pamphlet" 2021858 2021884 2023269 2023366) (-1121 "bookvol10.3.pamphlet" 2019314 2019334 2019687 2019814) (-1120 "bookvol10.4.pamphlet" 2018151 2018176 2019304 2019309) (-1119 "bookvol10.2.pamphlet" 2016259 2016289 2018083 2018146) (-1118 NIL 2014311 2014343 2016137 2016142) (-1117 "bookvol10.2.pamphlet" 2012913 2012924 2014267 2014306) (-1116 "bookvol10.3.pamphlet" 2011276 2011285 2012779 2012908) (-1115 "bookvol10.4.pamphlet" 2011019 2011028 2011266 2011271) (-1114 "bookvol10.4.pamphlet" 2010109 2010120 2011009 2011014) (-1113 "bookvol10.4.pamphlet" 2009368 2009385 2010099 2010104) (-1112 "bookvol10.4.pamphlet" 2007332 2007347 2009324 2009329) (-1111 "bookvol10.3.pamphlet" 1999045 1999072 1999547 1999678) (-1110 "bookvol10.2.pamphlet" 1998357 1998366 1999035 1999040) (-1109 NIL 1997667 1997678 1998347 1998352) (-1108 "bookvol10.4.pamphlet" 1991179 1991188 1997657 1997662) (-1107 "bookvol10.2.pamphlet" 1990742 1990759 1991135 1991174) (-1106 "bookvol10.4.pamphlet" 1990441 1990461 1990732 1990737) (-1105 "bookvol10.4.pamphlet" 1986358 1986378 1990431 1990436) (-1104 "bookvol10.3.pamphlet" 1985819 1985833 1986348 1986353) (-1103 "bookvol10.3.pamphlet" 1985662 1985702 1985809 1985814) (-1102 "bookvol10.3.pamphlet" 1985554 1985563 1985652 1985657) (-1101 "bookvol10.2.pamphlet" 1982805 1982845 1985544 1985549) (-1100 "bookvol10.3.pamphlet" 1981169 1981180 1982282 1982321) (-1099 "bookvol10.3.pamphlet" 1979649 1979666 1981159 1981164) (-1098 "bookvol10.2.pamphlet" 1979139 1979148 1979639 1979644) (-1097 NIL 1978627 1978638 1979129 1979134) (-1096 "bookvol10.2.pamphlet" 1978518 1978527 1978617 1978622) (-1095 "bookvol10.2.pamphlet" 1975408 1975419 1978486 1978513) (-1094 NIL 1972318 1972331 1975398 1975403) (-1093 "bookvol10.2.pamphlet" 1971380 1971393 1972298 1972313) (-1092 "bookvol10.3.pamphlet" 1971193 1971204 1971299 1971304) (-1091 "bookvol10.2.pamphlet" 1969981 1969992 1971173 1971188) (-1090 "bookvol10.3.pamphlet" 1969067 1969078 1969936 1969941) (-1089 "bookvol10.4.pamphlet" 1968773 1968786 1969057 1969062) (-1088 "bookvol10.4.pamphlet" 1968192 1968205 1968729 1968734) (-1087 "bookvol10.3.pamphlet" 1967490 1967501 1968182 1968187) (-1086 "bookvol10.3.pamphlet" 1964894 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1928755 1928760) (-1069 NIL 1925575 1925607 1927161 1927166) (-1068 "bookvol10.2.pamphlet" 1908817 1908832 1925443 1925570) (-1067 NIL 1891772 1891789 1908400 1908405) (-1066 "bookvol10.3.pamphlet" 1888257 1888266 1891001 1891028) (-1065 "bookvol10.3.pamphlet" 1887504 1887513 1888123 1888252) (-1064 "bookvol10.3.pamphlet" 1886638 1886670 1887494 1887499) (-1063 "bookvol10.2.pamphlet" 1885461 1885470 1886540 1886633) (-1062 NIL 1884370 1884381 1885451 1885456) (-1061 "bookvol10.2.pamphlet" 1883890 1883899 1884360 1884365) (-1060 "bookvol10.2.pamphlet" 1883405 1883416 1883880 1883885) (-1059 "bookvol10.4.pamphlet" 1882833 1882890 1883395 1883400) (-1058 "bookvol10.3.pamphlet" 1881568 1881587 1882056 1882095) (-1057 "bookvol10.2.pamphlet" 1877204 1877235 1881512 1881563) (-1056 NIL 1872742 1872775 1877052 1877057) (-1055 "bookvol10.4.pamphlet" 1872630 1872650 1872732 1872737) (-1054 "bookvol10.2.pamphlet" 1871989 1871998 1872610 1872625) (-1053 NIL 1871356 1871367 1871979 1871984) (-1052 "bookvol10.4.pamphlet" 1870384 1870393 1871346 1871351) (-1051 "bookvol10.3.pamphlet" 1869063 1869079 1869944 1869971) (-1050 "bookvol10.4.pamphlet" 1867113 1867124 1869053 1869058) (-1049 "bookvol10.4.pamphlet" 1864769 1864780 1867103 1867108) (-1048 "bookvol10.4.pamphlet" 1864231 1864242 1864759 1864764) (-1047 "bookvol10.4.pamphlet" 1863966 1863978 1864221 1864226) (-1046 "bookvol10.4.pamphlet" 1862962 1862971 1863956 1863961) (-1045 "bookvol10.4.pamphlet" 1862381 1862394 1862952 1862957) (-1044 "bookvol10.2.pamphlet" 1861723 1861734 1862371 1862376) (-1043 NIL 1861063 1861076 1861713 1861718) (-1042 "bookvol10.3.pamphlet" 1859707 1859716 1860292 1860319) (-1041 "bookvol10.3.pamphlet" 1859054 1859101 1859645 1859702) (-1040 "bookvol10.4.pamphlet" 1858380 1858391 1859044 1859049) (-1039 "bookvol10.4.pamphlet" 1858111 1858122 1858370 1858375) (-1038 "bookvol10.4.pamphlet" 1855667 1855676 1858101 1858106) (-1037 "bookvol10.4.pamphlet" 1855366 1855377 1855657 1855662) (-1036 "bookvol10.4.pamphlet" 1845386 1845397 1855208 1855213) (-1035 "bookvol10.4.pamphlet" 1839774 1839785 1845336 1845341) (-1034 "bookvol10.3.pamphlet" 1838069 1838086 1839476 1839503) (-1033 "bookvol10.3.pamphlet" 1837419 1837430 1838024 1838029) (-1032 "bookvol10.4.pamphlet" 1836549 1836566 1837409 1837414) (-1031 "bookvol10.4.pamphlet" 1834956 1834973 1836504 1836509) (-1030 "bookvol10.3.pamphlet" 1833789 1833809 1834443 1834536) (-1029 "bookvol10.4.pamphlet" 1832362 1832371 1833779 1833784) (-1028 "bookvol10.2.pamphlet" 1832246 1832255 1832352 1832357) (-1027 "bookvol10.4.pamphlet" 1829597 1829612 1832236 1832241) (-1026 "bookvol10.4.pamphlet" 1826506 1826521 1829587 1829592) (-1025 "bookvol10.4.pamphlet" 1826255 1826280 1826496 1826501) (-1024 "bookvol10.4.pamphlet" 1825822 1825833 1826245 1826250) (-1023 "bookvol10.4.pamphlet" 1824676 1824694 1825812 1825817) (-1022 "bookvol10.4.pamphlet" 1822641 1822659 1824666 1824671) (-1021 "bookvol10.4.pamphlet" 1821882 1821899 1822631 1822636) (-1020 "bookvol10.4.pamphlet" 1820938 1820955 1821872 1821877) (-1019 "bookvol10.2.pamphlet" 1818267 1818276 1820840 1820933) (-1018 NIL 1815682 1815693 1818257 1818262) (-1017 "bookvol10.2.pamphlet" 1813655 1813666 1815662 1815677) (-1016 NIL 1811565 1811578 1813574 1813579) (-1015 "bookvol10.4.pamphlet" 1810986 1810997 1811555 1811560) (-1014 "bookvol10.4.pamphlet" 1810170 1810182 1810976 1810981) (-1013 "bookvol10.4.pamphlet" 1809527 1809536 1810160 1810165) (-1012 "bookvol10.4.pamphlet" 1809283 1809292 1809517 1809522) (-1011 "bookvol10.3.pamphlet" 1806098 1806112 1807750 1807843) (-1010 "bookvol10.3.pamphlet" 1804527 1804564 1804630 1804786) (-1009 "bookvol10.2.pamphlet" 1804158 1804167 1804517 1804522) (-1008 NIL 1803787 1803798 1804148 1804153) (-1007 "bookvol10.3.pamphlet" 1799604 1799615 1803617 1803644) (-1006 "bookvol10.3.pamphlet" 1798234 1798245 1798528 1798593) (-1005 "bookvol10.4.pamphlet" 1797638 1797657 1798224 1798229) (-1004 "bookvol10.2.pamphlet" 1795844 1795855 1797568 1797633) (-1003 NIL 1793801 1793814 1795527 1795532) (-1002 "bookvol10.2.pamphlet" 1792614 1792625 1793757 1793796) (-1001 "bookvol10.3.pamphlet" 1792082 1792097 1792604 1792609) (-1000 "bookvol10.2.pamphlet" 1790776 1790787 1791972 1792077) (-999 NIL 1789074 1789086 1790271 1790276) (-998 "bookvol10.4.pamphlet" 1788775 1788791 1789064 1789069) (-997 "bookvol10.3.pamphlet" 1788350 1788358 1788765 1788770) (-996 "bookvol10.4.pamphlet" 1784334 1784353 1788340 1788345) (-995 "bookvol10.3.pamphlet" 1780507 1780539 1784248 1784253) (-994 "bookvol10.4.pamphlet" 1778519 1778537 1780497 1780502) (-993 "bookvol10.4.pamphlet" 1775847 1775868 1778509 1778514) (-992 "bookvol10.4.pamphlet" 1775184 1775203 1775837 1775842) (-991 "bookvol10.2.pamphlet" 1771463 1771473 1775174 1775179) (-990 "bookvol10.4.pamphlet" 1768589 1768599 1771453 1771458) (-989 "bookvol10.4.pamphlet" 1768408 1768422 1768579 1768584) (-988 "bookvol10.2.pamphlet" 1767500 1767510 1768364 1768403) (-987 "bookvol10.4.pamphlet" 1766811 1766835 1767490 1767495) (-986 "bookvol10.4.pamphlet" 1765681 1765691 1766801 1766806) (-985 "bookvol10.4.pamphlet" 1753190 1753206 1765559 1765564) (-984 "bookvol10.2.pamphlet" 1748045 1748068 1753158 1753185) (-983 NIL 1742886 1742911 1748001 1748006) (-982 "bookvol10.2.pamphlet" 1741911 1741919 1742876 1742881) (-981 "bookvol10.2.pamphlet" 1740674 1740703 1741809 1741906) (-980 NIL 1739527 1739558 1740664 1740669) (-979 "bookvol10.3.pamphlet" 1738330 1738338 1739517 1739522) (-978 "bookvol10.2.pamphlet" 1735825 1735835 1738320 1738325) (-977 "bookvol10.4.pamphlet" 1727494 1727511 1735781 1735786) (-976 "bookvol10.2.pamphlet" 1726917 1726927 1727450 1727489) (-975 "bookvol10.3.pamphlet" 1726801 1726817 1726907 1726912) (-974 "bookvol10.3.pamphlet" 1726691 1726701 1726791 1726796) (-973 "bookvol10.3.pamphlet" 1726581 1726591 1726681 1726686) (-972 "bookvol10.3.pamphlet" 1724020 1724032 1724547 1724602) (-971 "bookvol10.3.pamphlet" 1722418 1722430 1723111 1723238) (-970 "bookvol10.4.pamphlet" 1721672 1721711 1722408 1722413) (-969 "bookvol10.4.pamphlet" 1721424 1721432 1721662 1721667) (-968 "bookvol10.4.pamphlet" 1719657 1719667 1721414 1721419) (-967 "bookvol10.4.pamphlet" 1717744 1717758 1719647 1719652) (-966 "bookvol10.2.pamphlet" 1717355 1717363 1717734 1717739) (-965 "bookvol10.3.pamphlet" 1716608 1716618 1716761 1716788) (-964 "bookvol10.4.pamphlet" 1714714 1714726 1716598 1716603) (-963 "bookvol10.4.pamphlet" 1714080 1714092 1714704 1714709) (-962 "bookvol10.2.pamphlet" 1713445 1713453 1714070 1714075) (-961 "bookvol10.4.pamphlet" 1708254 1708262 1713435 1713440) (-960 "bookvol10.4.pamphlet" 1706998 1707020 1708210 1708215) (-959 "bookvol10.3.pamphlet" 1704316 1704326 1704812 1704939) (-958 "bookvol10.4.pamphlet" 1703605 1703628 1704306 1704311) (-957 "bookvol10.4.pamphlet" 1701615 1701637 1703595 1703600) (-956 "bookvol10.2.pamphlet" 1695045 1695066 1701483 1701610) (-955 NIL 1687777 1687800 1694217 1694222) (-954 "bookvol10.4.pamphlet" 1687223 1687237 1687767 1687772) (-953 "bookvol10.4.pamphlet" 1686829 1686841 1687213 1687218) (-952 "bookvol10.4.pamphlet" 1685870 1685899 1686785 1686790) (-951 "bookvol10.4.pamphlet" 1684618 1684633 1685860 1685865) (-950 "bookvol10.3.pamphlet" 1683679 1683689 1683766 1683793) (-949 "bookvol10.4.pamphlet" 1680351 1680359 1683669 1683674) (-948 "bookvol10.4.pamphlet" 1679172 1679186 1680341 1680346) (-947 "bookvol10.4.pamphlet" 1678729 1678739 1679162 1679167) (-946 "bookvol10.4.pamphlet" 1678328 1678342 1678719 1678724) (-945 "bookvol10.4.pamphlet" 1677848 1677862 1678318 1678323) (-944 "bookvol10.4.pamphlet" 1677343 1677365 1677838 1677843) (-943 "bookvol10.4.pamphlet" 1676423 1676441 1677275 1677280) (-942 "bookvol10.4.pamphlet" 1676008 1676022 1676413 1676418) (-941 "bookvol10.4.pamphlet" 1675587 1675599 1675998 1676003) (-940 "bookvol10.4.pamphlet" 1675167 1675177 1675577 1675582) (-939 "bookvol10.4.pamphlet" 1674752 1674770 1675157 1675162) (-938 "bookvol10.4.pamphlet" 1674062 1674076 1674742 1674747) (-937 "bookvol10.4.pamphlet" 1673129 1673137 1674052 1674057) (-936 "bookvol10.4.pamphlet" 1672153 1672169 1673119 1673124) (-935 "bookvol10.4.pamphlet" 1671051 1671089 1672143 1672148) (-934 "bookvol10.4.pamphlet" 1670831 1670839 1671041 1671046) (-933 "bookvol10.3.pamphlet" 1665683 1665691 1670821 1670826) (-932 "bookvol10.3.pamphlet" 1662297 1662305 1665673 1665678) (-931 "bookvol10.4.pamphlet" 1661448 1661458 1662287 1662292) (-930 "bookvol10.4.pamphlet" 1647561 1647588 1661438 1661443) (-929 "bookvol10.3.pamphlet" 1647468 1647482 1647551 1647556) (-928 "bookvol10.3.pamphlet" 1647379 1647389 1647458 1647463) (-927 "bookvol10.3.pamphlet" 1647290 1647300 1647369 1647374) (-926 "bookvol10.2.pamphlet" 1646332 1646346 1647280 1647285) (-925 "bookvol10.4.pamphlet" 1645954 1645973 1646322 1646327) (-924 "bookvol10.4.pamphlet" 1645738 1645754 1645944 1645949) (-923 "bookvol10.3.pamphlet" 1645362 1645370 1645712 1645733) (-922 "bookvol10.2.pamphlet" 1644342 1644350 1645288 1645357) (-921 "bookvol10.4.pamphlet" 1644087 1644097 1644332 1644337) (-920 "bookvol10.4.pamphlet" 1642705 1642719 1644077 1644082) (-919 "bookvol10.4.pamphlet" 1634663 1634671 1642695 1642700) (-918 "bookvol10.4.pamphlet" 1633237 1633254 1634653 1634658) (-917 "bookvol10.4.pamphlet" 1632288 1632298 1633227 1633232) (-916 "bookvol10.3.pamphlet" 1627858 1627868 1632190 1632283) (-915 "bookvol10.4.pamphlet" 1627205 1627221 1627848 1627853) (-914 "bookvol10.4.pamphlet" 1625346 1625375 1627195 1627200) (-913 "bookvol10.4.pamphlet" 1624716 1624734 1625336 1625341) (-912 "bookvol10.4.pamphlet" 1624137 1624164 1624706 1624711) (-911 "bookvol10.3.pamphlet" 1623812 1623824 1623942 1624035) (-910 "bookvol10.2.pamphlet" 1621520 1621528 1623738 1623807) (-909 NIL 1619256 1619266 1621476 1621481) (-908 "bookvol10.4.pamphlet" 1617163 1617175 1619246 1619251) (-907 "bookvol10.4.pamphlet" 1614823 1614846 1617153 1617158) (-906 "bookvol10.3.pamphlet" 1610145 1610155 1614653 1614668) (-905 "bookvol10.3.pamphlet" 1604910 1604920 1610135 1610140) (-904 "bookvol10.2.pamphlet" 1603573 1603583 1604890 1604905) (-903 "bookvol10.4.pamphlet" 1602332 1602346 1603563 1603568) (-902 "bookvol10.3.pamphlet" 1601604 1601614 1602184 1602189) (-901 "bookvol10.2.pamphlet" 1599979 1599989 1601584 1601599) (-900 NIL 1598362 1598374 1599969 1599974) (-899 "bookvol10.3.pamphlet" 1596541 1596549 1598352 1598357) (-898 "bookvol10.4.pamphlet" 1590617 1590625 1596531 1596536) (-897 "bookvol10.4.pamphlet" 1589969 1589986 1590607 1590612) (-896 "bookvol10.2.pamphlet" 1588119 1588127 1589959 1589964) (-895 "bookvol10.4.pamphlet" 1587854 1587867 1588109 1588114) (-894 "bookvol10.3.pamphlet" 1586496 1586513 1587844 1587849) (-893 "bookvol10.3.pamphlet" 1580781 1580791 1586486 1586491) (-892 "bookvol10.4.pamphlet" 1580512 1580524 1580771 1580776) (-891 "bookvol10.4.pamphlet" 1578810 1578826 1580502 1580507) (-890 "bookvol10.3.pamphlet" 1576471 1576483 1578800 1578805) (-889 "bookvol10.4.pamphlet" 1576183 1576197 1576461 1576466) (-888 "bookvol10.4.pamphlet" 1574404 1574435 1575891 1575896) (-887 "bookvol10.2.pamphlet" 1573843 1573853 1574394 1574399) (-886 "bookvol10.3.pamphlet" 1572953 1572967 1573833 1573838) (-885 "bookvol10.2.pamphlet" 1572659 1572669 1572943 1572948) (-884 "bookvol10.4.pamphlet" 1570177 1570185 1572649 1572654) (-883 "bookvol10.3.pamphlet" 1569635 1569663 1570167 1570172) (-882 "bookvol10.4.pamphlet" 1569428 1569444 1569625 1569630) (-881 "bookvol10.3.pamphlet" 1568886 1568914 1569418 1569423) (-880 "bookvol10.4.pamphlet" 1568673 1568689 1568876 1568881) (-879 "bookvol10.3.pamphlet" 1568143 1568171 1568663 1568668) (-878 "bookvol10.4.pamphlet" 1567930 1567946 1568133 1568138) (-877 "bookvol10.4.pamphlet" 1566753 1566802 1567920 1567925) (-876 "bookvol10.4.pamphlet" 1566167 1566175 1566743 1566748) (-875 "bookvol10.3.pamphlet" 1565175 1565183 1566157 1566162) (-874 "bookvol10.4.pamphlet" 1559622 1559645 1565131 1565136) (-873 "bookvol10.4.pamphlet" 1553503 1553526 1559571 1559576) (-872 "bookvol10.3.pamphlet" 1550879 1550897 1552008 1552101) (-871 "bookvol10.3.pamphlet" 1548942 1548954 1549115 1549208) (-870 "bookvol10.3.pamphlet" 1548687 1548699 1548868 1548937) (-869 "bookvol10.2.pamphlet" 1547233 1547245 1548613 1548682) (-868 "bookvol10.4.pamphlet" 1546178 1546197 1547223 1547228) (-867 "bookvol10.4.pamphlet" 1545183 1545199 1546168 1546173) (-866 "bookvol10.3.pamphlet" 1544018 1544026 1544854 1544947) (-865 "bookvol10.2.pamphlet" 1543002 1543010 1543920 1544013) (-864 "bookvol10.2.pamphlet" 1541301 1541309 1542904 1542997) (-863 "bookvol10.3.pamphlet" 1540260 1540270 1541097 1541190) (-862 "bookvol10.2.pamphlet" 1539247 1539255 1540162 1540255) (-861 "bookvol10.3.pamphlet" 1537786 1537806 1538637 1538730) (-860 "bookvol10.2.pamphlet" 1536762 1536770 1537688 1537781) (-859 "bookvol10.3.pamphlet" 1535770 1535800 1536620 1536687) (-858 "bookvol10.3.pamphlet" 1535551 1535574 1535760 1535765) (-857 "bookvol10.4.pamphlet" 1534677 1534685 1535541 1535546) (-856 "bookvol10.3.pamphlet" 1524091 1524099 1534667 1534672) (-855 "bookvol10.3.pamphlet" 1523696 1523704 1524081 1524086) (-854 "bookvol10.4.pamphlet" 1522153 1522163 1523613 1523618) (-853 "bookvol10.3.pamphlet" 1521503 1521531 1521833 1521872) (-852 "bookvol10.3.pamphlet" 1520788 1520812 1521183 1521222) (-851 "bookvol10.4.pamphlet" 1518548 1518560 1520708 1520713) (-850 "bookvol10.2.pamphlet" 1512560 1512570 1518504 1518543) (-849 NIL 1506462 1506474 1512408 1512413) (-848 "bookvol10.2.pamphlet" 1505602 1505610 1506452 1506457) (-847 NIL 1504740 1504750 1505592 1505597) (-846 "bookvol10.2.pamphlet" 1504074 1504082 1504720 1504735) (-845 NIL 1503416 1503426 1504064 1504069) (-844 "bookvol10.2.pamphlet" 1503140 1503148 1503406 1503411) (-843 "bookvol10.4.pamphlet" 1502287 1502303 1503130 1503135) (-842 "bookvol10.2.pamphlet" 1502221 1502229 1502277 1502282) (-841 "bookvol10.3.pamphlet" 1500713 1500723 1501768 1501797) (-840 "bookvol10.4.pamphlet" 1500065 1500077 1500703 1500708) (-839 "bookvol10.3.pamphlet" 1497831 1497839 1500055 1500060) (-838 "bookvol10.4.pamphlet" 1490283 1490291 1497821 1497826) (-837 "bookvol10.2.pamphlet" 1487761 1487769 1490273 1490278) (-836 "bookvol10.4.pamphlet" 1487316 1487324 1487751 1487756) (-835 "bookvol10.3.pamphlet" 1487058 1487068 1487138 1487205) (-834 "bookvol10.3.pamphlet" 1485834 1485844 1486605 1486634) (-833 "bookvol10.4.pamphlet" 1485325 1485337 1485824 1485829) (-832 "bookvol10.4.pamphlet" 1484375 1484383 1485315 1485320) (-831 "bookvol10.2.pamphlet" 1484159 1484169 1484319 1484370) (-830 "bookvol10.4.pamphlet" 1482835 1482843 1484149 1484154) (-829 "bookvol10.2.pamphlet" 1481910 1481918 1482825 1482830) (-828 "bookvol10.3.pamphlet" 1481327 1481339 1481796 1481835) (-827 "bookvol10.4.pamphlet" 1481161 1481171 1481317 1481322) (-826 "bookvol10.3.pamphlet" 1480714 1480722 1481151 1481156) (-825 "bookvol10.3.pamphlet" 1479766 1479774 1480704 1480709) (-824 "bookvol10.3.pamphlet" 1479112 1479120 1479756 1479761) (-823 "bookvol10.3.pamphlet" 1473855 1473863 1479102 1479107) (-822 "bookvol10.3.pamphlet" 1473272 1473280 1473845 1473850) (-821 "bookvol10.2.pamphlet" 1473049 1473057 1473198 1473267) (-820 "bookvol10.3.pamphlet" 1466676 1466686 1473039 1473044) (-819 "bookvol10.3.pamphlet" 1465959 1465969 1466666 1466671) (-818 "bookvol10.3.pamphlet" 1465407 1465433 1465771 1465920) (-817 "bookvol10.3.pamphlet" 1462767 1462777 1463093 1463220) (-816 "bookvol10.3.pamphlet" 1454624 1454644 1454982 1455113) (-815 "bookvol10.4.pamphlet" 1453149 1453168 1454614 1454619) (-814 "bookvol10.4.pamphlet" 1450609 1450626 1453139 1453144) (-813 "bookvol10.4.pamphlet" 1446538 1446555 1450566 1450571) (-812 "bookvol10.4.pamphlet" 1445899 1445923 1446528 1446533) (-811 "bookvol10.4.pamphlet" 1443343 1443360 1445889 1445894) (-810 "bookvol10.4.pamphlet" 1440358 1440380 1443333 1443338) (-809 "bookvol10.3.pamphlet" 1439014 1439022 1440348 1440353) (-808 "bookvol10.4.pamphlet" 1436272 1436294 1439004 1439009) (-807 "bookvol10.4.pamphlet" 1435638 1435662 1436262 1436267) (-806 "bookvol10.4.pamphlet" 1423382 1423390 1435628 1435633) (-805 "bookvol10.4.pamphlet" 1422801 1422817 1423372 1423377) (-804 "bookvol10.3.pamphlet" 1420204 1420212 1422791 1422796) (-803 "bookvol10.4.pamphlet" 1415521 1415537 1420194 1420199) (-802 "bookvol10.4.pamphlet" 1415030 1415048 1415511 1415516) (-801 "bookvol10.2.pamphlet" 1413421 1413429 1415020 1415025) (-800 "bookvol10.3.pamphlet" 1411589 1411599 1412271 1412310) (-799 "bookvol10.4.pamphlet" 1411235 1411256 1411579 1411584) (-798 "bookvol10.2.pamphlet" 1409183 1409193 1411191 1411230) (-797 NIL 1406856 1406868 1408866 1408871) (-796 "bookvol10.2.pamphlet" 1406706 1406714 1406846 1406851) (-795 "bookvol10.2.pamphlet" 1406472 1406480 1406696 1406701) (-794 "bookvol10.2.pamphlet" 1405826 1405834 1406462 1406467) (-793 "bookvol10.2.pamphlet" 1405689 1405697 1405816 1405821) (-792 "bookvol10.2.pamphlet" 1405553 1405561 1405679 1405684) (-791 "bookvol10.4.pamphlet" 1405280 1405296 1405543 1405548) (-790 "bookvol10.4.pamphlet" 1394009 1394017 1405270 1405275) (-789 "bookvol10.4.pamphlet" 1385576 1385584 1393999 1394004) (-788 "bookvol10.2.pamphlet" 1382931 1382939 1385566 1385571) (-787 "bookvol10.4.pamphlet" 1381773 1381781 1382921 1382926) (-786 "bookvol10.4.pamphlet" 1373931 1373941 1381578 1381583) (-785 "bookvol10.2.pamphlet" 1373338 1373354 1373887 1373926) (-784 "bookvol10.4.pamphlet" 1372889 1372899 1373255 1373260) (-783 "bookvol10.3.pamphlet" 1366790 1366800 1370439 1370592) (-782 "bookvol10.4.pamphlet" 1366186 1366198 1366780 1366785) (-781 "bookvol10.3.pamphlet" 1362396 1362415 1362688 1362815) (-780 "bookvol10.3.pamphlet" 1360920 1360930 1360997 1361090) (-779 "bookvol10.4.pamphlet" 1359310 1359324 1360910 1360915) (-778 "bookvol10.4.pamphlet" 1359202 1359231 1359300 1359305) (-777 "bookvol10.4.pamphlet" 1358450 1358470 1359192 1359197) (-776 "bookvol10.3.pamphlet" 1358338 1358352 1358430 1358445) (-775 "bookvol10.4.pamphlet" 1357932 1357971 1358328 1358333) (-774 "bookvol10.4.pamphlet" 1356780 1356799 1357922 1357927) (-773 "bookvol10.4.pamphlet" 1356462 1356488 1356770 1356775) (-772 "bookvol10.3.pamphlet" 1356203 1356211 1356452 1356457) (-771 "bookvol10.4.pamphlet" 1355879 1355889 1356193 1356198) (-770 "bookvol10.4.pamphlet" 1355336 1355352 1355869 1355874) (-769 "bookvol10.3.pamphlet" 1354226 1354234 1355310 1355331) (-768 "bookvol10.4.pamphlet" 1352852 1352862 1354216 1354221) (-767 "bookvol10.3.pamphlet" 1350540 1350548 1352842 1352847) (-766 "bookvol10.4.pamphlet" 1348008 1348025 1350530 1350535) (-765 "bookvol10.4.pamphlet" 1347327 1347341 1347998 1348003) (-764 "bookvol10.4.pamphlet" 1345467 1345483 1347317 1347322) (-763 "bookvol10.4.pamphlet" 1345124 1345138 1345457 1345462) (-762 "bookvol10.4.pamphlet" 1343302 1343316 1345114 1345119) (-761 "bookvol10.2.pamphlet" 1342900 1342908 1343292 1343297) (-760 NIL 1342496 1342506 1342890 1342895) (-759 "bookvol10.2.pamphlet" 1341874 1341882 1342486 1342491) (-758 NIL 1341250 1341260 1341864 1341869) (-757 "bookvol10.4.pamphlet" 1340327 1340335 1341240 1341245) (-756 "bookvol10.4.pamphlet" 1330769 1330777 1340317 1340322) (-755 "bookvol10.4.pamphlet" 1329269 1329277 1330759 1330764) (-754 "bookvol10.4.pamphlet" 1323733 1323741 1329259 1329264) (-753 "bookvol10.4.pamphlet" 1317889 1317897 1323723 1323728) (-752 "bookvol10.4.pamphlet" 1313699 1313707 1317879 1317884) (-751 "bookvol10.4.pamphlet" 1307493 1307501 1313689 1313694) (-750 "bookvol10.4.pamphlet" 1298250 1298258 1307483 1307488) (-749 "bookvol10.4.pamphlet" 1294341 1294349 1298240 1298245) (-748 "bookvol10.4.pamphlet" 1292380 1292388 1294331 1294336) (-747 "bookvol10.4.pamphlet" 1285186 1285194 1292370 1292375) (-746 "bookvol10.4.pamphlet" 1279730 1279738 1285176 1285181) (-745 "bookvol10.4.pamphlet" 1275662 1275670 1279720 1279725) (-744 "bookvol10.4.pamphlet" 1274208 1274216 1275652 1275657) (-743 "bookvol10.4.pamphlet" 1273538 1273546 1274198 1274203) (-742 "bookvol10.2.pamphlet" 1273090 1273100 1273506 1273533) (-741 NIL 1272662 1272674 1273080 1273085) (-740 "bookvol10.3.pamphlet" 1269889 1269903 1270212 1270365) (-739 "bookvol10.3.pamphlet" 1268008 1268022 1268080 1268300) (-738 "bookvol10.4.pamphlet" 1264976 1264993 1267998 1268003) (-737 "bookvol10.4.pamphlet" 1264374 1264391 1264966 1264971) (-736 "bookvol10.2.pamphlet" 1262404 1262425 1264272 1264369) (-735 "bookvol10.4.pamphlet" 1262063 1262073 1262394 1262399) (-734 "bookvol10.4.pamphlet" 1261521 1261529 1262053 1262058) (-733 "bookvol10.3.pamphlet" 1259584 1259594 1261283 1261322) (-732 "bookvol10.2.pamphlet" 1259417 1259427 1259540 1259579) (-731 "bookvol10.3.pamphlet" 1256452 1256464 1259125 1259192) (-730 "bookvol10.4.pamphlet" 1256014 1256028 1256442 1256447) (-729 "bookvol10.4.pamphlet" 1255575 1255592 1256004 1256009) (-728 "bookvol10.4.pamphlet" 1253648 1253667 1255565 1255570) (-727 "bookvol10.3.pamphlet" 1251100 1251115 1251442 1251569) (-726 "bookvol10.4.pamphlet" 1250379 1250398 1251090 1251095) (-725 "bookvol10.4.pamphlet" 1250189 1250232 1250369 1250374) (-724 "bookvol10.4.pamphlet" 1249937 1249973 1250179 1250184) (-723 "bookvol10.4.pamphlet" 1248308 1248325 1249927 1249932) (-722 "bookvol10.2.pamphlet" 1247210 1247218 1248298 1248303) (-721 NIL 1246110 1246120 1247200 1247205) (-720 "bookvol10.2.pamphlet" 1244838 1244851 1245970 1246105) (-719 NIL 1243588 1243603 1244722 1244727) (-718 "bookvol10.2.pamphlet" 1241741 1241749 1243578 1243583) (-717 NIL 1239892 1239902 1241731 1241736) (-716 "bookvol10.2.pamphlet" 1239083 1239091 1239882 1239887) (-715 NIL 1238272 1238282 1239073 1239078) (-714 "bookvol10.3.pamphlet" 1236929 1236943 1238252 1238267) (-713 "bookvol10.2.pamphlet" 1236642 1236652 1236897 1236924) (-712 NIL 1236375 1236387 1236632 1236637) (-711 "bookvol10.3.pamphlet" 1235694 1235733 1236355 1236370) (-710 "bookvol10.3.pamphlet" 1234314 1234326 1235516 1235583) (-709 "bookvol10.3.pamphlet" 1233827 1233845 1234304 1234309) (-708 "bookvol10.3.pamphlet" 1230487 1230503 1231305 1231458) (-707 "bookvol10.3.pamphlet" 1229854 1229893 1230389 1230482) (-706 "bookvol10.3.pamphlet" 1228659 1228667 1229844 1229849) (-705 "bookvol10.4.pamphlet" 1228393 1228427 1228649 1228654) (-704 "bookvol10.2.pamphlet" 1226811 1226821 1228349 1228388) (-703 "bookvol10.4.pamphlet" 1225427 1225444 1226801 1226806) (-702 "bookvol10.4.pamphlet" 1224867 1224885 1225417 1225422) (-701 "bookvol10.4.pamphlet" 1224459 1224472 1224857 1224862) (-700 "bookvol10.4.pamphlet" 1223744 1223754 1224449 1224454) (-699 "bookvol10.4.pamphlet" 1222594 1222604 1223734 1223739) (-698 "bookvol10.3.pamphlet" 1222372 1222382 1222584 1222589) (-697 "bookvol10.4.pamphlet" 1221811 1221829 1222362 1222367) (-696 "bookvol10.3.pamphlet" 1221250 1221258 1221713 1221806) (-695 "bookvol10.4.pamphlet" 1219889 1219899 1221240 1221245) (-694 "bookvol10.3.pamphlet" 1218337 1218345 1219779 1219884) (-693 "bookvol10.4.pamphlet" 1217737 1217759 1218327 1218332) (-692 "bookvol10.4.pamphlet" 1215649 1215657 1217727 1217732) (-691 "bookvol10.4.pamphlet" 1213902 1213912 1215639 1215644) (-690 "bookvol10.2.pamphlet" 1213183 1213193 1213870 1213897) (-689 "bookvol10.3.pamphlet" 1209156 1209164 1209770 1209971) (-688 "bookvol10.4.pamphlet" 1208358 1208370 1209146 1209151) (-687 "bookvol10.4.pamphlet" 1205618 1205644 1208348 1208353) (-686 "bookvol10.4.pamphlet" 1202898 1202908 1205608 1205613) (-685 "bookvol10.3.pamphlet" 1201791 1201801 1202273 1202300) (-684 "bookvol10.4.pamphlet" 1199199 1199223 1201675 1201680) (-683 "bookvol10.2.pamphlet" 1185327 1185349 1199155 1199194) (-682 NIL 1171303 1171327 1185133 1185138) (-681 "bookvol10.4.pamphlet" 1170585 1170633 1171293 1171298) (-680 "bookvol10.4.pamphlet" 1169379 1169391 1170575 1170580) (-679 "bookvol10.4.pamphlet" 1168254 1168268 1169369 1169374) (-678 "bookvol10.4.pamphlet" 1167560 1167572 1168244 1168249) (-677 "bookvol10.4.pamphlet" 1166382 1166392 1167550 1167555) (-676 "bookvol10.4.pamphlet" 1166194 1166208 1166372 1166377) (-675 "bookvol10.4.pamphlet" 1165963 1165975 1166184 1166189) (-674 "bookvol10.4.pamphlet" 1165599 1165609 1165953 1165958) (-673 "bookvol10.4.pamphlet" 1161271 1161295 1165589 1165594) (-672 "bookvol10.3.pamphlet" 1159555 1159572 1161261 1161266) (-671 "bookvol10.2.pamphlet" 1157411 1157426 1159545 1159550) (-670 "bookvol10.3.pamphlet" 1155396 1155406 1157012 1157017) (-669 "bookvol10.2.pamphlet" 1151144 1151154 1155376 1155391) (-668 NIL 1146900 1146912 1151134 1151139) (-667 "bookvol10.3.pamphlet" 1144138 1144155 1146890 1146895) (-666 "bookvol10.3.pamphlet" 1142436 1142450 1142818 1142869) (-665 "bookvol10.4.pamphlet" 1141979 1141996 1142426 1142431) (-664 "bookvol10.4.pamphlet" 1140781 1140809 1141969 1141974) (-663 "bookvol10.4.pamphlet" 1138543 1138557 1140771 1140776) (-662 "bookvol10.2.pamphlet" 1138200 1138210 1138499 1138538) (-661 NIL 1137889 1137901 1138190 1138195) (-660 "bookvol10.3.pamphlet" 1137037 1137056 1137745 1137814) (-659 "bookvol10.4.pamphlet" 1136298 1136308 1137027 1137032) (-658 "bookvol10.4.pamphlet" 1134774 1134823 1136288 1136293) (-657 "bookvol10.4.pamphlet" 1133447 1133457 1134764 1134769) (-656 "bookvol10.3.pamphlet" 1132844 1132858 1133381 1133408) (-655 "bookvol10.2.pamphlet" 1132476 1132484 1132834 1132839) (-654 NIL 1132106 1132116 1132466 1132471) (-653 "bookvol10.4.pamphlet" 1131036 1131048 1132096 1132101) (-652 "bookvol10.3.pamphlet" 1130407 1130423 1130716 1130755) (-651 "bookvol10.4.pamphlet" 1129455 1129472 1130364 1130369) (-650 "bookvol10.2.pamphlet" 1128104 1128114 1129411 1129450) (-649 NIL 1126751 1126763 1128060 1128065) (-648 "bookvol10.3.pamphlet" 1126011 1126023 1126431 1126470) (-647 "bookvol10.3.pamphlet" 1125398 1125408 1125691 1125730) (-646 "bookvol10.4.pamphlet" 1124124 1124142 1125388 1125393) (-645 "bookvol10.2.pamphlet" 1122547 1122557 1124026 1124119) (-644 "bookvol10.2.pamphlet" 1119023 1119033 1122527 1122542) (-643 NIL 1115473 1115485 1118979 1118984) (-642 "bookvol10.3.pamphlet" 1112085 1112102 1115463 1115468) (-641 "bookvol10.2.pamphlet" 1111600 1111610 1112075 1112080) (-640 "bookvol10.3.pamphlet" 1110722 1110732 1111374 1111401) (-639 "bookvol10.4.pamphlet" 1110173 1110187 1110712 1110717) (-638 "bookvol10.3.pamphlet" 1108136 1108146 1109543 1109570) (-637 "bookvol10.4.pamphlet" 1107451 1107465 1108126 1108131) (-636 "bookvol10.4.pamphlet" 1106131 1106143 1107441 1107446) (-635 "bookvol10.4.pamphlet" 1102994 1103006 1106121 1106126) (-634 "bookvol10.2.pamphlet" 1102372 1102382 1102974 1102989) (-633 "bookvol10.4.pamphlet" 1101245 1101257 1102284 1102289) (-632 "bookvol10.4.pamphlet" 1099203 1099213 1101235 1101240) (-631 "bookvol10.4.pamphlet" 1098078 1098091 1099193 1099198) (-630 "bookvol10.3.pamphlet" 1096108 1096120 1097368 1097513) (-629 "bookvol10.2.pamphlet" 1095693 1095703 1096034 1096103) (-628 NIL 1095306 1095318 1095649 1095654) (-627 "bookvol10.3.pamphlet" 1093841 1093849 1094547 1094562) (-626 "bookvol10.4.pamphlet" 1091219 1091238 1093831 1093836) (-625 "bookvol10.4.pamphlet" 1089998 1090014 1091209 1091214) (-624 "bookvol10.2.pamphlet" 1088851 1088859 1089988 1089993) (-623 "bookvol10.4.pamphlet" 1084683 1084698 1088841 1088846) (-622 "bookvol10.3.pamphlet" 1082918 1082945 1084663 1084678) (-621 "bookvol10.4.pamphlet" 1081348 1081365 1082908 1082913) (-620 "bookvol10.4.pamphlet" 1080458 1080480 1081338 1081343) (-619 "bookvol10.3.pamphlet" 1079234 1079247 1080051 1080120) (-618 "bookvol10.4.pamphlet" 1078779 1078795 1079224 1079229) (-617 "bookvol10.3.pamphlet" 1078189 1078203 1078701 1078740) (-616 "bookvol10.2.pamphlet" 1077965 1077975 1078169 1078184) (-615 NIL 1077749 1077761 1077955 1077960) (-614 "bookvol10.4.pamphlet" 1076430 1076447 1077739 1077744) (-613 "bookvol10.2.pamphlet" 1076154 1076164 1076420 1076425) (-612 "bookvol10.2.pamphlet" 1075891 1075901 1076144 1076149) (-611 "bookvol10.3.pamphlet" 1074452 1074462 1075675 1075680) (-610 "bookvol10.4.pamphlet" 1074155 1074167 1074442 1074447) (-609 "bookvol10.2.pamphlet" 1073294 1073316 1074123 1074150) (-608 NIL 1072453 1072477 1073284 1073289) (-607 "bookvol10.3.pamphlet" 1071091 1071107 1071800 1071827) (-606 "bookvol10.3.pamphlet" 1069100 1069112 1070381 1070526) (-605 "bookvol10.2.pamphlet" 1067344 1067368 1069080 1069095) (-604 NIL 1065453 1065479 1067191 1067196) (-603 "bookvol10.3.pamphlet" 1064461 1064476 1064601 1064628) (-602 "bookvol10.3.pamphlet" 1063581 1063591 1064451 1064456) (-601 "bookvol10.4.pamphlet" 1062344 1062363 1063571 1063576) (-600 "bookvol10.4.pamphlet" 1061850 1061864 1062334 1062339) (-599 "bookvol10.4.pamphlet" 1061594 1061606 1061840 1061845) (-598 "bookvol10.3.pamphlet" 1059402 1059417 1061430 1061555) (-597 "bookvol10.3.pamphlet" 1051790 1051805 1058376 1058473) (-596 "bookvol10.4.pamphlet" 1051257 1051273 1051780 1051785) (-595 "bookvol10.3.pamphlet" 1050487 1050500 1050653 1050680) (-594 "bookvol10.4.pamphlet" 1049482 1049501 1050477 1050482) (-593 "bookvol10.4.pamphlet" 1047550 1047558 1049472 1049477) (-592 "bookvol10.4.pamphlet" 1046097 1046107 1047506 1047511) (-591 "bookvol10.4.pamphlet" 1045698 1045709 1046087 1046092) (-590 "bookvol10.4.pamphlet" 1044014 1044024 1045688 1045693) (-589 "bookvol10.3.pamphlet" 1041737 1041751 1043869 1043896) (-588 "bookvol10.4.pamphlet" 1040881 1040897 1041727 1041732) (-587 "bookvol10.4.pamphlet" 1040058 1040074 1040871 1040876) (-586 "bookvol10.4.pamphlet" 1039834 1039842 1040048 1040053) (-585 "bookvol10.3.pamphlet" 1039535 1039547 1039639 1039732) (-584 "bookvol10.3.pamphlet" 1039306 1039332 1039461 1039530) (-583 "bookvol10.4.pamphlet" 1038903 1038919 1039296 1039301) (-582 "bookvol10.4.pamphlet" 1031925 1031942 1038893 1038898) (-581 "bookvol10.4.pamphlet" 1029790 1029806 1031499 1031504) (-580 "bookvol10.4.pamphlet" 1029110 1029118 1029780 1029785) (-579 "bookvol10.3.pamphlet" 1028886 1028896 1029024 1029105) (-578 "bookvol10.4.pamphlet" 1027250 1027264 1028876 1028881) (-577 "bookvol10.4.pamphlet" 1026743 1026753 1027240 1027245) (-576 "bookvol10.4.pamphlet" 1025412 1025429 1026733 1026738) (-575 "bookvol10.4.pamphlet" 1023725 1023741 1025055 1025060) (-574 "bookvol10.4.pamphlet" 1021382 1021400 1023657 1023662) (-573 "bookvol10.4.pamphlet" 1011907 1011915 1021372 1021377) (-572 "bookvol10.3.pamphlet" 1011268 1011276 1011761 1011902) (-571 "bookvol10.4.pamphlet" 1010534 1010551 1011258 1011263) (-570 "bookvol10.4.pamphlet" 1010179 1010203 1010524 1010529) (-569 "bookvol10.4.pamphlet" 1006558 1006566 1010169 1010174) (-568 "bookvol10.4.pamphlet" 999716 999734 1006490 1006495) (-567 "bookvol10.3.pamphlet" 993714 993722 999706 999711) (-566 "bookvol10.4.pamphlet" 992866 992923 993704 993709) (-565 "bookvol10.4.pamphlet" 991952 991962 992856 992861) (-564 "bookvol10.4.pamphlet" 991820 991844 991942 991947) (-563 "bookvol10.4.pamphlet" 990178 990194 991810 991815) (-562 "bookvol10.2.pamphlet" 988830 988838 990104 990173) (-561 NIL 987544 987554 988820 988825) (-560 "bookvol10.4.pamphlet" 986690 986777 987534 987539) (-559 "bookvol10.2.pamphlet" 985311 985321 986604 986685) (-558 "bookvol10.4.pamphlet" 984842 984850 985301 985306) (-557 "bookvol10.4.pamphlet" 984000 984027 984832 984837) (-556 "bookvol10.4.pamphlet" 983476 983492 983990 983995) (-555 "bookvol10.3.pamphlet" 982556 982587 982719 982746) (-554 "bookvol10.2.pamphlet" 979890 979898 982458 982551) (-553 NIL 977310 977320 979880 979885) (-552 "bookvol10.4.pamphlet" 976758 976771 977300 977305) (-551 "bookvol10.4.pamphlet" 975854 975873 976748 976753) (-550 "bookvol10.4.pamphlet" 974942 974966 975844 975849) (-549 "bookvol10.4.pamphlet" 973948 973965 974932 974937) (-548 "bookvol10.4.pamphlet" 973105 973135 973938 973943) (-547 "bookvol10.4.pamphlet" 971450 971472 973095 973100) (-546 "bookvol10.4.pamphlet" 970530 970549 971440 971445) (-545 "bookvol10.3.pamphlet" 967451 967459 970520 970525) (-544 "bookvol10.4.pamphlet" 967096 967106 967441 967446) (-543 "bookvol10.4.pamphlet" 966684 966692 967086 967091) (-542 "bookvol10.3.pamphlet" 966101 966164 966674 966679) (-541 "bookvol10.3.pamphlet" 965543 965566 966091 966096) (-540 "bookvol10.2.pamphlet" 964196 964259 965533 965538) (-539 "bookvol10.4.pamphlet" 962740 962762 964186 964191) (-538 "bookvol10.3.pamphlet" 962646 962663 962730 962735) (-537 "bookvol10.4.pamphlet" 962063 962073 962636 962641) (-536 "bookvol10.4.pamphlet" 957957 957968 962053 962058) (-535 "bookvol10.3.pamphlet" 957089 957115 957601 957628) (-534 "bookvol10.4.pamphlet" 956181 956225 957045 957050) (-533 "bookvol10.4.pamphlet" 954794 954818 956137 956142) (-532 "bookvol10.3.pamphlet" 953681 953696 954200 954227) (-531 "bookvol10.3.pamphlet" 953406 953444 953511 953538) (-530 "bookvol10.3.pamphlet" 952836 952852 953087 953180) (-529 "bookvol10.3.pamphlet" 950069 950084 952242 952269) (-528 "bookvol10.3.pamphlet" 949907 949924 950025 950030) (-527 "bookvol10.2.pamphlet" 949304 949316 949897 949902) (-526 NIL 948699 948713 949294 949299) (-525 "bookvol10.3.pamphlet" 948512 948524 948689 948694) (-524 "bookvol10.3.pamphlet" 948285 948297 948502 948507) (-523 "bookvol10.3.pamphlet" 948020 948032 948275 948280) (-522 "bookvol10.2.pamphlet" 946958 946970 948010 948015) (-521 "bookvol10.3.pamphlet" 946718 946730 946948 946953) (-520 "bookvol10.3.pamphlet" 946480 946492 946708 946713) (-519 "bookvol10.4.pamphlet" 943752 943770 946470 946475) (-518 "bookvol10.3.pamphlet" 938832 938871 943687 943692) (-517 "bookvol10.3.pamphlet" 938289 938312 938822 938827) (-516 "bookvol10.4.pamphlet" 937522 937538 938279 938284) (-515 "bookvol10.3.pamphlet" 936805 936813 937512 937517) (-514 "bookvol10.4.pamphlet" 935448 935465 936795 936800) (-513 "bookvol10.3.pamphlet" 934730 934743 935142 935169) (-512 "bookvol10.4.pamphlet" 931657 931676 934720 934725) (-511 "bookvol10.4.pamphlet" 930567 930582 931647 931652) (-510 "bookvol10.3.pamphlet" 930298 930324 930397 930424) (-509 "bookvol10.3.pamphlet" 929611 929626 929704 929731) (-508 "bookvol10.3.pamphlet" 927834 927842 929427 929520) (-507 "bookvol10.4.pamphlet" 927391 927424 927824 927829) (-506 "bookvol10.2.pamphlet" 926769 926777 927381 927386) (-505 NIL 926145 926155 926759 926764) (-504 "bookvol10.3.pamphlet" 924997 925005 926135 926140) (-503 "bookvol10.2.pamphlet" 922791 922801 924977 924992) (-502 NIL 920426 920438 922614 922619) (-501 "bookvol10.3.pamphlet" 918295 918303 918893 918986) (-500 "bookvol10.4.pamphlet" 917247 917258 918285 918290) (-499 "bookvol10.3.pamphlet" 916879 916903 917237 917242) (-498 "bookvol10.3.pamphlet" 913016 913026 916709 916736) (-497 "bookvol10.3.pamphlet" 904871 904887 905231 905362) (-496 "bookvol10.3.pamphlet" 902066 902081 902665 902792) (-495 "bookvol10.4.pamphlet" 900662 900670 902056 902061) (-494 "bookvol10.3.pamphlet" 899696 899727 899905 899932) (-493 "bookvol10.3.pamphlet" 899307 899315 899598 899691) (-492 "bookvol10.4.pamphlet" 885404 885416 899297 899302) (-491 "bookvol10.4.pamphlet" 885149 885157 885249 885254) (-490 "bookvol10.4.pamphlet" 869446 869482 885019 885024) (-489 "bookvol10.4.pamphlet" 869207 869215 869305 869310) (-488 "bookvol10.4.pamphlet" 869028 869042 869141 869146) (-487 "bookvol10.4.pamphlet" 868905 868919 869018 869023) (-486 "bookvol10.4.pamphlet" 868738 868746 868838 868843) (-485 "bookvol10.3.pamphlet" 867954 867970 868440 868467) (-484 "bookvol10.3.pamphlet" 867037 867072 867209 867224) (-483 "bookvol10.3.pamphlet" 864210 864237 865169 865318) (-482 "bookvol10.2.pamphlet" 863188 863196 864190 864205) (-481 NIL 862174 862184 863178 863183) (-480 "bookvol10.4.pamphlet" 860765 860786 862164 862169) (-479 "bookvol10.2.pamphlet" 859405 859417 860755 860760) (-478 NIL 858043 858057 859395 859400) (-477 "bookvol10.3.pamphlet" 851082 851090 858033 858038) (-476 "bookvol10.4.pamphlet" 849477 849485 851072 851077) (-475 "bookvol10.4.pamphlet" 848018 848026 849467 849472) (-474 "bookvol10.2.pamphlet" 847221 847233 848008 848013) (-473 NIL 846422 846436 847211 847216) (-472 "bookvol10.3.pamphlet" 845948 845971 846160 846187) (-471 "bookvol10.4.pamphlet" 840722 840809 845904 845909) (-470 "bookvol10.4.pamphlet" 839991 840009 840712 840717) (-469 "bookvol10.3.pamphlet" 834284 834292 839981 839986) (-468 "bookvol10.3.pamphlet" 830699 830707 834274 834279) (-467 "bookvol10.3.pamphlet" 829816 829843 830667 830694) (-466 "bookvol10.4.pamphlet" 828988 829002 829806 829811) (-465 "bookvol10.4.pamphlet" 824801 824814 828978 828983) (-464 "bookvol10.4.pamphlet" 824405 824415 824791 824796) (-463 "bookvol10.4.pamphlet" 824055 824072 824395 824400) (-462 "bookvol10.4.pamphlet" 823522 823541 824045 824050) (-461 "bookvol10.4.pamphlet" 822004 822017 823512 823517) (-460 "bookvol10.4.pamphlet" 820469 820477 821994 821999) (-459 "bookvol10.3.pamphlet" 817510 817527 818263 818390) (-458 "bookvol10.3.pamphlet" 811481 811508 817304 817371) (-457 "bookvol10.2.pamphlet" 810435 810443 811407 811476) (-456 NIL 809451 809461 810425 810430) (-455 "bookvol10.4.pamphlet" 804998 805036 809407 809412) (-454 "bookvol10.4.pamphlet" 801096 801134 804988 804993) (-453 "bookvol10.4.pamphlet" 796561 796599 801086 801091) (-452 "bookvol10.4.pamphlet" 793214 793252 796551 796556) (-451 "bookvol10.4.pamphlet" 792537 792545 793204 793209) (-450 "bookvol10.4.pamphlet" 790863 790873 792493 792498) (-449 "bookvol10.4.pamphlet" 789330 789343 790853 790858) (-448 "bookvol10.4.pamphlet" 787535 787554 789320 789325) (-447 "bookvol10.4.pamphlet" 777973 777984 787525 787530) (-446 "bookvol10.2.pamphlet" 774916 774924 777953 777968) (-445 "bookvol10.2.pamphlet" 773960 773968 774896 774911) (-444 "bookvol10.3.pamphlet" 773809 773821 773950 773955) (-443 "bookvol10.3.pamphlet" 772041 772049 773799 773804) (-442 "bookvol10.3.pamphlet" 771212 771220 772031 772036) (-441 "bookvol10.4.pamphlet" 770258 770277 771148 771153) (-440 "bookvol10.3.pamphlet" 768402 768410 770248 770253) (-439 "bookvol10.4.pamphlet" 767826 767842 768392 768397) (-438 "bookvol10.4.pamphlet" 766686 766702 767783 767788) (-437 "bookvol10.4.pamphlet" 763973 763989 766676 766681) (-436 "bookvol10.2.pamphlet" 757883 757893 763736 763968) (-435 NIL 751583 751595 757438 757443) (-434 "bookvol10.4.pamphlet" 751199 751215 751573 751578) (-433 "bookvol10.3.pamphlet" 750527 750539 751019 751118) (-432 "bookvol10.4.pamphlet" 749791 749807 750517 750522) (-431 "bookvol10.2.pamphlet" 748968 748978 749735 749786) (-430 NIL 748119 748131 748888 748893) (-429 "bookvol10.4.pamphlet" 746862 746878 748109 748114) (-428 "bookvol10.4.pamphlet" 741353 741387 746852 746857) (-427 "bookvol10.4.pamphlet" 740965 740981 741343 741348) (-426 "bookvol10.4.pamphlet" 740128 740151 740955 740960) (-425 "bookvol10.4.pamphlet" 739128 739138 740118 740123) (-424 "bookvol10.3.pamphlet" 731104 731114 738152 738221) (-423 "bookvol10.2.pamphlet" 726287 726297 731046 731099) (-422 NIL 721482 721494 726243 726248) (-421 "bookvol10.4.pamphlet" 720930 720948 721472 721477) (-420 "bookvol10.3.pamphlet" 720340 720370 720861 720866) (-419 "bookvol10.3.pamphlet" 719573 719594 720320 720335) (-418 "bookvol10.4.pamphlet" 719311 719343 719563 719568) (-417 "bookvol10.2.pamphlet" 718985 718995 719301 719306) (-416 NIL 718525 718537 718843 718848) (-415 "bookvol10.2.pamphlet" 716931 716944 718481 718520) (-414 NIL 715369 715384 716921 716926) (-413 "bookvol10.3.pamphlet" 712486 712496 712871 713044) (-412 "bookvol10.4.pamphlet" 712099 712111 712476 712481) (-411 "bookvol10.4.pamphlet" 711457 711469 712089 712094) (-410 "bookvol10.2.pamphlet" 708406 708414 711347 711452) (-409 NIL 705383 705393 708326 708331) (-408 "bookvol10.2.pamphlet" 704437 704445 705285 705378) (-407 NIL 703577 703587 704427 704432) (-406 "bookvol10.2.pamphlet" 703329 703339 703557 703572) (-405 "bookvol10.3.pamphlet" 702079 702096 703319 703324) (-404 "bookvol10.3.pamphlet" 700564 700613 702069 702074) (-403 "bookvol10.4.pamphlet" 699513 699521 700554 700559) (-402 "bookvol10.2.pamphlet" 696603 696611 699493 699508) (-401 "bookvol10.2.pamphlet" 696306 696314 696583 696598) (-400 "bookvol10.3.pamphlet" 693700 693708 696296 696301) (-399 "bookvol10.4.pamphlet" 693179 693189 693690 693695) (-398 "bookvol10.4.pamphlet" 692960 692984 693169 693174) (-397 "bookvol10.4.pamphlet" 692161 692169 692950 692955) (-396 "bookvol10.3.pamphlet" 691583 691605 692129 692156) (-395 "bookvol10.2.pamphlet" 689927 689935 691573 691578) (-394 "bookvol10.3.pamphlet" 689819 689827 689917 689922) (-393 "bookvol10.2.pamphlet" 689617 689625 689745 689814) (-392 "bookvol10.3.pamphlet" 686387 686397 689573 689578) (-391 "bookvol10.3.pamphlet" 686090 686102 686321 686348) (-390 "bookvol10.2.pamphlet" 683040 683048 686070 686085) (-389 "bookvol10.2.pamphlet" 682084 682092 683020 683035) (-388 "bookvol10.2.pamphlet" 679778 679796 682052 682079) (-387 "bookvol10.3.pamphlet" 679240 679252 679712 679739) (-386 "bookvol10.4.pamphlet" 677048 677062 679230 679235) (-385 "bookvol10.3.pamphlet" 673953 673961 676914 677043) (-384 "bookvol10.4.pamphlet" 671419 671433 673943 673948) (-383 "bookvol10.2.pamphlet" 671121 671131 671399 671414) (-382 NIL 670777 670789 671057 671062) (-381 "bookvol10.4.pamphlet" 670033 670045 670767 670772) (-380 "bookvol10.2.pamphlet" 668100 668119 669959 670028) (-379 "bookvol10.2.pamphlet" 665306 665316 668068 668095) (-378 NIL 662425 662437 665189 665194) (-377 "bookvol10.4.pamphlet" 661146 661162 662415 662420) (-376 "bookvol10.2.pamphlet" 659267 659280 661102 661141) (-375 NIL 657314 657329 659151 659156) (-374 "bookvol10.2.pamphlet" 656309 656317 657304 657309) (-373 NIL 655302 655312 656299 656304) (-372 "bookvol10.2.pamphlet" 644651 644661 655244 655297) (-371 NIL 634012 634024 644607 644612) (-370 "bookvol10.3.pamphlet" 633599 633609 634002 634007) (-369 "bookvol10.2.pamphlet" 632046 632063 633589 633594) (-368 "bookvol10.2.pamphlet" 631384 631392 631948 632041) (-367 NIL 630808 630818 631374 631379) (-366 "bookvol10.3.pamphlet" 629349 629359 630788 630803) (-365 "bookvol10.4.pamphlet" 628256 628271 629339 629344) (-364 "bookvol10.3.pamphlet" 627685 627700 627972 628065) (-363 "bookvol10.4.pamphlet" 627558 627575 627675 627680) (-362 "bookvol10.4.pamphlet" 627061 627082 627548 627553) (-361 "bookvol10.4.pamphlet" 618460 618471 627051 627056) (-360 "bookvol10.4.pamphlet" 617542 617559 618450 618455) (-359 "bookvol10.3.pamphlet" 617038 617058 617258 617351) (-358 "bookvol10.3.pamphlet" 616506 616522 616719 616812) (-357 "bookvol10.3.pamphlet" 615056 615076 616222 616315) (-356 "bookvol10.3.pamphlet" 613592 613609 614772 614865) (-355 "bookvol10.3.pamphlet" 612133 612154 613273 613366) (-354 "bookvol10.4.pamphlet" 609503 609522 612123 612128) (-353 "bookvol10.2.pamphlet" 607101 607109 609405 609498) (-352 NIL 604785 604795 607091 607096) (-351 "bookvol10.4.pamphlet" 603578 603595 604775 604780) (-350 "bookvol10.4.pamphlet" 601053 601064 603568 603573) (-349 "bookvol10.4.pamphlet" 595175 595191 601043 601048) (-348 "bookvol10.4.pamphlet" 593850 593869 595165 595170) (-347 "bookvol10.4.pamphlet" 593269 593286 593840 593845) (-346 "bookvol10.4.pamphlet" 593190 593207 593259 593264) (-345 "bookvol10.3.pamphlet" 592071 592091 592906 592999) (-344 "bookvol10.3.pamphlet" 590986 591006 591787 591880) (-343 "bookvol10.3.pamphlet" 589813 589834 590667 590760) (-342 "bookvol10.2.pamphlet" 578618 578640 589652 589808) (-341 NIL 567502 567526 578538 578543) (-340 "bookvol10.4.pamphlet" 567241 567281 567492 567497) (-339 "bookvol10.3.pamphlet" 559917 559963 566997 567036) (-338 "bookvol10.2.pamphlet" 559627 559637 559907 559912) (-337 NIL 559122 559134 559404 559409) (-336 "bookvol10.3.pamphlet" 558573 558597 559112 559117) (-335 "bookvol10.2.pamphlet" 556585 556609 558563 558568) (-334 NIL 554595 554621 556575 556580) (-333 "bookvol10.4.pamphlet" 554341 554381 554585 554590) (-332 "bookvol10.4.pamphlet" 552902 552910 554331 554336) (-331 "bookvol10.3.pamphlet" 552433 552443 552892 552897) (-330 "bookvol10.3.pamphlet" 542398 542406 552423 552428) (-329 "bookvol10.2.pamphlet" 535675 535689 542300 542393) (-328 NIL 529004 529020 535631 535636) (-327 "bookvol10.3.pamphlet" 527432 527442 528410 528437) (-326 "bookvol10.2.pamphlet" 525574 525586 527330 527427) (-325 NIL 523700 523714 525458 525463) (-324 "bookvol10.4.pamphlet" 523274 523296 523690 523695) (-323 "bookvol10.3.pamphlet" 522931 522941 523228 523233) (-322 "bookvol10.2.pamphlet" 521114 521126 522921 522926) (-321 "bookvol10.3.pamphlet" 520728 520738 521010 521037) (-320 "bookvol10.4.pamphlet" 518940 518957 520718 520723) (-319 "bookvol10.4.pamphlet" 518822 518832 518930 518935) (-318 "bookvol10.4.pamphlet" 518016 518026 518812 518817) (-317 "bookvol10.4.pamphlet" 517898 517908 518006 518011) (-316 "bookvol10.3.pamphlet" 514735 514758 516030 516179) (-315 "bookvol10.4.pamphlet" 512203 512211 514725 514730) (-314 "bookvol10.4.pamphlet" 512105 512134 512193 512198) (-313 "bookvol10.4.pamphlet" 508849 508865 512095 512100) (-312 "bookvol10.3.pamphlet" 504116 504126 504838 505245) (-311 "bookvol10.4.pamphlet" 500206 500219 504106 504111) (-310 "bookvol10.4.pamphlet" 499976 499988 500196 500201) (-309 "bookvol10.3.pamphlet" 496910 496935 497548 497641) (-308 "bookvol10.4.pamphlet" 496763 496771 496900 496905) (-307 "bookvol10.3.pamphlet" 496434 496442 496753 496758) (-306 "bookvol10.4.pamphlet" 495928 495942 496424 496429) (-305 "bookvol10.2.pamphlet" 495492 495502 495918 495923) (-304 NIL 495054 495066 495482 495487) (-303 "bookvol10.2.pamphlet" 492626 492634 494980 495049) (-302 NIL 490260 490270 492616 492621) (-301 "bookvol10.4.pamphlet" 482118 482126 490250 490255) (-300 "bookvol10.4.pamphlet" 481713 481727 482108 482113) (-299 "bookvol10.4.pamphlet" 481398 481409 481703 481708) (-298 "bookvol10.2.pamphlet" 474345 474353 481388 481393) (-297 NIL 467198 467208 474243 474248) (-296 "bookvol10.4.pamphlet" 464007 464015 467188 467193) (-295 "bookvol10.4.pamphlet" 463748 463760 463997 464002) (-294 "bookvol10.4.pamphlet" 463255 463271 463738 463743) (-293 "bookvol10.4.pamphlet" 462813 462829 463245 463250) (-292 "bookvol10.4.pamphlet" 460289 460297 462803 462808) (-291 "bookvol10.3.pamphlet" 459323 459345 459532 459559) (-290 "bookvol10.3.pamphlet" 454249 454259 456996 457108) (-289 "bookvol10.4.pamphlet" 453967 453979 454239 454244) (-288 "bookvol10.4.pamphlet" 450321 450331 453957 453962) (-287 "bookvol10.2.pamphlet" 449865 449873 450265 450316) (-286 "bookvol10.3.pamphlet" 449061 449102 449791 449860) (-285 "bookvol10.2.pamphlet" 447517 447536 449051 449056) (-284 NIL 445937 445958 447473 447478) (-283 "bookvol10.2.pamphlet" 445469 445487 445927 445932) (-282 "bookvol10.4.pamphlet" 444858 444877 445459 445464) (-281 "bookvol10.2.pamphlet" 444555 444563 444848 444853) (-280 NIL 444250 444260 444545 444550) (-279 "bookvol10.2.pamphlet" 442166 442176 444218 444245) (-278 NIL 440031 440043 442085 442090) (-277 "bookvol10.3.pamphlet" 436806 436836 439987 439992) (-276 "bookvol10.3.pamphlet" 433642 433665 436762 436767) (-275 "bookvol10.4.pamphlet" 431639 431655 433632 433637) (-274 "bookvol10.4.pamphlet" 426415 426431 431629 431634) (-273 "bookvol10.3.pamphlet" 424729 424737 426405 426410) (-272 "bookvol10.3.pamphlet" 424267 424275 424719 424724) (-271 "bookvol10.3.pamphlet" 423846 423854 424257 424262) (-270 "bookvol10.3.pamphlet" 423428 423436 423836 423841) (-269 "bookvol10.3.pamphlet" 422966 422974 423418 423423) (-268 "bookvol10.3.pamphlet" 422504 422512 422956 422961) (-267 "bookvol10.3.pamphlet" 422042 422050 422494 422499) (-266 "bookvol10.3.pamphlet" 421580 421588 422032 422037) (-265 "bookvol10.4.pamphlet" 417322 417330 421570 421575) (-264 "bookvol10.2.pamphlet" 414071 414081 417312 417317) (-263 NIL 410818 410830 414061 414066) (-262 "bookvol10.4.pamphlet" 407903 407990 410808 410813) (-261 "bookvol10.3.pamphlet" 407109 407119 407733 407760) (-260 "bookvol10.2.pamphlet" 406703 406713 407065 407104) (-259 "bookvol10.3.pamphlet" 404146 404160 404439 404566) (-258 "bookvol10.3.pamphlet" 397909 397917 404136 404141) (-257 "bookvol10.4.pamphlet" 397580 397590 397899 397904) (-256 "bookvol10.4.pamphlet" 392539 392547 397570 397575) (-255 "bookvol10.4.pamphlet" 390780 390788 392529 392534) (-254 "bookvol10.4.pamphlet" 383688 383701 390770 390775) (-253 "bookvol10.4.pamphlet" 382951 382961 383678 383683) (-252 "bookvol10.4.pamphlet" 380376 380384 382941 382946) (-251 "bookvol10.4.pamphlet" 379923 379938 380366 380371) (-250 "bookvol10.4.pamphlet" 369363 369371 379913 379918) (-249 "bookvol10.2.pamphlet" 367573 367583 369319 369358) (-248 "bookvol10.2.pamphlet" 362970 362986 367441 367568) (-247 NIL 358453 358471 362926 362931) (-246 "bookvol10.3.pamphlet" 351828 351844 351950 352251) (-245 "bookvol10.3.pamphlet" 345200 345218 345325 345626) (-244 "bookvol10.3.pamphlet" 342441 342456 342994 343121) (-243 "bookvol10.4.pamphlet" 341781 341791 342431 342436) (-242 "bookvol10.3.pamphlet" 340496 340506 341187 341214) (-241 "bookvol10.2.pamphlet" 338943 338953 340476 340491) (-240 "bookvol10.2.pamphlet" 338384 338392 338887 338938) (-239 NIL 337869 337879 338374 338379) (-238 "bookvol10.3.pamphlet" 337722 337732 337801 337828) (-237 "bookvol10.2.pamphlet" 336487 336497 337690 337717) (-236 "bookvol10.4.pamphlet" 334701 334709 336477 336482) (-235 "bookvol10.3.pamphlet" 333981 333996 334537 334662) (-234 "bookvol10.3.pamphlet" 325571 325587 326196 326327) (-233 "bookvol10.4.pamphlet" 324432 324450 325561 325566) (-232 "bookvol10.2.pamphlet" 323363 323379 324284 324427) (-231 NIL 322035 322053 322958 322963) (-230 "bookvol10.4.pamphlet" 320880 320888 322025 322030) (-229 "bookvol10.2.pamphlet" 319960 319970 320848 320875) (-228 NIL 319026 319038 319916 319921) (-227 "bookvol10.2.pamphlet" 318147 318155 319006 319021) (-226 NIL 317276 317286 318137 318142) (-225 "bookvol10.2.pamphlet" 316427 316437 317256 317271) (-224 NIL 315495 315507 316326 316331) (-223 "bookvol10.2.pamphlet" 315115 315125 315463 315490) (-222 NIL 314755 314767 315105 315110) (-221 "bookvol10.3.pamphlet" 313037 313047 314399 314426) (-220 "bookvol10.3.pamphlet" 311775 311783 312161 312188) (-219 "bookvol10.4.pamphlet" 302969 302977 311765 311770) (-218 "bookvol10.3.pamphlet" 302186 302194 302601 302628) (-217 "bookvol10.3.pamphlet" 298571 298579 302076 302181) (-216 "bookvol10.4.pamphlet" 296806 296822 298561 298566) (-215 "bookvol10.3.pamphlet" 294764 294796 296786 296801) (-214 "bookvol10.3.pamphlet" 288954 288964 294594 294621) (-213 "bookvol10.4.pamphlet" 288569 288583 288944 288949) (-212 "bookvol10.4.pamphlet" 286034 286044 288559 288564) (-211 "bookvol10.4.pamphlet" 284514 284530 286024 286029) (-210 "bookvol10.3.pamphlet" 282395 282403 282981 283074) (-209 "bookvol10.4.pamphlet" 280272 280289 282385 282390) (-208 "bookvol10.4.pamphlet" 279880 279904 280262 280267) (-207 "bookvol10.3.pamphlet" 278533 278543 279870 279875) (-206 "bookvol10.3.pamphlet" 278361 278369 278523 278528) (-205 "bookvol10.3.pamphlet" 278181 278189 278351 278356) (-204 "bookvol10.4.pamphlet" 277126 277134 278171 278176) (-203 "bookvol10.3.pamphlet" 276590 276598 277116 277121) (-202 "bookvol10.3.pamphlet" 276070 276078 276580 276585) (-201 "bookvol10.3.pamphlet" 275562 275570 276060 276065) (-200 "bookvol10.3.pamphlet" 275054 275062 275552 275557) (-199 "bookvol10.4.pamphlet" 269999 270007 275044 275049) (-198 "bookvol10.4.pamphlet" 268322 268330 269989 269994) (-197 "bookvol10.3.pamphlet" 268299 268307 268312 268317) (-196 "bookvol10.3.pamphlet" 267823 267831 268289 268294) (-195 "bookvol10.3.pamphlet" 267347 267355 267813 267818) (-194 "bookvol10.3.pamphlet" 266817 266825 267337 267342) (-193 "bookvol10.3.pamphlet" 266312 266320 266807 266812) (-192 "bookvol10.3.pamphlet" 265794 265802 266302 266307) (-191 "bookvol10.3.pamphlet" 265290 265298 265784 265789) (-190 "bookvol10.3.pamphlet" 264802 264810 265280 265285) (-189 "bookvol10.3.pamphlet" 264344 264352 264792 264797) (-188 "bookvol10.3.pamphlet" 263874 263882 264334 264339) (-187 "bookvol10.3.pamphlet" 263399 263407 263864 263869) (-186 "bookvol10.4.pamphlet" 259506 259514 263389 263394) (-185 "bookvol10.4.pamphlet" 259010 259018 259496 259501) (-184 "bookvol10.4.pamphlet" 255821 255829 259000 259005) (-183 "bookvol10.4.pamphlet" 255206 255216 255811 255816) (-182 "bookvol10.4.pamphlet" 253674 253690 255196 255201) (-181 "bookvol10.4.pamphlet" 252463 252476 253664 253669) (-180 "bookvol10.4.pamphlet" 246478 246491 252453 252458) (-179 "bookvol10.4.pamphlet" 245635 245645 246468 246473) (-178 "bookvol10.4.pamphlet" 245147 245162 245560 245565) (-177 "bookvol10.4.pamphlet" 244852 244871 245137 245142) (-176 "bookvol10.4.pamphlet" 239867 239877 244842 244847) (-175 "bookvol10.3.pamphlet" 235868 235878 239769 239862) (-174 "bookvol10.2.pamphlet" 235547 235555 235806 235863) (-173 "bookvol10.3.pamphlet" 235047 235055 235537 235542) (-172 "bookvol10.4.pamphlet" 234814 234829 235037 235042) (-171 "bookvol10.3.pamphlet" 228832 228842 229081 229342) (-170 "bookvol10.4.pamphlet" 228555 228567 228822 228827) (-169 "bookvol10.4.pamphlet" 228351 228365 228545 228550) (-168 "bookvol10.2.pamphlet" 226457 226467 228073 228346) (-167 NIL 224267 224279 225885 225890) (-166 "bookvol10.2.pamphlet" 224006 224014 224257 224262) (-165 "bookvol10.4.pamphlet" 223780 223798 223996 224001) (-164 "bookvol10.4.pamphlet" 223319 223327 223770 223775) (-163 "bookvol10.3.pamphlet" 223128 223136 223309 223314) (-162 "bookvol10.2.pamphlet" 222163 222171 223118 223123) (-161 "bookvol10.4.pamphlet" 220655 220665 222153 222158) (-160 "bookvol10.4.pamphlet" 218105 218121 220645 220650) (-159 "bookvol10.3.pamphlet" 216943 216951 218095 218100) (-158 "bookvol10.4.pamphlet" 216277 216294 216933 216938) (-157 "bookvol10.4.pamphlet" 212397 212405 216267 216272) (-156 "bookvol10.3.pamphlet" 211112 211128 212353 212392) (-155 "bookvol10.2.pamphlet" 208132 208142 211092 211107) (-154 NIL 205033 205045 207995 208000) (-153 "bookvol10.4.pamphlet" 204372 204385 205023 205028) (-152 "bookvol10.4.pamphlet" 202342 202364 204362 204367) (-151 "bookvol10.2.pamphlet" 202257 202265 202322 202337) (-150 "bookvol10.4.pamphlet" 201771 201781 202247 202252) (-149 "bookvol10.2.pamphlet" 201524 201532 201751 201766) (-148 "bookvol10.3.pamphlet" 197885 197893 201514 201519) (-147 "bookvol10.2.pamphlet" 197058 197066 197875 197880) (-146 "bookvol10.3.pamphlet" 195365 195373 195996 196023) (-145 "bookvol10.3.pamphlet" 194497 194505 194921 194948) (-144 "bookvol10.4.pamphlet" 193737 193751 194487 194492) (-143 "bookvol10.3.pamphlet" 192148 192156 193206 193245) (-142 "bookvol10.3.pamphlet" 183327 183351 192138 192143) (-141 "bookvol10.4.pamphlet" 182717 182744 183317 183322) (-140 "bookvol10.3.pamphlet" 179055 179063 182691 182712) (-139 "bookvol10.2.pamphlet" 178671 178679 179045 179050) (-138 "bookvol10.2.pamphlet" 178164 178172 178661 178666) (-137 "bookvol10.3.pamphlet" 177256 177266 177994 178021) (-136 "bookvol10.3.pamphlet" 176498 176508 177086 177113) (-135 "bookvol10.2.pamphlet" 175872 175882 176454 176493) (-134 NIL 175278 175290 175862 175867) (-133 "bookvol10.2.pamphlet" 174381 174389 175234 175273) (-132 NIL 173516 173526 174371 174376) (-131 "bookvol10.3.pamphlet" 172174 172184 173346 173373) (-130 "Makefile.pamphlet" 170064 170072 172164 172169) (-129 "bookvol10.4.pamphlet" 168837 168848 170054 170059) (-128 "bookvol10.2.pamphlet" 167797 167807 168817 168832) (-127 NIL 166731 166743 167753 167758) (-126 "bookvol10.3.pamphlet" 164776 164788 164967 165060) (-125 "bookvol10.3.pamphlet" 164504 164516 164702 164771) (-124 "bookvol10.4.pamphlet" 164162 164179 164494 164499) (-123 "bookvol10.3.pamphlet" 159694 159702 164152 164157) (-122 "bookvol10.4.pamphlet" 157180 157190 159650 159655) (-121 "bookvol10.3.pamphlet" 156050 156058 157170 157175) (-120 "bookvol10.2.pamphlet" 155694 155706 156018 156045) (-119 "bookvol10.4.pamphlet" 153972 154008 155684 155689) (-118 "bookvol10.3.pamphlet" 153862 153870 153937 153967) (-117 "bookvol10.2.pamphlet" 153839 153847 153852 153857) (-116 "bookvol10.3.pamphlet" 153731 153739 153806 153834) (-115 "bookvol10.5.pamphlet" 142003 142011 153721 153726) (-114 "bookvol10.3.pamphlet" 141482 141490 141697 141724) (-113 "bookvol10.3.pamphlet" 140839 140847 141472 141477) (-112 "bookvol10.3.pamphlet" 138687 138695 139306 139399) (-111 "bookvol10.2.pamphlet" 137932 137942 138655 138682) (-110 NIL 137197 137209 137922 137927) (-109 "bookvol10.3.pamphlet" 136618 136626 137177 137192) (-108 "bookvol10.4.pamphlet" 135758 135785 136568 136573) (-107 "bookvol10.4.pamphlet" 133621 133631 135748 135753) (-106 "bookvol10.3.pamphlet" 129253 129263 133451 133478) (-105 "bookvol10.2.pamphlet" 128947 128955 129243 129248) (-104 NIL 128639 128649 128937 128942) (-103 "bookvol10.4.pamphlet" 128058 128071 128629 128634) (-102 "bookvol10.4.pamphlet" 127918 127926 128048 128053) (-101 "bookvol10.3.pamphlet" 127362 127372 127898 127913) (-100 "bookvol10.2.pamphlet" 123917 123925 127102 127357) (-99 "bookvol10.3.pamphlet" 120042 120049 123897 123912) (-98 "bookvol10.2.pamphlet" 119512 119519 120032 120037) (-97 NIL 118980 118989 119502 119507) (-96 "bookvol10.3.pamphlet" 114684 114693 118810 118837) (-95 "bookvol10.4.pamphlet" 113474 113485 114640 114645) (-94 "bookvol10.3.pamphlet" 112631 112644 113464 113469) (-93 "bookvol10.3.pamphlet" 111574 111587 112621 112626) (-92 "bookvol10.3.pamphlet" 110906 110919 111564 111569) (-91 "bookvol10.3.pamphlet" 110104 110117 110896 110901) (-90 "bookvol10.3.pamphlet" 109583 109596 110094 110099) (-89 "bookvol10.3.pamphlet" 108956 108969 109573 109578) (-88 "bookvol10.3.pamphlet" 107983 107996 108946 108951) (-87 "bookvol10.3.pamphlet" 107246 107259 107973 107978) (-86 "bookvol10.3.pamphlet" 105926 105939 107236 107241) (-85 "bookvol10.3.pamphlet" 104363 104376 105916 105921) (-84 "bookvol10.3.pamphlet" 102019 102032 104353 104358) (-83 "bookvol10.3.pamphlet" 101308 101321 102009 102014) (-82 "bookvol10.3.pamphlet" 100297 100310 101298 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. -43) 139023) ((-74 . -611) 139005) ((-315 . -505) 138971) ((-1177 . -284) 138950) ((-1110 . -1109) 138860) ((-88 . -1203) T) ((-66 . -611) 138842) ((-493 . -284) 138821) ((-1271 . -1043) 138798) ((-1157 . -1097) T) ((-1110 . -23) 138668) ((-816 . -900) 138604) ((-1230 . -721) T) ((-1099 . -1203) T) ((-1085 . -286) 138535) ((-893 . -105) T) ((-782 . -286) 138446) ((-326 . -19) 138430) ((-64 . -284) 138407) ((-780 . -286) 138338) ((-852 . -721) T) ((-126 . -845) NIL) ((-528 . -284) 138315) ((-326 . -604) 138292) ((-508 . -284) 138269) ((-458 . -286) 138200) ((-1041 . -304) 138051) ((-578 . -721) T) ((-655 . -611) 138033) ((-241 . -612) 137994) ((-241 . -611) 137933) ((-1139 . -39) T) ((-949 . -1203) T) ((-342 . -712) 137878) ((-862 . -1053) T) ((-779 . -1053) T) ((-665 . -25) T) ((-665 . -21) T) ((-1115 . -1143) T) ((-482 . -1053) T) ((-629 . -422) 137843) ((-605 . -422) 137808) ((-927 . -1097) T) ((-862 . -226) T) ((-862 . -239) T) ((-779 . -226) 137767) ((-779 . -239) T) ((-584 . 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. -1095) T) ((-1241 . -721) T) ((-1220 . -721) T) ((-53 . -712) 125811) ((-1163 . -286) 125722) ((-216 . -1027) T) ((-354 . -1265) 125699) ((-1243 . -416) 125665) ((-713 . -721) T) ((-1230 . -900) 125608) ((-121 . -611) 125590) ((-121 . -612) 125572) ((-713 . -481) T) ((-496 . -21) 125482) ((-137 . -502) 125466) ((-131 . -502) 125450) ((-496 . -25) 125301) ((-618 . -286) T) ((-779 . -39) T) ((-1209 . -502) 125283) ((-588 . -1059) 125258) ((-1208 . -62) 125224) ((-442 . -1097) T) ((-1064 . -302) T) ((-126 . -286) T) ((-1101 . -105) T) ((-1009 . -105) T) ((-588 . -120) 125185) ((-1253 . -1060) T) ((-1134 . -304) 125123) ((-1198 . -1053) T) ((-1064 . -1027) T) ((-71 . -1203) T) ((-1057 . -25) T) ((-1057 . -21) T) ((-706 . -1053) T) ((-390 . -21) T) ((-390 . -25) T) ((-688 . -526) NIL) ((-1029 . -173) T) ((-706 . -239) T) ((-1064 . -553) T) ((-862 . -721) T) ((-779 . -721) T) ((-514 . -105) T) ((-357 . -173) T) ((-342 . -611) 125105) ((-399 . -611) 125087) ((-482 . -721) T) ((-1115 . -845) 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. -1016) 122168) ((-1177 . -39) T) ((-922 . -611) 122150) ((-1110 . -847) 122101) ((-768 . -611) 122083) ((-666 . -611) 122065) ((-1149 . -304) 122003) ((-1089 . -1203) T) ((-493 . -39) T) ((-1085 . -1053) T) ((-492 . -456) T) ((-865 . -1275) 121978) ((-860 . -1275) 121938) ((-1133 . -39) T) ((-782 . -1053) T) ((-780 . -1053) T) ((-639 . -228) 121922) ((-626 . -228) 121868) ((-1230 . -302) 121847) ((-1209 . -19) 121829) ((-1209 . -604) 121804) ((-1085 . -325) 121765) ((-458 . -1053) T) ((-1171 . -21) T) ((-1085 . -226) 121744) ((-782 . -325) 121721) ((-782 . -226) T) ((-780 . -325) 121693) ((-326 . -643) 121677) ((-726 . -1213) 121656) ((-1171 . -25) T) ((-64 . -39) T) ((-530 . -39) T) ((-528 . -39) T) ((-458 . -325) 121635) ((-326 . -378) 121619) ((-509 . -39) T) ((-508 . -39) T) ((-1009 . -1143) NIL) ((-629 . -105) T) ((-605 . -105) T) ((-726 . -561) 121550) ((-358 . -721) T) ((-355 . -721) T) ((-343 . -721) T) ((-258 . -721) T) ((-243 . -721) T) ((-739 . -25) T) ((-739 . -21) T) 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T) ((-193 . -787) T) ((-192 . -787) T) ((-191 . -787) T) ((-190 . -787) T) ((-189 . -787) T) ((-188 . -787) T) ((-187 . -787) T) ((-507 . -1008) T) ((-271 . -836) T) ((-270 . -836) T) ((-269 . -836) T) ((-268 . -836) T) ((-53 . -286) T) ((-267 . -836) T) ((-266 . -836) T) ((-265 . -836) T) ((-186 . -787) T) ((-610 . -847) T) ((-647 . -416) 120699) ((-114 . -847) T) ((-646 . -21) T) ((-646 . -25) T) ((-467 . -611) 120681) ((-1279 . -43) 120651) ((-1258 . -19) 120635) ((-126 . -282) 120565) ((-217 . -105) T) ((-145 . -105) T) ((-1258 . -604) 120542) ((-1269 . -1097) T) ((-1253 . -712) 120439) ((-1076 . -1097) T) ((-994 . -1097) T) ((-970 . -138) T) ((-732 . -1097) T) ((-730 . -138) T) ((-710 . -138) T) ((-523 . -793) T) ((-412 . -1143) 120417) ((-457 . -138) T) ((-523 . -794) T) ((-214 . -1053) T) ((-289 . -105) 120199) ((-143 . -1097) T) ((-693 . -1008) T) ((-96 . -1203) T) ((-137 . -611) 120166) ((-131 . -611) 120133) ((-738 . -173) T) ((-1284 . -173) T) ((-1209 . -612) 120115) ((-1209 . -611) 120097) ((-1166 . -367) 120076) ((-1159 . -367) 120055) ((-311 . -1097) T) ((-423 . -138) T) ((-308 . -1097) T) ((-412 . -43) 120007) ((-1128 . -105) T) ((-1243 . -712) 119864) ((-647 . -1060) T) ((-315 . -149) 119843) ((-315 . -151) 119822) ((-142 . -1097) T) ((-123 . -1097) T) ((-854 . -105) T) ((-583 . -611) 119804) ((-571 . -612) 119703) ((-571 . -611) 119685) ((-507 . -611) 119667) ((-507 . -612) 119612) ((-498 . -23) T) ((-496 . -847) 119563) ((-118 . -1097) T) ((-500 . -633) 119545) ((-779 . -1016) 119497) ((-209 . -633) 119479) ((-216 . -409) T) ((-655 . -640) 119463) ((-1165 . -921) 119442) ((-726 . -1109) T) ((-354 . -105) T) ((-818 . -847) T) ((-726 . -23) T) ((-342 . -1059) 119387) ((-1151 . -1150) T) ((-1139 . -111) 119371) ((-1253 . -173) 119322) ((-1167 . -1109) T) ((-1166 . -1109) T) ((-1159 . -1109) T) ((-1121 . -1109) T) ((-527 . -1043) 119306) ((-342 . -120) 119223) ((-217 . -304) NIL) ((-145 . -304) NIL) ((-1010 . -1213) T) ((-136 . -1203) T) ((-915 . -1213) T) ((-1259 . -611) 119205) ((-1207 . -1097) T) ((-688 . -282) NIL) ((-1167 . -23) T) ((-1166 . -23) T) ((-1159 . -23) T) ((-1134 . -224) 119189) ((-1121 . -23) T) ((-1074 . -1097) T) ((-1010 . -561) T) ((-915 . -561) T) ((-799 . -138) T) ((-219 . -1203) T) ((-146 . -1203) T) ((-738 . -526) 119155) ((-705 . -611) 119137) ((-34 . -1097) T) ((-311 . -712) 119047) ((-308 . -712) 118976) ((-693 . -611) 118958) ((-693 . -612) 118903) ((-412 . -405) 118887) ((-443 . -1097) T) ((-500 . -25) T) ((-500 . -21) T) ((-1115 . -1097) T) ((-209 . -25) T) ((-209 . -21) T) ((-707 . -416) 118871) ((-709 . -1043) 118840) ((-1258 . -611) 118779) ((-1258 . -612) 118740) ((-1243 . -173) T) ((-241 . -39) T) ((-1163 . -612) NIL) ((-1163 . -611) 118722) ((-931 . -981) T) ((-1190 . -1203) T) ((-655 . -791) 118701) ((-655 . -794) 118680) ((-403 . -400) T) ((-534 . -105) 118658) ((-1041 . -1097) T) ((-213 . -1001) 118642) ((-517 . -105) T) ((-618 . -611) 118624) ((-50 . -847) NIL) ((-618 . -612) 118601) ((-1041 . 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117372) ((-344 . -151) 117351) ((-344 . -149) 117302) ((-315 . -40) 117268) ((-483 . -1180) 117247) ((0 . |EnumerationCategory|) T) ((-315 . -98) 117213) ((-384 . -1027) T) ((-112 . -151) T) ((-112 . -149) NIL) ((-50 . -228) 117163) ((-647 . -1097) T) ((-606 . -111) 117110) ((-498 . -138) T) ((-483 . -111) 117060) ((-233 . -1109) 116970) ((-1084 . -1109) T) ((-871 . -382) 116954) ((-871 . -337) 116938) ((-233 . -23) 116808) ((-1064 . -921) T) ((-1064 . -820) T) ((-584 . -373) T) ((-529 . -373) T) ((-739 . -847) 116787) ((-1209 . -284) 116762) ((-354 . -1143) T) ((-326 . -39) T) ((-49 . -422) 116746) ((-1084 . -23) T) ((-395 . -741) 116730) ((-1269 . -526) 116663) ((-726 . -138) T) ((-1253 . -286) 116642) ((-1249 . -561) 116621) ((-1242 . -1213) 116600) ((-1242 . -561) 116551) ((-1221 . -1213) 116530) ((-1221 . -561) 116481) ((-732 . -526) 116414) ((-1220 . -1203) 116393) ((-1220 . -886) 116266) ((-893 . -1097) T) ((-148 . -841) T) ((-1220 . -884) 116236) ((-1215 . -561) 116215) ((-1167 . -138) T) ((-534 . -304) 116153) ((-1166 . -138) T) ((-143 . -526) NIL) ((-1159 . -138) T) ((-1121 . -138) T) ((-1029 . -1008) T) ((-1010 . -23) T) ((-354 . -43) 116118) ((-1010 . -1109) T) ((-915 . -1109) T) ((-87 . -611) 116100) ((-45 . -1053) T) ((-869 . -1059) 116087) ((-871 . -900) 116046) ((-779 . -52) 116023) ((-695 . -105) T) ((-1009 . -352) NIL) ((-602 . -1203) T) ((-978 . -23) T) ((-915 . -23) T) ((-869 . -120) 116008) ((-432 . -1109) T) ((-482 . -52) 115978) ((-140 . -105) T) ((-45 . -226) 115950) ((-45 . -239) T) ((-125 . -105) T) ((-597 . -561) 115929) ((-596 . -561) 115908) ((-688 . -611) 115890) ((-688 . -612) 115798) ((-311 . -526) 115764) ((-308 . -526) 115515) ((-1241 . -1043) 115499) ((-1220 . -1043) 115285) ((-1005 . -416) 115269) ((-432 . -23) T) ((-1115 . -173) T) ((-865 . -721) T) ((-860 . -721) T) ((-1243 . -286) T) ((-647 . -712) 115239) ((-148 . -1097) T) ((-53 . -1008) T) ((-412 . -224) 115223) ((-290 . -228) 115173) ((-870 . -921) T) ((-870 . -820) NIL) 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-120) 114224) ((-507 . -120) 114173) ((-1169 . -886) 114140) ((-35 . -105) T) ((-901 . -502) 114124) ((-116 . -611) 114106) ((-53 . -611) 114088) ((-53 . -612) 114033) ((-260 . -502) 114017) ((-233 . -138) 113887) ((-1230 . -921) 113866) ((-816 . -1213) 113845) ((-1041 . -526) 113653) ((-1084 . -138) T) ((-393 . -611) 113635) ((-816 . -561) 113566) ((-588 . -640) 113541) ((-258 . -52) 113513) ((-243 . -52) 113470) ((-537 . -521) 113447) ((-1006 . -1203) T) ((-1249 . -23) T) ((-1249 . -1109) T) ((-693 . -1059) 113412) ((-779 . -900) 113325) ((-1242 . -1109) T) ((-1242 . -23) T) ((-1221 . -1109) T) ((-1215 . -1109) T) ((-1009 . -375) 113297) ((-121 . -373) T) ((-482 . -900) 113203) ((-1221 . -23) T) ((-1215 . -23) T) ((-904 . -611) 113185) ((-96 . -111) 113169) ((-1198 . -721) T) ((-905 . -847) 113120) ((-695 . -1143) T) ((-693 . -120) 113069) ((-1205 . -1097) T) ((-597 . -1109) T) ((-596 . -1109) T) ((-707 . -712) 112898) ((-706 . -721) T) ((-1115 . -286) T) ((-1010 . -138) T) ((-500 . 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-105) T) ((-512 . -105) T) ((-1128 . -1129) 107852) ((-156 . -1265) 107836) ((-241 . -1203) T) ((-1207 . -19) 107818) ((-779 . -668) 107770) ((-1165 . -1213) 107749) ((-1120 . -1213) 107728) ((-233 . -21) 107638) ((-233 . -25) 107489) ((-137 . -128) 107473) ((-131 . -128) 107457) ((-1209 . -643) 107439) ((-49 . -741) 107423) ((-1207 . -604) 107398) ((-1165 . -561) 107309) ((-1120 . -561) 107240) ((-1209 . -378) 107222) ((-1041 . -282) 107197) ((-1084 . -25) T) ((-1084 . -21) T) ((-816 . -138) T) ((-126 . -795) NIL) ((-126 . -792) NIL) ((-358 . -302) T) ((-355 . -302) T) ((-343 . -302) T) ((-1091 . -1203) T) ((-245 . -1109) 107107) ((-244 . -1109) 107017) ((-1029 . -1053) T) ((-1009 . -1060) T) ((-342 . -640) 106962) ((-616 . -43) 106946) ((-1269 . -611) 106908) ((-1269 . -612) 106869) ((-1076 . -611) 106851) ((-1029 . -239) T) ((-357 . -1053) T) ((-815 . -1265) 106821) ((-245 . -23) T) ((-244 . -23) T) ((-994 . -611) 106803) ((-732 . -612) 106764) ((-732 . -611) 106746) ((-799 . -847) 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. -561) T) ((-1204 . -62) 104985) ((-958 . -561) 104916) ((-1165 . -23) T) ((-1120 . -23) T) ((-851 . -23) T) ((-495 . -561) 104847) ((-1134 . -712) 104779) ((-1138 . -526) 104712) ((-1041 . -612) NIL) ((-1041 . -611) 104694) ((-858 . -712) 104664) ((-1284 . -1059) 104651) ((-1284 . -120) 104636) ((-1198 . -52) 104605) ((-245 . -138) T) ((-244 . -138) T) ((-1101 . -1097) T) ((-1009 . -1097) T) ((-67 . -611) 104587) ((-1159 . -847) NIL) ((-1029 . -792) T) ((-1029 . -795) T) ((-1249 . -25) T) ((-738 . -1059) 104511) ((-1249 . -21) T) ((-1242 . -21) T) ((-869 . -640) 104498) ((-1242 . -25) T) ((-1221 . -21) T) ((-1221 . -25) T) ((-1215 . -25) T) ((-1215 . -21) T) ((-1033 . -155) 104482) ((-871 . -820) 104461) ((-871 . -921) T) ((-738 . -120) 104364) ((-707 . -282) 104291) ((-597 . -21) T) ((-597 . -25) T) ((-596 . -21) T) ((-45 . -721) T) ((-213 . -526) 104224) ((-596 . -25) T) ((-484 . -155) 104208) ((-471 . -155) 104192) ((-922 . -721) T) ((-768 . -793) T) ((-768 . -794) T) ((-514 . 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-561) 102972) ((-1220 . -921) 102951) ((-583 . -640) 102938) ((-412 . -1097) T) ((-571 . -640) 102925) ((-257 . -1097) T) ((-507 . -640) 102890) ((-216 . -23) T) ((-1220 . -820) 102843) ((-972 . -1097) T) ((-1278 . -105) T) ((-357 . -1275) 102820) ((-1276 . -105) T) ((-1243 . -120) 102670) ((-148 . -611) 102652) ((-1000 . -138) T) ((-49 . -105) T) ((-233 . -847) 102603) ((-1279 . -712) 102573) ((-1230 . -1213) 102552) ((-106 . -502) 102536) ((-1230 . -561) 102447) ((-1205 . -19) 102429) ((-1085 . -52) 102390) ((-1064 . -1109) T) ((-958 . -1109) T) ((-137 . -39) T) ((-131 . -39) T) ((-1209 . -39) T) ((-1207 . -284) 102365) ((-782 . -52) 102342) ((-780 . -52) 102314) ((-1205 . -604) 102289) ((-1165 . -138) T) ((-357 . -373) T) ((-495 . -1109) T) ((-1120 . -138) T) ((-1064 . -23) T) ((-458 . -52) 102268) ((-870 . -367) T) ((-851 . -138) T) ((-156 . -105) T) ((-739 . -456) 102199) ((-958 . -23) T) ((-578 . -561) T) ((-816 . -25) T) ((-816 . -21) T) ((-1134 . -526) 102132) ((-588 . -1043) 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100773) ((-860 . -302) T) ((-1138 . -502) 100757) ((-1085 . -886) NIL) ((-870 . -1109) T) ((-126 . -909) NIL) ((-1278 . -1277) 100733) ((-1276 . -1277) 100712) ((-782 . -886) NIL) ((-780 . -886) 100571) ((-1271 . -25) T) ((-1271 . -21) T) ((-1201 . -105) 100549) ((-1103 . -400) T) ((-618 . -640) 100536) ((-458 . -886) NIL) ((-669 . -105) 100514) ((-1085 . -1043) 100341) ((-870 . -23) T) ((-782 . -1043) 100200) ((-780 . -1043) 100057) ((-126 . -640) 100002) ((-458 . -1043) 99878) ((-641 . -1043) 99862) ((-621 . -105) T) ((-213 . -502) 99846) ((-1258 . -39) T) ((-629 . -712) 99830) ((-605 . -712) 99814) ((-665 . -43) 99774) ((-315 . -105) T) ((-217 . -1097) T) ((-145 . -1097) T) ((-90 . -611) 99756) ((-55 . -1043) 99740) ((-1115 . -1059) 99727) ((-1085 . -382) 99711) ((-782 . -382) 99695) ((-65 . -62) 99657) ((-693 . -794) T) ((-693 . -791) T) ((-584 . -1043) 99644) ((-529 . -1043) 99621) ((-693 . -721) T) ((-322 . -138) T) ((-311 . -1053) 99511) ((-308 . -1053) T) ((-170 . -1109) T) 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. -138) T) ((-1120 . -25) T) ((-1120 . -21) T) ((-851 . -25) T) ((-851 . -21) T) ((-782 . -302) 96629) ((-35 . -37) 96613) ((-1152 . -304) 96408) ((-1149 . -502) 96392) ((-639 . -105) 96370) ((-626 . -105) T) ((-1142 . -155) 96320) ((-578 . -138) T) ((-616 . -845) 96299) ((-1138 . -611) 96261) ((-1138 . -612) 96222) ((-1029 . -791) T) ((-1029 . -794) T) ((-1029 . -721) T) ((-497 . -304) 96160) ((-457 . -422) 96130) ((-354 . -173) T) ((-217 . -526) NIL) ((-145 . -526) NIL) ((-285 . -43) 96117) ((-271 . -105) T) ((-270 . -105) T) ((-269 . -105) T) ((-268 . -105) T) ((-267 . -105) T) ((-266 . -105) T) ((-265 . -105) T) ((-342 . -1043) 96094) ((-205 . -105) T) ((-204 . -105) T) ((-202 . -105) T) ((-201 . -105) T) ((-200 . -105) T) ((-199 . -105) T) ((-196 . -105) T) ((-195 . -105) T) ((-707 . -1059) 95917) ((-194 . -105) T) ((-193 . -105) T) ((-192 . -105) T) ((-191 . -105) T) ((-190 . -105) T) ((-189 . -105) T) ((-188 . -105) T) ((-187 . -105) T) ((-186 . -105) T) ((-357 . -721) T) ((-707 . -120) 95719) ((-665 . -224) 95703) ((-584 . -302) T) ((-529 . -302) T) ((-289 . -526) 95652) ((-112 . -304) NIL) ((-77 . -400) T) ((-1110 . -105) 95442) ((-833 . -416) 95426) ((-1115 . -795) T) ((-1115 . -792) T) ((-695 . -1097) T) ((-384 . -367) T) ((-170 . -505) 95404) ((-213 . -611) 95371) ((-140 . -1097) T) ((-125 . -1097) T) ((-53 . -721) T) ((-1050 . -502) 95336) ((-143 . -430) 95318) ((-143 . -373) T) ((-1033 . -105) T) ((-524 . -521) 95297) ((-484 . -105) T) ((-471 . -105) T) ((-1040 . -1109) T) ((-739 . -1233) 95281) ((-1167 . -40) 95247) ((-1167 . -98) 95213) ((-1167 . -1192) 95179) ((-1167 . -1189) 95145) ((-1166 . -1189) 95111) ((-1151 . -304) NIL) ((-94 . -401) T) ((-94 . -400) T) ((-1079 . -1143) 95090) ((-1166 . -1192) 95056) ((-1166 . -98) 95022) ((-1040 . -23) T) ((-1166 . -40) 94988) ((-578 . -505) T) ((-1159 . -1189) 94954) ((-1159 . -1192) 94920) ((-1159 . -98) 94886) ((-1159 . -40) 94852) ((-365 . -1109) T) ((-363 . -1143) 94831) ((-356 . -1143) 94810) ((-344 . 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. -173) T) ((-101 . -721) T) ((-496 . -105) 92226) ((-101 . -481) T) ((-125 . -173) T) ((-1110 . -43) 92196) ((-170 . -633) 92144) ((-217 . -502) 92126) ((-145 . -502) 92101) ((-1057 . -105) T) ((-870 . -25) T) ((-815 . -231) 92080) ((-870 . -21) T) ((-818 . -105) T) ((-1208 . -304) NIL) ((-419 . -105) T) ((-390 . -105) T) ((-114 . -304) NIL) ((-220 . -105) 92058) ((-137 . -1203) T) ((-131 . -1203) T) ((-1209 . -1203) T) ((-1040 . -138) T) ((-665 . -371) 92042) ((-1253 . -640) 91967) ((-1284 . -721) T) ((-1249 . -149) 91946) ((-1005 . -1053) T) ((-1249 . -151) 91925) ((-1230 . -633) 91873) ((-1242 . -151) 91852) ((-1101 . -611) 91834) ((-1009 . -611) 91816) ((-527 . -23) T) ((-522 . -23) T) ((-342 . -302) T) ((-520 . -23) T) ((-320 . -138) T) ((-3 . -1097) T) ((-1009 . -612) 91800) ((-1005 . -239) 91779) ((-1005 . -226) 91758) ((-1242 . -149) 91737) ((-1241 . -1213) 91716) ((-833 . -1097) T) ((-1221 . -149) 91623) ((-1221 . -151) 91530) ((-1220 . -1213) 91509) ((-1215 . -149) 91488) 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. -886) 90700) ((-1258 . -1203) T) ((-220 . -304) 90638) ((-148 . -373) T) ((-1050 . -612) 90580) ((-1050 . -611) 90523) ((-862 . -1213) T) ((-308 . -909) NIL) ((-779 . -1213) T) ((-1253 . -721) T) ((-693 . -1043) 90468) ((-706 . -921) T) ((-482 . -1213) 90447) ((-1166 . -456) 90426) ((-1159 . -456) 90405) ((-862 . -561) T) ((-329 . -105) T) ((-779 . -561) T) ((-871 . -1109) T) ((-311 . -640) 90226) ((-308 . -640) 90155) ((-482 . -561) 90106) ((-338 . -526) 90072) ((-554 . -155) 90022) ((-45 . -302) T) ((-1163 . -886) NIL) ((-840 . -611) 90004) ((-695 . -286) T) ((-871 . -23) T) ((-384 . -505) T) ((-1079 . -224) 89974) ((-524 . -105) T) ((-412 . -612) 89775) ((-412 . -611) 89757) ((-257 . -611) 89739) ((-125 . -286) T) ((-1163 . -1043) 89619) ((-972 . -611) 89601) ((-1243 . -721) T) ((-1241 . -367) 89580) ((-1220 . -367) 89559) ((-1269 . -39) T) ((-126 . -1203) T) ((-112 . -224) 89541) ((-1171 . -105) T) ((-492 . -1097) T) ((-534 . -502) 89525) ((-739 . -105) T) ((-732 . -39) T) ((-496 . -43) 89495) ((-143 . -39) T) ((-126 . -884) 89472) ((-126 . -886) NIL) ((-618 . -1043) 89355) ((-637 . -847) 89334) ((-1268 . -105) T) ((-290 . -105) T) ((-707 . -373) 89313) ((-126 . -1043) 89290) ((-395 . -712) 89274) ((-1163 . -382) 89258) ((-616 . -712) 89242) ((-50 . -304) 89046) ((-816 . -149) 89025) ((-816 . -151) 89004) ((-1279 . -387) 88983) ((-819 . -847) T) ((-1260 . -1097) T) ((-1249 . -40) 88949) ((-1249 . -98) 88915) ((-1249 . -1192) 88881) ((-1152 . -222) 88828) ((-1249 . -1189) 88794) ((-391 . -847) 88773) ((-1242 . -1189) 88739) ((-1242 . -1192) 88705) ((-1242 . -98) 88671) ((-217 . -682) 88639) ((-145 . -682) 88600) ((-1242 . -40) 88566) ((-1241 . -1109) T) ((-1221 . -1189) 88532) ((-527 . -138) T) ((-1221 . -1192) 88498) ((-1215 . -1192) 88464) ((-1215 . -1189) 88430) ((-1221 . -98) 88396) ((-1221 . -40) 88362) ((-629 . -611) 88331) ((-605 . -611) 88300) ((-33 . -105) T) ((-216 . -847) T) ((-1220 . -1109) T) ((-1215 . -40) 88266) ((-1215 . -98) 88232) ((-1115 . 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-224) 87508) ((-495 . -847) 87487) ((-1151 . -828) T) ((-1134 . -1059) 87471) ((-395 . -758) T) ((-739 . -304) 87458) ((-688 . -1203) T) ((-358 . -561) T) ((-355 . -561) T) ((-343 . -561) T) ((-258 . -561) 87389) ((-243 . -561) 87320) ((-1134 . -120) 87299) ((-457 . -741) 87269) ((-858 . -1059) 87239) ((-817 . -43) 87176) ((-688 . -884) 87158) ((-688 . -886) 87140) ((-290 . -304) 86944) ((-910 . -1213) T) ((-862 . -1109) T) ((-858 . -120) 86909) ((-665 . -416) 86893) ((-779 . -1109) T) ((-688 . -1043) 86838) ((-1149 . -284) 86815) ((-1010 . -456) T) ((-910 . -561) T) ((-584 . -921) T) ((-482 . -1109) T) ((-529 . -921) T) ((-915 . -456) T) ((-217 . -611) 86797) ((-145 . -611) 86779) ((-70 . -611) 86761) ((-862 . -23) T) ((-626 . -222) 86707) ((-779 . -23) T) ((-482 . -23) T) ((-1115 . -794) T) ((-871 . -138) T) ((-1115 . -791) T) ((-1271 . -1273) 86686) ((-1115 . -721) T) ((-647 . -640) 86660) ((-289 . -611) 86401) ((-1041 . -39) T) ((-815 . -845) 86380) ((-583 . -302) T) ((-571 . -302) T) ((-507 . -302) T) ((-1280 . -712) 86350) ((-688 . -382) 86332) ((-688 . -337) 86314) ((-492 . -173) T) ((-386 . -712) 86284) ((-739 . -1143) 86262) ((-870 . -847) NIL) ((-571 . -1027) T) ((-507 . -1027) T) ((-1128 . -611) 86244) ((-1110 . -231) 86223) ((-206 . -105) T) ((-1142 . -105) T) ((-76 . -611) 86205) ((-1134 . -1053) T) ((-1171 . -43) 86102) ((-854 . -611) 86084) ((-571 . -553) T) ((-739 . -43) 85913) ((-665 . -1060) T) ((-726 . -955) 85866) ((-1134 . -226) 85845) ((-1081 . -1097) T) ((-1040 . -25) T) ((-1040 . -21) T) ((-1009 . -1059) 85790) ((-905 . -105) T) ((-858 . -1053) T) ((-775 . -1109) T) ((-688 . -900) NIL) ((-358 . -328) 85774) ((-358 . -367) T) ((-355 . -328) 85758) ((-355 . -367) T) ((-343 . -328) 85742) ((-343 . -367) T) ((-500 . -105) T) ((-1268 . -43) 85712) ((-534 . -682) 85662) ((-209 . -105) T) ((-1029 . -1043) 85542) ((-1009 . -120) 85459) ((-1167 . -980) 85428) ((-1166 . -980) 85390) ((-531 . -155) 85374) ((-1079 . -375) 85353) ((-354 . -611) 85335) 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83833) ((-1166 . -1238) 83817) ((-209 . -1143) T) ((-342 . -921) T) ((-818 . -263) 83801) ((-629 . -120) 83780) ((-605 . -120) 83759) ((-1159 . -1219) 83720) ((-840 . -1053) 83699) ((-1159 . -1235) 83676) ((-527 . -25) T) ((-507 . -297) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-1159 . -1217) 83660) ((-412 . -1053) T) ((-315 . -1060) T) ((-688 . -302) T) ((-112 . -845) T) ((-412 . -239) T) ((-412 . -226) 83639) ((-707 . -721) T) ((-500 . -43) 83589) ((-209 . -43) 83539) ((-482 . -505) 83505) ((-1151 . -1136) T) ((-1098 . -105) T) ((-695 . -611) 83487) ((-695 . -612) 83402) ((-709 . -21) T) ((-709 . -25) T) ((-140 . -611) 83384) ((-125 . -611) 83366) ((-159 . -25) T) ((-1278 . -1097) T) ((-871 . -633) 83314) ((-1276 . -1097) T) ((-970 . -105) T) ((-730 . -105) T) ((-710 . -105) T) ((-457 . -105) T) ((-1205 . -39) T) ((-816 . -456) 83265) ((-49 . -1097) T) ((-1086 . -847) T) ((-659 . -138) T) ((-1065 . -304) 83116) ((-665 . -712) 83100) ((-285 . -1060) T) 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80897) ((-412 . -792) 80876) ((-512 . -502) 80858) ((-1243 . -1043) 80824) ((-1241 . -21) T) ((-1241 . -25) T) ((-1220 . -21) T) ((-1220 . -25) T) ((-815 . -712) 80766) ((-1206 . -105) T) ((-865 . -367) T) ((-860 . -367) T) ((-693 . -409) T) ((-1269 . -1203) T) ((-1110 . -416) 80735) ((-1009 . -373) NIL) ((-106 . -39) T) ((-732 . -1203) T) ((-49 . -758) T) ((-594 . -105) T) ((-82 . -401) T) ((-82 . -400) T) ((-646 . -649) 80719) ((-143 . -1203) T) ((-870 . -151) T) ((-870 . -149) NIL) ((-1253 . -900) 80632) ((-354 . -1053) T) ((-75 . -388) T) ((-75 . -400) T) ((-1158 . -105) T) ((-665 . -526) 80565) ((-684 . -304) 80503) ((-970 . -43) 80400) ((-730 . -43) 80370) ((-554 . -304) 80174) ((-311 . -1203) T) ((-354 . -226) T) ((-354 . -239) T) ((-308 . -1203) T) ((-285 . -1097) T) ((-1173 . -611) 80156) ((-706 . -1213) T) ((-1149 . -643) 80140) ((-1198 . -561) 80119) ((-862 . -25) T) ((-862 . -21) T) ((-706 . -561) T) ((-311 . -884) 80103) ((-311 . -886) 80028) ((-308 . -884) 79989) ((-308 . -886) NIL) ((-799 . -304) 79954) ((-779 . -25) T) ((-315 . -712) 79795) ((-779 . -21) T) ((-322 . -321) 79772) ((-498 . -105) T) ((-482 . -25) T) ((-482 . -21) T) ((-423 . -43) 79746) ((-311 . -1043) 79409) ((-216 . -1189) T) ((-216 . -1192) T) ((-3 . -611) 79391) ((-308 . -1043) 79321) ((-865 . -1109) T) ((-2 . -1097) T) ((-2 . |RecordCategory|) T) ((-860 . -1109) T) ((-833 . -611) 79303) ((-1110 . -1060) 79233) ((-583 . -921) T) ((-571 . -820) T) ((-571 . -921) T) ((-507 . -921) T) ((-142 . -1043) 79217) ((-216 . -98) T) ((-80 . -445) T) ((-80 . -400) T) ((0 . -611) 79199) ((-170 . -151) 79178) ((-170 . -149) 79129) ((-216 . -40) T) ((-54 . -611) 79111) ((-865 . -23) T) ((-492 . -1060) T) ((-860 . -23) T) ((-500 . -224) 79093) ((-497 . -975) 79077) ((-496 . -845) 79056) ((-209 . -224) 79038) ((-86 . -445) T) ((-86 . -400) T) ((-1138 . -39) T) ((-815 . -173) 79017) ((-726 . -105) T) ((-1032 . -611) 78984) ((-512 . -282) 78959) ((-311 . -382) 78928) ((-308 . -382) 78889) ((-308 . -337) 78850) ((-1206 . -304) NIL) ((-816 . -955) 78797) ((-655 . -138) T) ((-1230 . -149) 78776) ((-1230 . -151) 78755) ((-1207 . -1203) T) ((-1167 . -105) T) ((-1166 . -105) T) ((-1159 . -105) T) ((-1152 . -1097) T) ((-1121 . -105) T) ((-213 . -39) T) ((-285 . -712) 78742) ((-1152 . -608) 78718) ((-594 . -304) NIL) ((-1249 . -1248) 78702) ((-1249 . -1235) 78679) ((-497 . -1097) 78657) ((-1242 . -1240) 78618) ((-395 . -611) 78600) ((-522 . -847) T) ((-1142 . -222) 78550) ((-1242 . -1235) 78520) ((-1242 . -1238) 78504) ((-1221 . -1219) 78465) ((-1221 . -1235) 78442) ((-1221 . -1217) 78426) ((-1215 . -1248) 78410) ((-1215 . -1235) 78387) ((-616 . -611) 78369) ((-1167 . -280) 78335) ((-693 . -921) T) ((-1166 . -280) 78301) ((-1159 . -280) 78267) ((-1121 . -280) 78233) ((-1079 . -1097) T) ((-1063 . -1097) T) ((-53 . -297) T) ((-311 . -900) 78199) ((-308 . -900) NIL) ((-1063 . -1069) 78178) ((-1115 . -886) 78160) ((-799 . -43) 78144) ((-258 . -633) 78092) ((-243 . -633) 78040) ((-695 . -1059) 78027) ((-596 . -1235) 78004) ((-1115 . -1043) 77986) ((-315 . -173) 77917) ((-363 . -1097) T) ((-356 . -1097) T) ((-344 . -1097) T) ((-512 . -19) 77899) ((-1099 . -155) 77883) ((-738 . -302) 77862) ((-112 . -1097) T) ((-125 . -1059) 77849) ((-706 . -367) T) ((-512 . -604) 77824) ((-695 . -120) 77809) ((-441 . -105) T) ((-1163 . -921) 77788) ((-50 . -1141) 77738) ((-125 . -120) 77723) ((-219 . -847) T) ((-146 . -847) 77693) ((-629 . -715) T) ((-605 . -715) T) ((-815 . -526) 77626) ((-1041 . -1203) T) ((-949 . -155) 77610) ((-531 . -105) 77560) ((-1085 . -1213) 77539) ((-782 . -1213) 77518) ((-780 . -1213) 77497) ((-67 . -1203) T) ((-492 . -611) 77449) ((-492 . -612) 77371) ((-1165 . -456) 77302) ((-1151 . -1097) T) ((-1134 . -640) 77276) ((-1085 . -561) 77207) ((-496 . -416) 77176) ((-618 . -921) 77155) ((-458 . -1213) 77134) ((-1120 . -456) 77085) ((-782 . -561) 76996) ((-403 . -611) 76978) ((-780 . -561) 76909) ((-669 . -526) 76842) ((-726 . -304) 76829) ((-659 . -25) T) ((-659 . -21) T) ((-458 . -561) 76760) ((-126 . -921) T) ((-126 . -820) NIL) ((-358 . -25) T) ((-358 . -21) T) ((-355 . -25) T) ((-355 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-258 . -25) T) ((-258 . -21) T) ((-88 . -389) T) ((-88 . -400) T) ((-243 . -25) T) ((-243 . -21) T) ((-1260 . -611) 76742) ((-1198 . -1109) T) ((-1198 . -23) T) ((-1159 . -304) 76627) ((-1121 . -304) 76614) ((-1079 . -712) 76482) ((-858 . -640) 76442) ((-949 . -987) 76426) ((-910 . -21) T) ((-285 . -173) T) ((-910 . -25) T) ((-871 . -847) 76377) ((-865 . -138) T) ((-706 . -1109) T) ((-706 . -23) T) ((-639 . -1097) 76355) ((-626 . -608) 76330) ((-626 . -1097) T) ((-584 . -1213) T) ((-529 . -1213) T) ((-584 . -561) T) ((-529 . -561) T) ((-363 . -712) 76282) ((-356 . -712) 76234) ((-344 . -712) 76186) ((-338 . -1059) 76170) ((-174 . -120) 76069) ((-174 . -1059) 76001) ((-112 . -712) 75951) ((-338 . -120) 75930) ((-271 . -1097) T) ((-270 . -1097) T) ((-269 . -1097) T) ((-268 . -1097) T) ((-695 . -1053) T) ((-267 . -1097) T) ((-266 . -1097) T) ((-265 . -1097) T) ((-205 . -1097) T) ((-204 . -1097) T) ((-202 . -1097) T) ((-170 . -1192) 75908) ((-170 . -1189) 75886) ((-201 . -1097) T) ((-200 . -1097) T) ((-125 . -1053) T) ((-199 . -1097) T) ((-196 . -1097) T) ((-695 . -226) T) ((-195 . -1097) T) ((-194 . -1097) T) ((-193 . -1097) T) ((-192 . -1097) T) ((-191 . -1097) T) ((-190 . -1097) T) ((-189 . -1097) T) ((-188 . -1097) T) ((-187 . -1097) T) ((-186 . -1097) T) ((-233 . -105) 75676) ((-170 . -40) 75654) ((-170 . -98) 75632) ((-860 . -138) T) ((-647 . -1043) 75528) ((-496 . -1060) 75458) ((-1134 . -39) T) ((-1110 . -1097) 75248) ((-1084 . -105) T) ((-665 . -502) 75232) ((-78 . -1203) T) ((-109 . -611) 75214) ((-1280 . -611) 75196) ((-386 . -611) 75178) ((-578 . -1192) T) ((-578 . -1189) T) ((-726 . -43) 75027) ((-537 . -611) 75009) ((-531 . -304) 74947) ((-512 . -611) 74929) ((-512 . -612) 74911) ((-1159 . -1143) NIL) ((-1033 . -1072) 74880) ((-1033 . -1097) T) ((-1010 . -105) T) ((-978 . -105) T) ((-915 . -105) T) ((-893 . -1043) 74857) ((-1134 . -721) T) ((-1009 . -640) 74802) ((-484 . -1097) T) ((-471 . -1097) T) ((-588 . -23) T) ((-578 . -40) T) ((-578 . -98) T) ((-432 . -105) T) ((-1065 . -222) 74748) ((-1167 . -43) 74645) ((-858 . -721) T) ((-688 . -921) T) ((-523 . -25) T) ((-519 . -21) T) ((-519 . -25) T) ((-1166 . -43) 74486) ((-338 . -1053) T) ((-1159 . -43) 74282) ((-1079 . -173) T) ((-174 . -1053) T) ((-1121 . -43) 74179) ((-707 . -52) 74156) ((-363 . -173) T) ((-356 . -173) T) ((-530 . -62) 74130) ((-509 . -62) 74080) ((-354 . -1275) 74057) ((-216 . -456) T) ((-315 . -286) 74008) ((-344 . -173) T) ((-174 . -239) T) ((-1220 . -847) 73907) ((-112 . -173) T) ((-871 . -999) 73891) ((-651 . -1109) T) ((-584 . -367) T) ((-584 . -328) 73878) ((-529 . -328) 73855) ((-529 . -367) T) ((-311 . -302) 73834) ((-308 . -302) T) ((-602 . -847) 73813) ((-1110 . -712) 73755) ((-531 . -278) 73739) ((-651 . -23) T) ((-423 . -224) 73723) ((-1204 . -105) T) ((-308 . -1027) NIL) ((-335 . -23) T) 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-526) NIL) ((-529 . -23) T) ((-170 . -414) 72801) ((-216 . -1131) T) ((-1132 . -1097) T) ((-1271 . -1270) 72785) ((-695 . -795) T) ((-695 . -792) T) ((-384 . -151) T) ((-1115 . -302) T) ((-1220 . -999) 72755) ((-53 . -921) T) ((-669 . -502) 72739) ((-245 . -1265) 72709) ((-244 . -1265) 72679) ((-1169 . -847) T) ((-1110 . -173) 72658) ((-1115 . -1027) T) ((-1050 . -39) T) ((-834 . -151) 72637) ((-834 . -149) 72616) ((-732 . -111) 72600) ((-610 . -139) T) ((-496 . -1097) 72390) ((-1171 . -1060) T) ((-870 . -456) T) ((-90 . -1203) T) ((-233 . -43) 72360) ((-143 . -111) 72342) ((-928 . -1095) T) ((-707 . -382) 72326) ((-739 . -1060) T) ((-1115 . -553) T) ((-1204 . -304) NIL) ((-395 . -1059) 72310) ((-1279 . -721) T) ((-1268 . -1060) T) ((-1165 . -955) 72279) ((-57 . -611) 72261) ((-1120 . -955) 72228) ((-646 . -416) 72212) ((-1249 . -105) T) ((-1242 . -105) T) ((-616 . -1059) 72196) ((-655 . -25) T) ((-655 . -21) T) ((-1151 . -526) NIL) ((-1221 . -105) T) ((-1205 . -1203) T) ((-395 . -120) 72175) ((-213 . -248) 72159) ((-1215 . -105) T) ((-1057 . -1097) T) ((-1010 . -1143) T) ((-1057 . -1056) 72099) ((-818 . -1097) T) ((-342 . -1213) T) ((-629 . -640) 72083) ((-616 . -120) 72062) ((-605 . -640) 72046) ((-597 . -105) T) ((-588 . -138) T) ((-596 . -105) T) ((-419 . -1097) T) ((-390 . -1097) T) ((-220 . -1097) 72024) ((-639 . -526) 71957) ((-626 . -526) 71765) ((-833 . -1053) 71744) ((-637 . -155) 71728) ((-342 . -561) T) ((-707 . -900) 71671) ((-554 . -222) 71621) ((-1249 . -280) 71587) ((-1242 . -280) 71553) ((-1079 . -286) 71504) ((-500 . -845) T) ((-214 . -1109) T) ((-1221 . -280) 71470) ((-1215 . -280) 71436) ((-1010 . -43) 71386) ((-209 . -845) T) ((-1198 . -505) 71352) ((-915 . -43) 71304) ((-840 . -794) 71283) ((-840 . -791) 71262) ((-840 . -721) 71241) ((-363 . -286) T) ((-356 . -286) T) ((-344 . -286) T) ((-170 . -456) 71172) ((-432 . -43) 71156) ((-112 . -286) T) ((-214 . -23) T) ((-412 . -794) 71135) ((-412 . -791) 71114) ((-412 . -721) T) ((-512 . -284) 71089) 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-561) T) ((-384 . -1189) T) ((-384 . -1192) T) ((-1041 . -1180) 69780) ((-1177 . -228) 69730) ((-1159 . -224) 69682) ((-1041 . -111) 69628) ((-329 . -1097) T) ((-384 . -98) T) ((-384 . -40) T) ((-865 . -21) T) ((-865 . -25) T) ((-860 . -25) T) ((-492 . -1053) T) ((-541 . -539) 69572) ((-860 . -21) T) ((-493 . -228) 69522) ((-1152 . -502) 69456) ((-1280 . -1059) 69440) ((-386 . -1059) 69424) ((-492 . -239) T) ((-816 . -105) T) ((-709 . -151) 69403) ((-709 . -149) 69382) ((-497 . -502) 69366) ((-1280 . -120) 69345) ((-498 . -334) 69314) ((-1005 . -382) 69298) ((-524 . -1097) T) ((-496 . -173) 69277) ((-1005 . -337) 69261) ((-418 . -105) T) ((-386 . -120) 69240) ((-276 . -990) 69224) ((-275 . -990) 69208) ((-217 . -39) T) ((-145 . -39) T) ((-1208 . -526) NIL) ((-1278 . -611) 69190) ((-1276 . -611) 69172) ((-114 . -526) NIL) ((-1165 . -1233) 69156) ((-851 . -849) 69140) ((-1171 . -1097) T) ((-106 . -1203) T) ((-958 . -955) 69101) ((-739 . -1097) T) ((-817 . -712) 69038) ((-1221 . -1143) NIL) ((-495 . -955) 68983) ((-1064 . -147) T) ((-65 . -105) 68961) ((-49 . -611) 68943) ((-83 . -611) 68925) ((-354 . -640) 68870) ((-1268 . -1097) T) ((-523 . -847) T) ((-342 . -1109) T) ((-290 . -1097) T) ((-1005 . -900) 68829) ((-290 . -608) 68808) ((-1249 . -43) 68705) ((-1242 . -43) 68546) ((-540 . -1095) T) ((-1221 . -43) 68342) ((-500 . -1060) T) ((-1215 . -43) 68239) ((-209 . -1060) T) ((-342 . -23) T) ((-156 . -611) 68221) ((-833 . -795) 68200) ((-833 . -792) 68179) ((-738 . -921) 68158) ((-597 . -43) 68131) ((-596 . -43) 68028) ((-869 . -561) T) ((-214 . -138) T) ((-315 . -1008) 67994) ((-84 . -611) 67976) ((-707 . -302) 67955) ((-289 . -721) 67857) ((-824 . -105) T) ((-857 . -841) T) ((-289 . -481) 67836) ((-1271 . -105) T) ((-45 . -367) T) ((-871 . -151) 67815) ((-33 . -1097) T) ((-871 . -149) 67794) ((-1151 . -502) 67776) ((-1280 . -1053) T) ((-496 . -526) 67709) ((-1138 . -1203) T) ((-971 . -611) 67691) ((-639 . -502) 67675) ((-626 . -502) 67607) ((-815 . -611) 67365) 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66328) ((-1241 . -149) 66307) ((-1033 . -502) 66291) ((-1220 . -149) 66216) ((-1220 . -151) 66141) ((-1271 . -1277) 66120) ((-484 . -502) 66104) ((-471 . -502) 66088) ((-534 . -39) T) ((-646 . -712) 66058) ((-655 . -847) 66037) ((-1171 . -173) 65988) ((-369 . -105) T) ((-233 . -231) 65967) ((-245 . -105) T) ((-244 . -105) T) ((-1230 . -955) 65936) ((-113 . -105) T) ((-241 . -847) 65915) ((-816 . -43) 65764) ((-739 . -173) 65655) ((-50 . -526) 65415) ((-1151 . -282) 65390) ((-206 . -1097) T) ((-1142 . -1097) T) ((-926 . -105) T) ((-1142 . -608) 65369) ((-588 . -25) T) ((-588 . -21) T) ((-1099 . -304) 65307) ((-970 . -416) 65291) ((-693 . -1213) T) ((-626 . -282) 65266) ((-1085 . -633) 65214) ((-782 . -633) 65162) ((-780 . -633) 65110) ((-342 . -138) T) ((-285 . -611) 65092) ((-926 . -925) 65064) ((-693 . -561) T) ((-905 . -1097) T) ((-869 . -1109) T) ((-458 . -633) 65012) ((-905 . -903) 64996) ((-862 . -861) T) ((-862 . -863) T) ((-949 . -304) 64934) ((-384 . -456) T) ((-869 . -23) T) 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-25) T) ((-126 . -561) T) ((-466 . -21) T) ((-458 . -25) T) ((-458 . -21) T) ((-1134 . -1043) 64307) ((-817 . -286) 64286) ((-738 . -435) 64270) ((-823 . -1097) T) ((-665 . -120) 64249) ((-290 . -526) 64009) ((-1278 . -1059) 63993) ((-1276 . -1059) 63977) ((-1241 . -1189) 63943) ((-245 . -304) 63881) ((-244 . -304) 63819) ((-1224 . -105) 63797) ((-1152 . -612) NIL) ((-1152 . -611) 63779) ((-1241 . -1192) 63745) ((-1221 . -224) 63697) ((-1220 . -1189) 63663) ((-1220 . -1192) 63629) ((-1134 . -382) 63613) ((-1115 . -820) T) ((-1115 . -921) T) ((-1110 . -604) 63590) ((-1079 . -612) 63574) ((-541 . -105) T) ((-497 . -611) 63541) ((-815 . -284) 63518) ((-606 . -155) 63465) ((-423 . -1060) T) ((-500 . -712) 63415) ((-496 . -502) 63399) ((-326 . -847) 63378) ((-338 . -640) 63352) ((-55 . -21) T) ((-55 . -25) T) ((-209 . -712) 63302) ((-170 . -719) 63273) ((-174 . -640) 63205) ((-584 . -21) T) ((-584 . -25) T) ((-529 . -25) T) ((-529 . -21) T) ((-483 . -155) 63155) ((-1079 . -611) 63137) 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-612) NIL) ((-1151 . -611) 62451) ((-1065 . -608) 62426) ((-1065 . -1097) T) ((-79 . -445) T) ((-79 . -400) T) ((-665 . -226) 62405) ((-156 . -1059) 62389) ((-578 . -558) 62373) ((-358 . -151) 62352) ((-358 . -149) 62303) ((-355 . -151) 62282) ((-697 . -1097) T) ((-355 . -149) 62233) ((-343 . -151) 62212) ((-343 . -149) 62163) ((-258 . -149) 62142) ((-258 . -151) 62121) ((-245 . -43) 62091) ((-243 . -151) 62070) ((-126 . -367) T) ((-243 . -149) 62049) ((-244 . -43) 62019) ((-156 . -120) 61998) ((-1009 . -1043) 61873) ((-927 . -1095) T) ((-688 . -1213) T) ((-799 . -1060) T) ((-693 . -1109) T) ((-1278 . -1053) T) ((-1276 . -1053) T) ((-1163 . -1109) T) ((-1149 . -1203) T) ((-1009 . -382) 61850) ((-910 . -149) T) ((-910 . -151) 61832) ((-869 . -138) T) ((-815 . -1059) 61729) ((-688 . -561) T) ((-693 . -23) T) ((-639 . -611) 61696) ((-639 . -612) 61657) ((-626 . -612) NIL) ((-626 . -611) 61639) ((-500 . -173) T) ((-214 . -21) T) ((-214 . -25) T) ((-209 . -173) T) ((-482 . -1192) 61605) 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-304) 60411) ((-1120 . -304) 60398) ((-126 . -1109) T) ((-1208 . -682) 60364) ((-819 . -105) T) ((-618 . -23) T) ((-1142 . -526) 60124) ((-391 . -105) T) ((-322 . -105) T) ((-1009 . -900) 60076) ((-970 . -1097) T) ((-156 . -1053) T) ((-126 . -23) T) ((-726 . -416) 60060) ((-730 . -1097) T) ((-710 . -1097) T) ((-697 . -139) T) ((-457 . -1097) T) ((-311 . -435) 60044) ((-412 . -1203) T) ((-1033 . -612) 60005) ((-1033 . -611) 59967) ((-1029 . -1213) T) ((-216 . -105) T) ((-234 . -43) 59913) ((-816 . -224) 59897) ((-1029 . -561) T) ((-833 . -640) 59870) ((-357 . -1213) T) ((-484 . -611) 59832) ((-484 . -612) 59793) ((-471 . -612) 59754) ((-471 . -611) 59716) ((-412 . -884) 59700) ((-315 . -1059) 59535) ((-412 . -886) 59460) ((-840 . -1043) 59356) ((-500 . -526) NIL) ((-496 . -604) 59333) ((-357 . -561) T) ((-209 . -526) NIL) ((-871 . -456) T) ((-423 . -1097) T) ((-412 . -1043) 59197) ((-315 . -120) 59011) ((-688 . -367) T) ((-216 . -280) T) ((-53 . -1213) T) ((-815 . -1053) 58941) ((-583 . -138) T) ((-571 . -138) T) ((-507 . -138) T) ((-53 . -561) T) ((-1152 . -284) 58917) ((-1165 . -1143) 58895) ((-311 . -27) 58874) ((-1064 . -105) T) ((-815 . -226) 58826) ((-233 . -845) 58805) ((-958 . -105) T) ((-708 . -105) T) ((-290 . -502) 58742) ((-495 . -105) T) ((-726 . -1060) T) ((-610 . -611) 58724) ((-610 . -612) 58585) ((-412 . -382) 58569) ((-412 . -337) 58553) ((-1165 . -43) 58382) ((-1120 . -43) 58231) ((-851 . -43) 58201) ((-395 . -640) 58185) ((-637 . -304) 58123) ((-1208 . -611) 58105) ((-970 . -712) 58002) ((-730 . -712) 57972) ((-213 . -111) 57956) ((-50 . -282) 57881) ((-616 . -640) 57855) ((-306 . -1097) T) ((-285 . -1059) 57842) ((-114 . -611) 57824) ((-114 . -612) 57806) ((-457 . -712) 57776) ((-816 . -247) 57715) ((-684 . -1097) 57693) ((-554 . -1097) T) ((-1167 . -1060) T) ((-1166 . -1060) T) ((-285 . -120) 57678) ((-1159 . -1060) T) ((-1121 . -1060) T) ((-554 . -608) 57657) ((-1010 . -845) T) ((-220 . -682) 57615) ((-688 . -1109) T) ((-1198 . -735) 57591) 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. -712) 24384) ((-1084 . -120) 24349) ((-1040 . -1060) T) ((-495 . -526) 24287) ((-949 . -19) 24271) ((-949 . -604) 24248) ((-816 . -612) NIL) ((-816 . -611) 24230) ((-1010 . -1059) 24180) ((-418 . -611) 24162) ((-245 . -282) 24139) ((-244 . -282) 24116) ((-500 . -909) NIL) ((-311 . -29) 24086) ((-112 . -1203) T) ((-1009 . -1109) T) ((-209 . -909) NIL) ((-915 . -1059) 24038) ((-1207 . -847) T) ((-1079 . -1043) 23934) ((-1010 . -120) 23861) ((-732 . -689) 23845) ((-258 . -224) 23829) ((-432 . -1059) 23813) ((-384 . -1060) T) ((-1009 . -23) T) ((-915 . -120) 23744) ((-688 . -1192) NIL) ((-500 . -640) 23694) ((-112 . -884) 23676) ((-112 . -886) 23658) ((-688 . -1189) NIL) ((-209 . -640) 23608) ((-363 . -1043) 23592) ((-356 . -1043) 23576) ((-326 . -304) 23514) ((-344 . -1043) 23498) ((-216 . -286) T) ((-432 . -120) 23477) ((-65 . -611) 23444) ((-170 . -173) T) ((-1115 . -847) T) ((-112 . -1043) 23404) ((-892 . -1097) T) ((-834 . -1060) T) ((-827 . -1060) T) ((-688 . -40) NIL) ((-688 . 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127291) ((-116 . -1098) T) ((-53 . -1098) T) ((-708 . -225) 127275) ((-871 . -901) NIL) ((-1231 . -887) NIL) ((-890 . -105) T) ((-886 . -105) T) ((-394 . -1098) T) ((-171 . -383) 127259) ((-171 . -338) 127243) ((-1231 . -1044) 127123) ((-853 . -1044) 127019) ((-1135 . -105) T) ((-647 . -138) T) ((-126 . -527) 126882) ((-656 . -793) 126861) ((-656 . -796) 126840) ((-579 . -1044) 126822) ((-290 . -1266) 126792) ((-859 . -105) T) ((-971 . -562) 126771) ((-1199 . -1060) 126654) ((-497 . -634) 126560) ((-905 . -1098) T) ((-1030 . -713) 126497) ((-707 . -1060) 126462) ((-863 . -641) 126414) ((-780 . -641) 126366) ((-603 . -39) T) ((-1140 . -1204) T) ((-1199 . -120) 126228) ((-483 . -641) 126125) ((-358 . -713) 126070) ((-171 . -901) 126029) ((-694 . -287) T) ((-739 . -1061) T) ((-689 . -174) T) ((-707 . -120) 125978) ((-1285 . -1061) T) ((-1231 . -383) 125962) ((-424 . -1214) 125940) ((-309 . -846) NIL) ((-424 . -562) T) ((-217 . -303) T) ((-1221 . -792) 125893) ((-1221 . -795) 125846) ((-33 . -1096) T) ((-1242 . -722) T) ((-1221 . -722) T) ((-53 . -713) 125811) ((-1164 . -287) 125722) ((-217 . -1028) T) ((-355 . -1266) 125699) ((-1244 . -417) 125665) ((-714 . -722) T) ((-1231 . -901) 125608) ((-121 . -612) 125590) ((-121 . -613) 125572) ((-714 . -482) T) ((-497 . -21) 125482) ((-137 . -503) 125466) ((-131 . -503) 125450) ((-497 . -25) 125301) ((-619 . -287) T) ((-780 . -39) T) ((-1210 . -503) 125283) ((-589 . -1060) 125258) ((-1209 . -62) 125224) ((-443 . -1098) T) ((-1065 . -303) T) ((-126 . -287) T) ((-1102 . -105) T) ((-1010 . -105) T) ((-589 . -120) 125185) ((-1254 . -1061) T) ((-1135 . -305) 125123) ((-1199 . -1054) T) ((-1065 . -1028) T) ((-71 . -1204) T) ((-1058 . -25) T) ((-1058 . -21) T) ((-707 . -1054) T) ((-391 . -21) T) ((-391 . -25) T) ((-689 . -527) NIL) ((-1030 . -174) T) ((-707 . -240) T) ((-1065 . -554) T) ((-863 . -722) T) ((-780 . -722) T) ((-515 . -105) T) ((-358 . -174) T) ((-343 . -612) 125105) ((-400 . -612) 125087) ((-483 . -722) T) ((-1116 . -846) T) ((-893 . -1044) 125055) ((-112 . -848) T) ((-652 . -1060) 125039) ((-501 . -138) T) ((-1244 . -1061) T) ((-210 . -138) T) ((-238 . -1060) 125021) ((-1150 . -105) 124999) ((-101 . -1098) T) ((-242 . -662) 124983) ((-242 . -644) 124967) ((-652 . -120) 124946) ((-312 . -417) 124930) ((-242 . -379) 124914) ((-1153 . -229) 124861) ((-1006 . -225) 124845) ((-238 . -120) 124820) ((-79 . -1204) T) ((-53 . -174) T) ((-696 . -393) T) ((-696 . -147) T) ((-1280 . -105) T) ((-1086 . -1060) 124663) ((-259 . -910) 124642) ((-244 . -910) 124621) ((-783 . -1060) 124444) ((-781 . -1060) 124287) ((-607 . -1204) T) ((-1158 . -612) 124269) ((-1086 . -120) 124091) ((-1051 . -105) T) ((-484 . -1204) T) ((-467 . -1060) 124062) ((-459 . -1060) 123905) ((-660 . -641) 123889) ((-871 . -303) T) ((-783 . -120) 123691) ((-781 . -120) 123513) ((-359 . -641) 123465) ((-356 . -641) 123417) ((-344 . -641) 123369) ((-259 . -641) 123294) ((-244 . -641) 123219) ((-1152 . -848) T) ((-467 . -120) 123180) ((-459 . -120) 123002) ((-1087 . -1044) 122986) ((-1076 . -1044) 122963) ((-1007 . -39) T) ((-965 . -1204) T) ((-136 . -1017) 122947) ((-971 . -1110) T) ((-871 . -1028) NIL) ((-731 . -1110) T) ((-711 . -1110) T) ((-1259 . -503) 122931) ((-1135 . -43) 122891) ((-971 . -23) T) ((-911 . -641) 122856) ((-841 . -105) T) ((-818 . -21) T) ((-818 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-114 . -655) T) ((-776 . -722) T) ((-585 . -1060) 122821) ((-530 . -1060) 122766) ((-221 . -62) 122724) ((-458 . -23) T) ((-413 . -105) T) ((-258 . -105) T) ((-776 . -482) T) ((-973 . -105) T) ((-689 . -287) T) ((-859 . -43) 122694) ((-1210 . -283) 122669) ((-585 . -120) 122618) ((-530 . -120) 122535) ((-740 . -634) 122483) ((-424 . -1110) T) ((-312 . -1061) 122373) ((-309 . -1061) T) ((-928 . -612) 122355) ((-739 . -1098) T) ((-652 . -1054) T) ((-1285 . -1098) T) ((-171 . -303) 122286) ((-424 . -23) T) ((-45 . -612) 122268) ((-45 . -613) 122252) ((-112 . -1000) 122234) ((-125 . -869) 122218) ((-53 . -527) 122184) 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-21) T) ((-1051 . -305) 121458) ((-1269 . -21) T) ((-1269 . -25) T) ((-902 . -1098) 121436) ((-55 . -1054) T) ((-1254 . -1098) T) ((-1168 . -562) 121415) ((-1167 . -1214) 121394) ((-1167 . -562) 121345) ((-1160 . -1214) 121324) ((-585 . -1054) T) ((-530 . -1054) T) ((-517 . -105) T) ((-1030 . -287) T) ((-366 . -1044) 121308) ((-321 . -1044) 121292) ((-261 . -1098) 121270) ((-385 . -887) 121252) ((-1160 . -562) 121203) ((-1122 . -562) 121182) ((-1010 . -43) 121127) ((-800 . -1110) T) ((-911 . -722) T) ((-585 . -240) T) ((-585 . -227) T) ((-530 . -227) T) ((-530 . -240) T) ((-739 . -713) 121051) ((-358 . -287) T) ((-640 . -690) 121035) ((-385 . -1044) 120995) ((-261 . -260) 120979) ((-1116 . -1061) T) ((-106 . -135) 120963) ((-800 . -23) T) ((-1279 . -1274) 120939) ((-1277 . -1274) 120918) ((-1259 . -283) 120895) ((-413 . -305) 120860) ((-1244 . -1098) T) ((-1164 . -283) 120787) ((-870 . -612) 120769) ((-835 . -1044) 120738) ((-197 . -788) T) ((-196 . -788) T) ((-34 . -37) 120715) ((-195 . -788) T) ((-194 . -788) T) ((-193 . -788) T) ((-192 . -788) T) ((-191 . -788) T) ((-190 . -788) T) ((-189 . -788) T) ((-188 . -788) T) ((-508 . -1009) T) ((-272 . -837) T) ((-271 . -837) T) ((-270 . -837) T) ((-269 . -837) T) ((-53 . -287) T) ((-268 . -837) T) ((-267 . -837) T) ((-266 . -837) T) ((-187 . -788) T) ((-611 . -848) T) ((-648 . -417) 120699) ((-114 . -848) T) ((-647 . -21) T) ((-647 . -25) T) ((-468 . -612) 120681) ((-1280 . -43) 120651) ((-1259 . -19) 120635) ((-126 . -283) 120565) ((-218 . -105) T) ((-145 . -105) T) ((-1259 . -605) 120542) ((-1270 . -1098) T) ((-1254 . -713) 120439) ((-1077 . -1098) T) ((-995 . -1098) T) ((-971 . -138) T) ((-733 . -1098) T) ((-731 . -138) T) ((-711 . -138) T) ((-524 . -794) T) ((-413 . -1144) 120417) ((-458 . -138) T) ((-524 . -795) T) ((-215 . -1054) T) ((-290 . -105) 120199) ((-143 . -1098) T) ((-694 . -1009) T) ((-96 . -1204) T) ((-137 . -612) 120166) ((-131 . -612) 120133) ((-739 . -174) T) ((-1285 . -174) T) ((-1210 . -613) 120115) ((-1210 . -612) 120097) ((-1167 . -368) 120076) ((-1160 . -368) 120055) ((-312 . -1098) T) ((-424 . -138) T) ((-309 . -1098) T) ((-413 . -43) 120007) ((-1129 . -105) T) ((-1244 . -713) 119864) ((-648 . -1061) T) ((-316 . -149) 119843) ((-316 . -151) 119822) ((-142 . -1098) T) ((-123 . -1098) T) ((-855 . -105) T) ((-584 . -612) 119804) ((-572 . -613) 119703) ((-572 . -612) 119685) ((-508 . -612) 119667) ((-508 . -613) 119612) ((-499 . -23) T) ((-497 . -848) 119563) ((-118 . -1098) T) ((-501 . -634) 119545) ((-780 . -1017) 119497) ((-210 . -634) 119479) ((-217 . -410) T) ((-656 . -641) 119463) ((-1166 . -922) 119442) ((-727 . -1110) T) ((-355 . -105) T) ((-819 . -848) T) ((-727 . -23) T) ((-343 . -1060) 119387) ((-1152 . -1151) T) ((-1140 . -111) 119371) ((-1254 . -174) 119322) ((-1168 . -1110) T) ((-1167 . -1110) T) ((-1160 . -1110) T) ((-1122 . -1110) T) ((-528 . -1044) 119306) ((-343 . -120) 119223) ((-218 . -305) NIL) ((-145 . -305) NIL) ((-1011 . -1214) T) ((-136 . -1204) T) ((-916 . -1214) T) ((-1260 . -612) 119205) ((-1208 . -1098) T) ((-689 . -283) NIL) ((-1168 . -23) T) ((-1167 . -23) T) ((-1160 . -23) T) ((-1135 . -225) 119189) ((-1122 . -23) T) ((-1075 . -1098) T) ((-1011 . -562) T) ((-916 . -562) T) ((-800 . -138) T) ((-220 . -1204) T) ((-146 . -1204) T) ((-739 . -527) 119155) ((-706 . -612) 119137) ((-34 . -1098) T) ((-312 . -713) 119047) ((-309 . -713) 118976) ((-694 . -612) 118958) ((-694 . -613) 118903) ((-413 . -406) 118887) ((-444 . -1098) T) ((-501 . -25) T) ((-501 . -21) T) ((-1116 . -1098) T) ((-210 . -25) T) ((-210 . -21) T) ((-708 . -417) 118871) ((-710 . -1044) 118840) ((-1259 . -612) 118779) ((-1259 . -613) 118740) ((-1244 . -174) T) ((-242 . -39) T) ((-1164 . -613) NIL) ((-1164 . -612) 118722) ((-932 . -982) T) ((-1191 . -1204) T) ((-656 . -792) 118701) ((-656 . -795) 118680) ((-404 . -401) T) ((-535 . -105) 118658) ((-1042 . -1098) T) ((-214 . -1002) 118642) ((-518 . -105) T) ((-619 . -612) 118624) ((-50 . -848) NIL) ((-619 . -613) 118601) ((-1042 . -609) 118576) ((-902 . -527) 118509) ((-343 . -1054) T) ((-130 . -612) 118491) ((-126 . -613) NIL) ((-126 . -612) 118473) ((-872 . -1204) T) ((-666 . -423) 118457) ((-666 . -1119) 118402) ((-261 . -527) 118335) ((-513 . -155) 118317) ((-343 . -227) T) ((-343 . -240) T) ((-45 . -1060) 118262) ((-872 . -885) 118246) ((-872 . -887) 118171) ((-708 . -1061) T) ((-689 . -1009) NIL) ((-1242 . -52) 118141) ((-1221 . -52) 118118) ((-1134 . -1017) 118089) ((-1116 . -713) 118076) ((-1103 . -612) 118058) ((-872 . -1044) 117922) ((-217 . -922) T) ((-45 . -120) 117839) ((-739 . -287) T) ((-1080 . -151) 117818) ((-1080 . -149) 117769) ((-1011 . -368) T) ((-866 . -641) 117734) ((-861 . -641) 117684) ((-316 . -1193) 117650) ((-385 . -303) T) ((-316 . -1190) 117616) ((-312 . -174) 117595) ((-309 . -174) T) ((-1010 . -225) 117572) ((-916 . -368) T) ((-585 . -1276) 117559) ((-530 . -1276) 117536) ((-364 . -151) 117515) ((-364 . -149) 117466) ((-357 . -151) 117445) ((-357 . -149) 117396) ((-607 . -1181) 117372) ((-345 . -151) 117351) ((-345 . -149) 117302) ((-316 . -40) 117268) ((-484 . -1181) 117247) ((0 . |EnumerationCategory|) T) ((-316 . -98) 117213) ((-385 . -1028) T) ((-112 . -151) T) ((-112 . -149) NIL) ((-50 . -229) 117163) ((-648 . -1098) T) ((-607 . -111) 117110) ((-499 . -138) T) ((-484 . -111) 117060) ((-234 . -1110) 116970) ((-1085 . -1110) T) ((-872 . -383) 116954) ((-872 . -338) 116938) ((-234 . -23) 116808) ((-1065 . -922) T) ((-1065 . -821) T) ((-585 . -374) T) ((-530 . -374) T) ((-740 . -848) 116787) ((-1210 . -285) 116762) ((-355 . -1144) T) ((-327 . -39) T) ((-49 . -423) 116746) ((-1085 . -23) T) ((-396 . -742) 116730) ((-1270 . -527) 116663) ((-727 . -138) T) ((-1254 . -287) 116642) ((-1250 . -562) 116621) ((-1243 . -1214) 116600) ((-1243 . -562) 116551) ((-1222 . -1214) 116530) ((-1222 . -562) 116481) ((-733 . -527) 116414) ((-1221 . -1204) 116393) ((-1221 . -887) 116266) ((-894 . -1098) T) ((-148 . -842) T) ((-1221 . -885) 116236) ((-1216 . -562) 116215) ((-1168 . -138) T) ((-535 . -305) 116153) ((-1167 . -138) T) ((-143 . -527) NIL) ((-1160 . -138) T) ((-1122 . -138) T) ((-1030 . -1009) T) ((-1011 . -23) T) ((-355 . -43) 116118) ((-1011 . -1110) T) ((-916 . -1110) T) ((-87 . -612) 116100) ((-45 . -1054) T) ((-870 . -1060) 116087) ((-872 . -901) 116046) ((-780 . -52) 116023) ((-696 . -105) T) ((-1010 . -353) NIL) ((-603 . -1204) T) ((-979 . -23) T) ((-916 . -23) T) ((-870 . -120) 116008) ((-433 . -1110) T) ((-483 . -52) 115978) ((-140 . -105) T) ((-45 . -227) 115950) ((-45 . -240) T) ((-125 . -105) T) ((-598 . -562) 115929) ((-597 . -562) 115908) ((-689 . -612) 115890) ((-689 . -613) 115798) ((-312 . -527) 115764) ((-309 . -527) 115515) ((-1242 . -1044) 115499) ((-1221 . -1044) 115285) ((-1006 . -417) 115269) ((-433 . -23) T) ((-1116 . -174) T) ((-866 . -722) T) ((-861 . -722) T) ((-1244 . -287) T) ((-648 . -713) 115239) ((-148 . -1098) T) ((-53 . -1009) T) ((-413 . -225) 115223) ((-291 . -229) 115173) ((-871 . -922) T) ((-871 . -821) NIL) ((-975 . -612) 115155) ((-858 . -848) T) ((-1221 . -338) 115125) ((-1221 . -383) 115095) ((-214 . -1117) 115079) ((-780 . -1204) T) ((-1259 . -285) 115056) ((-504 . -105) T) ((-1199 . -641) 114981) ((-971 . -21) T) ((-971 . -25) T) ((-731 . -21) T) ((-731 . -25) T) ((-711 . -21) T) ((-711 . -25) T) ((-707 . -641) 114946) ((-458 . -21) T) ((-458 . -25) T) ((-339 . -105) T) ((-175 . -105) T) ((-1006 . -1061) T) ((-870 . -1054) T) ((-863 . -1044) 114930) ((-772 . -105) T) ((-1208 . -527) NIL) ((-1243 . -368) 114909) ((-1242 . -901) 114815) ((-1222 . -368) 114794) ((-1221 . -901) 114645) ((-1030 . -612) 114627) ((-413 . -829) 114580) ((-1168 . -506) 114546) ((-171 . -922) 114477) ((-1167 . -506) 114443) ((-1160 . -506) 114409) ((-708 . -1098) T) ((-1122 . -506) 114375) ((-584 . -1060) 114362) ((-572 . -1060) 114349) ((-508 . -1060) 114314) ((-312 . -287) 114293) ((-309 . -287) T) ((-358 . -612) 114275) ((-424 . -25) T) ((-424 . -21) T) ((-101 . -283) 114254) ((-584 . -120) 114239) 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97638) ((-727 . -149) 97617) ((-1030 . -641) 97554) ((-535 . -1098) 97532) ((-364 . -105) T) ((-357 . -105) T) ((-345 . -105) T) ((-235 . -21) T) ((-235 . -25) T) ((-112 . -105) T) ((-518 . -1098) T) ((-358 . -641) 97477) ((-1166 . -634) 97425) ((-1121 . -634) 97373) ((-391 . -522) 97352) ((-834 . -846) 97331) ((-385 . -1214) T) ((-689 . -722) T) ((-339 . -1061) T) ((-1222 . -1000) 97283) ((-175 . -1061) T) ((-106 . -612) 97250) ((-1168 . -149) 97229) ((-1168 . -151) 97208) ((-385 . -562) T) ((-1167 . -151) 97187) ((-1167 . -149) 97166) ((-1160 . -149) 97073) ((-413 . -287) T) ((-1160 . -151) 96980) ((-1122 . -151) 96959) ((-1122 . -149) 96938) ((-316 . -43) 96779) ((-171 . -138) T) ((-309 . -796) NIL) ((-309 . -793) NIL) ((-648 . -1054) T) ((-53 . -641) 96744) ((-1001 . -21) T) ((-137 . -1017) 96728) ((-131 . -1017) 96712) ((-1001 . -25) T) ((-902 . -128) 96696) ((-1152 . -105) T) ((-817 . -848) 96675) ((-1231 . -138) T) ((-1206 . -285) 96650) ((-1166 . -25) T) ((-1166 . -21) T) 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. -229) 93650) ((-69 . -402) T) ((-69 . -401) T) ((-114 . -105) T) ((-45 . -383) 93627) ((-35 . -1098) T) ((-1208 . -644) 93609) ((-647 . -850) 93593) ((-1208 . -379) 93575) ((-1065 . -21) T) ((-1065 . -25) T) ((-816 . -225) 93544) ((-959 . -25) T) ((-959 . -21) T) ((-617 . -1061) T) ((-496 . -25) T) ((-496 . -21) T) ((-1034 . -305) 93482) ((-890 . -612) 93464) ((-886 . -612) 93446) ((-246 . -848) 93397) ((-245 . -848) 93348) ((-535 . -527) 93281) ((-871 . -634) 93258) ((-485 . -305) 93196) ((-472 . -305) 93134) ((-355 . -287) T) ((-1150 . -1246) 93118) ((-1135 . -612) 93080) ((-1135 . -613) 93041) ((-1133 . -105) T) ((-1006 . -1060) 92937) ((-45 . -901) 92889) ((-1150 . -605) 92866) ((-739 . -641) 92790) ((-1285 . -641) 92777) ((-1066 . -155) 92723) ((-872 . -1214) T) ((-1006 . -120) 92598) ((-339 . -713) 92582) ((-859 . -612) 92564) ((-175 . -713) 92496) ((-413 . -283) 92454) ((-872 . -562) T) ((-112 . -406) 92436) ((-89 . -390) T) ((-89 . -401) T) ((-866 . -922) T) ((-861 . -922) T) 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91488) ((-1216 . -151) 91467) ((-739 . -482) 91446) ((-739 . -722) T) ((-385 . -138) T) ((-572 . -887) 91428) ((0 . -1098) T) ((-175 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-54 . -1098) T) ((-1244 . -641) 91317) ((-1242 . -562) 91268) ((-710 . -1110) T) ((-1221 . -562) 91219) ((-572 . -1044) 91201) ((-597 . -151) 91180) ((-597 . -149) 91159) ((-508 . -1044) 91102) ((-92 . -390) T) ((-92 . -401) T) ((-872 . -368) T) ((-1164 . -52) 91079) ((-835 . -138) T) ((-828 . -138) T) ((-710 . -23) T) ((-515 . -612) 91061) ((-1281 . -1061) T) ((-385 . -1063) T) ((-1033 . -1098) 91039) ((-902 . -39) T) ((-497 . -305) 90977) ((-1150 . -613) 90938) ((-1150 . -612) 90905) ((-261 . -39) T) ((-1166 . -848) 90884) ((-50 . -105) T) ((-1121 . -848) 90863) ((-818 . -105) T) ((-1231 . -25) T) ((-1231 . -21) T) ((-853 . -25) T) ((-49 . -372) 90847) ((-853 . -21) T) ((-727 . -457) 90798) ((-1280 . -612) 90780) ((-579 . -25) T) ((-579 . -21) T) ((-396 . -1098) T) ((-1058 . -305) 90718) ((-617 . -1098) T) 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. -383) 81761) ((-53 . -1028) T) ((-1221 . -634) 81669) ((-685 . -105) 81647) ((-49 . -713) 81631) ((-555 . -105) T) ((-72 . -389) T) ((-261 . -1204) T) ((-72 . -401) T) ((-35 . -612) 81613) ((-656 . -23) T) ((-666 . -759) T) ((-1202 . -1098) 81591) ((-355 . -1060) 81536) ((-670 . -1098) 81514) ((-1065 . -151) T) ((-959 . -151) 81493) ((-959 . -149) 81472) ((-800 . -105) T) ((-156 . -713) 81456) ((-496 . -151) 81435) ((-496 . -149) 81414) ((-355 . -120) 81331) ((-1080 . -1061) T) ((-321 . -848) 81310) ((-974 . -1096) T) ((-1250 . -981) 81279) ((-1243 . -981) 81241) ((-1222 . -981) 81210) ((-622 . -1098) T) ((-739 . -901) 81191) ((-524 . -138) T) ((-520 . -138) T) ((-291 . -223) 81141) ((-364 . -1061) T) ((-357 . -1061) T) ((-345 . -1061) T) ((-290 . -1054) 81083) ((-1216 . -981) 81052) ((-385 . -848) T) ((-112 . -1061) T) ((-1006 . -722) T) ((-870 . -922) T) ((-841 . -796) 81031) ((-841 . -793) 81010) ((-424 . -305) 80949) ((-477 . -105) T) ((-597 . -981) 80918) ((-316 . -1098) T) 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. -105) T) ((-916 . -105) T) ((-894 . -1044) 74857) ((-1135 . -722) T) ((-1010 . -641) 74802) ((-485 . -1098) T) ((-472 . -1098) T) ((-589 . -23) T) ((-579 . -40) T) ((-579 . -98) T) ((-433 . -105) T) ((-1066 . -223) 74748) ((-1168 . -43) 74645) ((-859 . -722) T) ((-689 . -922) T) ((-524 . -25) T) ((-520 . -21) T) ((-520 . -25) T) ((-1167 . -43) 74486) ((-339 . -1054) T) ((-1160 . -43) 74282) ((-1080 . -174) T) ((-175 . -1054) T) ((-1122 . -43) 74179) ((-708 . -52) 74156) ((-364 . -174) T) ((-357 . -174) T) ((-531 . -62) 74130) ((-510 . -62) 74080) ((-355 . -1276) 74057) ((-217 . -457) T) ((-316 . -287) 74008) ((-345 . -174) T) ((-175 . -240) T) ((-1221 . -848) 73907) ((-112 . -174) T) ((-872 . -1000) 73891) ((-652 . -1110) T) ((-585 . -368) T) ((-585 . -329) 73878) ((-530 . -329) 73855) ((-530 . -368) T) ((-312 . -303) 73834) ((-309 . -303) T) ((-603 . -848) 73813) ((-1111 . -713) 73755) ((-532 . -279) 73739) ((-652 . -23) T) ((-424 . -225) 73723) ((-1205 . -105) T) ((-309 . -1028) 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. -23) T) ((-112 . -527) NIL) ((-530 . -23) T) ((-171 . -415) 72801) ((-217 . -1132) T) ((-1133 . -1098) T) ((-1272 . -1271) 72785) ((-696 . -796) T) ((-696 . -793) T) ((-385 . -151) T) ((-1116 . -303) T) ((-1221 . -1000) 72755) ((-53 . -922) T) ((-670 . -503) 72739) ((-246 . -1266) 72709) ((-245 . -1266) 72679) ((-1170 . -848) T) ((-1111 . -174) 72658) ((-1116 . -1028) T) ((-1051 . -39) T) ((-835 . -151) 72637) ((-835 . -149) 72616) ((-733 . -111) 72600) ((-611 . -139) T) ((-497 . -1098) 72390) ((-1172 . -1061) T) ((-871 . -457) T) ((-90 . -1204) T) ((-234 . -43) 72360) ((-143 . -111) 72342) ((-929 . -1096) T) ((-708 . -383) 72326) ((-740 . -1061) T) ((-1116 . -554) T) ((-1205 . -305) NIL) ((-396 . -1060) 72310) ((-1280 . -722) T) ((-1269 . -1061) T) ((-1166 . -956) 72279) ((-57 . -612) 72261) ((-1121 . -956) 72228) ((-647 . -417) 72212) ((-1250 . -105) T) ((-1243 . -105) T) ((-617 . -1060) 72196) ((-656 . -25) T) ((-656 . -21) T) ((-1152 . -527) NIL) ((-1222 . -105) T) ((-1206 . 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. -722) T) ((-112 . -910) NIL) ((-685 . -612) 40119) ((-685 . -613) 40080) ((-1080 . -641) 39990) ((-602 . -612) 39972) ((-555 . -613) NIL) ((-555 . -612) 39954) ((-1160 . -283) 39802) ((-501 . -1060) 39752) ((-707 . -457) T) ((-524 . -522) 39731) ((-520 . -522) 39710) ((-210 . -1060) 39660) ((-364 . -641) 39612) ((-357 . -641) 39564) ((-217 . -846) T) ((-345 . -641) 39516) ((-603 . -105) 39466) ((-497 . -374) 39445) ((-112 . -641) 39395) ((-501 . -120) 39322) ((-234 . -503) 39306) ((-343 . -151) 39288) ((-343 . -149) T) ((-171 . -376) 39259) ((-950 . -1257) 39243) ((-210 . -120) 39170) ((-872 . -305) 39135) ((-950 . -1098) 39085) ((-800 . -613) 39046) ((-800 . -612) 39028) ((-714 . -105) T) ((-331 . -1098) T) ((-1116 . -138) T) ((-710 . -43) 38998) ((-312 . -506) 38977) ((-513 . -1204) T) ((-1242 . -281) 38943) ((-1221 . -281) 38909) ((-327 . -155) 38893) ((-1066 . -285) 38868) ((-1272 . -713) 38838) ((-1153 . -39) T) ((-1281 . -1044) 38815) ((-739 . -634) 38721) ((-477 . -612) 38703) 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|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&| 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|FiniteFieldNormalBasisExtension| |FiniteField| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteFieldExtension| |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite&| |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&| 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|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&| 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|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| |FiniteFieldFactorization| |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&| |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| |ModularAlgebraicGcdOperations| |Magma| |MatrixManipulation| |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| |U32VectorPolynomialOperations| |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| |StochasticDifferential| |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| |StreamTensor| |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| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U8Matrix| |U8Vector| |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| |pointColorPalette| |acoshIfCan| |bivariateSLPEBR| |coerceP| |filterUpTo| |resetVariableOrder| |primitive?| |setErrorBound| |cRationalPower| |setOfMinN| |nullSpace| |solid| |node?| |squareMatrix| |fortranLinkerArgs| |irreducibleFactor| |zCoord| |deleteRoutine!| |translateToOrigin| |fractRadix| |lfintegrate| |top!| |call| |homogeneous| |withPredicates| |elem?| |representationType| |retract| |exptMod| |univariatePolynomialsGcds| |maxPower| |trace2PowMod| |subResultantChain| = |repeatUntilLoop| |sechIfCan| |fresnelC| |linearPart| |resetBadValues| |contractSolve| |nsqfree| |double| |nthCoef| < |insert!| |inGroundField?| |tower| > |subscript| |mapmult| |transform| |zero?| <= |clipSurface| |cyclotomicDecomposition| |mainVariable?| |pole?| |bit?| >= |uniform| |rotatex| |child| |sincos| |structuralConstants| |scale| |nextSubsetGray| |btwFact| |generalPosition| |vedf2vef| |vark| |nodeOf?| |transcendentalDecompose| |element?| |new| |middle| |purelyAlgebraic?| + |rk4qc| |mat| |OMopenFile| |iipolygamma| |subresultantSequence| - |setStatus| |polCase| |mix| |removeSquaresIfCan| |chiSquare1| / |hyperelliptic| |polyRing2UPUP| |supDimElseRittWu?| |powers| |rightFactorIfCan| |iicosh| |Is| |plus!| |fortranCharacter| |maxSubst| |iiasech| |close!| |identityMatrix| |iiBesselY| |ParCond| |getZechTable| |figureUnits| |antiCommutator| |yCoord| |normFactors| |coshIfCan| |generalSqFr| |alterDrift!| |normalise| |primintegrate| |rowEch| |makeSin| |radicalEigenvector| |numberOfChildren| |OMgetEndBind| |numFunEvals3D| |ffactor| |satisfy?| |projectivePoint| |reducedForm| |summation| |expandPower| |ldf2lst| |ramified?| |factorset| |scalarTypeOf| |nonLinearPart| |splitNodeOf!| |ode1| |setAttributeButtonStep| |sPol| |primlimintfrac| |stoseInvertibleSet| |open| |factorByRecursion| |numberOfDivisors| |root| |genericRightDiscriminant| |certainlySubVariety?| |qfactor| |mindegTerm| |dot| |contract| |exprex| |quasiMonic?| |tube| |range| |false| |clearDenominator| |transpose| |goto| |morphism| |alternative?| |integerIfCan| |pseudoDivide| |stirling2| |nthRoot| |removeConjugate| |ratDenom| |sqfree| |height| |leftRank| |topPredicate| |numberOfOperations| |polygamma| |label| |perfectSquare?| |intcompBasis| |addPoint| |opeval| |airyAi| |squareFree| |exactQuotient| |scalarMatrix| |operation| |mainVariable| |cycleLength| |SturmHabichtSequence| |randomR| |f2st| |subSet| |extension| |Ei6| 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|rationalApproximation| |norm| |previousTower| |getMatch| |enterInCache| |enterPointData| |toseInvertibleSet| |interpolate| |setvalue!| |supRittWu?| |genericRightTraceForm| |pfaffian| |generalizedEigenvector| |monicRightDivide| |reduceBasisAtInfinity| |setLegalFortranSourceExtensions| |algebraicDecompose| |interpretString| |zag| |edf2efi| |point?| |iiperm| |tanQ| |ravel| |irreducible?| |calcRanges| |localReal?| |tubePlot| |complexSolve| |adjunctionDivisor| |primintfldpoly| |convertIfCan| |cotIfCan| |high| |set| |viewWriteDefault| |pointToPlace| |digits| |open?| |members| |pushdterm| |tanSum| |quadraticNorm| |viewport3D| |negative?| |sizeMultiplication| |laguerre| |merge| |cycle| |ran| |fortranCompilerName| |diagonal| |extendedIntegrate| |exists?| |newSubProgram| |halfExtendedSubResultantGcd2| |linearAssociatedLog| |eval| |primeFrobenius| |numer| |startStats!| |positiveRemainder| |cCosh| |PollardSmallFactor| |denom| |desingTreeAtPoint| |dequeue!| |genusTreeNeg| |kernel| |inR?| |headReduce| |removeCoshSq| |concat| |listConjugateBases| |draw| |integralAtInfinity?| |monomialIntPoly| |lfunc| |countable?| |makeObject| |expPot| |localAbs| |stoseInvertible?reg| |rightUnits| |integralLastSubResultant| |coef| |dAndcExp| |convergents| |hypergeometric0F1| |palgLODE0| |monom| |normalDenom| |introduce!| |series| |getMultiplicationMatrix| |real?| |gcdprim| |quadraticBezier| |ParCondList| |polarCoordinates| |OMputAttr| |tablePow| |options| |mapSolve| |tensorProduct| |indicialEquationAtInfinity| |repack1| |rightRankPolynomial| |clearTheIFTable| |radPoly| |shrinkable| |hconcat| |smith| |dihedralGroup| |goodnessOfFit| |pointDominateBy| |computePowers| |bat| |argscript| |factors| |setTex!| |rightExactQuotient| |pToHdmp| |asinhIfCan| |removeSuperfluousCases| |iiacosh| |normInvertible?| |binary| |partitions| |generalInterpolation| |setlocalParam!| |permanent| |chartV| |dmpToHdmp| |setsymbName!| |noKaratsuba| |operator| |tree| |measure2Result| |tanNa| |times!| |cAsinh| |subHeight| |weighted| |getStream| |innerEigenvectors| |smaller?| |supp| |iicot| |rewriteSetWithReduction| |pr2dmp| |bottom!| |column| |monomial?| |forLoop| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|) \ No newline at end of file diff --git a/src/share/algebra/dependents.daase/dependents.daase/index.kaf b/src/share/algebra/dependents.daase/dependents.daase/index.kaf deleted file mode 100644 index 426e4e3..0000000 --- a/src/share/algebra/dependents.daase/dependents.daase/index.kaf +++ /dev/null @@ -1,279 +0,0 @@ -77354 (|AbelianGroup&| |FourierSeries| |FreeAbelianGroup| |IndexedDirectProductAbelianGroup| |QuadraticForm|) -(|AbelianMonoid&| |CardinalNumber| |EuclideanModularRing| |GradedAlgebra| |GradedAlgebra&| |GradedModule| |GradedModule&| |IndexedDirectProductAbelianMonoid| |ListMonoidOps| |ModularField| |ModularRing| |RecurrenceOperator|) -(|AbelianMonoidRing&| |FractionFreeFastGaussian|) -(|AbelianSemiGroup&| |Color| |IncrementingMaps| |PositiveInteger|) -(|AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace|) -(|Aggregate&| |SplittingNode| |SplittingTree|) -(|Algebra&| |CliffordAlgebra| |ContinuedFraction| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |EvaluateCycleIndicators| |Factored| |FortranExpression| |FourierSeries| |LocalAlgebra| |PartialFraction| |RealClosure| |ResidueRing| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesODESolver|) -(|AlgFactor| |AlgebraicMultFact|) -(|AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicNumber| |AlgebraicallyClosedField&| |ComplexTrigonometricManipulations| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |InnerAlgebraicNumber| |Kovacic| |PatternMatchIntegration| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|AlgebraicallyClosedFunctionSpace&| |ConstantLODE| |DefiniteIntegrationTools| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultToFunction| |InverseLaplaceTransform| |LaplaceTransform| |NonLinearFirstOrderODESolver| |ODEIntegration|) -(|Library| |Result| |RoutinesTable|) -(|ArcTrigonometricFunctionCategory&|) -(|AssociationList|) -(|SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial|) -(|BagAggregate&|) -(|BalancedPAdicRational|) -(|ModuleOperator| |Operator|) -(|BasicType&|) -(|FreeModule| |OrdinaryDifferentialRing|) -(|BinaryRecursiveAggregate&| |PendantTree|) -(|BalancedBinaryTree| |BinarySearchTree| |BinaryTournament| |BinaryTree| |BinaryTreeCategory&|) -(|BitAggregate&| |Bits| |IndexedBits|) -(|BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |DesingTreePackage| |GeneralPackageForAlgebraicFunctionField| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |IntersectionDivisorPackage| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) -(|GeneralModulePolynomial| |InnerPAdicInteger| |ModuleMonomial| |OrderedDirectProduct|) -(|Kernel| |MakeCachableSet| |SortedCache|) -(|FreeAbelianMonoidCategory| |InnerFreeAbelianMonoid|) -(|CharacterClass|) -(|AlgebraicNumber| |BalancedFactorisation| |ConstantLODE| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |FullPartialFractionExpansion| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |GenusZeroIntegration| |GroebnerFactorizationPackage| |InfiniteProductCharacteristicZero| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerMultFact| |InternalRationalUnivariateRepresentationPackage| |InverseLaplaceTransform| |Kovacic| |LaplaceTransform| |LinearOrdinaryDifferentialOperatorFactorizer| |MRationalFactorize| |MachineFloat| |MultivariateFactorize| |NonLinearFirstOrderODESolver| |ODEIntegration| |ParametricLinearEquations| |PartialFractionPackage| |Pi| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |PureAlgebraicIntegration| |PureAlgebraicLODE| |RadicalSolvePackage| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalIntegration| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor| |StreamInfiniteProduct| |TransSolvePackage| |TranscendentalRischDE| |TranscendentalRischDESystem| |UnivariatePolynomialDecompositionPackage| |ZeroDimensionalSolvePackage|) -(|AssociatedJordanAlgebra| |AssociatedLieAlgebra| |Float| |FortranScalarType| |InfiniteTuple| |LieSquareMatrix| |MakeCachableSet| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |Pi| |QuasiAlgebraicSet| |QueryEquation| |RectangularMatrix| |SquareMatrix| |Switch| |SymbolTable| |TheSymbolTable| |Tuple| |Variable|) -(|Collection&|) -(|FunctionSpaceSum| |Guess| |MyExpression| |RecurrenceOperator|) -(|Algebra| |Algebra&| |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|) -(|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| |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&|) -(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) -(|DesingTreePackage| |Divisor| |GeneralPackageForAlgebraicFunctionField| |InfinitlyClosePoint| |InfinitlyClosePointCategory| |InterpolateFormsPackage| |IntersectionDivisorPackage|) -(|ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |DoubleFloatMatrix| |DoubleFloatVector| |ExpertSystemContinuityPackage1| |Float| |InputForm| |Pi| |SExpression|) -(|DoubleFloatMatrix|) -(|ElementaryFunctionCategory&| |GaloisGroupFactorizationUtilities|) -(|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|) -(|Evalable&|) -(|UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|DeRhamComplex| |StochasticDifferential|) -(|AlgebraicManipulations| |AlgebraicNumber| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |FortranExpression| |InnerAlgebraicNumber|) -(|ExtensibleLinearAggregate&| |FlexibleArray| |IndexedFlexibleArray|) -(|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| |MatrixManipulation| |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| |Finite&| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |IntegerMod| |ReducedDivisor| |SetOfMIntegersInOneToN|) -(|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|) -(|AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |ChineseRemainderToolsForIntegralBases| |DistinctDegreeFactorize| |FiniteFieldCategory&| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorization| |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| |MatrixManipulation| |MultiVariableCalculusFunctions| |SmithNormalForm| |TriangularMatrixOperations| |TwoDimensionalArrayCategory| |TwoDimensionalArrayCategory&|) -(|FiniteRankAlgebra&|) -(|FiniteRankNonAssociativeAlgebra&|) -(|CharacterClass| |FiniteSetAggregate&| |FiniteSetAggregateFunctions2| |Set|) -(|AlgebraicNumber| |DrawNumericHack| |InnerAlgebraicNumber| |MachineFloat| |Numeric| |OrderedVariableList| |Pi| |Symbol|) -(|DoubleFloat| |Float| |FloatingPointSystem&| |GaloisGroupFactorizationUtilities| |Interval| |IntervalCategory| |MachineFloat| |NumericContinuedFraction|) -(|Asp1| |Asp24| |Asp4| |Asp49| |Asp9|) -(|FortranExpression| |MachineComplex| |MachineFloat| |MachineInteger|) -(|Asp27| |Asp28| |Asp30| |Asp34|) -(|Asp20| |Asp74| |Asp77| |Asp80|) -(|Asp12| |Asp29| |Asp33| |FortranProgram| |SimpleFortranProgram|) -(|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| |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|) -(|LiePolynomial|) -(|FreeModule1| |LiePolynomial| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomialRing|) -(|Factored| |FullyEvalableOver&|) -(|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| |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| |NottinghamGroup|) -(|HomogeneousAggregate&| |ThreeDimensionalMatrix|) -(|HomogeneousDistributedMultivariatePolynomial|) -(|HyperbolicFunctionCategory&|) -(|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| |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| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U8Matrix| |U8Vector| |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| |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| |StochasticDifferential| |StreamInfiniteProduct| |SubResultantPackage| |SystemSolvePackage| |TopLevelDrawFunctionsForAlgebraicCurves| |TransSolvePackageService| |TriangularMatrixOperations| |TriangularSetCategory| |TriangularSetCategory&| |UnivariatePolynomialCommonDenominator| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialDivisionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeriesWithExponentialSingularity| |WuWenTsunTriangularSet|) -(|Interval|) -(|PatternMatchFunctionSpace| |PatternMatchKernel|) -(|KeyedDictionary&|) -(|CyclicStreamTools| |LazyStreamAggregate&| |NeitherSparseOrDensePowerSeries| |Stream|) -(|AntiSymm| |DeRhamComplex| |LeftAlgebra&|) -(|AlgebraGivenByStructuralConstants| |ApplyUnivariateSkewPolynomial| |DirectProductMatrixModule| |DirectProductModule| |GenericNonAssociativeAlgebra| |LinearOrdinaryDifferentialOperator2| |ModuleOperator|) -(|LieAlgebra&|) -(|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|) -(|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| |ComplexDoubleFloatMatrix| |DenavitHartenbergMatrix| |DoubleFloatMatrix| |IndexedMatrix| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |LinearSystemMatrixPackage| |Matrix| |MatrixCategory&| |MatrixCategoryFunctions2| |MatrixLinearAlgebraFunctions| |MatrixManipulation| |SmithNormalForm| |TriangularMatrixOperations| |U16Matrix| |U32Matrix| |U8Matrix|) -(|FreeAbelianGroup| |GeneralModulePolynomial| |IntegrationResult| |LieExponentials| |Localize| |Module&| |StochasticDifferential| |XExponentialPackage|) -(|Monad&|) -(|MonadWithUnit&|) -(|CharacteristicPolynomialInMonogenicalAlgebra| |InfiniteProductFiniteField| |InnerAlgFactor| |MonogenicAlgebra&| |NormInMonogenicAlgebra| |PAdicWildFunctionFieldIntegralBasis| |ReduceLODE| |SAERationalFunctionAlgFactor| |SimpleAlgebraicExtension| |SimpleAlgebraicExtensionAlgFactor|) -(|NonCommutativeOperatorDivision| |OppositeMonogenicLinearOperator|) -(|CardinalNumber| |DiscreteLogarithmPackage| |FramedModule| |FreeMonoid| |IncrementingMaps| |LocalAlgebra| |Localize| |Monoid&| |MonoidRing| |MonoidRingFunctions2| |NonNegativeInteger| |PositiveInteger|) -(|ListMultiDictionary|) -(|Multiset|) -(|SparseMultivariateTaylorSeries| |TaylorSeries|) -(|MyExpression|) -(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField|) -(|RegularChain|) -(|AssociatedJordanAlgebra| |AssociatedLieAlgebra| |FreeNilpotentLie| |NonAssociativeAlgebra&|) -(|NonAssociativeRing&|) -(|NonAssociativeRng&|) -(|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| |U16Vector| |U32Vector| |U8Vector|) -(|DoubleFloat| |ExpressionToOpenMath| |Float| |Integer| |SingleInteger| |Symbol|) -(|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| |BasicStochasticDifferential| |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| |StochasticDifferential| |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| |QuasiAlgebraicSet| |QueryEquation| |SExpression| |Switch| |SymbolTable| |TheSymbolTable|) -(|PAdicRational|) -(|BalancedPAdicInteger| |InnerPAdicInteger| |PAdicInteger| |PAdicRationalConstructor|) -(|d03eefAnnaType| |d03fafAnnaType|) -(|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|) -(|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| |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&| 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|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| |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| |StochasticDifferential|) -(|InputForm|) -(|InputForm| |SExpression| |SExpressionOf|) -(|Segment| |UniversalSegment|) -(|SemiGroup&|) -(|SequentialDifferentialPolynomial|) -(|SetAggregate&|) -(|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|) -(|DoubleFloat| |InverseLaplaceTransform|) -(|SplittingTree|) -(|InternalRationalUnivariateRepresentationPackage| |LazardSetSolvingPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet|) -(|AlgebraGivenByStructuralConstants| |GenericNonAssociativeAlgebra|) -(|DirectProductMatrixModule| |LieSquareMatrix| |SquareMatrix| |SquareMatrixCategory&|) -(|ArrayStack| |Stack|) -(|IntegerMod|) -(|SegmentExpansionCategory| |StreamAggregate&|) -(|CharacterClass| |Float| |FortranTemplate| |HashTable| |InputForm| |Integer| |KeyedAccessFile| |Library| |SExpression| |StringTable| |TextFile|) -(|IndexedString| |StringAggregate&|) -(|String|) -(|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|) -(|ComplexTrigonometricManipulations| |ConstantLODE| |CoordinateSystems| |DefiniteIntegrationTools| |DenavitHartenbergMatrix| |DoubleFloat| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExponentialExpansion| |ExpressionToUnivariatePowerSeries| |Float| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |GaloisGroupFactorizationUtilities| |GenerateUnivariatePowerSeries| |GenusZeroIntegration| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |Interval| |IntervalCategory| |InverseLaplaceTransform| |LaplaceTransform| |LiouvillianFunction| |NonLinearFirstOrderODESolver| |ODEIntegration| |PartialTranscendentalFunctions| |PatternMatchIntegration| |PowerSeriesLimitPackage| |PureAlgebraicIntegration| |TranscendentalFunctionCategory&| |TranscendentalManipulations| |TrigonometricManipulations| |UnivariatePuiseuxSeriesWithExponentialSingularity|) -(|GeneralTriangularSet| |TriangularSetCategory&| |WuWenTsunTriangularSet|) -(|TrigonometricFunctionCategory&|) -(|IndexedTwoDimensionalArray| |InnerIndexedTwoDimensionalArray| |TwoDimensionalArray| |TwoDimensionalArrayCategory&|) -(|AnyFunctions1| |AttachPredicates| |BagAggregate| |BagAggregate&| |BinaryRecursiveAggregate| |BinaryRecursiveAggregate&| |CoercibleTo| |Collection| |Collection&| |ConvertibleTo| |CyclicStreamTools| |DequeueAggregate| |DirectProduct| |DirectProductCategory| |DirectProductCategory&| |DirectProductFunctions2| |DoublyLinkedAggregate| |DrawOptionFunctions1| |Eltable| 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|ModularAlgebraicGcdOperations| |NoneFunctions1| |OneDimensionalArray| |OneDimensionalArrayAggregate| |OneDimensionalArrayAggregate&| |OneDimensionalArrayFunctions2| |ParadoxicalCombinatorsForStreams| |ParametricPlaneCurve| |ParametricPlaneCurveFunctions2| |ParametricSpaceCurve| |ParametricSpaceCurveFunctions2| |ParametricSurface| |ParametricSurfaceFunctions2| |PatternFunctions1| |Patternable| |PrimitiveArray| |PrimitiveArrayFunctions2| |QueueAggregate| |RecursiveAggregate| |RecursiveAggregate&| |Reference| |ResolveLatticeCompletion| |RetractableTo| |RetractableTo&| |Segment| |SegmentBinding| |SegmentBindingFunctions2| |SegmentCategory| |SegmentFunctions2| |SortPackage| |StackAggregate| |Stream| |StreamAggregate| |StreamAggregate&| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamTensor| |Tuple| |TwoDimensionalArray| |TwoDimensionalArrayCategory| |TwoDimensionalArrayCategory&| |UnaryRecursiveAggregate| |UnaryRecursiveAggregate&| |UniversalSegment| 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T) ((-909) |has| |#1| (-909)) ((-1043 (-412 (-571))) |has| |#1| (-1043 (-412 (-571)))) ((-1043 (-571)) |has| |#1| (-1043 (-571))) ((-1043 |#1|) . T) ((-1043 |#2|) . T) ((-1043 |#3|) . T) ((-1059 (-412 (-571))) |has| |#1| (-43 (-412 (-571)))) ((-1059 |#1|) . T) ((-1059 $) -1831 (|has| |#1| (-909)) (|has| |#1| (-561)) (|has| |#1| (-456)) (|has| |#1| (-173))) ((-1053) . T) ((-1060) . T) ((-1109) . T) ((-1097) . 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both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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"))))))) $)) (-15 -4279 ((-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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")))) (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216))))))) (T -566)) -((-4279 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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 (-566)))) (-3909 (*1 *2 *1) (-12 (-5 *2 (-637 (-2 (|:| -4080 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (|:| -4279 (-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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 (-566)))) (-3213 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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 (-566)))) (-2863 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -4080 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (|:| -4279 (-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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 (-566)))) (-3172 (*1 *1 *2) (-12 (-5 *2 (-637 (-2 (|:| -4080 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (|:| -4279 (-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| (-1149 (-216))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1981 (-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 (-566)))) (-3359 (*1 *2 *1) (-12 (-5 *2 (-637 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216))))) (-5 *1 (-566)))) (-2312 (*1 *2) (-12 (-5 *2 (-1263)) (-5 *1 (-566)))) (-3667 (*1 *1) (-5 *1 (-566)))) -(-10 -8 (-15 -3667 ($)) (-15 -2312 ((-1263))) (-15 -3359 ((-637 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) $)) (-15 -3172 ($ (-637 (-2 (|:| -4080 (-2 (|:| |var| (-1169)) (|:| |fn| (-311 (-216))) (|:| -1981 (-1091 (-840 (-216)))) (|:| |abserr| (-216)) (|:| |relerr| (-216)))) (|:| -4279 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| 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3504757 "URAGG-" 3504762 NIL URAGG- (NIL T T) -8 NIL NIL) (-1243 3498449 3501385 3501857 "UPXSSING" 3502435 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1242 3490336 3497566 3497847 "UPXS" 3498226 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1241 3483364 3490240 3490312 "UPXSCONS" 3490317 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1240 3473576 3480401 3480464 "UPXSCCA" 3481120 NIL UPXSCCA (NIL T T) -9 NIL 3481362) (-1239 3473214 3473299 3473473 "UPXSCCA-" 3473478 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1238 3463358 3469956 3470000 "UPXSCAT" 3470648 NIL UPXSCAT (NIL T) -9 NIL 3471250) (-1237 3462788 3462867 3463046 "UPXS2" 3463273 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1236 3461442 3461695 3462046 "UPSQFREE" 3462531 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1235 3455277 3458327 3458383 "UPSCAT" 3459544 NIL UPSCAT (NIL T T) -9 NIL 3460312) (-1234 3454481 3454688 3455015 "UPSCAT-" 3455020 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1233 3440470 3448510 3448554 "UPOLYC" 3450655 NIL UPOLYC (NIL T) -9 NIL 3451870) (-1232 3431799 3434224 3437371 "UPOLYC-" 3437376 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1231 3431426 3431469 3431602 "UPOLYC2" 3431750 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1230 3422837 3430992 3431130 "UP" 3431336 NIL UP (NIL NIL T) -8 NIL NIL) (-1229 3422176 3422283 3422447 "UPMP" 3422726 NIL UPMP (NIL T T) -7 NIL NIL) (-1228 3421729 3421810 3421949 "UPDIVP" 3422089 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1227 3420297 3420546 3420862 "UPDECOMP" 3421478 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1226 3419532 3419644 3419829 "UPCDEN" 3420181 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1225 3419051 3419120 3419269 "UP2" 3419457 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1224 3417572 3418259 3418534 "UNISEG" 3418811 NIL UNISEG (NIL T) -8 NIL NIL) (-1223 3416789 3416916 3417120 "UNISEG2" 3417416 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1222 3415849 3416029 3416255 "UNIFACT" 3416605 NIL UNIFACT (NIL T) -7 NIL NIL) (-1221 3399733 3415028 3415278 "ULS" 3415657 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1220 3387688 3399637 3399709 "ULSCONS" 3399714 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1219 3370355 3382372 3382435 "ULSCCAT" 3383155 NIL ULSCCAT (NIL T T) -9 NIL 3383451) (-1218 3369405 3369650 3370038 "ULSCCAT-" 3370043 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1217 3359341 3365853 3365897 "ULSCAT" 3366760 NIL ULSCAT (NIL T) -9 NIL 3367483) (-1216 3358771 3358850 3359029 "ULS2" 3359256 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1215 3350909 3356762 3357262 "UFPS" 3358306 NIL UFPS (NIL T) -8 NIL NIL) (-1214 3350606 3350663 3350761 "UFPS1" 3350846 NIL UFPS1 (NIL T) -7 NIL NIL) (-1213 3348999 3349966 3349997 "UFD" 3350209 T UFD (NIL) -9 NIL 3350323) (-1212 3348793 3348839 3348934 "UFD-" 3348939 NIL UFD- (NIL T) -8 NIL NIL) (-1211 3347875 3348058 3348274 "UDVO" 3348599 T UDVO (NIL) -7 NIL NIL) (-1210 3345693 3346102 3346572 "UDPO" 3347440 NIL UDPO (NIL T) -7 NIL NIL) (-1209 3341656 3345638 3345674 "U8VEC" 3345679 T U8VEC (NIL) -8 NIL NIL) (-1208 3337850 3341420 3341518 "U8MAT" 3341580 T U8MAT (NIL) -8 NIL NIL) (-1207 3333813 3337795 3337831 "U32VEC" 3337836 T U32VEC (NIL) -8 NIL NIL) (-1206 3330007 3333577 3333675 "U32MAT" 3333737 T U32MAT (NIL) -8 NIL NIL) (-1205 3325970 3329952 3329988 "U16VEC" 3329993 T U16VEC (NIL) -8 NIL NIL) (-1204 3322164 3325734 3325832 "U16MAT" 3325894 T U16MAT (NIL) -8 NIL NIL) (-1203 3322096 3322101 3322132 "TYPE" 3322137 T TYPE (NIL) -9 NIL NIL) (-1202 3321067 3321269 3321509 "TWOFACT" 3321890 NIL TWOFACT (NIL T) -7 NIL NIL) (-1201 3320139 3320470 3320669 "TUPLE" 3320903 NIL TUPLE (NIL T) -8 NIL NIL) (-1200 3317830 3318349 3318888 "TUBETOOL" 3319622 T TUBETOOL (NIL) -7 NIL NIL) (-1199 3316679 3316884 3317125 "TUBE" 3317623 NIL TUBE (NIL T) -8 NIL NIL) (-1198 3311399 3315653 3315935 "TS" 3316432 NIL TS (NIL T) -8 NIL NIL) (-1197 3300073 3304158 3304256 "TSETCAT" 3309525 NIL TSETCAT (NIL T T T T) -9 NIL 3311055) (-1196 3294808 3296405 3298296 "TSETCAT-" 3298301 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1195 3289078 3289925 3290863 "TRMANIP" 3293948 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1194 3288519 3288582 3288745 "TRIMAT" 3289010 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1193 3286315 3286552 3286916 "TRIGMNIP" 3288268 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1192 3285834 3285947 3285978 "TRIGCAT" 3286191 T TRIGCAT (NIL) -9 NIL NIL) (-1191 3285503 3285582 3285723 "TRIGCAT-" 3285728 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1190 3282406 3284361 3284642 "TREE" 3285257 NIL TREE (NIL T) -8 NIL NIL) (-1189 3281679 3282207 3282238 "TRANFUN" 3282273 T TRANFUN (NIL) -9 NIL 3282339) (-1188 3280958 3281149 3281429 "TRANFUN-" 3281434 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1187 3280762 3280794 3280855 "TOPSP" 3280919 T TOPSP (NIL) -7 NIL NIL) (-1186 3280110 3280225 3280379 "TOOLSIGN" 3280643 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1185 3278745 3279287 3279526 "TEXTFILE" 3279893 T TEXTFILE (NIL) -8 NIL NIL) (-1184 3276610 3277124 3277562 "TEX" 3278329 T TEX (NIL) -8 NIL NIL) (-1183 3276391 3276422 3276494 "TEX1" 3276573 NIL TEX1 (NIL T) -7 NIL NIL) (-1182 3276039 3276102 3276192 "TEMUTL" 3276323 T TEMUTL (NIL) -7 NIL NIL) (-1181 3274193 3274473 3274798 "TBCMPPK" 3275762 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1180 3265938 3272198 3272255 "TBAGG" 3272655 NIL TBAGG (NIL T T) -9 NIL 3272866) (-1179 3261008 3262496 3264250 "TBAGG-" 3264255 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1178 3260392 3260499 3260644 "TANEXP" 3260897 NIL TANEXP (NIL T) -7 NIL NIL) (-1177 3253905 3260249 3260342 "TABLE" 3260347 NIL TABLE (NIL T T) -8 NIL NIL) (-1176 3253318 3253416 3253554 "TABLEAU" 3253802 NIL TABLEAU (NIL T) -8 NIL NIL) (-1175 3247926 3249146 3250394 "TABLBUMP" 3252104 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1174 3244389 3245084 3245867 "SYSSOLP" 3247177 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1173 3241523 3242131 3242769 "SYMTAB" 3243773 T SYMTAB (NIL) -8 NIL NIL) (-1172 3236772 3237674 3238657 "SYMS" 3240562 T SYMS (NIL) -8 NIL NIL) (-1171 3234004 3236236 3236463 "SYMPOLY" 3236580 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1170 3233521 3233596 3233719 "SYMFUNC" 3233916 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1169 3229499 3230758 3231580 "SYMBOL" 3232721 T SYMBOL (NIL) -8 NIL NIL) (-1168 3223038 3224727 3226447 "SWITCH" 3227801 T SWITCH (NIL) -8 NIL NIL) (-1167 3216264 3221861 3222163 "SUTS" 3222794 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1166 3208150 3215381 3215662 "SUPXS" 3216041 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1165 3199635 3207768 3207894 "SUP" 3208059 NIL SUP (NIL T) -8 NIL NIL) (-1164 3198794 3198921 3199138 "SUPFRACF" 3199503 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1163 3189366 3198596 3198710 "SUPEXPR" 3198715 NIL SUPEXPR (NIL T) -8 NIL NIL) (-1162 3188987 3189046 3189159 "SUP2" 3189301 NIL SUP2 (NIL T T) -7 NIL NIL) (-1161 3187400 3187674 3188037 "SUMRF" 3188686 NIL SUMRF (NIL T) -7 NIL NIL) (-1160 3186714 3186780 3186979 "SUMFS" 3187321 NIL SUMFS (NIL T T) -7 NIL NIL) (-1159 3170638 3185893 3186143 "SULS" 3186522 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1158 3169960 3170163 3170303 "SUCH" 3170546 NIL SUCH (NIL T T) -8 NIL NIL) (-1157 3163854 3164866 3165825 "SUBSPACE" 3169048 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1156 3163286 3163376 3163539 "SUBRESP" 3163743 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1155 3156655 3157951 3159262 "STTF" 3162022 NIL STTF (NIL T) -7 NIL NIL) (-1154 3150828 3151948 3153095 "STTFNC" 3155555 NIL STTFNC (NIL T) -7 NIL NIL) (-1153 3142147 3144014 3145806 "STTAYLOR" 3149071 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1152 3135403 3142011 3142094 "STRTBL" 3142099 NIL STRTBL (NIL T) -8 NIL NIL) (-1151 3130794 3135358 3135389 "STRING" 3135394 T STRING (NIL) -8 NIL NIL) (-1150 3125658 3130136 3130167 "STRICAT" 3130226 T STRICAT (NIL) -9 NIL 3130288) (-1149 3118385 3123185 3123803 "STREAM" 3125075 NIL STREAM (NIL T) -8 NIL NIL) (-1148 3117895 3117972 3118116 "STREAM3" 3118302 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1147 3116877 3117060 3117295 "STREAM2" 3117708 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1146 3116565 3116617 3116710 "STREAM1" 3116819 NIL STREAM1 (NIL T) -7 NIL NIL) (-1145 3116209 3116275 3116382 "STNSR" 3116493 NIL STNSR (NIL T) -7 NIL NIL) (-1144 3115225 3115406 3115637 "STINPROD" 3116025 NIL STINPROD (NIL T) -7 NIL NIL) (-1143 3114802 3114986 3115017 "STEP" 3115097 T STEP (NIL) -9 NIL 3115175) (-1142 3108357 3114701 3114778 "STBL" 3114783 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1141 3103571 3107609 3107653 "STAGG" 3107806 NIL STAGG (NIL T) -9 NIL 3107895) (-1140 3101273 3101875 3102747 "STAGG-" 3102752 NIL STAGG- (NIL T T) -8 NIL NIL) (-1139 3094765 3096334 3097449 "STACK" 3100193 NIL STACK (NIL T) -8 NIL NIL) (-1138 3087490 3092906 3093362 "SREGSET" 3094395 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1137 3079916 3081284 3082797 "SRDCMPK" 3086096 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1136 3072894 3077354 3077385 "SRAGG" 3078688 T SRAGG (NIL) -9 NIL 3079296) (-1135 3071911 3072166 3072545 "SRAGG-" 3072550 NIL SRAGG- (NIL T) -8 NIL NIL) (-1134 3066359 3070834 3071258 "SQMATRIX" 3071534 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1133 3060115 3063077 3063804 "SPLTREE" 3065704 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1132 3056105 3056771 3057417 "SPLNODE" 3059541 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1131 3055151 3055384 3055415 "SPFCAT" 3055859 T SPFCAT (NIL) -9 NIL NIL) (-1130 3053888 3054098 3054362 "SPECOUT" 3054909 T SPECOUT (NIL) -7 NIL NIL) (-1129 3045858 3047605 3047649 "SPACEC" 3052022 NIL SPACEC (NIL T) -9 NIL 3053838) (-1128 3044029 3045790 3045839 "SPACE3" 3045844 NIL SPACE3 (NIL T) -8 NIL NIL) (-1127 3042783 3042954 3043244 "SORTPAK" 3043835 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1126 3040833 3041136 3041555 "SOLVETRA" 3042447 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1125 3039844 3040066 3040340 "SOLVESER" 3040606 NIL SOLVESER (NIL T) -7 NIL NIL) (-1124 3035064 3035945 3036947 "SOLVERAD" 3038896 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1123 3030879 3031488 3032217 "SOLVEFOR" 3034431 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1122 3025182 3030227 3030325 "SNTSCAT" 3030330 NIL SNTSCAT (NIL T T T T) -9 NIL 3030400) (-1121 3019280 3023507 3023897 "SMTS" 3024873 NIL SMTS (NIL T T T) -8 NIL NIL) (-1120 3013684 3019168 3019245 "SMP" 3019250 NIL SMP (NIL T T) -8 NIL NIL) (-1119 3011843 3012144 3012542 "SMITH" 3013381 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1118 3004785 3008983 3009087 "SMATCAT" 3010438 NIL SMATCAT (NIL NIL T T T) -9 NIL 3010985) (-1117 3001725 3002548 3003726 "SMATCAT-" 3003731 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1116 2999478 3000995 3001039 "SKAGG" 3001300 NIL SKAGG (NIL T) -9 NIL 3001435) (-1115 2995536 2998582 2998860 "SINT" 2999222 T SINT (NIL) -8 NIL NIL) (-1114 2995308 2995346 2995412 "SIMPAN" 2995492 T SIMPAN (NIL) -7 NIL NIL) (-1113 2994146 2994367 2994642 "SIGNRF" 2995067 NIL SIGNRF (NIL T) -7 NIL NIL) (-1112 2992951 2993102 2993393 "SIGNEF" 2993975 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1111 2990643 2991097 2991602 "SHP" 2992493 NIL SHP (NIL T NIL) -7 NIL NIL) (-1110 2984424 2990544 2990620 "SHDP" 2990625 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1109 2983912 2984104 2984135 "SGROUP" 2984287 T SGROUP (NIL) -9 NIL 2984374) (-1108 2983682 2983734 2983838 "SGROUP-" 2983843 NIL SGROUP- (NIL T) -8 NIL NIL) (-1107 2980518 2981215 2981938 "SGCF" 2982981 T SGCF (NIL) -7 NIL NIL) (-1106 2974919 2979964 2980062 "SFRTCAT" 2980067 NIL SFRTCAT (NIL T T T T) -9 NIL 2980106) (-1105 2968343 2969358 2970494 "SFRGCD" 2973902 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1104 2961471 2962542 2963728 "SFQCMPK" 2967276 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1103 2961093 2961182 2961292 "SFORT" 2961412 NIL SFORT (NIL T T) -8 NIL NIL) (-1102 2960238 2960933 2961054 "SEXOF" 2961059 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1101 2959372 2960119 2960187 "SEX" 2960192 T SEX (NIL) -8 NIL NIL) (-1100 2954147 2954836 2954932 "SEXCAT" 2958703 NIL SEXCAT (NIL T T T T T) -9 NIL 2959322) (-1099 2951282 2954081 2954129 "SET" 2954134 NIL SET (NIL T) -8 NIL NIL) (-1098 2949516 2949995 2950300 "SETMN" 2951023 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1097 2949121 2949247 2949278 "SETCAT" 2949395 T SETCAT (NIL) -9 NIL 2949480) (-1096 2948901 2948953 2949052 "SETCAT-" 2949057 NIL SETCAT- (NIL T) -8 NIL NIL) (-1095 2948564 2948714 2948745 "SETCATD" 2948804 T SETCATD (NIL) -9 NIL 2948851) (-1094 2944950 2947024 2947068 "SETAGG" 2947938 NIL SETAGG (NIL T) -9 NIL 2948278) (-1093 2944408 2944524 2944761 "SETAGG-" 2944766 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1092 2943611 2943904 2943966 "SEGXCAT" 2944252 NIL SEGXCAT (NIL T T) -9 NIL 2944372) (-1091 2942671 2943281 2943461 "SEG" 2943466 NIL SEG (NIL T) -8 NIL NIL) (-1090 2941577 2941790 2941834 "SEGCAT" 2942416 NIL SEGCAT (NIL T) -9 NIL 2942654) (-1089 2940628 2940958 2941157 "SEGBIND" 2941413 NIL SEGBIND (NIL T) -8 NIL NIL) (-1088 2940249 2940308 2940421 "SEGBIND2" 2940563 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1087 2939470 2939596 2939799 "SEG2" 2940094 NIL SEG2 (NIL T T) -7 NIL NIL) (-1086 2938907 2939405 2939452 "SDVAR" 2939457 NIL SDVAR (NIL T) -8 NIL NIL) (-1085 2931151 2938677 2938807 "SDPOL" 2938812 NIL SDPOL (NIL T) -8 NIL NIL) (-1084 2927174 2928203 2928850 "SD" 2930551 NIL SD (NIL T) -8 NIL NIL) (-1083 2925767 2926033 2926352 "SCPKG" 2926889 NIL SCPKG (NIL T) -7 NIL NIL) (-1082 2924988 2925121 2925300 "SCACHE" 2925622 NIL SCACHE (NIL T) -7 NIL NIL) (-1081 2924427 2924748 2924833 "SAOS" 2924925 T SAOS (NIL) -8 NIL NIL) (-1080 2923992 2924027 2924200 "SAERFFC" 2924386 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1079 2917836 2923889 2923969 "SAE" 2923974 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1078 2917429 2917464 2917623 "SAEFACT" 2917795 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1077 2915750 2916064 2916465 "RURPK" 2917095 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1076 2914386 2914665 2914977 "RULESET" 2915584 NIL RULESET (NIL T T T) -8 NIL NIL) (-1075 2911573 2912076 2912541 "RULE" 2914067 NIL RULE (NIL T T T) -8 NIL NIL) (-1074 2911212 2911367 2911450 "RULECOLD" 2911525 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1073 2906061 2906855 2907775 "RSETGCD" 2910411 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1072 2895324 2900369 2900467 "RSETCAT" 2904586 NIL RSETCAT (NIL T T T T) -9 NIL 2905683) (-1071 2893251 2893790 2894614 "RSETCAT-" 2894619 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1070 2885638 2887013 2888533 "RSDCMPK" 2891850 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1069 2883642 2884083 2884158 "RRCC" 2885244 NIL RRCC (NIL T T) -9 NIL 2885588) (-1068 2882993 2883167 2883446 "RRCC-" 2883451 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1067 2857140 2866769 2866837 "RPOLCAT" 2877501 NIL RPOLCAT (NIL T T T) -9 NIL 2880649) (-1066 2848640 2850978 2854100 "RPOLCAT-" 2854105 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1065 2839699 2846851 2847333 "ROUTINE" 2848180 T ROUTINE (NIL) -8 NIL NIL) (-1064 2836399 2839250 2839399 "ROMAN" 2839572 T ROMAN (NIL) -8 NIL NIL) (-1063 2834674 2835259 2835519 "ROIRC" 2836204 NIL ROIRC (NIL T T) -8 NIL NIL) (-1062 2831012 2833312 2833343 "RNS" 2833647 T RNS (NIL) -9 NIL 2833921) (-1061 2829521 2829904 2830438 "RNS-" 2830513 NIL RNS- (NIL T) -8 NIL NIL) (-1060 2828943 2829351 2829382 "RNG" 2829387 T RNG (NIL) -9 NIL 2829408) (-1059 2828334 2828696 2828740 "RMODULE" 2828802 NIL RMODULE (NIL T) -9 NIL 2828844) (-1058 2827170 2827264 2827600 "RMCAT2" 2828235 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1057 2823879 2826348 2826671 "RMATRIX" 2826906 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1056 2816825 2819059 2819175 "RMATCAT" 2822534 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2823511) (-1055 2816200 2816347 2816654 "RMATCAT-" 2816659 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1054 2815767 2815842 2815970 "RINTERP" 2816119 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1053 2814810 2815374 2815405 "RING" 2815517 T RING (NIL) -9 NIL 2815612) (-1052 2814602 2814646 2814743 "RING-" 2814748 NIL RING- (NIL T) -8 NIL NIL) (-1051 2813443 2813680 2813938 "RIDIST" 2814366 T RIDIST (NIL) -7 NIL NIL) (-1050 2804759 2812911 2813117 "RGCHAIN" 2813291 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1049 2803559 2803800 2804079 "RFP" 2804514 NIL RFP (NIL T) -7 NIL NIL) (-1048 2800553 2801167 2801837 "RF" 2802923 NIL RF (NIL T) -7 NIL NIL) (-1047 2800199 2800262 2800365 "RFFACTOR" 2800484 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1046 2799924 2799959 2800056 "RFFACT" 2800158 NIL RFFACT (NIL T) -7 NIL NIL) (-1045 2798041 2798405 2798787 "RFDIST" 2799564 T RFDIST (NIL) -7 NIL NIL) (-1044 2797494 2797586 2797749 "RETSOL" 2797943 NIL RETSOL (NIL T T) -7 NIL NIL) (-1043 2797081 2797161 2797205 "RETRACT" 2797398 NIL RETRACT (NIL T) -9 NIL NIL) (-1042 2796930 2796955 2797042 "RETRACT-" 2797047 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1041 2789796 2796583 2796710 "RESULT" 2796825 T RESULT (NIL) -8 NIL NIL) (-1040 2788376 2789065 2789264 "RESRING" 2789699 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1039 2788012 2788061 2788159 "RESLATC" 2788313 NIL RESLATC (NIL T) -7 NIL NIL) (-1038 2787718 2787752 2787859 "REPSQ" 2787971 NIL REPSQ (NIL T) -7 NIL NIL) (-1037 2785140 2785720 2786322 "REP" 2787138 T REP (NIL) -7 NIL NIL) (-1036 2784838 2784872 2784983 "REPDB" 2785099 NIL REPDB (NIL T) -7 NIL NIL) (-1035 2778756 2780135 2781354 "REP2" 2783654 NIL REP2 (NIL T) -7 NIL NIL) (-1034 2775137 2775818 2776624 "REP1" 2777985 NIL REP1 (NIL T) -7 NIL NIL) (-1033 2767863 2773278 2773734 "REGSET" 2774767 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1032 2766678 2767013 2767262 "REF" 2767649 NIL REF (NIL T) -8 NIL NIL) (-1031 2766055 2766158 2766325 "REDORDER" 2766562 NIL REDORDER (NIL T T) -7 NIL NIL) (-1030 2762917 2763383 2763992 "RECOP" 2765589 NIL RECOP (NIL T T) -7 NIL NIL) (-1029 2758857 2762130 2762357 "RECLOS" 2762745 NIL RECLOS (NIL T) -8 NIL NIL) (-1028 2757909 2758090 2758305 "REALSOLV" 2758664 T REALSOLV (NIL) -7 NIL NIL) (-1027 2757754 2757795 2757826 "REAL" 2757831 T REAL (NIL) -9 NIL 2757866) (-1026 2754237 2755039 2755923 "REAL0Q" 2756919 NIL REAL0Q (NIL T) -7 NIL NIL) (-1025 2749838 2750826 2751887 "REAL0" 2753218 NIL REAL0 (NIL T) -7 NIL NIL) (-1024 2749243 2749315 2749522 "RDIV" 2749760 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1023 2748311 2748485 2748698 "RDIST" 2749065 NIL RDIST (NIL T) -7 NIL NIL) (-1022 2746908 2747195 2747567 "RDETRS" 2748019 NIL RDETRS (NIL T T) -7 NIL NIL) (-1021 2744720 2745174 2745712 "RDETR" 2746450 NIL RDETR (NIL T T) -7 NIL NIL) (-1020 2743331 2743609 2744013 "RDEEFS" 2744436 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1019 2741826 2742132 2742564 "RDEEF" 2743019 NIL RDEEF (NIL T T) -7 NIL NIL) (-1018 2736017 2738952 2738983 "RCFIELD" 2740278 T RCFIELD (NIL) -9 NIL 2741009) (-1017 2734081 2734585 2735281 "RCFIELD-" 2735356 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1016 2730439 2732218 2732262 "RCAGG" 2733346 NIL RCAGG (NIL T) -9 NIL 2733809) (-1015 2730067 2730161 2730324 "RCAGG-" 2730329 NIL RCAGG- (NIL T T) -8 NIL NIL) (-1014 2729403 2729514 2729679 "RATRET" 2729951 NIL RATRET (NIL T) -7 NIL NIL) (-1013 2728956 2729023 2729144 "RATFACT" 2729331 NIL RATFACT (NIL T) -7 NIL NIL) (-1012 2728264 2728384 2728536 "RANDSRC" 2728826 T RANDSRC (NIL) -7 NIL NIL) (-1011 2727998 2728042 2728115 "RADUTIL" 2728213 T RADUTIL (NIL) -7 NIL NIL) (-1010 2720986 2726731 2727050 "RADIX" 2727713 NIL RADIX (NIL NIL) -8 NIL NIL) (-1009 2712497 2720828 2720958 "RADFF" 2720963 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-1008 2712143 2712218 2712249 "RADCAT" 2712409 T RADCAT (NIL) -9 NIL NIL) (-1007 2711925 2711973 2712073 "RADCAT-" 2712078 NIL RADCAT- (NIL T) -8 NIL NIL) (-1006 2705170 2706788 2707942 "QUEUE" 2710806 NIL QUEUE (NIL T) -8 NIL NIL) (-1005 2701657 2705103 2705151 "QUAT" 2705156 NIL QUAT (NIL T) -8 NIL NIL) (-1004 2701288 2701331 2701462 "QUATCT2" 2701608 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-1003 2695012 2698396 2698439 "QUATCAT" 2699230 NIL QUATCAT (NIL T) -9 NIL 2699988) (-1002 2691151 2692188 2693578 "QUATCAT-" 2693674 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-1001 2688703 2690261 2690305 "QUAGG" 2690686 NIL QUAGG (NIL T) -9 NIL 2690861) (-1000 2687623 2688096 2688270 "QFORM" 2688575 NIL QFORM (NIL NIL T) -8 NIL NIL) (-999 2678850 2684117 2684158 "QFCAT" 2684816 NIL QFCAT (NIL T) -9 NIL 2685805) (-998 2674422 2675623 2677214 "QFCAT-" 2677308 NIL QFCAT- (NIL T T) -8 NIL NIL) (-997 2674060 2674103 2674230 "QFCAT2" 2674373 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-996 2673520 2673630 2673760 "QEQUAT" 2673950 T QEQUAT (NIL) -8 NIL NIL) (-995 2666668 2667739 2668923 "QCMPACK" 2672453 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-994 2664248 2664669 2665095 "QALGSET" 2666325 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-993 2663493 2663667 2663899 "QALGSET2" 2664068 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-992 2662184 2662407 2662724 "PWFFINTB" 2663266 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-991 2660366 2660534 2660888 "PUSHVAR" 2661998 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-990 2656283 2657337 2657379 "PTRANFN" 2659263 NIL PTRANFN (NIL T) -9 NIL NIL) (-989 2654685 2654976 2655298 "PTPACK" 2655994 NIL PTPACK (NIL T) -7 NIL NIL) (-988 2654317 2654374 2654483 "PTFUNC2" 2654622 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-987 2648817 2653151 2653193 "PTCAT" 2653566 NIL PTCAT (NIL T) -9 NIL 2653728) (-986 2648475 2648510 2648634 "PSQFR" 2648776 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-985 2647062 2647362 2647698 "PSEUDLIN" 2648171 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-984 2633838 2636202 2638523 "PSETPK" 2644825 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-983 2626882 2629596 2629693 "PSETCAT" 2632714 NIL PSETCAT (NIL T T T T) -9 NIL 2633527) (-982 2624718 2625352 2626173 "PSETCAT-" 2626178 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-981 2624067 2624231 2624260 "PSCURVE" 2624528 T PSCURVE (NIL) -9 NIL 2624695) (-980 2620456 2621982 2622048 "PSCAT" 2622892 NIL PSCAT (NIL T T T) -9 NIL 2623132) (-979 2619519 2619735 2620135 "PSCAT-" 2620140 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-978 2618172 2618804 2619018 "PRTITION" 2619325 T PRTITION (NIL) -8 NIL NIL) (-977 2615336 2615985 2616026 "PRSPCAT" 2617540 NIL PRSPCAT (NIL T) -9 NIL 2618108) (-976 2604436 2606642 2608829 "PRS" 2613199 NIL PRS (NIL T T) -7 NIL NIL) (-975 2602334 2603820 2603861 "PRQAGG" 2604044 NIL PRQAGG (NIL T) -9 NIL 2604146) (-974 2601603 2602259 2602316 "PROJSP" 2602321 NIL PROJSP (NIL NIL T) -8 NIL NIL) (-973 2600785 2601526 2601578 "PROJPLPS" 2601583 NIL PROJPLPS (NIL T) -8 NIL NIL) (-972 2600044 2600722 2600767 "PROJPL" 2600772 NIL PROJPL (NIL T) -8 NIL NIL) (-971 2593779 2598242 2599046 "PRODUCT" 2599286 NIL PRODUCT (NIL T T) -8 NIL NIL) (-970 2591054 2593243 2593474 "PR" 2593593 NIL PR (NIL T T) -8 NIL NIL) (-969 2589606 2589763 2590058 "PRJALGPK" 2590894 NIL PRJALGPK (NIL T NIL T T T) -7 NIL NIL) (-968 2589402 2589434 2589493 "PRINT" 2589567 T PRINT (NIL) -7 NIL NIL) (-967 2588742 2588859 2589011 "PRIMES" 2589282 NIL PRIMES (NIL T) -7 NIL NIL) (-966 2586807 2587208 2587674 "PRIMELT" 2588321 NIL PRIMELT (NIL T) -7 NIL NIL) (-965 2586535 2586584 2586613 "PRIMCAT" 2586737 T PRIMCAT (NIL) -9 NIL NIL) (-964 2582702 2586473 2586518 "PRIMARR" 2586523 NIL PRIMARR (NIL T) -8 NIL NIL) (-963 2581709 2581887 2582115 "PRIMARR2" 2582520 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-962 2581352 2581408 2581519 "PREASSOC" 2581647 NIL PREASSOC (NIL T T) -7 NIL NIL) (-961 2580827 2580959 2580988 "PPCURVE" 2581193 T PPCURVE (NIL) -9 NIL 2581329) (-960 2575225 2576376 2577555 "POLYVEC" 2579668 T POLYVEC (NIL) -7 NIL NIL) (-959 2572586 2572985 2573576 "POLYROOT" 2574807 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-958 2566487 2572192 2572351 "POLY" 2572460 NIL POLY (NIL T) -8 NIL NIL) (-957 2565870 2565928 2566162 "POLYLIFT" 2566423 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-956 2562145 2562594 2563223 "POLYCATQ" 2565415 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-955 2549107 2554507 2554573 "POLYCAT" 2558087 NIL POLYCAT (NIL T T T) -9 NIL 2560000) (-954 2542557 2544418 2546802 "POLYCAT-" 2546807 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-953 2542144 2542212 2542332 "POLY2UP" 2542483 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-952 2541776 2541833 2541942 "POLY2" 2542081 NIL POLY2 (NIL T T) -7 NIL NIL) (-951 2540463 2540702 2540977 "POLUTIL" 2541551 NIL POLUTIL (NIL T T) -7 NIL NIL) (-950 2538818 2539095 2539426 "POLTOPOL" 2540185 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-949 2534340 2538754 2538800 "POINT" 2538805 NIL POINT (NIL T) -8 NIL NIL) (-948 2532527 2532884 2533259 "PNTHEORY" 2533985 T PNTHEORY (NIL) -7 NIL NIL) (-947 2530946 2531243 2531655 "PMTOOLS" 2532225 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-946 2530539 2530617 2530734 "PMSYM" 2530862 NIL PMSYM (NIL T) -7 NIL NIL) (-945 2530049 2530118 2530292 "PMQFCAT" 2530464 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-944 2529404 2529514 2529670 "PMPRED" 2529926 NIL PMPRED (NIL T) -7 NIL NIL) (-943 2528800 2528886 2529047 "PMPREDFS" 2529305 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-942 2527445 2527653 2528037 "PMPLCAT" 2528563 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-941 2526977 2527056 2527208 "PMLSAGG" 2527360 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-940 2526452 2526528 2526709 "PMKERNEL" 2526895 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-939 2526069 2526144 2526257 "PMINS" 2526371 NIL PMINS (NIL T) -7 NIL NIL) (-938 2525497 2525566 2525782 "PMFS" 2525994 NIL PMFS (NIL T T T) -7 NIL NIL) (-937 2524725 2524843 2525048 "PMDOWN" 2525374 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-936 2523888 2524047 2524229 "PMASS" 2524563 T PMASS (NIL) -7 NIL NIL) (-935 2523162 2523273 2523436 "PMASSFS" 2523774 NIL PMASSFS (NIL T T) -7 NIL NIL) (-934 2520922 2521175 2521558 "PLPKCRV" 2522886 NIL PLPKCRV (NIL T T T NIL T) -7 NIL NIL) (-933 2520577 2520645 2520739 "PLOTTOOL" 2520848 T PLOTTOOL (NIL) -7 NIL NIL) (-932 2515199 2516388 2517536 "PLOT" 2519449 T PLOT (NIL) -8 NIL NIL) (-931 2511013 2512047 2512968 "PLOT3D" 2514298 T PLOT3D (NIL) -8 NIL NIL) (-930 2509925 2510102 2510337 "PLOT1" 2510817 NIL PLOT1 (NIL T) -7 NIL NIL) (-929 2485344 2490009 2494854 "PLEQN" 2505197 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-928 2484584 2485254 2485321 "PLCS" 2485326 NIL PLCS (NIL T T) -8 NIL NIL) (-927 2483735 2484469 2484540 "PLACESPS" 2484545 NIL PLACESPS (NIL T) -8 NIL NIL) (-926 2482942 2483648 2483705 "PLACES" 2483710 NIL PLACES (NIL T) -8 NIL NIL) (-925 2479666 2480330 2480389 "PLACESC" 2482307 NIL PLACESC (NIL T T) -9 NIL 2482878) (-924 2478984 2479106 2479286 "PINTERP" 2479531 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-923 2478677 2478724 2478827 "PINTERPA" 2478931 NIL PINTERPA (NIL T T) -7 NIL NIL) (-922 2477904 2478471 2478564 "PI" 2478604 T PI (NIL) -8 NIL NIL) (-921 2476291 2477276 2477305 "PID" 2477487 T PID (NIL) -9 NIL 2477621) (-920 2476016 2476053 2476141 "PICOERCE" 2476248 NIL PICOERCE (NIL T) -7 NIL NIL) (-919 2475337 2475475 2475651 "PGROEB" 2475872 NIL PGROEB (NIL T) -7 NIL NIL) (-918 2470924 2471738 2472643 "PGE" 2474452 T PGE (NIL) -7 NIL NIL) (-917 2469048 2469294 2469660 "PGCD" 2470641 NIL PGCD (NIL T T T T) -7 NIL NIL) (-916 2468386 2468489 2468650 "PFRPAC" 2468932 NIL PFRPAC (NIL T) -7 NIL NIL) (-915 2465001 2466934 2467287 "PFR" 2468065 NIL PFR (NIL T) -8 NIL NIL) (-914 2463390 2463634 2463959 "PFOTOOLS" 2464748 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-913 2458255 2458920 2459669 "PFORP" 2462732 NIL PFORP (NIL T T T NIL) -7 NIL NIL) (-912 2456788 2457027 2457378 "PFOQ" 2458012 NIL PFOQ (NIL T T T) -7 NIL NIL) (-911 2455261 2455473 2455836 "PFO" 2456572 NIL PFO (NIL T T T T T) -7 NIL NIL) (-910 2451759 2455150 2455219 "PF" 2455224 NIL PF (NIL NIL) -8 NIL NIL) (-909 2449184 2450465 2450494 "PFECAT" 2451079 T PFECAT (NIL) -9 NIL 2451462) (-908 2448629 2448783 2448997 "PFECAT-" 2449002 NIL PFECAT- (NIL T) -8 NIL NIL) (-907 2447233 2447484 2447785 "PFBRU" 2448378 NIL PFBRU (NIL T T) -7 NIL NIL) (-906 2445100 2445451 2445883 "PFBR" 2446884 NIL PFBR (NIL T T T T) -7 NIL NIL) (-905 2440956 2442480 2443154 "PERM" 2444459 NIL PERM (NIL T) -8 NIL NIL) (-904 2436223 2437163 2438033 "PERMGRP" 2440119 NIL PERMGRP (NIL T) -8 NIL NIL) (-903 2434294 2435287 2435329 "PERMCAT" 2435775 NIL PERMCAT (NIL T) -9 NIL 2436078) (-902 2433947 2433988 2434112 "PERMAN" 2434247 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-901 2431393 2433516 2433647 "PENDTREE" 2433849 NIL PENDTREE (NIL T) -8 NIL NIL) (-900 2429461 2430239 2430281 "PDRING" 2430938 NIL PDRING (NIL T) -9 NIL 2431224) (-899 2428564 2428782 2429144 "PDRING-" 2429149 NIL PDRING- (NIL T T) -8 NIL NIL) (-898 2425706 2426456 2427147 "PDEPROB" 2427893 T PDEPROB (NIL) -8 NIL NIL) (-897 2423253 2423755 2424310 "PDEPACK" 2425171 T PDEPACK (NIL) -7 NIL NIL) (-896 2422165 2422355 2422606 "PDECOMP" 2423052 NIL PDECOMP (NIL T T) -7 NIL NIL) (-895 2419769 2420586 2420615 "PDECAT" 2421402 T PDECAT (NIL) -9 NIL 2422115) (-894 2419520 2419553 2419643 "PCOMP" 2419730 NIL PCOMP (NIL T T) -7 NIL NIL) (-893 2417725 2418321 2418618 "PBWLB" 2419249 NIL PBWLB (NIL T) -8 NIL NIL) (-892 2410230 2411798 2413136 "PATTERN" 2416408 NIL PATTERN (NIL T) -8 NIL NIL) (-891 2409862 2409919 2410028 "PATTERN2" 2410167 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-890 2407619 2408007 2408464 "PATTERN1" 2409451 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-889 2405014 2405568 2406049 "PATRES" 2407184 NIL PATRES (NIL T T) -8 NIL NIL) (-888 2404578 2404645 2404777 "PATRES2" 2404941 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-887 2402461 2402866 2403273 "PATMATCH" 2404245 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-886 2401996 2402179 2402221 "PATMAB" 2402328 NIL PATMAB (NIL T) -9 NIL 2402411) (-885 2400541 2400850 2401108 "PATLRES" 2401801 NIL PATLRES (NIL T T T) -8 NIL NIL) (-884 2400088 2400211 2400253 "PATAB" 2400258 NIL PATAB (NIL T) -9 NIL 2400428) (-883 2397569 2398101 2398674 "PARTPERM" 2399535 T PARTPERM (NIL) -7 NIL NIL) (-882 2397190 2397253 2397355 "PARSURF" 2397500 NIL PARSURF (NIL T) -8 NIL NIL) (-881 2396822 2396879 2396988 "PARSU2" 2397127 NIL PARSU2 (NIL T T) -7 NIL NIL) (-880 2396443 2396506 2396608 "PARSCURV" 2396753 NIL PARSCURV (NIL T) -8 NIL NIL) (-879 2396075 2396132 2396241 "PARSC2" 2396380 NIL PARSC2 (NIL T T) -7 NIL NIL) (-878 2395714 2395772 2395869 "PARPCURV" 2396011 NIL PARPCURV (NIL T) -8 NIL NIL) (-877 2395346 2395403 2395512 "PARPC2" 2395651 NIL PARPC2 (NIL T T) -7 NIL NIL) (-876 2393826 2393944 2394263 "PARAMP" 2395201 NIL PARAMP (NIL T NIL T T T T T) -7 NIL NIL) (-875 2393346 2393432 2393551 "PAN2EXPR" 2393727 T PAN2EXPR (NIL) -7 NIL NIL) (-874 2392152 2392467 2392695 "PALETTE" 2393138 T PALETTE (NIL) -8 NIL NIL) (-873 2379785 2381951 2384067 "PAFF" 2390100 NIL PAFF (NIL T NIL T) -7 NIL NIL) (-872 2366781 2369109 2371320 "PAFFFF" 2377638 NIL PAFFFF (NIL T NIL T) -7 NIL NIL) (-871 2360622 2366040 2366234 "PADICRC" 2366636 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-870 2353821 2359968 2360152 "PADICRAT" 2360470 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-869 2352125 2353758 2353803 "PADIC" 2353808 NIL PADIC (NIL NIL) -8 NIL NIL) (-868 2349325 2350899 2350940 "PADICCT" 2351521 NIL PADICCT (NIL NIL) -9 NIL 2351803) (-867 2348282 2348482 2348750 "PADEPAC" 2349112 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-866 2347494 2347627 2347833 "PADE" 2348144 NIL PADE (NIL T T T) -7 NIL NIL) (-865 2343971 2347112 2347231 "PACRAT" 2347395 T PACRAT (NIL) -8 NIL NIL) (-864 2340032 2343082 2343111 "PACRATC" 2343116 T PACRATC (NIL) -9 NIL 2343196) (-863 2336154 2338119 2338148 "PACPERC" 2339094 T PACPERC (NIL) -9 NIL 2339534) (-862 2332799 2335928 2336019 "PACOFF" 2336095 NIL PACOFF (NIL T) -8 NIL NIL) (-861 2329469 2332154 2332183 "PACFFC" 2332188 T PACFFC (NIL) -9 NIL 2332209) (-860 2325559 2329152 2329253 "PACEXT" 2329400 NIL PACEXT (NIL NIL) -8 NIL NIL) (-859 2320937 2324454 2324483 "PACEXTC" 2324488 T PACEXTC (NIL) -9 NIL 2324532) (-858 2318945 2319777 2320092 "OWP" 2320706 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-857 2318029 2318550 2318722 "OVAR" 2318813 NIL OVAR (NIL NIL) -8 NIL NIL) (-856 2317293 2317414 2317575 "OUT" 2317888 T OUT (NIL) -7 NIL NIL) (-855 2306339 2308518 2310688 "OUTFORM" 2315143 T OUTFORM (NIL) -8 NIL NIL) (-854 2305747 2306068 2306157 "OSI" 2306270 T OSI (NIL) -8 NIL NIL) (-853 2304494 2304721 2305005 "ORTHPOL" 2305495 NIL ORTHPOL (NIL T) -7 NIL NIL) (-852 2301856 2304151 2304291 "OREUP" 2304437 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-851 2299243 2301545 2301673 "ORESUP" 2301798 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-850 2296751 2297257 2297822 "OREPCTO" 2298728 NIL OREPCTO (NIL T T) -7 NIL NIL) (-849 2290621 2292832 2292874 "OREPCAT" 2295222 NIL OREPCAT (NIL T) -9 NIL 2296322) (-848 2287768 2288550 2289608 "OREPCAT-" 2289613 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-847 2286944 2287216 2287245 "ORDSET" 2287554 T ORDSET (NIL) -9 NIL 2287718) (-846 2286463 2286585 2286778 "ORDSET-" 2286783 NIL ORDSET- (NIL T) -8 NIL NIL) (-845 2285072 2285873 2285902 "ORDRING" 2286104 T ORDRING (NIL) -9 NIL 2286229) (-844 2284717 2284811 2284955 "ORDRING-" 2284960 NIL ORDRING- (NIL T) -8 NIL NIL) (-843 2284091 2284572 2284601 "ORDMON" 2284606 T ORDMON (NIL) -9 NIL 2284627) (-842 2283253 2283400 2283595 "ORDFUNS" 2283940 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-841 2282739 2283122 2283151 "ORDFIN" 2283156 T ORDFIN (NIL) -9 NIL 2283177) (-840 2279251 2281331 2281737 "ORDCOMP" 2282366 NIL ORDCOMP (NIL T) -8 NIL NIL) (-839 2278517 2278644 2278830 "ORDCOMP2" 2279111 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-838 2275025 2275907 2276744 "OPTPROB" 2277700 T OPTPROB (NIL) -8 NIL NIL) (-837 2271827 2272466 2273170 "OPTPACK" 2274341 T OPTPACK (NIL) -7 NIL NIL) (-836 2269539 2270279 2270308 "OPTCAT" 2271127 T OPTCAT (NIL) -9 NIL 2271777) (-835 2269307 2269346 2269412 "OPQUERY" 2269493 T OPQUERY (NIL) -7 NIL NIL) (-834 2266433 2267624 2268125 "OP" 2268839 NIL OP (NIL T) -8 NIL NIL) (-833 2263198 2265236 2265602 "ONECOMP" 2266100 NIL ONECOMP (NIL T) -8 NIL NIL) (-832 2262503 2262618 2262792 "ONECOMP2" 2263070 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-831 2261922 2262028 2262158 "OMSERVER" 2262393 T OMSERVER (NIL) -7 NIL NIL) (-830 2258809 2261361 2261402 "OMSAGG" 2261463 NIL OMSAGG (NIL T) -9 NIL 2261527) (-829 2257432 2257695 2257977 "OMPKG" 2258547 T OMPKG (NIL) -7 NIL NIL) (-828 2256861 2256964 2256993 "OM" 2257292 T OM (NIL) -9 NIL NIL) (-827 2255399 2256412 2256580 "OMLO" 2256743 NIL OMLO (NIL T T) -8 NIL NIL) (-826 2254324 2254471 2254698 "OMEXPR" 2255225 NIL OMEXPR (NIL T) -7 NIL NIL) (-825 2253642 2253870 2254006 "OMERR" 2254208 T OMERR (NIL) -8 NIL NIL) (-824 2252820 2253063 2253223 "OMERRK" 2253502 T OMERRK (NIL) -8 NIL NIL) (-823 2252298 2252497 2252605 "OMENC" 2252732 T OMENC (NIL) -8 NIL NIL) (-822 2246193 2247378 2248549 "OMDEV" 2251147 T OMDEV (NIL) -8 NIL NIL) (-821 2245262 2245433 2245627 "OMCONN" 2246019 T OMCONN (NIL) -8 NIL NIL) (-820 2243873 2244859 2244888 "OINTDOM" 2244893 T OINTDOM (NIL) -9 NIL 2244914) (-819 2239524 2240779 2241523 "OFMONOID" 2243161 NIL OFMONOID (NIL T) -8 NIL NIL) (-818 2238962 2239461 2239506 "ODVAR" 2239511 NIL ODVAR (NIL T) -8 NIL NIL) (-817 2236089 2238461 2238645 "ODR" 2238838 NIL ODR (NIL T T NIL) -8 NIL NIL) (-816 2228387 2235865 2235991 "ODPOL" 2235996 NIL ODPOL (NIL T) -8 NIL NIL) (-815 2222138 2228259 2228364 "ODP" 2228369 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-814 2220904 2221119 2221394 "ODETOOLS" 2221912 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-813 2217873 2218529 2219245 "ODESYS" 2220237 NIL ODESYS (NIL T T) -7 NIL NIL) (-812 2212757 2213665 2214689 "ODERTRIC" 2216949 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-811 2212183 2212265 2212459 "ODERED" 2212669 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-810 2209071 2209619 2210296 "ODERAT" 2211606 NIL ODERAT (NIL T T) -7 NIL NIL) (-809 2206031 2206495 2207092 "ODEPRRIC" 2208600 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-808 2203902 2204469 2204978 "ODEPROB" 2205542 T ODEPROB (NIL) -8 NIL NIL) (-807 2200424 2200907 2201554 "ODEPRIM" 2203381 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-806 2199673 2199775 2200035 "ODEPAL" 2200316 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-805 2195835 2196626 2197490 "ODEPACK" 2198829 T ODEPACK (NIL) -7 NIL NIL) (-804 2194868 2194975 2195204 "ODEINT" 2195724 NIL ODEINT (NIL T T) -7 NIL NIL) (-803 2188969 2190394 2191841 "ODEIFTBL" 2193441 T ODEIFTBL (NIL) -8 NIL NIL) (-802 2184304 2185090 2186049 "ODEEF" 2188128 NIL ODEEF (NIL T T) -7 NIL NIL) (-801 2183639 2183728 2183958 "ODECONST" 2184209 NIL ODECONST (NIL T T T) -7 NIL NIL) (-800 2181789 2182424 2182453 "ODECAT" 2183058 T ODECAT (NIL) -9 NIL 2183589) (-799 2178588 2181494 2181616 "OCT" 2181699 NIL OCT (NIL T) -8 NIL NIL) (-798 2178226 2178269 2178396 "OCTCT2" 2178539 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-797 2173006 2175494 2175535 "OC" 2176632 NIL OC (NIL T) -9 NIL 2177482) (-796 2170233 2170981 2171971 "OC-" 2172065 NIL OC- (NIL T T) -8 NIL NIL) (-795 2169610 2170052 2170081 "OCAMON" 2170086 T OCAMON (NIL) -9 NIL 2170107) (-794 2169062 2169469 2169498 "OASGP" 2169503 T OASGP (NIL) -9 NIL 2169523) (-793 2168348 2168811 2168840 "OAMONS" 2168880 T OAMONS (NIL) -9 NIL 2168923) (-792 2167787 2168194 2168223 "OAMON" 2168228 T OAMON (NIL) -9 NIL 2168248) (-791 2167090 2167582 2167611 "OAGROUP" 2167616 T OAGROUP (NIL) -9 NIL 2167636) (-790 2166780 2166830 2166918 "NUMTUBE" 2167034 NIL NUMTUBE (NIL T) -7 NIL NIL) (-789 2160353 2161871 2163407 "NUMQUAD" 2165264 T NUMQUAD (NIL) -7 NIL NIL) (-788 2156109 2157097 2158122 "NUMODE" 2159348 T NUMODE (NIL) -7 NIL NIL) (-787 2153489 2154343 2154372 "NUMINT" 2155295 T NUMINT (NIL) -9 NIL 2156059) (-786 2152437 2152634 2152852 "NUMFMT" 2153291 T NUMFMT (NIL) -7 NIL NIL) (-785 2138815 2141757 2144281 "NUMERIC" 2149952 NIL NUMERIC (NIL T) -7 NIL NIL) (-784 2133218 2138263 2138359 "NTSCAT" 2138364 NIL NTSCAT (NIL T T T T) -9 NIL 2138403) (-783 2132414 2132579 2132771 "NTPOLFN" 2133058 NIL NTPOLFN (NIL T) -7 NIL NIL) (-782 2120210 2129241 2130052 "NSUP" 2131636 NIL NSUP (NIL T) -8 NIL NIL) (-781 2119842 2119899 2120008 "NSUP2" 2120147 NIL NSUP2 (NIL T T) -7 NIL NIL) (-780 2109793 2119616 2119749 "NSMP" 2119754 NIL NSMP (NIL T T) -8 NIL NIL) (-779 2097885 2109375 2109539 "NSDPS" 2109661 NIL NSDPS (NIL T) -8 NIL NIL) (-778 2096317 2096618 2096975 "NREP" 2097573 NIL NREP (NIL T) -7 NIL NIL) (-777 2093406 2093954 2094603 "NPOLYGON" 2095759 NIL NPOLYGON (NIL T T T NIL) -7 NIL NIL) (-776 2091997 2092249 2092607 "NPCOEF" 2093149 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-775 2091279 2091781 2091865 "NOTTING" 2091945 NIL NOTTING (NIL T) -8 NIL NIL) (-774 2090345 2090460 2090676 "NORMRETR" 2091160 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-773 2088386 2088676 2089085 "NORMPK" 2090053 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-772 2088071 2088099 2088223 "NORMMA" 2088352 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-771 2087898 2088028 2088057 "NONE" 2088062 T NONE (NIL) -8 NIL NIL) (-770 2087687 2087716 2087785 "NONE1" 2087862 NIL NONE1 (NIL T) -7 NIL NIL) (-769 2087170 2087232 2087418 "NODE1" 2087619 NIL NODE1 (NIL T T) -7 NIL NIL) (-768 2085464 2086333 2086588 "NNI" 2086935 T NNI (NIL) -8 NIL NIL) (-767 2083884 2084197 2084561 "NLINSOL" 2085132 NIL NLINSOL (NIL T) -7 NIL NIL) (-766 2080052 2081019 2081941 "NIPROB" 2082982 T NIPROB (NIL) -8 NIL NIL) (-765 2078809 2079043 2079345 "NFINTBAS" 2079814 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-764 2078538 2078581 2078662 "NEWTON" 2078760 NIL NEWTON (NIL T) -7 NIL NIL) (-763 2077246 2077477 2077758 "NCODIV" 2078306 NIL NCODIV (NIL T T) -7 NIL NIL) (-762 2077008 2077045 2077120 "NCNTFRAC" 2077203 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-761 2075188 2075552 2075972 "NCEP" 2076633 NIL NCEP (NIL T) -7 NIL NIL) (-760 2074098 2074837 2074866 "NASRING" 2074976 T NASRING (NIL) -9 NIL 2075050) (-759 2073893 2073937 2074031 "NASRING-" 2074036 NIL NASRING- (NIL T) -8 NIL NIL) (-758 2073045 2073544 2073573 "NARNG" 2073690 T NARNG (NIL) -9 NIL 2073781) (-757 2072737 2072804 2072938 "NARNG-" 2072943 NIL NARNG- (NIL T) -8 NIL NIL) (-756 2071616 2071823 2072058 "NAGSP" 2072522 T NAGSP (NIL) -7 NIL NIL) (-755 2062888 2064572 2066245 "NAGS" 2069963 T NAGS (NIL) -7 NIL NIL) (-754 2061436 2061744 2062075 "NAGF07" 2062577 T NAGF07 (NIL) -7 NIL NIL) (-753 2055974 2057265 2058572 "NAGF04" 2060149 T NAGF04 (NIL) -7 NIL NIL) (-752 2048942 2050556 2052189 "NAGF02" 2054361 T NAGF02 (NIL) -7 NIL NIL) (-751 2044166 2045266 2046383 "NAGF01" 2047845 T NAGF01 (NIL) -7 NIL NIL) (-750 2037794 2039360 2040945 "NAGE04" 2042601 T NAGE04 (NIL) -7 NIL NIL) (-749 2028963 2031084 2033214 "NAGE02" 2035684 T NAGE02 (NIL) -7 NIL NIL) (-748 2024916 2025863 2026827 "NAGE01" 2028019 T NAGE01 (NIL) -7 NIL NIL) (-747 2022711 2023245 2023803 "NAGD03" 2024378 T NAGD03 (NIL) -7 NIL NIL) (-746 2014461 2016389 2018343 "NAGD02" 2020777 T NAGD02 (NIL) -7 NIL NIL) (-745 2008272 2009697 2011137 "NAGD01" 2013041 T NAGD01 (NIL) -7 NIL NIL) (-744 2004481 2005303 2006140 "NAGC06" 2007455 T NAGC06 (NIL) -7 NIL NIL) (-743 2002946 2003278 2003634 "NAGC05" 2004145 T NAGC05 (NIL) -7 NIL NIL) (-742 2002322 2002441 2002585 "NAGC02" 2002822 T NAGC02 (NIL) -7 NIL NIL) (-741 2001381 2001938 2001979 "NAALG" 2002058 NIL NAALG (NIL T) -9 NIL 2002119) (-740 2001216 2001245 2001335 "NAALG-" 2001340 NIL NAALG- (NIL T T) -8 NIL NIL) (-739 1992092 2000332 2000607 "MYUP" 2000987 NIL MYUP (NIL NIL T) -8 NIL NIL) (-738 1982455 1990548 1990919 "MYEXPR" 1991787 NIL MYEXPR (NIL NIL T) -8 NIL NIL) (-737 1976405 1977513 1978700 "MULTSQFR" 1981351 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-736 1975724 1975799 1975983 "MULTFACT" 1976317 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-735 1968849 1972758 1972812 "MTSCAT" 1973882 NIL MTSCAT (NIL T T) -9 NIL 1974396) (-734 1968561 1968615 1968707 "MTHING" 1968789 NIL MTHING (NIL T) -7 NIL NIL) (-733 1968353 1968386 1968446 "MSYSCMD" 1968521 T MSYSCMD (NIL) -7 NIL NIL) (-732 1964465 1967108 1967428 "MSET" 1968066 NIL MSET (NIL T) -8 NIL NIL) (-731 1961559 1964025 1964067 "MSETAGG" 1964072 NIL MSETAGG (NIL T) -9 NIL 1964106) (-730 1957337 1958950 1959689 "MRING" 1960865 NIL MRING (NIL T T) -8 NIL NIL) (-729 1956903 1956970 1957101 "MRF2" 1957264 NIL MRF2 (NIL T T T) -7 NIL NIL) (-728 1956521 1956556 1956700 "MRATFAC" 1956862 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-727 1954133 1954428 1954859 "MPRFF" 1956226 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-726 1948147 1953987 1954084 "MPOLY" 1954089 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-725 1947637 1947672 1947880 "MPCPF" 1948106 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-724 1947151 1947194 1947378 "MPC3" 1947588 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-723 1946346 1946427 1946648 "MPC2" 1947066 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-722 1944647 1944984 1945374 "MONOTOOL" 1946006 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-721 1943770 1944105 1944134 "MONOID" 1944411 T MONOID (NIL) -9 NIL 1944583) (-720 1943148 1943311 1943554 "MONOID-" 1943559 NIL MONOID- (NIL T) -8 NIL NIL) (-719 1934029 1940059 1940119 "MONOGEN" 1940793 NIL MONOGEN (NIL T T) -9 NIL 1941246) (-718 1931247 1931982 1932982 "MONOGEN-" 1933101 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-717 1930105 1930525 1930554 "MONADWU" 1930946 T MONADWU (NIL) -9 NIL 1931184) (-716 1929477 1929636 1929884 "MONADWU-" 1929889 NIL MONADWU- (NIL T) -8 NIL NIL) (-715 1928861 1929079 1929108 "MONAD" 1929315 T MONAD (NIL) -9 NIL 1929427) (-714 1928546 1928624 1928756 "MONAD-" 1928761 NIL MONAD- (NIL T) -8 NIL NIL) (-713 1926797 1927459 1927738 "MOEBIUS" 1928299 NIL MOEBIUS (NIL T) -8 NIL NIL) (-712 1926188 1926566 1926607 "MODULE" 1926612 NIL MODULE (NIL T) -9 NIL 1926638) (-711 1925756 1925852 1926042 "MODULE-" 1926047 NIL MODULE- (NIL T T) -8 NIL NIL) (-710 1923425 1924120 1924447 "MODRING" 1925580 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-709 1920371 1921536 1922054 "MODOP" 1922957 NIL MODOP (NIL T T) -8 NIL NIL) (-708 1918558 1919010 1919351 "MODMONOM" 1920170 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-707 1908178 1916754 1917175 "MODMON" 1918188 NIL MODMON (NIL T T) -8 NIL NIL) (-706 1905304 1907022 1907298 "MODFIELD" 1908053 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-705 1904308 1904585 1904775 "MMLFORM" 1905134 T MMLFORM (NIL) -8 NIL NIL) (-704 1903834 1903877 1904056 "MMAP" 1904259 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-703 1902059 1902836 1902878 "MLO" 1903301 NIL MLO (NIL T) -9 NIL 1903542) (-702 1899426 1899941 1900543 "MLIFT" 1901540 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-701 1898817 1898901 1899055 "MKUCFUNC" 1899337 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-700 1898416 1898486 1898609 "MKRECORD" 1898740 NIL MKRECORD (NIL T T) -7 NIL NIL) (-699 1897464 1897625 1897853 "MKFUNC" 1898227 NIL MKFUNC (NIL T) -7 NIL NIL) (-698 1896852 1896956 1897112 "MKFLCFN" 1897347 NIL MKFLCFN (NIL T) -7 NIL NIL) (-697 1896278 1896645 1896734 "MKCHSET" 1896796 NIL MKCHSET (NIL T) -8 NIL NIL) (-696 1895555 1895657 1895842 "MKBCFUNC" 1896171 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-695 1892239 1895109 1895245 "MINT" 1895439 T MINT (NIL) -8 NIL NIL) (-694 1891051 1891294 1891571 "MHROWRED" 1891994 NIL MHROWRED (NIL T) -7 NIL NIL) (-693 1886318 1889492 1889918 "MFLOAT" 1890645 T MFLOAT (NIL) -8 NIL NIL) (-692 1885675 1885751 1885922 "MFINFACT" 1886230 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-691 1881990 1882838 1883722 "MESH" 1884811 T MESH (NIL) -7 NIL NIL) (-690 1880380 1880692 1881045 "MDDFACT" 1881677 NIL MDDFACT (NIL T) -7 NIL NIL) (-689 1877262 1879573 1879615 "MDAGG" 1879870 NIL MDAGG (NIL T) -9 NIL 1880013) (-688 1866903 1876555 1876762 "MCMPLX" 1877075 T MCMPLX (NIL) -8 NIL NIL) (-687 1866044 1866190 1866390 "MCDEN" 1866752 NIL MCDEN (NIL T T) -7 NIL NIL) (-686 1863934 1864204 1864584 "MCALCFN" 1865774 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-685 1861546 1862069 1862631 "MATSTOR" 1863405 NIL MATSTOR (NIL T) -7 NIL NIL) (-684 1857412 1860922 1861168 "MATRIX" 1861333 NIL MATRIX (NIL T) -8 NIL NIL) (-683 1853188 1853891 1854624 "MATLIN" 1856772 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-682 1842699 1845967 1846045 "MATCAT" 1851327 NIL MATCAT (NIL T T T) -9 NIL 1852889) (-681 1838737 1839852 1841320 "MATCAT-" 1841325 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-680 1837331 1837484 1837817 "MATCAT2" 1838572 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-679 1836071 1836337 1836652 "MAPPKG4" 1837062 NIL MAPPKG4 (NIL T T) -7 NIL NIL) (-678 1834183 1834507 1834891 "MAPPKG3" 1835746 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-677 1833164 1833337 1833559 "MAPPKG2" 1834007 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-676 1831663 1831947 1832274 "MAPPKG1" 1832870 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-675 1831274 1831332 1831455 "MAPHACK3" 1831599 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-674 1830866 1830927 1831041 "MAPHACK2" 1831206 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-673 1830304 1830407 1830549 "MAPHACK1" 1830757 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-672 1823472 1824413 1825510 "MAMA" 1829300 NIL MAMA (NIL T T T T) -7 NIL NIL) (-671 1821578 1822172 1822476 "MAGMA" 1823200 NIL MAGMA (NIL T) -8 NIL NIL) (-670 1819814 1820186 1820241 "MAGCDOC" 1821178 NIL MAGCDOC (NIL T T) -9 NIL NIL) (-669 1816289 1818055 1818515 "M3D" 1819387 NIL M3D (NIL T) -8 NIL NIL) (-668 1810483 1814689 1814731 "LZSTAGG" 1815513 NIL LZSTAGG (NIL T) -9 NIL 1815808) (-667 1806457 1807614 1809071 "LZSTAGG-" 1809076 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-666 1803571 1804348 1804835 "LWORD" 1806002 NIL LWORD (NIL T) -8 NIL NIL) (-665 1796726 1803342 1803476 "LSQM" 1803481 NIL LSQM (NIL NIL T) -8 NIL NIL) (-664 1795950 1796089 1796317 "LSPP" 1796581 NIL LSPP (NIL T T T T) -7 NIL NIL) (-663 1793762 1794063 1794519 "LSMP" 1795639 NIL LSMP (NIL T T T T) -7 NIL NIL) (-662 1790541 1791215 1791945 "LSMP1" 1793064 NIL LSMP1 (NIL T) -7 NIL NIL) (-661 1784498 1789731 1789773 "LSAGG" 1789835 NIL LSAGG (NIL T) -9 NIL 1789913) (-660 1781193 1782117 1783330 "LSAGG-" 1783335 NIL LSAGG- (NIL T T) -8 NIL NIL) (-659 1778819 1780337 1780586 "LPOLY" 1780988 NIL LPOLY (NIL T T) -8 NIL NIL) (-658 1778401 1778486 1778609 "LPEFRAC" 1778728 NIL LPEFRAC (NIL T) -7 NIL NIL) (-657 1775965 1776214 1776646 "LPARSPT" 1778143 NIL LPARSPT (NIL T NIL T T T T T) -7 NIL NIL) (-656 1774440 1774767 1775127 "LOP" 1775637 NIL LOP (NIL T) -7 NIL NIL) (-655 1772789 1773536 1773788 "LO" 1774273 NIL LO (NIL T T T) -8 NIL NIL) (-654 1772440 1772552 1772581 "LOGIC" 1772692 T LOGIC (NIL) -9 NIL 1772773) (-653 1772302 1772325 1772396 "LOGIC-" 1772401 NIL LOGIC- (NIL T) -8 NIL NIL) (-652 1771495 1771635 1771828 "LODOOPS" 1772158 NIL LODOOPS (NIL T T) -7 NIL NIL) (-651 1768907 1771411 1771477 "LODO" 1771482 NIL LODO (NIL T NIL) -8 NIL NIL) (-650 1767447 1767682 1768034 "LODOF" 1768655 NIL LODOF (NIL T T) -7 NIL NIL) (-649 1763846 1766287 1766329 "LODOCAT" 1766767 NIL LODOCAT (NIL T) -9 NIL 1766977) (-648 1763579 1763637 1763764 "LODOCAT-" 1763769 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-647 1760888 1763420 1763538 "LODO2" 1763543 NIL LODO2 (NIL T T) -8 NIL NIL) (-646 1758312 1760825 1760870 "LODO1" 1760875 NIL LODO1 (NIL T) -8 NIL NIL) (-645 1757172 1757337 1757649 "LODEEF" 1758135 NIL LODEEF (NIL T T T) -7 NIL NIL) (-644 1749999 1754164 1754205 "LOCPOWC" 1755667 NIL LOCPOWC (NIL T) -9 NIL 1756244) (-643 1745323 1748161 1748203 "LNAGG" 1749150 NIL LNAGG (NIL T) -9 NIL 1749593) (-642 1744470 1744684 1745026 "LNAGG-" 1745031 NIL LNAGG- (NIL T T) -8 NIL NIL) (-641 1740633 1741395 1742034 "LMOPS" 1743885 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-640 1740027 1740389 1740431 "LMODULE" 1740492 NIL LMODULE (NIL T) -9 NIL 1740534) (-639 1737279 1739672 1739795 "LMDICT" 1739937 NIL LMDICT (NIL T) -8 NIL NIL) (-638 1736436 1736570 1736757 "LISYSER" 1737141 NIL LISYSER (NIL T T) -7 NIL NIL) (-637 1729673 1735386 1735682 "LIST" 1736173 NIL LIST (NIL T) -8 NIL NIL) (-636 1729198 1729272 1729411 "LIST3" 1729593 NIL LIST3 (NIL T T T) -7 NIL NIL) (-635 1728205 1728383 1728611 "LIST2" 1729016 NIL LIST2 (NIL T T) -7 NIL NIL) (-634 1726339 1726651 1727050 "LIST2MAP" 1727852 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-633 1725044 1725724 1725766 "LINEXP" 1726021 NIL LINEXP (NIL T) -9 NIL 1726170) (-632 1723691 1723951 1724248 "LINDEP" 1724796 NIL LINDEP (NIL T T) -7 NIL NIL) (-631 1720458 1721177 1721954 "LIMITRF" 1722946 NIL LIMITRF (NIL T) -7 NIL NIL) (-630 1718734 1719029 1719445 "LIMITPS" 1720153 NIL LIMITPS (NIL T T) -7 NIL NIL) (-629 1713193 1718249 1718475 "LIE" 1718557 NIL LIE (NIL T T) -8 NIL NIL) (-628 1712242 1712685 1712726 "LIECAT" 1712866 NIL LIECAT (NIL T) -9 NIL 1713016) (-627 1712083 1712110 1712198 "LIECAT-" 1712203 NIL LIECAT- (NIL T T) -8 NIL NIL) (-626 1704617 1711462 1711645 "LIB" 1711920 T LIB (NIL) -8 NIL NIL) (-625 1700254 1701135 1702070 "LGROBP" 1703734 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-624 1697735 1698059 1698470 "LF" 1699927 NIL LF (NIL T T) -7 NIL NIL) (-623 1696432 1697162 1697191 "LFCAT" 1697466 T LFCAT (NIL) -9 NIL 1697641) (-622 1693336 1693964 1694652 "LEXTRIPK" 1695796 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-621 1690042 1690906 1691409 "LEXP" 1692916 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-620 1688440 1688753 1689154 "LEADCDET" 1689724 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-619 1687630 1687704 1687933 "LAZM3PK" 1688361 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-618 1682546 1685713 1686248 "LAUPOL" 1687145 NIL LAUPOL (NIL T T) -8 NIL NIL) (-617 1682111 1682155 1682323 "LAPLACE" 1682496 NIL LAPLACE (NIL T T) -7 NIL NIL) (-616 1680041 1681214 1681464 "LA" 1681945 NIL LA (NIL T T T) -8 NIL NIL) (-615 1679097 1679691 1679733 "LALG" 1679795 NIL LALG (NIL T) -9 NIL 1679854) (-614 1678811 1678870 1679006 "LALG-" 1679011 NIL LALG- (NIL T T) -8 NIL NIL) (-613 1677715 1677902 1678201 "KOVACIC" 1678611 NIL KOVACIC (NIL T T) -7 NIL NIL) (-612 1677549 1677573 1677615 "KONVERT" 1677677 NIL KONVERT (NIL T) -9 NIL NIL) (-611 1677383 1677407 1677449 "KOERCE" 1677511 NIL KOERCE (NIL T) -9 NIL NIL) (-610 1675119 1675879 1676271 "KERNEL" 1677023 NIL KERNEL (NIL T) -8 NIL NIL) (-609 1674621 1674702 1674832 "KERNEL2" 1675033 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-608 1668304 1672986 1673041 "KDAGG" 1673418 NIL KDAGG (NIL T T) -9 NIL 1673624) (-607 1667833 1667957 1668162 "KDAGG-" 1668167 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-606 1660982 1667494 1667649 "KAFILE" 1667711 NIL KAFILE (NIL T) -8 NIL NIL) (-605 1655441 1660497 1660723 "JORDAN" 1660805 NIL JORDAN (NIL T T) -8 NIL NIL) (-604 1651784 1653684 1653739 "IXAGG" 1654668 NIL IXAGG (NIL T T) -9 NIL 1655123) (-603 1650703 1651009 1651428 "IXAGG-" 1651433 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-602 1646287 1650625 1650684 "IVECTOR" 1650689 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-601 1645053 1645290 1645556 "ITUPLE" 1646054 NIL ITUPLE (NIL T) -8 NIL NIL) (-600 1643477 1643654 1643962 "ITRIGMNP" 1644875 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-599 1642222 1642426 1642709 "ITFUN3" 1643253 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-598 1641854 1641911 1642020 "ITFUN2" 1642159 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-597 1639647 1640718 1641016 "ITAYLOR" 1641589 NIL ITAYLOR (NIL T) -8 NIL NIL) (-596 1628586 1633786 1634948 "ISUPS" 1638518 NIL ISUPS (NIL T) -8 NIL NIL) (-595 1627690 1627830 1628066 "ISUMP" 1628433 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-594 1622960 1627491 1627570 "ISTRING" 1627643 NIL ISTRING (NIL NIL) -8 NIL NIL) (-593 1622170 1622251 1622467 "IRURPK" 1622874 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-592 1621106 1621307 1621547 "IRSN" 1621950 T IRSN (NIL) -7 NIL NIL) (-591 1619137 1619492 1619927 "IRRF2F" 1620745 NIL IRRF2F (NIL T) -7 NIL NIL) (-590 1618884 1618922 1618998 "IRREDFFX" 1619093 NIL IRREDFFX (NIL T) -7 NIL NIL) (-589 1617499 1617758 1618057 "IROOT" 1618617 NIL IROOT (NIL T) -7 NIL NIL) (-588 1614135 1615187 1615877 "IR" 1616841 NIL IR (NIL T) -8 NIL NIL) (-587 1611748 1612243 1612809 "IR2" 1613613 NIL IR2 (NIL T T) -7 NIL NIL) (-586 1610820 1610933 1611154 "IR2F" 1611631 NIL IR2F (NIL T T) -7 NIL NIL) (-585 1610611 1610645 1610705 "IPRNTPK" 1610780 T IPRNTPK (NIL) -7 NIL NIL) (-584 1607140 1610500 1610569 "IPF" 1610574 NIL IPF (NIL NIL) -8 NIL NIL) (-583 1605457 1607065 1607122 "IPADIC" 1607127 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-582 1604954 1605012 1605202 "INVLAPLA" 1605393 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-581 1594603 1596956 1599342 "INTTR" 1602618 NIL INTTR (NIL T T) -7 NIL NIL) (-580 1590961 1591703 1592560 "INTTOOLS" 1593795 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-579 1590547 1590638 1590755 "INTSLPE" 1590864 T INTSLPE (NIL) -7 NIL NIL) (-578 1588497 1590470 1590529 "INTRVL" 1590534 NIL INTRVL (NIL T) -8 NIL NIL) (-577 1586099 1586611 1587186 "INTRF" 1587982 NIL INTRF (NIL T) -7 NIL NIL) (-576 1585510 1585607 1585749 "INTRET" 1585997 NIL INTRET (NIL T) -7 NIL NIL) (-575 1583507 1583896 1584366 "INTRAT" 1585118 NIL INTRAT (NIL T T) -7 NIL NIL) (-574 1580743 1581326 1581948 "INTPM" 1582996 NIL INTPM (NIL T T) -7 NIL NIL) (-573 1577448 1578047 1578791 "INTPAF" 1580130 NIL INTPAF (NIL T T T) -7 NIL NIL) (-572 1572627 1573589 1574640 "INTPACK" 1576417 T INTPACK (NIL) -7 NIL NIL) (-571 1569481 1572356 1572483 "INT" 1572520 T INT (NIL) -8 NIL NIL) (-570 1568733 1568885 1569093 "INTHERTR" 1569323 NIL INTHERTR (NIL T T) -7 NIL NIL) (-569 1568172 1568252 1568440 "INTHERAL" 1568647 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-568 1566018 1566461 1566918 "INTHEORY" 1567735 T INTHEORY (NIL) -7 NIL NIL) (-567 1557329 1558949 1560727 "INTG0" 1564371 NIL INTG0 (NIL T T T) -7 NIL NIL) (-566 1537902 1542692 1547502 "INTFTBL" 1552539 T INTFTBL (NIL) -8 NIL NIL) (-565 1535939 1536146 1536547 "INTFRSP" 1537692 NIL INTFRSP (NIL T NIL T T T T T T) -7 NIL NIL) (-564 1535188 1535326 1535499 "INTFACT" 1535798 NIL INTFACT (NIL T) -7 NIL NIL) (-563 1534778 1534820 1534971 "INTERGB" 1535140 NIL INTERGB (NIL T NIL T T T) -7 NIL NIL) (-562 1532163 1532609 1533173 "INTEF" 1534332 NIL INTEF (NIL T T) -7 NIL NIL) (-561 1530620 1531369 1531398 "INTDOM" 1531699 T INTDOM (NIL) -9 NIL 1531906) (-560 1529989 1530163 1530405 "INTDOM-" 1530410 NIL INTDOM- (NIL T) -8 NIL NIL) (-559 1528593 1528698 1529088 "INTDIVP" 1529879 NIL INTDIVP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-558 1525079 1527009 1527064 "INTCAT" 1527863 NIL INTCAT (NIL T) -9 NIL 1528184) (-557 1524552 1524654 1524782 "INTBIT" 1524971 T INTBIT (NIL) -7 NIL NIL) (-556 1523223 1523377 1523691 "INTALG" 1524397 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-555 1522680 1522770 1522940 "INTAF" 1523127 NIL INTAF (NIL T T) -7 NIL NIL) (-554 1516146 1522490 1522630 "INTABL" 1522635 NIL INTABL (NIL T T T) -8 NIL NIL) (-553 1511091 1513817 1513846 "INS" 1514814 T INS (NIL) -9 NIL 1515497) (-552 1508331 1509102 1510076 "INS-" 1510149 NIL INS- (NIL T) -8 NIL NIL) (-551 1507106 1507333 1507631 "INPSIGN" 1508084 NIL INPSIGN (NIL T T) -7 NIL NIL) (-550 1506224 1506341 1506538 "INPRODPF" 1506986 NIL INPRODPF (NIL T T) -7 NIL NIL) (-549 1505118 1505235 1505472 "INPRODFF" 1506104 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-548 1504118 1504270 1504530 "INNMFACT" 1504954 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-547 1503315 1503412 1503600 "INMODGCD" 1504017 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-546 1501824 1502068 1502392 "INFSP" 1503060 NIL INFSP (NIL T T T) -7 NIL NIL) (-545 1501008 1501125 1501308 "INFPROD0" 1501704 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-544 1497889 1499073 1499588 "INFORM" 1500501 T INFORM (NIL) -8 NIL NIL) (-543 1497499 1497559 1497657 "INFORM1" 1497824 NIL INFORM1 (NIL T) -7 NIL NIL) (-542 1497022 1497111 1497225 "INFINITY" 1497405 T INFINITY (NIL) -7 NIL NIL) (-541 1494705 1495702 1496045 "INFCLSPT" 1496882 NIL INFCLSPT (NIL T NIL T T T T T T T) -8 NIL NIL) (-540 1492582 1493827 1494121 "INFCLSPS" 1494475 NIL INFCLSPS (NIL T NIL T) -8 NIL NIL) (-539 1485132 1486055 1486276 "INFCLCT" 1491707 NIL INFCLCT (NIL T NIL T T T T T T T) -9 NIL 1492518) (-538 1483750 1483998 1484319 "INEP" 1484880 NIL INEP (NIL T T T) -7 NIL NIL) (-537 1483026 1483647 1483712 "INDE" 1483717 NIL INDE (NIL T) -8 NIL NIL) (-536 1482590 1482658 1482775 "INCRMAPS" 1482953 NIL INCRMAPS (NIL T) -7 NIL NIL) (-535 1477901 1478826 1479770 "INBFF" 1481678 NIL INBFF (NIL T) -7 NIL NIL) (-534 1474248 1477745 1477849 "IMATRIX" 1477854 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-533 1472962 1473085 1473399 "IMATQF" 1474105 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-532 1471184 1471411 1471747 "IMATLIN" 1472719 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-531 1465816 1471108 1471166 "ILIST" 1471171 NIL ILIST (NIL T NIL) -8 NIL NIL) (-530 1463775 1465676 1465789 "IIARRAY2" 1465794 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-529 1459091 1463686 1463750 "IFF" 1463755 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-528 1454140 1458383 1458571 "IFARRAY" 1458948 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-527 1453347 1454044 1454117 "IFAMON" 1454122 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-526 1452930 1452995 1453050 "IEVALAB" 1453257 NIL IEVALAB (NIL T T) -9 NIL NIL) (-525 1452605 1452673 1452833 "IEVALAB-" 1452838 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-524 1452263 1452519 1452582 "IDPO" 1452587 NIL IDPO (NIL T T) -8 NIL NIL) (-523 1451540 1452152 1452227 "IDPOAMS" 1452232 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-522 1450874 1451429 1451504 "IDPOAM" 1451509 NIL IDPOAM (NIL T T) -8 NIL NIL) (-521 1449958 1450208 1450262 "IDPC" 1450675 NIL IDPC (NIL T T) -9 NIL 1450824) (-520 1449454 1449850 1449923 "IDPAM" 1449928 NIL IDPAM (NIL T T) -8 NIL NIL) (-519 1448857 1449346 1449419 "IDPAG" 1449424 NIL IDPAG (NIL T T) -8 NIL NIL) (-518 1445112 1445960 1446855 "IDECOMP" 1448014 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-517 1437988 1439037 1440083 "IDEAL" 1444149 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-516 1436005 1437152 1437425 "ICP" 1437779 NIL ICP (NIL T NIL T) -8 NIL NIL) (-515 1435169 1435281 1435480 "ICDEN" 1435889 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-514 1434268 1434649 1434796 "ICARD" 1435042 T ICARD (NIL) -8 NIL NIL) (-513 1432328 1432641 1433046 "IBPTOOLS" 1433945 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-512 1427942 1431948 1432061 "IBITS" 1432247 NIL IBITS (NIL NIL) -8 NIL NIL) (-511 1424665 1425241 1425936 "IBATOOL" 1427359 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-510 1422445 1422906 1423439 "IBACHIN" 1424200 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-509 1420328 1422291 1422394 "IARRAY2" 1422399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-508 1416487 1420254 1420311 "IARRAY1" 1420316 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-507 1410417 1414899 1415380 "IAN" 1416026 T IAN (NIL) -8 NIL NIL) (-506 1409928 1409985 1410158 "IALGFACT" 1410354 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-505 1409455 1409568 1409597 "HYPCAT" 1409804 T HYPCAT (NIL) -9 NIL NIL) (-504 1408993 1409110 1409296 "HYPCAT-" 1409301 NIL HYPCAT- (NIL T) -8 NIL NIL) (-503 1407997 1408274 1408464 "HTMLFORM" 1408823 T HTMLFORM (NIL) -8 NIL NIL) (-502 1404786 1406111 1406153 "HOAGG" 1407134 NIL HOAGG (NIL T) -9 NIL 1407743) (-501 1403380 1403779 1404305 "HOAGG-" 1404310 NIL HOAGG- (NIL T T) -8 NIL NIL) (-500 1397198 1402818 1402985 "HEXADEC" 1403233 T HEXADEC (NIL) -8 NIL NIL) (-499 1395946 1396168 1396431 "HEUGCD" 1396975 NIL HEUGCD (NIL T) -7 NIL NIL) (-498 1395049 1395783 1395913 "HELLFDIV" 1395918 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-497 1388766 1390309 1391390 "HEAP" 1394000 NIL HEAP (NIL T) -8 NIL NIL) (-496 1382561 1388681 1388743 "HDP" 1388748 NIL HDP (NIL NIL T) -8 NIL NIL) (-495 1376266 1382196 1382348 "HDMP" 1382462 NIL HDMP (NIL NIL T) -8 NIL NIL) (-494 1375591 1375730 1375894 "HB" 1376122 T HB (NIL) -7 NIL NIL) (-493 1369100 1375437 1375541 "HASHTBL" 1375546 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-492 1366847 1368722 1368904 "HACKPI" 1368938 T HACKPI (NIL) -8 NIL NIL) (-491 1348995 1352864 1356867 "GUESSUP" 1362877 NIL GUESSUP (NIL NIL) -7 NIL NIL) (-490 1320092 1327133 1333829 "GUESSP" 1342319 T GUESSP (NIL) -7 NIL NIL) (-489 1286907 1292178 1297562 "GUESS" 1315036 NIL GUESS (NIL T T T T NIL NIL) -7 NIL NIL) (-488 1260412 1266809 1272945 "GUESSINT" 1280791 T GUESSINT (NIL) -7 NIL NIL) (-487 1235783 1241233 1246800 "GUESSF" 1254897 NIL GUESSF (NIL T) -7 NIL NIL) (-486 1235505 1235542 1235637 "GUESSF1" 1235740 NIL GUESSF1 (NIL T) -7 NIL NIL) (-485 1211666 1217200 1222815 "GUESSAN" 1229910 T GUESSAN (NIL) -7 NIL NIL) (-484 1207361 1211519 1211632 "GTSET" 1211637 NIL GTSET (NIL T T T T) -8 NIL NIL) (-483 1200899 1207239 1207337 "GSTBL" 1207342 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-482 1193129 1199932 1200196 "GSERIES" 1200691 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-481 1192150 1192603 1192632 "GROUP" 1192893 T GROUP (NIL) -9 NIL 1193052) (-480 1191266 1191489 1191833 "GROUP-" 1191838 NIL GROUP- (NIL T) -8 NIL NIL) (-479 1189635 1189954 1190341 "GROEBSOL" 1190943 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-478 1188574 1188836 1188888 "GRMOD" 1189417 NIL GRMOD (NIL T T) -9 NIL 1189585) (-477 1188342 1188378 1188506 "GRMOD-" 1188511 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-476 1183671 1184696 1185696 "GRIMAGE" 1187362 T GRIMAGE (NIL) -8 NIL NIL) (-475 1182138 1182398 1182722 "GRDEF" 1183367 T GRDEF (NIL) -7 NIL NIL) (-474 1181582 1181698 1181839 "GRAY" 1182017 T GRAY (NIL) -7 NIL NIL) (-473 1180812 1181192 1181244 "GRALG" 1181397 NIL GRALG (NIL T T) -9 NIL 1181490) (-472 1180473 1180546 1180709 "GRALG-" 1180714 NIL GRALG- (NIL T T T) -8 NIL NIL) (-471 1177277 1180058 1180236 "GPOLSET" 1180380 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-470 1159480 1160970 1162559 "GPAFF" 1175968 NIL GPAFF (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-469 1158834 1158891 1159149 "GOSPER" 1159417 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-468 1155184 1156020 1156747 "GOPT" 1158127 T GOPT (NIL) -8 NIL NIL) (-467 1150663 1151681 1152589 "GOPT0" 1154296 T GOPT0 (NIL) -8 NIL NIL) (-466 1146422 1147101 1147627 "GMODPOL" 1150362 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-465 1145427 1145611 1145849 "GHENSEL" 1146234 NIL GHENSEL (NIL T T) -7 NIL NIL) (-464 1139478 1140321 1141348 "GENUPS" 1144511 NIL GENUPS (NIL T T) -7 NIL NIL) (-463 1139175 1139226 1139315 "GENUFACT" 1139421 NIL GENUFACT (NIL T) -7 NIL NIL) (-462 1138587 1138664 1138829 "GENPGCD" 1139093 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-461 1138061 1138096 1138309 "GENMFACT" 1138546 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-460 1136629 1136884 1137191 "GENEEZ" 1137804 NIL GENEEZ (NIL T T) -7 NIL NIL) (-459 1135173 1135450 1135774 "GDRAW" 1136325 T GDRAW (NIL) -7 NIL NIL) (-458 1129040 1134784 1134946 "GDMP" 1135096 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-457 1118424 1122813 1123918 "GCNAALG" 1128024 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-456 1116841 1117713 1117742 "GCDDOM" 1117997 T GCDDOM (NIL) -9 NIL 1118154) (-455 1116311 1116438 1116653 "GCDDOM-" 1116658 NIL GCDDOM- (NIL T) -8 NIL NIL) (-454 1114985 1115170 1115473 "GB" 1116091 NIL GB (NIL T T T T) -7 NIL NIL) (-453 1103605 1105931 1108323 "GBINTERN" 1112676 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-452 1101442 1101734 1102155 "GBF" 1103280 NIL GBF (NIL T T T T) -7 NIL NIL) (-451 1100223 1100388 1100655 "GBEUCLID" 1101258 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-450 1099572 1099697 1099846 "GAUSSFAC" 1100094 T GAUSSFAC (NIL) -7 NIL NIL) (-449 1097941 1098243 1098556 "GALUTIL" 1099292 NIL GALUTIL (NIL T) -7 NIL NIL) (-448 1096249 1096523 1096847 "GALPOLYU" 1097668 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-447 1093614 1093904 1094311 "GALFACTU" 1095946 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-446 1085420 1086919 1088527 "GALFACT" 1092046 NIL GALFACT (NIL T) -7 NIL NIL) (-445 1082808 1083465 1083494 "FVFUN" 1084650 T FVFUN (NIL) -9 NIL 1085370) (-444 1082074 1082255 1082284 "FVC" 1082575 T FVC (NIL) -9 NIL 1082758) (-443 1081716 1081871 1081952 "FUNCTION" 1082026 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-442 1079386 1079937 1080426 "FT" 1081247 T FT (NIL) -8 NIL NIL) (-441 1078178 1078687 1078890 "FTEM" 1079203 T FTEM (NIL) -8 NIL NIL) (-440 1076436 1076725 1077128 "FSUPFACT" 1077870 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-439 1074833 1075122 1075454 "FST" 1076124 T FST (NIL) -8 NIL NIL) (-438 1074004 1074110 1074305 "FSRED" 1074715 NIL FSRED (NIL T T) -7 NIL NIL) (-437 1072685 1072940 1073293 "FSPRMELT" 1073720 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-436 1068051 1068756 1069513 "FSPECF" 1071990 NIL FSPECF (NIL T T) -7 NIL NIL) (-435 1050309 1058898 1058939 "FS" 1062787 NIL FS (NIL T) -9 NIL 1065065) (-434 1038959 1041949 1046005 "FS-" 1046302 NIL FS- (NIL T T) -8 NIL NIL) (-433 1038473 1038527 1038704 "FSINT" 1038900 NIL FSINT (NIL T T) -7 NIL NIL) (-432 1036758 1037470 1037771 "FSERIES" 1038254 NIL FSERIES (NIL T T) -8 NIL NIL) (-431 1035772 1035888 1036119 "FSCINT" 1036638 NIL FSCINT (NIL T T) -7 NIL NIL) (-430 1031963 1034717 1034759 "FSAGG" 1035129 NIL FSAGG (NIL T) -9 NIL 1035386) (-429 1029725 1030326 1031122 "FSAGG-" 1031217 NIL FSAGG- (NIL T T) -8 NIL NIL) (-428 1028767 1028910 1029137 "FSAGG2" 1029578 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-427 1026422 1026701 1027255 "FS2UPS" 1028485 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-426 1026004 1026047 1026202 "FS2" 1026373 NIL FS2 (NIL T T T T) -7 NIL NIL) (-425 1024861 1025032 1025341 "FS2EXPXP" 1025829 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-424 1024287 1024402 1024554 "FRUTIL" 1024741 NIL FRUTIL (NIL T) -7 NIL NIL) (-423 1015713 1019798 1021148 "FR" 1022969 NIL FR (NIL T) -8 NIL NIL) (-422 1010793 1013431 1013472 "FRNAALG" 1014868 NIL FRNAALG (NIL T) -9 NIL 1015474) (-421 1006472 1007542 1008817 "FRNAALG-" 1009567 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-420 1006110 1006153 1006280 "FRNAAF2" 1006423 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-419 1004473 1004966 1005260 "FRMOD" 1005923 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-418 1002188 1002856 1003173 "FRIDEAL" 1004264 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-417 1001383 1001470 1001759 "FRIDEAL2" 1002095 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-416 1000626 1001040 1001082 "FRETRCT" 1001087 NIL FRETRCT (NIL T) -9 NIL 1001261) (-415 999738 999969 1000320 "FRETRCT-" 1000325 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-414 996943 998163 998223 "FRAMALG" 999105 NIL FRAMALG (NIL T T) -9 NIL 999397) (-413 995076 995532 996162 "FRAMALG-" 996385 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-412 988979 994561 994832 "FRAC" 994837 NIL FRAC (NIL T) -8 NIL NIL) (-411 988615 988672 988779 "FRAC2" 988916 NIL FRAC2 (NIL T T) -7 NIL NIL) (-410 988251 988308 988415 "FR2" 988552 NIL FR2 (NIL T T) -7 NIL NIL) (-409 982873 985782 985811 "FPS" 986930 T FPS (NIL) -9 NIL 987484) (-408 982322 982431 982595 "FPS-" 982741 NIL FPS- (NIL T) -8 NIL NIL) (-407 979718 981415 981444 "FPC" 981669 T FPC (NIL) -9 NIL 981811) (-406 979511 979551 979648 "FPC-" 979653 NIL FPC- (NIL T) -8 NIL NIL) (-405 978390 979000 979042 "FPATMAB" 979047 NIL FPATMAB (NIL T) -9 NIL 979197) (-404 976090 976566 976992 "FPARFRAC" 978027 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-403 971485 971982 972664 "FORTRAN" 975522 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-402 969201 969701 970240 "FORT" 970966 T FORT (NIL) -7 NIL NIL) (-401 966877 967438 967467 "FORTFN" 968527 T FORTFN (NIL) -9 NIL 969151) (-400 966640 966690 966719 "FORTCAT" 966778 T FORTCAT (NIL) -9 NIL 966840) (-399 964700 965183 965582 "FORMULA" 966261 T FORMULA (NIL) -8 NIL NIL) (-398 964488 964518 964587 "FORMULA1" 964664 NIL FORMULA1 (NIL T) -7 NIL NIL) (-397 964011 964063 964236 "FORDER" 964430 NIL FORDER (NIL T T T T) -7 NIL NIL) (-396 963107 963271 963464 "FOP" 963838 T FOP (NIL) -7 NIL NIL) (-395 961715 962387 962561 "FNLA" 962989 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-394 960382 960771 960800 "FNCAT" 961372 T FNCAT (NIL) -9 NIL 961665) (-393 959948 960341 960369 "FNAME" 960374 T FNAME (NIL) -8 NIL NIL) (-392 958601 959574 959603 "FMTC" 959608 T FMTC (NIL) -9 NIL 959644) (-391 954919 956126 956754 "FMONOID" 958006 NIL FMONOID (NIL T) -8 NIL NIL) (-390 954140 954663 954811 "FM" 954816 NIL FM (NIL T T) -8 NIL NIL) (-389 951564 952209 952238 "FMFUN" 953382 T FMFUN (NIL) -9 NIL 954090) (-388 950833 951013 951042 "FMC" 951332 T FMC (NIL) -9 NIL 951514) (-387 948045 948879 948934 "FMCAT" 950129 NIL FMCAT (NIL T T) -9 NIL 950623) (-386 946938 947811 947911 "FM1" 947990 NIL FM1 (NIL T T) -8 NIL NIL) (-385 944712 945128 945622 "FLOATRP" 946489 NIL FLOATRP (NIL T) -7 NIL NIL) (-384 938199 942368 942998 "FLOAT" 944102 T FLOAT (NIL) -8 NIL NIL) (-383 935637 936137 936715 "FLOATCP" 937666 NIL FLOATCP (NIL T) -7 NIL NIL) (-382 934422 935270 935312 "FLINEXP" 935317 NIL FLINEXP (NIL T) -9 NIL 935409) (-381 933576 933811 934139 "FLINEXP-" 934144 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-380 932652 932796 933020 "FLASORT" 933428 NIL FLASORT (NIL T T) -7 NIL NIL) (-379 929868 930710 930763 "FLALG" 931990 NIL FLALG (NIL T T) -9 NIL 932457) (-378 923687 927381 927423 "FLAGG" 928685 NIL FLAGG (NIL T) -9 NIL 929333) (-377 922413 922752 923242 "FLAGG-" 923247 NIL FLAGG- (NIL T T) -8 NIL NIL) (-376 921455 921598 921825 "FLAGG2" 922266 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-375 918426 919444 919504 "FINRALG" 920632 NIL FINRALG (NIL T T) -9 NIL 921137) (-374 917586 917815 918154 "FINRALG-" 918159 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-373 916889 917126 917155 "FINITE" 917406 T FINITE (NIL) -9 NIL 917536) (-372 916698 916742 916829 "FINITE-" 916834 NIL FINITE- (NIL T) -8 NIL NIL) (-371 909156 911317 911358 "FINAALG" 915025 NIL FINAALG (NIL T) -9 NIL 916477) (-370 904496 905538 906682 "FINAALG-" 908061 NIL FINAALG- (NIL T T) -8 NIL NIL) (-369 903866 904251 904354 "FILE" 904426 NIL FILE (NIL T) -8 NIL NIL) (-368 902406 902743 902798 "FILECAT" 903576 NIL FILECAT (NIL T T) -9 NIL 903816) (-367 900216 901772 901801 "FIELD" 901841 T FIELD (NIL) -9 NIL 901921) (-366 898836 899221 899732 "FIELD-" 899737 NIL FIELD- (NIL T) -8 NIL NIL) (-365 896649 897471 897818 "FGROUP" 898522 NIL FGROUP (NIL T) -8 NIL NIL) (-364 895739 895903 896123 "FGLMICPK" 896481 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-363 891496 895664 895721 "FFX" 895726 NIL FFX (NIL T NIL) -8 NIL NIL) (-362 891036 891103 891225 "FFSQFR" 891424 NIL FFSQFR (NIL T T) -7 NIL NIL) (-361 890637 890698 890833 "FFSLPE" 890969 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-360 886633 887409 888205 "FFPOLY" 889873 NIL FFPOLY (NIL T) -7 NIL NIL) (-359 886137 886173 886382 "FFPOLY2" 886591 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-358 881914 886056 886119 "FFP" 886124 NIL FFP (NIL T NIL) -8 NIL NIL) (-357 877230 881825 881889 "FF" 881894 NIL FF (NIL NIL NIL) -8 NIL NIL) (-356 872281 876573 876763 "FFNBX" 877084 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-355 867146 871416 871674 "FFNBP" 872135 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-354 861697 866430 866641 "FFNB" 866979 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-353 860529 860727 861042 "FFINTBAS" 861494 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-352 856680 858940 858969 "FFIELDC" 859589 T FFIELDC (NIL) -9 NIL 859965) (-351 855343 855713 856210 "FFIELDC-" 856215 NIL FFIELDC- (NIL T) -8 NIL NIL) (-350 854913 854958 855082 "FFHOM" 855285 NIL FFHOM (NIL T T T) -7 NIL NIL) (-349 852611 853095 853612 "FFF" 854428 NIL FFF (NIL T) -7 NIL NIL) (-348 848307 849072 849916 "FFFG" 851835 NIL FFFG (NIL T T) -7 NIL NIL) (-347 847033 847242 847564 "FFFGF" 848085 NIL FFFGF (NIL T T T) -7 NIL NIL) (-346 845784 845981 846229 "FFFACTSE" 846835 NIL FFFACTSE (NIL T T) -7 NIL NIL) (-345 844535 844732 844980 "FFFACTOR" 845586 NIL FFFACTOR (NIL T T) -7 NIL NIL) (-344 840078 844277 844378 "FFCGX" 844478 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-343 835635 839810 839917 "FFCGP" 840021 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-342 830736 835362 835470 "FFCG" 835571 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-341 812473 821647 821734 "FFCAT" 826899 NIL FFCAT (NIL T T T) -9 NIL 828384) (-340 807671 808718 810032 "FFCAT-" 811262 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-339 807082 807125 807360 "FFCAT2" 807622 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-338 796252 800058 801276 "FEXPR" 805936 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-337 795254 795689 795731 "FEVALAB" 795815 NIL FEVALAB (NIL T) -9 NIL 796073) (-336 794413 794623 794961 "FEVALAB-" 794966 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-335 793006 793796 793999 "FDIV" 794312 NIL FDIV (NIL T T T T) -8 NIL NIL) (-334 790071 790786 790902 "FDIVCAT" 792470 NIL FDIVCAT (NIL T T T T) -9 NIL 792907) (-333 789833 789860 790030 "FDIVCAT-" 790035 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-332 789053 789140 789417 "FDIV2" 789740 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-331 787739 787998 788287 "FCPAK1" 788784 T FCPAK1 (NIL) -7 NIL NIL) (-330 786867 787239 787380 "FCOMP" 787630 NIL FCOMP (NIL T) -8 NIL NIL) (-329 770495 773910 777473 "FC" 783324 T FC (NIL) -8 NIL NIL) (-328 762994 767082 767123 "FAXF" 768925 NIL FAXF (NIL T) -9 NIL 769616) (-327 760274 760928 761753 "FAXF-" 762218 NIL FAXF- (NIL T T) -8 NIL NIL) (-326 755380 759650 759826 "FARRAY" 760131 NIL FARRAY (NIL T) -8 NIL NIL) (-325 750698 752774 752828 "FAMR" 753851 NIL FAMR (NIL T T) -9 NIL 754308) (-324 749588 749890 750325 "FAMR-" 750330 NIL FAMR- (NIL T T T) -8 NIL NIL) (-323 749176 749219 749370 "FAMR2" 749539 NIL FAMR2 (NIL T T T T T) -7 NIL NIL) (-322 748372 749098 749151 "FAMONOID" 749156 NIL FAMONOID (NIL T) -8 NIL NIL) (-321 746202 746886 746940 "FAMONC" 747881 NIL FAMONC (NIL T T) -9 NIL 748266) (-320 744896 745958 746094 "FAGROUP" 746099 NIL FAGROUP (NIL T) -8 NIL NIL) (-319 742691 743010 743413 "FACUTIL" 744577 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-318 742107 742216 742362 "FACTRN" 742577 NIL FACTRN (NIL T) -7 NIL NIL) (-317 741206 741391 741613 "FACTFUNC" 741917 NIL FACTFUNC (NIL T) -7 NIL NIL) (-316 740622 740731 740877 "FACTEXT" 741092 NIL FACTEXT (NIL T) -7 NIL NIL) (-315 732942 739873 740085 "EXPUPXS" 740478 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-314 730425 730965 731551 "EXPRTUBE" 732376 T EXPRTUBE (NIL) -7 NIL NIL) (-313 729596 729691 729911 "EXPRSOL" 730325 NIL EXPRSOL (NIL T T T T) -7 NIL NIL) (-312 725790 726382 727119 "EXPRODE" 728935 NIL EXPRODE (NIL T T) -7 NIL NIL) (-311 710811 724451 724876 "EXPR" 725397 NIL EXPR (NIL T) -8 NIL NIL) (-310 705218 705805 706618 "EXPR2UPS" 710109 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-309 704854 704911 705018 "EXPR2" 705155 NIL EXPR2 (NIL T T) -7 NIL NIL) (-308 696194 703986 704283 "EXPEXPAN" 704691 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-307 695906 695957 696034 "EXP3D" 696137 T EXP3D (NIL) -7 NIL NIL) (-306 695733 695863 695892 "EXIT" 695897 T EXIT (NIL) -8 NIL NIL) (-305 695360 695422 695535 "EVALCYC" 695665 NIL EVALCYC (NIL T) -7 NIL NIL) (-304 694902 695018 695060 "EVALAB" 695230 NIL EVALAB (NIL T) -9 NIL 695334) (-303 694383 694505 694726 "EVALAB-" 694731 NIL EVALAB- (NIL T T) -8 NIL NIL) (-302 691841 693153 693182 "EUCDOM" 693737 T EUCDOM (NIL) -9 NIL 694087) (-301 690246 690688 691278 "EUCDOM-" 691283 NIL EUCDOM- (NIL T) -8 NIL NIL) (-300 677786 680544 683294 "ESTOOLS" 687516 T ESTOOLS (NIL) -7 NIL NIL) (-299 677418 677475 677584 "ESTOOLS2" 677723 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-298 677169 677211 677291 "ESTOOLS1" 677370 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-297 671095 672823 672852 "ES" 675620 T ES (NIL) -9 NIL 677027) (-296 666043 667329 669146 "ES-" 669310 NIL ES- (NIL T) -8 NIL NIL) (-295 662418 663178 663958 "ESCONT" 665283 T ESCONT (NIL) -7 NIL NIL) (-294 662163 662195 662277 "ESCONT1" 662380 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-293 661838 661888 661988 "ES2" 662107 NIL ES2 (NIL T T) -7 NIL NIL) (-292 661468 661526 661635 "ES1" 661774 NIL ES1 (NIL T T) -7 NIL NIL) (-291 660684 660813 660989 "ERROR" 661312 T ERROR (NIL) -7 NIL NIL) (-290 654199 660543 660634 "EQTBL" 660639 NIL EQTBL (NIL T T) -8 NIL NIL) (-289 646658 649541 650976 "EQ" 652797 NIL -2978 (NIL T) -8 NIL NIL) (-288 646290 646347 646456 "EQ2" 646595 NIL EQ2 (NIL T T) -7 NIL NIL) (-287 641582 642628 643721 "EP" 645229 NIL EP (NIL T) -7 NIL NIL) (-286 640736 641300 641329 "ENTIRER" 641334 T ENTIRER (NIL) -9 NIL 641380) (-285 637192 638691 639061 "EMR" 640535 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-284 636338 636521 636576 "ELTAGG" 636956 NIL ELTAGG (NIL T T) -9 NIL 637166) (-283 636057 636119 636260 "ELTAGG-" 636265 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-282 635845 635874 635929 "ELTAB" 636013 NIL ELTAB (NIL T T) -9 NIL NIL) (-281 634971 635117 635316 "ELFUTS" 635696 NIL ELFUTS (NIL T T) -7 NIL NIL) (-280 634712 634768 634797 "ELEMFUN" 634902 T ELEMFUN (NIL) -9 NIL NIL) (-279 634582 634603 634671 "ELEMFUN-" 634676 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-278 629512 632715 632757 "ELAGG" 633697 NIL ELAGG (NIL T) -9 NIL 634158) (-277 627797 628231 628894 "ELAGG-" 628899 NIL ELAGG- (NIL T T) -8 NIL NIL) (-276 620667 622466 623292 "EFUPXS" 627074 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-275 614119 615920 616729 "EFULS" 619944 NIL EFULS (NIL T T T) -8 NIL NIL) (-274 611541 611899 612378 "EFSTRUC" 613751 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-273 600553 602118 603679 "EF" 610056 NIL EF (NIL T T) -7 NIL NIL) (-272 599654 600038 600187 "EAB" 600424 T EAB (NIL) -8 NIL NIL) (-271 598863 599613 599641 "E04UCFA" 599646 T E04UCFA (NIL) -8 NIL NIL) (-270 598072 598822 598850 "E04NAFA" 598855 T E04NAFA (NIL) -8 NIL NIL) (-269 597281 598031 598059 "E04MBFA" 598064 T E04MBFA (NIL) -8 NIL NIL) (-268 596490 597240 597268 "E04JAFA" 597273 T E04JAFA (NIL) -8 NIL NIL) (-267 595701 596449 596477 "E04GCFA" 596482 T E04GCFA (NIL) -8 NIL NIL) (-266 594912 595660 595688 "E04FDFA" 595693 T E04FDFA (NIL) -8 NIL NIL) (-265 594121 594871 594899 "E04DGFA" 594904 T E04DGFA (NIL) -8 NIL NIL) (-264 588300 589646 591010 "E04AGNT" 592777 T E04AGNT (NIL) -7 NIL NIL) (-263 587023 587503 587544 "DVARCAT" 588019 NIL DVARCAT (NIL T) -9 NIL 588218) (-262 586227 586439 586753 "DVARCAT-" 586758 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-261 579196 579678 580427 "DTP" 585758 NIL DTP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-260 576645 578618 578775 "DSTREE" 579072 NIL DSTREE (NIL T) -8 NIL NIL) (-259 574114 575959 576001 "DSTRCAT" 576220 NIL DSTRCAT (NIL T) -9 NIL 576354) (-258 566968 573913 574042 "DSMP" 574047 NIL DSMP (NIL T T T) -8 NIL NIL) (-257 561778 562913 563981 "DROPT" 565920 T DROPT (NIL) -8 NIL NIL) (-256 561443 561502 561600 "DROPT1" 561713 NIL DROPT1 (NIL T) -7 NIL NIL) (-255 556558 557684 558821 "DROPT0" 560326 T DROPT0 (NIL) -7 NIL NIL) (-254 554903 555228 555614 "DRAWPT" 556192 T DRAWPT (NIL) -7 NIL NIL) (-253 549490 550413 551492 "DRAW" 553877 NIL DRAW (NIL T) -7 NIL NIL) (-252 549123 549176 549294 "DRAWHACK" 549431 NIL DRAWHACK (NIL T) -7 NIL NIL) (-251 547854 548123 548414 "DRAWCX" 548852 T DRAWCX (NIL) -7 NIL NIL) (-250 547370 547438 547589 "DRAWCURV" 547780 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-249 537842 539800 541915 "DRAWCFUN" 545275 T DRAWCFUN (NIL) -7 NIL NIL) (-248 534693 536569 536611 "DQAGG" 537240 NIL DQAGG (NIL T) -9 NIL 537514) (-247 523121 529862 529946 "DPOLCAT" 531798 NIL DPOLCAT (NIL T T T T) -9 NIL 532342) (-246 517960 519306 521264 "DPOLCAT-" 521269 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-245 510656 517821 517919 "DPMO" 517924 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-244 503255 510436 510603 "DPMM" 510608 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-243 496960 502890 503042 "DMP" 503156 NIL DMP (NIL NIL T) -8 NIL NIL) (-242 496560 496616 496760 "DLP" 496898 NIL DLP (NIL T) -7 NIL NIL) (-241 490210 495661 495888 "DLIST" 496365 NIL DLIST (NIL T) -8 NIL NIL) (-240 487095 489098 489140 "DLAGG" 489690 NIL DLAGG (NIL T) -9 NIL 489919) (-239 485752 486444 486473 "DIVRING" 486623 T DIVRING (NIL) -9 NIL 486731) (-238 484740 484993 485386 "DIVRING-" 485391 NIL DIVRING- (NIL T) -8 NIL NIL) (-237 483168 484333 484469 "DIV" 484637 NIL DIV (NIL T) -8 NIL NIL) (-236 480662 481730 481772 "DIVCAT" 482606 NIL DIVCAT (NIL T) -9 NIL 482937) (-235 478764 479121 479527 "DISPLAY" 480276 T DISPLAY (NIL) -7 NIL NIL) (-234 476257 477470 477852 "DIRRING" 478415 NIL DIRRING (NIL T) -8 NIL NIL) (-233 470074 476171 476234 "DIRPROD" 476239 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-232 468922 469125 469390 "DIRPROD2" 469867 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-231 458374 464446 464500 "DIRPCAT" 464910 NIL DIRPCAT (NIL NIL T) -9 NIL 465739) (-230 455700 456342 457223 "DIRPCAT-" 457560 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-229 454987 455147 455333 "DIOSP" 455534 T DIOSP (NIL) -7 NIL NIL) (-228 451730 453934 453976 "DIOPS" 454410 NIL DIOPS (NIL T) -9 NIL 454638) (-227 451279 451393 451584 "DIOPS-" 451589 NIL DIOPS- (NIL T T) -8 NIL NIL) (-226 450146 450784 450813 "DIFRING" 451000 T DIFRING (NIL) -9 NIL 451110) (-225 449792 449869 450021 "DIFRING-" 450026 NIL DIFRING- (NIL T) -8 NIL NIL) (-224 447574 448856 448898 "DIFEXT" 449261 NIL DIFEXT (NIL T) -9 NIL 449553) (-223 445859 446287 446953 "DIFEXT-" 446958 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-222 443221 445425 445467 "DIAGG" 445472 NIL DIAGG (NIL T) -9 NIL 445492) (-221 442605 442762 443014 "DIAGG-" 443019 NIL DIAGG- (NIL T T) -8 NIL NIL) (-220 437927 441564 441841 "DHMATRIX" 442374 NIL DHMATRIX (NIL T) -8 NIL NIL) (-219 433138 437741 437815 "DFVEC" 437873 T DFVEC (NIL) -8 NIL NIL) (-218 426739 428089 429526 "DFSFUN" 431721 T DFSFUN (NIL) -7 NIL NIL) (-217 422950 426510 426604 "DFMAT" 426665 T DFMAT (NIL) -8 NIL NIL) (-216 417227 421404 421837 "DFLOAT" 422537 T DFLOAT (NIL) -8 NIL NIL) (-215 415455 415736 416132 "DFINTTLS" 416935 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-214 412474 413476 413876 "DERHAM" 415121 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-213 404087 406004 407439 "DEQUEUE" 411072 NIL DEQUEUE (NIL T) -8 NIL NIL) (-212 403302 403435 403631 "DEGRED" 403949 NIL DEGRED (NIL T T) -7 NIL NIL) (-211 399697 400442 401295 "DEFINTRF" 402530 NIL DEFINTRF (NIL T) -7 NIL NIL) (-210 397224 397693 398292 "DEFINTEF" 399216 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-209 391042 396662 396829 "DECIMAL" 397077 T DECIMAL (NIL) -8 NIL NIL) (-208 388554 389012 389518 "DDFACT" 390586 NIL DDFACT (NIL T T) -7 NIL NIL) (-207 388150 388193 388344 "DBLRESP" 388505 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-206 385860 386194 386563 "DBASE" 387908 NIL DBASE (NIL T) -8 NIL NIL) (-205 384993 385819 385847 "D03FAFA" 385852 T D03FAFA (NIL) -8 NIL NIL) (-204 384127 384952 384980 "D03EEFA" 384985 T D03EEFA (NIL) -8 NIL NIL) (-203 382077 382543 383032 "D03AGNT" 383658 T D03AGNT (NIL) -7 NIL NIL) (-202 381393 382036 382064 "D02EJFA" 382069 T D02EJFA (NIL) -8 NIL NIL) (-201 380709 381352 381380 "D02CJFA" 381385 T D02CJFA (NIL) -8 NIL NIL) (-200 380025 380668 380696 "D02BHFA" 380701 T D02BHFA (NIL) -8 NIL NIL) (-199 379341 379984 380012 "D02BBFA" 380017 T D02BBFA (NIL) -8 NIL NIL) (-198 372540 374127 375733 "D02AGNT" 377755 T D02AGNT (NIL) -7 NIL NIL) (-197 370309 370831 371377 "D01WGTS" 372014 T D01WGTS (NIL) -7 NIL NIL) (-196 369404 370268 370296 "D01TRNS" 370301 T D01TRNS (NIL) -8 NIL NIL) (-195 368499 369363 369391 "D01GBFA" 369396 T D01GBFA (NIL) -8 NIL NIL) (-194 367594 368458 368486 "D01FCFA" 368491 T D01FCFA (NIL) -8 NIL NIL) (-193 366689 367553 367581 "D01ASFA" 367586 T D01ASFA (NIL) -8 NIL NIL) (-192 365784 366648 366676 "D01AQFA" 366681 T D01AQFA (NIL) -8 NIL NIL) (-191 364879 365743 365771 "D01APFA" 365776 T D01APFA (NIL) -8 NIL NIL) (-190 363974 364838 364866 "D01ANFA" 364871 T D01ANFA (NIL) -8 NIL NIL) (-189 363069 363933 363961 "D01AMFA" 363966 T D01AMFA (NIL) -8 NIL NIL) (-188 362164 363028 363056 "D01ALFA" 363061 T D01ALFA (NIL) -8 NIL NIL) (-187 361259 362123 362151 "D01AKFA" 362156 T D01AKFA (NIL) -8 NIL NIL) (-186 360354 361218 361246 "D01AJFA" 361251 T D01AJFA (NIL) -8 NIL NIL) (-185 353651 355202 356763 "D01AGNT" 358813 T D01AGNT (NIL) -7 NIL NIL) (-184 352988 353116 353268 "CYCLOTOM" 353519 T CYCLOTOM (NIL) -7 NIL NIL) (-183 349723 350436 351163 "CYCLES" 352281 T CYCLES (NIL) -7 NIL NIL) (-182 349035 349169 349340 "CVMP" 349584 NIL CVMP (NIL T) -7 NIL NIL) (-181 346807 347064 347440 "CTRIGMNP" 348763 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-180 346181 346280 346433 "CSTTOOLS" 346704 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 341980 342637 343395 "CRFP" 345493 NIL CRFP (NIL T T) -7 NIL NIL) (-178 341027 341212 341440 "CRAPACK" 341784 NIL CRAPACK (NIL T) -7 NIL NIL) (-177 340413 340514 340717 "CPMATCH" 340904 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-176 340138 340166 340272 "CPIMA" 340379 NIL CPIMA (NIL T T T) -7 NIL NIL) (-175 336486 337158 337877 "COORDSYS" 339473 NIL COORDSYS (NIL T) -7 NIL NIL) (-174 332347 334489 334981 "CONTFRAC" 336026 NIL CONTFRAC (NIL T) -8 NIL NIL) (-173 331495 332059 332088 "COMRING" 332093 T COMRING (NIL) -9 NIL 332145) (-172 330576 330853 331037 "COMPPROP" 331331 T COMPPROP (NIL) -8 NIL NIL) (-171 330237 330272 330400 "COMPLPAT" 330535 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-170 320163 330048 330156 "COMPLEX" 330161 NIL COMPLEX (NIL T) -8 NIL NIL) (-169 319799 319856 319963 "COMPLEX2" 320100 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-168 319517 319552 319650 "COMPFACT" 319758 NIL COMPFACT (NIL T T) -7 NIL NIL) (-167 303724 314069 314110 "COMPCAT" 315114 NIL COMPCAT (NIL T) -9 NIL 316495) (-166 293240 296163 299790 "COMPCAT-" 300146 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-165 292969 292997 293100 "COMMUPC" 293206 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-164 292764 292797 292856 "COMMONOP" 292930 T COMMONOP (NIL) -7 NIL NIL) (-163 292347 292515 292602 "COMM" 292697 T COMM (NIL) -8 NIL NIL) (-162 291595 291789 291818 "COMBOPC" 292156 T COMBOPC (NIL) -9 NIL 292331) (-161 290491 290701 290943 "COMBINAT" 291385 NIL COMBINAT (NIL T) -7 NIL NIL) (-160 286689 287262 287902 "COMBF" 289913 NIL COMBF (NIL T T) -7 NIL NIL) (-159 285475 285805 286040 "COLOR" 286474 T COLOR (NIL) -8 NIL NIL) (-158 285115 285162 285287 "CMPLXRT" 285422 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-157 280617 281645 282725 "CLIP" 284055 T CLIP (NIL) -7 NIL NIL) (-156 278948 279718 279958 "CLIF" 280444 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-155 275213 277131 277173 "CLAGG" 278102 NIL CLAGG (NIL T) -9 NIL 278635) (-154 273635 274092 274675 "CLAGG-" 274680 NIL CLAGG- (NIL T T) -8 NIL NIL) (-153 273179 273264 273404 "CINTSLPE" 273544 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-152 270680 271151 271699 "CHVAR" 272707 NIL CHVAR (NIL T T T) -7 NIL NIL) (-151 269898 270462 270491 "CHARZ" 270496 T CHARZ (NIL) -9 NIL 270511) (-150 269652 269692 269770 "CHARPOL" 269852 NIL CHARPOL (NIL T) -7 NIL NIL) (-149 268754 269351 269380 "CHARNZ" 269427 T CHARNZ (NIL) -9 NIL 269483) (-148 266752 267444 267779 "CHAR" 268439 T CHAR (NIL) -8 NIL NIL) (-147 266477 266538 266567 "CFCAT" 266678 T CFCAT (NIL) -9 NIL NIL) (-146 260610 266134 266252 "CDFVEC" 266379 T CDFVEC (NIL) -8 NIL NIL) (-145 256268 260367 260468 "CDFMAT" 260529 T CDFMAT (NIL) -8 NIL NIL) (-144 255513 255624 255806 "CDEN" 256152 NIL CDEN (NIL T T T) -7 NIL NIL) (-143 251458 254666 254946 "CCLASS" 255253 T CCLASS (NIL) -8 NIL NIL) (-142 246511 247487 248240 "CARTEN" 250761 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-141 245619 245767 245988 "CARTEN2" 246358 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-140 243914 244769 245026 "CARD" 245382 T CARD (NIL) -8 NIL NIL) (-139 243285 243613 243642 "CACHSET" 243774 T CACHSET (NIL) -9 NIL 243851) (-138 242780 243076 243105 "CABMON" 243155 T CABMON (NIL) -9 NIL 243211) (-137 240343 242472 242579 "BTREE" 242706 NIL BTREE (NIL T) -8 NIL NIL) (-136 237847 239991 240113 "BTOURN" 240253 NIL BTOURN (NIL T) -8 NIL NIL) (-135 235304 237351 237393 "BTCAT" 237461 NIL BTCAT (NIL T) -9 NIL 237538) (-134 234971 235051 235200 "BTCAT-" 235205 NIL BTCAT- (NIL T T) -8 NIL NIL) (-133 230161 234031 234060 "BTAGG" 234316 T BTAGG (NIL) -9 NIL 234495) (-132 229584 229728 229958 "BTAGG-" 229963 NIL BTAGG- (NIL T) -8 NIL NIL) (-131 226634 228862 229077 "BSTREE" 229401 NIL BSTREE (NIL T) -8 NIL NIL) (-130 225037 225584 225884 "BSD" 226354 T BSD (NIL) -8 NIL NIL) (-129 224175 224301 224485 "BRILL" 224893 NIL BRILL (NIL T) -7 NIL NIL) (-128 220915 222936 222978 "BRAGG" 223627 NIL BRAGG (NIL T) -9 NIL 223884) (-127 219444 219850 220405 "BRAGG-" 220410 NIL BRAGG- (NIL T T) -8 NIL NIL) (-126 212643 218790 218974 "BPADICRT" 219292 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-125 210947 212580 212625 "BPADIC" 212630 NIL BPADIC (NIL NIL) -8 NIL NIL) (-124 210645 210675 210789 "BOUNDZRO" 210911 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-123 206160 207251 208118 "BOP" 209798 T BOP (NIL) -8 NIL NIL) (-122 203783 204227 204746 "BOP1" 205674 NIL BOP1 (NIL T) -7 NIL NIL) (-121 202111 202826 203120 "BOOLEAN" 203509 T BOOLEAN (NIL) -8 NIL NIL) (-120 201472 201850 201905 "BMODULE" 201910 NIL BMODULE (NIL T T) -9 NIL 201975) (-119 197815 198485 199271 "BLUPPACK" 200804 NIL BLUPPACK (NIL T NIL T T T) -7 NIL NIL) (-118 197207 197692 197761 "BLQT" 197766 T BLQT (NIL) -8 NIL NIL) (-117 195636 196111 196140 "BLMETCT" 196785 T BLMETCT (NIL) -9 NIL 197157) (-116 195035 195517 195584 "BLHN" 195589 T BLHN (NIL) -8 NIL NIL) (-115 189872 191021 192180 "BLAS1" 193896 T BLAS1 (NIL) -7 NIL NIL) (-114 185682 189670 189743 "BITS" 189819 T BITS (NIL) -8 NIL NIL) (-113 184753 185214 185366 "BINFILE" 185550 T BINFILE (NIL) -8 NIL NIL) (-112 178575 184194 184360 "BINARY" 184607 T BINARY (NIL) -8 NIL NIL) (-111 176442 177864 177906 "BGAGG" 178166 NIL BGAGG (NIL T) -9 NIL 178303) (-110 176273 176305 176396 "BGAGG-" 176401 NIL BGAGG- (NIL T T) -8 NIL NIL) (-109 175371 175657 175862 "BFUNCT" 176088 T BFUNCT (NIL) -8 NIL NIL) (-108 174063 174241 174528 "BEZOUT" 175196 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-107 173026 173248 173507 "BEZIER" 173837 NIL BEZIER (NIL T) -7 NIL NIL) (-106 169549 171878 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(-92 153814 154549 154691 "ASP80" 154833 NIL ASP80 (NIL NIL) -8 NIL NIL) (-91 152713 153449 153581 "ASP7" 153713 NIL ASP7 (NIL NIL) -8 NIL NIL) (-90 151669 152390 152508 "ASP78" 152626 NIL ASP78 (NIL NIL) -8 NIL NIL) (-89 150640 151349 151466 "ASP77" 151583 NIL ASP77 (NIL NIL) -8 NIL NIL) (-88 149555 150278 150409 "ASP74" 150540 NIL ASP74 (NIL NIL) -8 NIL NIL) (-87 148456 149190 149322 "ASP73" 149454 NIL ASP73 (NIL NIL) -8 NIL NIL) (-86 147411 148133 148251 "ASP6" 148369 NIL ASP6 (NIL NIL) -8 NIL NIL) (-85 146360 147088 147206 "ASP55" 147324 NIL ASP55 (NIL NIL) -8 NIL NIL) (-84 145310 146034 146153 "ASP50" 146272 NIL ASP50 (NIL NIL) -8 NIL NIL) (-83 144398 145011 145121 "ASP4" 145231 NIL ASP4 (NIL NIL) -8 NIL NIL) (-82 143486 144099 144209 "ASP49" 144319 NIL ASP49 (NIL NIL) -8 NIL NIL) (-81 142271 143025 143193 "ASP42" 143375 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-80 141049 141804 141974 "ASP41" 142158 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-79 140001 140726 140844 "ASP35" 140962 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3165285 3166244 "SUBSPACE" 3169467 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1157 3163705 3163795 3163958 "SUBRESP" 3164162 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1156 3157074 3158370 3159681 "STTF" 3162441 NIL STTF (NIL T) -7 NIL NIL) (-1155 3151247 3152367 3153514 "STTFNC" 3155974 NIL STTFNC (NIL T) -7 NIL NIL) (-1154 3142566 3144433 3146225 "STTAYLOR" 3149490 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1153 3135822 3142430 3142513 "STRTBL" 3142518 NIL STRTBL (NIL T) -8 NIL NIL) (-1152 3131213 3135777 3135808 "STRING" 3135813 T STRING (NIL) -8 NIL NIL) (-1151 3126077 3130555 3130586 "STRICAT" 3130645 T STRICAT (NIL) -9 NIL 3130707) (-1150 3118804 3123604 3124222 "STREAM" 3125494 NIL STREAM (NIL T) -8 NIL NIL) (-1149 3118314 3118391 3118535 "STREAM3" 3118721 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1148 3117296 3117479 3117714 "STREAM2" 3118127 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1147 3116984 3117036 3117129 "STREAM1" 3117238 NIL STREAM1 (NIL T) -7 NIL NIL) (-1146 3116628 3116694 3116801 "STNSR" 3116912 NIL STNSR (NIL T) -7 NIL NIL) (-1145 3115644 3115825 3116056 "STINPROD" 3116444 NIL STINPROD (NIL T) -7 NIL NIL) (-1144 3115221 3115405 3115436 "STEP" 3115516 T STEP (NIL) -9 NIL 3115594) (-1143 3108776 3115120 3115197 "STBL" 3115202 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1142 3103990 3108028 3108072 "STAGG" 3108225 NIL STAGG (NIL T) -9 NIL 3108314) (-1141 3101692 3102294 3103166 "STAGG-" 3103171 NIL STAGG- (NIL T T) -8 NIL NIL) (-1140 3095184 3096753 3097868 "STACK" 3100612 NIL STACK (NIL T) -8 NIL NIL) (-1139 3087909 3093325 3093781 "SREGSET" 3094814 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1138 3080335 3081703 3083216 "SRDCMPK" 3086515 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1137 3073313 3077773 3077804 "SRAGG" 3079107 T SRAGG (NIL) -9 NIL 3079715) (-1136 3072330 3072585 3072964 "SRAGG-" 3072969 NIL SRAGG- (NIL T) -8 NIL NIL) (-1135 3066778 3071253 3071677 "SQMATRIX" 3071953 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1134 3060534 3063496 3064223 "SPLTREE" 3066123 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1133 3056524 3057190 3057836 "SPLNODE" 3059960 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1132 3055570 3055803 3055834 "SPFCAT" 3056278 T SPFCAT (NIL) -9 NIL NIL) (-1131 3054307 3054517 3054781 "SPECOUT" 3055328 T SPECOUT (NIL) -7 NIL NIL) (-1130 3046277 3048024 3048068 "SPACEC" 3052441 NIL SPACEC (NIL T) -9 NIL 3054257) (-1129 3044448 3046209 3046258 "SPACE3" 3046263 NIL SPACE3 (NIL T) -8 NIL NIL) (-1128 3043202 3043373 3043663 "SORTPAK" 3044254 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1127 3041252 3041555 3041974 "SOLVETRA" 3042866 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1126 3040263 3040485 3040759 "SOLVESER" 3041025 NIL SOLVESER (NIL T) -7 NIL NIL) (-1125 3035483 3036364 3037366 "SOLVERAD" 3039315 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1124 3031298 3031907 3032636 "SOLVEFOR" 3034850 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1123 3025601 3030646 3030744 "SNTSCAT" 3030749 NIL SNTSCAT (NIL T T T T) -9 NIL 3030819) (-1122 3019699 3023926 3024316 "SMTS" 3025292 NIL SMTS (NIL T T T) -8 NIL NIL) (-1121 3014103 3019587 3019664 "SMP" 3019669 NIL SMP (NIL T T) -8 NIL NIL) (-1120 3012262 3012563 3012961 "SMITH" 3013800 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1119 3005204 3009402 3009506 "SMATCAT" 3010857 NIL SMATCAT (NIL NIL T T T) -9 NIL 3011404) (-1118 3002144 3002967 3004145 "SMATCAT-" 3004150 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1117 2999897 3001414 3001458 "SKAGG" 3001719 NIL SKAGG (NIL T) -9 NIL 3001854) (-1116 2995955 2999001 2999279 "SINT" 2999641 T SINT (NIL) -8 NIL NIL) (-1115 2995727 2995765 2995831 "SIMPAN" 2995911 T SIMPAN (NIL) -7 NIL NIL) (-1114 2994565 2994786 2995061 "SIGNRF" 2995486 NIL SIGNRF (NIL T) -7 NIL NIL) (-1113 2993370 2993521 2993812 "SIGNEF" 2994394 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1112 2991062 2991516 2992021 "SHP" 2992912 NIL SHP (NIL T NIL) -7 NIL NIL) (-1111 2984843 2990963 2991039 "SHDP" 2991044 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1110 2984331 2984523 2984554 "SGROUP" 2984706 T SGROUP (NIL) -9 NIL 2984793) (-1109 2984101 2984153 2984257 "SGROUP-" 2984262 NIL SGROUP- (NIL T) -8 NIL NIL) (-1108 2980937 2981634 2982357 "SGCF" 2983400 T SGCF (NIL) -7 NIL NIL) (-1107 2975338 2980383 2980481 "SFRTCAT" 2980486 NIL SFRTCAT (NIL T T T T) -9 NIL 2980525) (-1106 2968762 2969777 2970913 "SFRGCD" 2974321 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1105 2961890 2962961 2964147 "SFQCMPK" 2967695 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1104 2961512 2961601 2961711 "SFORT" 2961831 NIL SFORT (NIL T T) -8 NIL NIL) (-1103 2960657 2961352 2961473 "SEXOF" 2961478 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1102 2959791 2960538 2960606 "SEX" 2960611 T SEX (NIL) -8 NIL NIL) (-1101 2954566 2955255 2955351 "SEXCAT" 2959122 NIL SEXCAT (NIL T T T T T) -9 NIL 2959741) (-1100 2951701 2954500 2954548 "SET" 2954553 NIL SET (NIL T) -8 NIL NIL) (-1099 2949935 2950414 2950719 "SETMN" 2951442 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1098 2949540 2949666 2949697 "SETCAT" 2949814 T SETCAT (NIL) -9 NIL 2949899) (-1097 2949320 2949372 2949471 "SETCAT-" 2949476 NIL SETCAT- (NIL T) -8 NIL NIL) (-1096 2948983 2949133 2949164 "SETCATD" 2949223 T SETCATD (NIL) -9 NIL 2949270) (-1095 2945369 2947443 2947487 "SETAGG" 2948357 NIL SETAGG (NIL T) -9 NIL 2948697) (-1094 2944827 2944943 2945180 "SETAGG-" 2945185 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1093 2944030 2944323 2944385 "SEGXCAT" 2944671 NIL SEGXCAT (NIL T T) -9 NIL 2944791) (-1092 2943090 2943700 2943880 "SEG" 2943885 NIL SEG (NIL T) -8 NIL NIL) (-1091 2941996 2942209 2942253 "SEGCAT" 2942835 NIL SEGCAT (NIL T) -9 NIL 2943073) (-1090 2941047 2941377 2941576 "SEGBIND" 2941832 NIL SEGBIND (NIL T) -8 NIL NIL) (-1089 2940668 2940727 2940840 "SEGBIND2" 2940982 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1088 2939889 2940015 2940218 "SEG2" 2940513 NIL SEG2 (NIL T T) -7 NIL NIL) (-1087 2939326 2939824 2939871 "SDVAR" 2939876 NIL SDVAR (NIL T) -8 NIL NIL) (-1086 2931570 2939096 2939226 "SDPOL" 2939231 NIL SDPOL (NIL T) -8 NIL NIL) (-1085 2927593 2928622 2929269 "SD" 2930970 NIL SD (NIL T) -8 NIL NIL) (-1084 2926186 2926452 2926771 "SCPKG" 2927308 NIL SCPKG (NIL T) -7 NIL NIL) (-1083 2925407 2925540 2925719 "SCACHE" 2926041 NIL SCACHE (NIL T) -7 NIL NIL) (-1082 2924846 2925167 2925252 "SAOS" 2925344 T SAOS (NIL) -8 NIL NIL) (-1081 2924411 2924446 2924619 "SAERFFC" 2924805 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1080 2918255 2924308 2924388 "SAE" 2924393 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1079 2917848 2917883 2918042 "SAEFACT" 2918214 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1078 2916169 2916483 2916884 "RURPK" 2917514 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1077 2914805 2915084 2915396 "RULESET" 2916003 NIL RULESET (NIL T T T) -8 NIL NIL) (-1076 2911992 2912495 2912960 "RULE" 2914486 NIL RULE (NIL T T T) -8 NIL NIL) (-1075 2911631 2911786 2911869 "RULECOLD" 2911944 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1074 2906480 2907274 2908194 "RSETGCD" 2910830 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1073 2895743 2900788 2900886 "RSETCAT" 2905005 NIL RSETCAT (NIL T T T T) -9 NIL 2906102) (-1072 2893670 2894209 2895033 "RSETCAT-" 2895038 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1071 2886057 2887432 2888952 "RSDCMPK" 2892269 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1070 2884061 2884502 2884577 "RRCC" 2885663 NIL RRCC (NIL T T) -9 NIL 2886007) (-1069 2883412 2883586 2883865 "RRCC-" 2883870 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1068 2857554 2867185 2867253 "RPOLCAT" 2877919 NIL RPOLCAT (NIL T T T) -9 NIL 2881068) (-1067 2849054 2851392 2854514 "RPOLCAT-" 2854519 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1066 2840113 2847265 2847747 "ROUTINE" 2848594 T ROUTINE (NIL) -8 NIL NIL) (-1065 2836813 2839664 2839813 "ROMAN" 2839986 T ROMAN (NIL) -8 NIL NIL) (-1064 2835088 2835673 2835933 "ROIRC" 2836618 NIL ROIRC (NIL T T) -8 NIL NIL) (-1063 2831426 2833726 2833757 "RNS" 2834061 T RNS (NIL) -9 NIL 2834335) (-1062 2829935 2830318 2830852 "RNS-" 2830927 NIL RNS- (NIL T) -8 NIL NIL) (-1061 2829357 2829765 2829796 "RNG" 2829801 T RNG (NIL) -9 NIL 2829822) (-1060 2828748 2829110 2829154 "RMODULE" 2829216 NIL RMODULE (NIL T) -9 NIL 2829258) (-1059 2827584 2827678 2828014 "RMCAT2" 2828649 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1058 2824293 2826762 2827085 "RMATRIX" 2827320 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1057 2817239 2819473 2819589 "RMATCAT" 2822948 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2823925) (-1056 2816614 2816761 2817068 "RMATCAT-" 2817073 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1055 2816181 2816256 2816384 "RINTERP" 2816533 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1054 2815224 2815788 2815819 "RING" 2815931 T RING (NIL) -9 NIL 2816026) (-1053 2815016 2815060 2815157 "RING-" 2815162 NIL RING- (NIL T) -8 NIL NIL) (-1052 2813857 2814094 2814352 "RIDIST" 2814780 T RIDIST (NIL) -7 NIL NIL) (-1051 2805173 2813325 2813531 "RGCHAIN" 2813705 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1050 2803973 2804214 2804493 "RFP" 2804928 NIL RFP (NIL T) -7 NIL NIL) (-1049 2800967 2801581 2802251 "RF" 2803337 NIL RF (NIL T) -7 NIL NIL) (-1048 2800613 2800676 2800779 "RFFACTOR" 2800898 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1047 2800338 2800373 2800470 "RFFACT" 2800572 NIL RFFACT (NIL T) -7 NIL NIL) (-1046 2798455 2798819 2799201 "RFDIST" 2799978 T RFDIST (NIL) -7 NIL NIL) (-1045 2797908 2798000 2798163 "RETSOL" 2798357 NIL RETSOL (NIL T T) -7 NIL NIL) (-1044 2797495 2797575 2797619 "RETRACT" 2797812 NIL RETRACT (NIL T) -9 NIL NIL) (-1043 2797344 2797369 2797456 "RETRACT-" 2797461 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1042 2790210 2796997 2797124 "RESULT" 2797239 T RESULT (NIL) -8 NIL NIL) (-1041 2788790 2789479 2789678 "RESRING" 2790113 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1040 2788426 2788475 2788573 "RESLATC" 2788727 NIL RESLATC (NIL T) -7 NIL NIL) (-1039 2788132 2788166 2788273 "REPSQ" 2788385 NIL REPSQ (NIL T) -7 NIL NIL) (-1038 2785554 2786134 2786736 "REP" 2787552 T REP (NIL) -7 NIL NIL) (-1037 2785252 2785286 2785397 "REPDB" 2785513 NIL REPDB (NIL T) -7 NIL NIL) (-1036 2779170 2780549 2781768 "REP2" 2784068 NIL REP2 (NIL T) -7 NIL NIL) (-1035 2775551 2776232 2777038 "REP1" 2778399 NIL REP1 (NIL T) -7 NIL NIL) (-1034 2768277 2773692 2774148 "REGSET" 2775181 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1033 2767092 2767427 2767676 "REF" 2768063 NIL REF (NIL T) -8 NIL NIL) (-1032 2766469 2766572 2766739 "REDORDER" 2766976 NIL REDORDER (NIL T T) -7 NIL NIL) (-1031 2763331 2763797 2764406 "RECOP" 2766003 NIL RECOP (NIL T T) -7 NIL NIL) (-1030 2759271 2762544 2762771 "RECLOS" 2763159 NIL RECLOS (NIL T) -8 NIL NIL) (-1029 2758323 2758504 2758719 "REALSOLV" 2759078 T REALSOLV (NIL) -7 NIL NIL) (-1028 2758168 2758209 2758240 "REAL" 2758245 T REAL (NIL) -9 NIL 2758280) (-1027 2754651 2755453 2756337 "REAL0Q" 2757333 NIL REAL0Q (NIL T) -7 NIL NIL) (-1026 2750252 2751240 2752301 "REAL0" 2753632 NIL REAL0 (NIL T) -7 NIL NIL) (-1025 2749657 2749729 2749936 "RDIV" 2750174 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-1024 2748725 2748899 2749112 "RDIST" 2749479 NIL RDIST (NIL T) -7 NIL NIL) (-1023 2747322 2747609 2747981 "RDETRS" 2748433 NIL RDETRS (NIL T T) -7 NIL NIL) (-1022 2745134 2745588 2746126 "RDETR" 2746864 NIL RDETR (NIL T T) -7 NIL NIL) (-1021 2743745 2744023 2744427 "RDEEFS" 2744850 NIL RDEEFS (NIL T T) -7 NIL NIL) (-1020 2742240 2742546 2742978 "RDEEF" 2743433 NIL RDEEF (NIL T T) -7 NIL NIL) (-1019 2736431 2739366 2739397 "RCFIELD" 2740692 T RCFIELD (NIL) -9 NIL 2741423) (-1018 2734495 2734999 2735695 "RCFIELD-" 2735770 NIL RCFIELD- (NIL T) -8 NIL NIL) (-1017 2730853 2732632 2732676 "RCAGG" 2733760 NIL RCAGG (NIL T) -9 NIL 2734223) (-1016 2730481 2730575 2730738 "RCAGG-" 2730743 NIL RCAGG- (NIL T T) -8 NIL NIL) (-1015 2729817 2729928 2730093 "RATRET" 2730365 NIL RATRET (NIL T) -7 NIL NIL) (-1014 2729370 2729437 2729558 "RATFACT" 2729745 NIL RATFACT (NIL T) -7 NIL NIL) (-1013 2728678 2728798 2728950 "RANDSRC" 2729240 T RANDSRC (NIL) -7 NIL NIL) (-1012 2728412 2728456 2728529 "RADUTIL" 2728627 T RADUTIL (NIL) -7 NIL NIL) (-1011 2721398 2727143 2727463 "RADIX" 2728126 NIL RADIX (NIL NIL) -8 NIL NIL) (-1010 2712909 2721240 2721370 "RADFF" 2721375 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-1009 2712555 2712630 2712661 "RADCAT" 2712821 T RADCAT (NIL) -9 NIL NIL) (-1008 2712337 2712385 2712485 "RADCAT-" 2712490 NIL RADCAT- (NIL T) -8 NIL NIL) (-1007 2705582 2707200 2708354 "QUEUE" 2711218 NIL QUEUE (NIL T) -8 NIL NIL) (-1006 2702069 2705515 2705563 "QUAT" 2705568 NIL QUAT (NIL T) -8 NIL NIL) (-1005 2701700 2701743 2701874 "QUATCT2" 2702020 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-1004 2695424 2698808 2698851 "QUATCAT" 2699642 NIL QUATCAT (NIL T) -9 NIL 2700400) (-1003 2691563 2692600 2693990 "QUATCAT-" 2694086 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-1002 2689115 2690673 2690717 "QUAGG" 2691098 NIL QUAGG (NIL T) -9 NIL 2691273) (-1001 2688035 2688508 2688682 "QFORM" 2688987 NIL QFORM (NIL NIL T) -8 NIL NIL) (-1000 2679250 2684517 2684560 "QFCAT" 2685228 NIL QFCAT (NIL T) -9 NIL 2686217) (-999 2674820 2676021 2677613 "QFCAT-" 2677708 NIL QFCAT- (NIL T T) -8 NIL NIL) (-998 2674454 2674497 2674626 "QFCAT2" 2674771 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-997 2673914 2674024 2674154 "QEQUAT" 2674344 T QEQUAT (NIL) -8 NIL NIL) (-996 2667062 2668133 2669317 "QCMPACK" 2672847 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-995 2664642 2665063 2665489 "QALGSET" 2666719 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-994 2663887 2664061 2664293 "QALGSET2" 2664462 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-993 2662578 2662801 2663118 "PWFFINTB" 2663660 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-992 2660760 2660928 2661282 "PUSHVAR" 2662392 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-991 2656677 2657731 2657773 "PTRANFN" 2659657 NIL PTRANFN (NIL T) -9 NIL NIL) (-990 2655079 2655370 2655692 "PTPACK" 2656388 NIL PTPACK (NIL T) -7 NIL NIL) (-989 2654711 2654768 2654877 "PTFUNC2" 2655016 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-988 2649211 2653545 2653587 "PTCAT" 2653960 NIL PTCAT (NIL T) -9 NIL 2654122) (-987 2648869 2648904 2649028 "PSQFR" 2649170 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-986 2647456 2647756 2648092 "PSEUDLIN" 2648565 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-985 2634232 2636596 2638917 "PSETPK" 2645219 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-984 2627276 2629990 2630087 "PSETCAT" 2633108 NIL PSETCAT (NIL T T T T) -9 NIL 2633921) (-983 2625112 2625746 2626567 "PSETCAT-" 2626572 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-982 2624461 2624625 2624654 "PSCURVE" 2624922 T PSCURVE (NIL) -9 NIL 2625089) (-981 2620850 2622376 2622442 "PSCAT" 2623286 NIL PSCAT (NIL T T T) -9 NIL 2623526) (-980 2619913 2620129 2620529 "PSCAT-" 2620534 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-979 2618566 2619198 2619412 "PRTITION" 2619719 T PRTITION (NIL) -8 NIL NIL) (-978 2615730 2616379 2616420 "PRSPCAT" 2617934 NIL PRSPCAT (NIL T) -9 NIL 2618502) (-977 2604830 2607036 2609223 "PRS" 2613593 NIL PRS (NIL T T) -7 NIL NIL) (-976 2602728 2604214 2604255 "PRQAGG" 2604438 NIL PRQAGG (NIL T) -9 NIL 2604540) (-975 2601997 2602653 2602710 "PROJSP" 2602715 NIL PROJSP (NIL NIL T) -8 NIL NIL) (-974 2601179 2601920 2601972 "PROJPLPS" 2601977 NIL PROJPLPS (NIL T) -8 NIL NIL) (-973 2600438 2601116 2601161 "PROJPL" 2601166 NIL PROJPL (NIL T) -8 NIL NIL) (-972 2594173 2598636 2599440 "PRODUCT" 2599680 NIL PRODUCT (NIL T T) -8 NIL NIL) (-971 2591448 2593637 2593868 "PR" 2593987 NIL PR (NIL T T) -8 NIL NIL) (-970 2590000 2590157 2590452 "PRJALGPK" 2591288 NIL PRJALGPK (NIL T NIL T T T) -7 NIL NIL) (-969 2589796 2589828 2589887 "PRINT" 2589961 T PRINT (NIL) -7 NIL NIL) (-968 2589136 2589253 2589405 "PRIMES" 2589676 NIL PRIMES (NIL T) -7 NIL NIL) (-967 2587201 2587602 2588068 "PRIMELT" 2588715 NIL PRIMELT (NIL T) -7 NIL NIL) (-966 2586929 2586978 2587007 "PRIMCAT" 2587131 T PRIMCAT (NIL) -9 NIL NIL) (-965 2583096 2586867 2586912 "PRIMARR" 2586917 NIL PRIMARR (NIL T) -8 NIL NIL) (-964 2582103 2582281 2582509 "PRIMARR2" 2582914 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-963 2581746 2581802 2581913 "PREASSOC" 2582041 NIL PREASSOC (NIL T T) -7 NIL NIL) (-962 2581221 2581353 2581382 "PPCURVE" 2581587 T PPCURVE (NIL) -9 NIL 2581723) (-961 2575619 2576770 2577949 "POLYVEC" 2580062 T POLYVEC (NIL) -7 NIL NIL) (-960 2572980 2573379 2573970 "POLYROOT" 2575201 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-959 2566881 2572586 2572745 "POLY" 2572854 NIL POLY (NIL T) -8 NIL NIL) (-958 2566264 2566322 2566556 "POLYLIFT" 2566817 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-957 2562539 2562988 2563617 "POLYCATQ" 2565809 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-956 2549501 2554901 2554967 "POLYCAT" 2558481 NIL POLYCAT (NIL T T T) -9 NIL 2560394) (-955 2542951 2544812 2547196 "POLYCAT-" 2547201 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-954 2542538 2542606 2542726 "POLY2UP" 2542877 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-953 2542170 2542227 2542336 "POLY2" 2542475 NIL POLY2 (NIL T T) -7 NIL NIL) (-952 2540857 2541096 2541371 "POLUTIL" 2541945 NIL POLUTIL (NIL T T) -7 NIL NIL) (-951 2539212 2539489 2539820 "POLTOPOL" 2540579 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-950 2534734 2539148 2539194 "POINT" 2539199 NIL POINT (NIL T) -8 NIL NIL) (-949 2532921 2533278 2533653 "PNTHEORY" 2534379 T PNTHEORY (NIL) -7 NIL NIL) (-948 2531340 2531637 2532049 "PMTOOLS" 2532619 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-947 2530933 2531011 2531128 "PMSYM" 2531256 NIL PMSYM (NIL T) -7 NIL NIL) (-946 2530441 2530510 2530685 "PMQFCAT" 2530858 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-945 2529796 2529906 2530062 "PMPRED" 2530318 NIL PMPRED (NIL T) -7 NIL NIL) (-944 2529192 2529278 2529439 "PMPREDFS" 2529697 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-943 2527837 2528045 2528429 "PMPLCAT" 2528955 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-942 2527369 2527448 2527600 "PMLSAGG" 2527752 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-941 2526844 2526920 2527101 "PMKERNEL" 2527287 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-940 2526461 2526536 2526649 "PMINS" 2526763 NIL PMINS (NIL T) -7 NIL NIL) (-939 2525889 2525958 2526174 "PMFS" 2526386 NIL PMFS (NIL T T T) -7 NIL NIL) (-938 2525117 2525235 2525440 "PMDOWN" 2525766 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-937 2524280 2524439 2524621 "PMASS" 2524955 T PMASS (NIL) -7 NIL NIL) (-936 2523554 2523665 2523828 "PMASSFS" 2524166 NIL PMASSFS (NIL T T) -7 NIL NIL) (-935 2521314 2521567 2521950 "PLPKCRV" 2523278 NIL PLPKCRV (NIL T T T NIL T) -7 NIL NIL) (-934 2520969 2521037 2521131 "PLOTTOOL" 2521240 T PLOTTOOL (NIL) -7 NIL NIL) (-933 2515591 2516780 2517928 "PLOT" 2519841 T PLOT (NIL) -8 NIL NIL) (-932 2511405 2512439 2513360 "PLOT3D" 2514690 T PLOT3D (NIL) -8 NIL NIL) (-931 2510317 2510494 2510729 "PLOT1" 2511209 NIL PLOT1 (NIL T) -7 NIL NIL) (-930 2485736 2490401 2495246 "PLEQN" 2505589 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-929 2484976 2485646 2485713 "PLCS" 2485718 NIL PLCS (NIL T T) -8 NIL NIL) (-928 2484127 2484861 2484932 "PLACESPS" 2484937 NIL PLACESPS (NIL T) -8 NIL NIL) (-927 2483334 2484040 2484097 "PLACES" 2484102 NIL PLACES (NIL T) -8 NIL NIL) (-926 2480058 2480722 2480781 "PLACESC" 2482699 NIL PLACESC (NIL T T) -9 NIL 2483270) (-925 2479376 2479498 2479678 "PINTERP" 2479923 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-924 2479069 2479116 2479219 "PINTERPA" 2479323 NIL PINTERPA (NIL T T) -7 NIL NIL) (-923 2478296 2478863 2478956 "PI" 2478996 T PI (NIL) -8 NIL NIL) (-922 2476683 2477668 2477697 "PID" 2477879 T PID (NIL) -9 NIL 2478013) (-921 2476408 2476445 2476533 "PICOERCE" 2476640 NIL PICOERCE (NIL T) -7 NIL NIL) (-920 2475729 2475867 2476043 "PGROEB" 2476264 NIL PGROEB (NIL T) -7 NIL NIL) (-919 2471316 2472130 2473035 "PGE" 2474844 T PGE (NIL) -7 NIL NIL) (-918 2469440 2469686 2470052 "PGCD" 2471033 NIL PGCD (NIL T T T T) -7 NIL NIL) (-917 2468778 2468881 2469042 "PFRPAC" 2469324 NIL PFRPAC (NIL T) -7 NIL NIL) (-916 2465393 2467326 2467679 "PFR" 2468457 NIL PFR (NIL T) -8 NIL NIL) (-915 2463782 2464026 2464351 "PFOTOOLS" 2465140 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-914 2458647 2459312 2460061 "PFORP" 2463124 NIL PFORP (NIL T T T NIL) -7 NIL NIL) (-913 2457180 2457419 2457770 "PFOQ" 2458404 NIL PFOQ (NIL T T T) -7 NIL NIL) (-912 2455653 2455865 2456228 "PFO" 2456964 NIL PFO (NIL T T T T T) -7 NIL NIL) (-911 2452151 2455542 2455611 "PF" 2455616 NIL PF (NIL NIL) -8 NIL NIL) (-910 2449576 2450857 2450886 "PFECAT" 2451471 T PFECAT (NIL) -9 NIL 2451854) (-909 2449021 2449175 2449389 "PFECAT-" 2449394 NIL PFECAT- (NIL T) -8 NIL NIL) (-908 2447625 2447876 2448177 "PFBRU" 2448770 NIL PFBRU (NIL T T) -7 NIL NIL) (-907 2445492 2445843 2446275 "PFBR" 2447276 NIL PFBR (NIL T T T T) -7 NIL NIL) (-906 2441348 2442872 2443546 "PERM" 2444851 NIL PERM (NIL T) -8 NIL NIL) (-905 2436615 2437555 2438425 "PERMGRP" 2440511 NIL PERMGRP (NIL T) -8 NIL NIL) (-904 2434686 2435679 2435721 "PERMCAT" 2436167 NIL PERMCAT (NIL T) -9 NIL 2436470) (-903 2434339 2434380 2434504 "PERMAN" 2434639 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-902 2431785 2433908 2434039 "PENDTREE" 2434241 NIL PENDTREE (NIL T) -8 NIL NIL) (-901 2429853 2430631 2430673 "PDRING" 2431330 NIL PDRING (NIL T) -9 NIL 2431616) (-900 2428956 2429174 2429536 "PDRING-" 2429541 NIL PDRING- (NIL T T) -8 NIL NIL) (-899 2426098 2426848 2427539 "PDEPROB" 2428285 T PDEPROB (NIL) -8 NIL NIL) (-898 2423645 2424147 2424702 "PDEPACK" 2425563 T PDEPACK (NIL) -7 NIL NIL) (-897 2422557 2422747 2422998 "PDECOMP" 2423444 NIL PDECOMP (NIL T T) -7 NIL NIL) (-896 2420161 2420978 2421007 "PDECAT" 2421794 T PDECAT (NIL) -9 NIL 2422507) (-895 2419912 2419945 2420035 "PCOMP" 2420122 NIL PCOMP (NIL T T) -7 NIL NIL) (-894 2418117 2418713 2419010 "PBWLB" 2419641 NIL PBWLB (NIL T) -8 NIL NIL) (-893 2410622 2412190 2413528 "PATTERN" 2416800 NIL PATTERN (NIL T) -8 NIL NIL) (-892 2410254 2410311 2410420 "PATTERN2" 2410559 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-891 2408011 2408399 2408856 "PATTERN1" 2409843 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-890 2405406 2405960 2406441 "PATRES" 2407576 NIL PATRES (NIL T T) -8 NIL NIL) (-889 2404970 2405037 2405169 "PATRES2" 2405333 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-888 2402853 2403258 2403665 "PATMATCH" 2404637 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-887 2402388 2402571 2402613 "PATMAB" 2402720 NIL PATMAB (NIL T) -9 NIL 2402803) (-886 2400933 2401242 2401500 "PATLRES" 2402193 NIL PATLRES (NIL T T T) -8 NIL NIL) (-885 2400480 2400603 2400645 "PATAB" 2400650 NIL PATAB (NIL T) -9 NIL 2400820) (-884 2397961 2398493 2399066 "PARTPERM" 2399927 T PARTPERM (NIL) -7 NIL NIL) (-883 2397582 2397645 2397747 "PARSURF" 2397892 NIL PARSURF (NIL T) -8 NIL NIL) (-882 2397214 2397271 2397380 "PARSU2" 2397519 NIL PARSU2 (NIL T T) -7 NIL NIL) (-881 2396835 2396898 2397000 "PARSCURV" 2397145 NIL PARSCURV (NIL T) -8 NIL NIL) (-880 2396467 2396524 2396633 "PARSC2" 2396772 NIL PARSC2 (NIL T T) -7 NIL NIL) (-879 2396106 2396164 2396261 "PARPCURV" 2396403 NIL PARPCURV (NIL T) -8 NIL NIL) (-878 2395738 2395795 2395904 "PARPC2" 2396043 NIL PARPC2 (NIL T T) -7 NIL NIL) (-877 2394218 2394336 2394655 "PARAMP" 2395593 NIL PARAMP (NIL T NIL T T T T T) -7 NIL NIL) (-876 2393738 2393824 2393943 "PAN2EXPR" 2394119 T PAN2EXPR (NIL) -7 NIL NIL) (-875 2392544 2392859 2393087 "PALETTE" 2393530 T PALETTE (NIL) -8 NIL NIL) (-874 2380177 2382343 2384459 "PAFF" 2390492 NIL PAFF (NIL T NIL T) -7 NIL NIL) (-873 2367173 2369501 2371712 "PAFFFF" 2378030 NIL PAFFFF (NIL T NIL T) -7 NIL NIL) (-872 2361012 2366430 2366625 "PADICRC" 2367027 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-871 2354209 2360356 2360541 "PADICRAT" 2360859 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-870 2352513 2354146 2354191 "PADIC" 2354196 NIL PADIC (NIL NIL) -8 NIL NIL) (-869 2349713 2351287 2351328 "PADICCT" 2351909 NIL PADICCT (NIL NIL) -9 NIL 2352191) (-868 2348670 2348870 2349138 "PADEPAC" 2349500 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-867 2347882 2348015 2348221 "PADE" 2348532 NIL PADE (NIL T T T) -7 NIL NIL) (-866 2344359 2347500 2347619 "PACRAT" 2347783 T PACRAT (NIL) -8 NIL NIL) (-865 2340420 2343470 2343499 "PACRATC" 2343504 T PACRATC (NIL) -9 NIL 2343584) (-864 2336542 2338507 2338536 "PACPERC" 2339482 T PACPERC (NIL) -9 NIL 2339922) (-863 2333187 2336316 2336407 "PACOFF" 2336483 NIL PACOFF (NIL T) -8 NIL NIL) (-862 2329857 2332542 2332571 "PACFFC" 2332576 T PACFFC (NIL) -9 NIL 2332597) (-861 2325947 2329540 2329641 "PACEXT" 2329788 NIL PACEXT (NIL NIL) -8 NIL NIL) (-860 2321325 2324842 2324871 "PACEXTC" 2324876 T PACEXTC (NIL) -9 NIL 2324920) (-859 2319333 2320165 2320480 "OWP" 2321094 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-858 2318417 2318938 2319110 "OVAR" 2319201 NIL OVAR (NIL NIL) -8 NIL NIL) (-857 2317681 2317802 2317963 "OUT" 2318276 T OUT (NIL) -7 NIL NIL) (-856 2306727 2308906 2311076 "OUTFORM" 2315531 T OUTFORM (NIL) -8 NIL NIL) (-855 2306135 2306456 2306545 "OSI" 2306658 T OSI (NIL) -8 NIL NIL) (-854 2304882 2305109 2305393 "ORTHPOL" 2305883 NIL ORTHPOL (NIL T) -7 NIL NIL) (-853 2302244 2304539 2304679 "OREUP" 2304825 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-852 2299631 2301933 2302061 "ORESUP" 2302186 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-851 2297139 2297645 2298210 "OREPCTO" 2299116 NIL OREPCTO (NIL T T) -7 NIL NIL) (-850 2291009 2293220 2293262 "OREPCAT" 2295610 NIL OREPCAT (NIL T) -9 NIL 2296710) (-849 2288156 2288938 2289996 "OREPCAT-" 2290001 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-848 2287332 2287604 2287633 "ORDSET" 2287942 T ORDSET (NIL) -9 NIL 2288106) (-847 2286851 2286973 2287166 "ORDSET-" 2287171 NIL ORDSET- (NIL T) -8 NIL NIL) (-846 2285460 2286261 2286290 "ORDRING" 2286492 T ORDRING (NIL) -9 NIL 2286617) (-845 2285105 2285199 2285343 "ORDRING-" 2285348 NIL ORDRING- (NIL T) -8 NIL NIL) (-844 2284479 2284960 2284989 "ORDMON" 2284994 T ORDMON (NIL) -9 NIL 2285015) (-843 2283641 2283788 2283983 "ORDFUNS" 2284328 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-842 2283127 2283510 2283539 "ORDFIN" 2283544 T ORDFIN (NIL) -9 NIL 2283565) (-841 2279639 2281719 2282125 "ORDCOMP" 2282754 NIL ORDCOMP (NIL T) -8 NIL NIL) (-840 2278905 2279032 2279218 "ORDCOMP2" 2279499 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-839 2275413 2276295 2277132 "OPTPROB" 2278088 T OPTPROB (NIL) -8 NIL NIL) (-838 2272215 2272854 2273558 "OPTPACK" 2274729 T OPTPACK (NIL) -7 NIL NIL) (-837 2269927 2270667 2270696 "OPTCAT" 2271515 T OPTCAT (NIL) -9 NIL 2272165) (-836 2269695 2269734 2269800 "OPQUERY" 2269881 T OPQUERY (NIL) -7 NIL NIL) (-835 2266821 2268012 2268513 "OP" 2269227 NIL OP (NIL T) -8 NIL NIL) (-834 2263586 2265624 2265990 "ONECOMP" 2266488 NIL ONECOMP (NIL T) -8 NIL NIL) (-833 2262891 2263006 2263180 "ONECOMP2" 2263458 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-832 2262310 2262416 2262546 "OMSERVER" 2262781 T OMSERVER (NIL) -7 NIL NIL) (-831 2259197 2261749 2261790 "OMSAGG" 2261851 NIL OMSAGG (NIL T) -9 NIL 2261915) (-830 2257820 2258083 2258365 "OMPKG" 2258935 T OMPKG (NIL) -7 NIL NIL) (-829 2257249 2257352 2257381 "OM" 2257680 T OM (NIL) -9 NIL NIL) (-828 2255787 2256800 2256968 "OMLO" 2257131 NIL OMLO (NIL T T) -8 NIL NIL) (-827 2254712 2254859 2255086 "OMEXPR" 2255613 NIL OMEXPR (NIL T) -7 NIL NIL) (-826 2254030 2254258 2254394 "OMERR" 2254596 T OMERR (NIL) -8 NIL NIL) (-825 2253208 2253451 2253611 "OMERRK" 2253890 T OMERRK (NIL) -8 NIL NIL) (-824 2252686 2252885 2252993 "OMENC" 2253120 T OMENC (NIL) -8 NIL NIL) (-823 2246581 2247766 2248937 "OMDEV" 2251535 T OMDEV (NIL) -8 NIL NIL) (-822 2245650 2245821 2246015 "OMCONN" 2246407 T OMCONN (NIL) -8 NIL NIL) (-821 2244261 2245247 2245276 "OINTDOM" 2245281 T OINTDOM (NIL) -9 NIL 2245302) (-820 2239912 2241167 2241911 "OFMONOID" 2243549 NIL OFMONOID (NIL T) -8 NIL NIL) (-819 2239350 2239849 2239894 "ODVAR" 2239899 NIL ODVAR (NIL T) -8 NIL NIL) (-818 2236477 2238849 2239033 "ODR" 2239226 NIL ODR (NIL T T NIL) -8 NIL NIL) (-817 2228775 2236253 2236379 "ODPOL" 2236384 NIL ODPOL (NIL T) -8 NIL NIL) (-816 2222526 2228647 2228752 "ODP" 2228757 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-815 2221292 2221507 2221782 "ODETOOLS" 2222300 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-814 2218261 2218917 2219633 "ODESYS" 2220625 NIL ODESYS (NIL T T) -7 NIL NIL) (-813 2213145 2214053 2215077 "ODERTRIC" 2217337 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-812 2212571 2212653 2212847 "ODERED" 2213057 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-811 2209459 2210007 2210684 "ODERAT" 2211994 NIL ODERAT (NIL T T) -7 NIL NIL) (-810 2206419 2206883 2207480 "ODEPRRIC" 2208988 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-809 2204290 2204857 2205366 "ODEPROB" 2205930 T ODEPROB (NIL) -8 NIL NIL) (-808 2200812 2201295 2201942 "ODEPRIM" 2203769 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-807 2200061 2200163 2200423 "ODEPAL" 2200704 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-806 2196223 2197014 2197878 "ODEPACK" 2199217 T ODEPACK (NIL) -7 NIL NIL) (-805 2195256 2195363 2195592 "ODEINT" 2196112 NIL ODEINT (NIL T T) -7 NIL NIL) (-804 2189357 2190782 2192229 "ODEIFTBL" 2193829 T ODEIFTBL (NIL) -8 NIL NIL) (-803 2184692 2185478 2186437 "ODEEF" 2188516 NIL ODEEF (NIL T T) -7 NIL NIL) (-802 2184027 2184116 2184346 "ODECONST" 2184597 NIL ODECONST (NIL T T T) -7 NIL NIL) (-801 2182177 2182812 2182841 "ODECAT" 2183446 T ODECAT (NIL) -9 NIL 2183977) (-800 2178976 2181882 2182004 "OCT" 2182087 NIL OCT (NIL T) -8 NIL NIL) (-799 2178614 2178657 2178784 "OCTCT2" 2178927 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-798 2173394 2175882 2175923 "OC" 2177020 NIL OC (NIL T) -9 NIL 2177870) (-797 2170621 2171369 2172359 "OC-" 2172453 NIL OC- (NIL T T) -8 NIL NIL) (-796 2169998 2170440 2170469 "OCAMON" 2170474 T OCAMON (NIL) -9 NIL 2170495) (-795 2169450 2169857 2169886 "OASGP" 2169891 T OASGP (NIL) -9 NIL 2169911) (-794 2168736 2169199 2169228 "OAMONS" 2169268 T OAMONS (NIL) -9 NIL 2169311) (-793 2168175 2168582 2168611 "OAMON" 2168616 T OAMON (NIL) -9 NIL 2168636) (-792 2167478 2167970 2167999 "OAGROUP" 2168004 T OAGROUP (NIL) -9 NIL 2168024) (-791 2167168 2167218 2167306 "NUMTUBE" 2167422 NIL NUMTUBE (NIL T) -7 NIL NIL) (-790 2160741 2162259 2163795 "NUMQUAD" 2165652 T NUMQUAD (NIL) -7 NIL NIL) (-789 2156497 2157485 2158510 "NUMODE" 2159736 T NUMODE (NIL) -7 NIL NIL) (-788 2153877 2154731 2154760 "NUMINT" 2155683 T NUMINT (NIL) -9 NIL 2156447) (-787 2152825 2153022 2153240 "NUMFMT" 2153679 T NUMFMT (NIL) -7 NIL NIL) (-786 2139203 2142145 2144669 "NUMERIC" 2150340 NIL NUMERIC (NIL T) -7 NIL NIL) (-785 2133606 2138651 2138747 "NTSCAT" 2138752 NIL NTSCAT (NIL T T T T) -9 NIL 2138791) (-784 2132802 2132967 2133159 "NTPOLFN" 2133446 NIL NTPOLFN (NIL T) -7 NIL NIL) (-783 2120598 2129629 2130440 "NSUP" 2132024 NIL NSUP (NIL T) -8 NIL NIL) (-782 2120230 2120287 2120396 "NSUP2" 2120535 NIL NSUP2 (NIL T T) -7 NIL NIL) (-781 2110179 2120004 2120137 "NSMP" 2120142 NIL NSMP (NIL T T) -8 NIL NIL) (-780 2098271 2109761 2109925 "NSDPS" 2110047 NIL NSDPS (NIL T) -8 NIL NIL) (-779 2096703 2097004 2097361 "NREP" 2097959 NIL NREP (NIL T) -7 NIL NIL) (-778 2093792 2094340 2094989 "NPOLYGON" 2096145 NIL NPOLYGON (NIL T T T NIL) -7 NIL NIL) (-777 2092383 2092635 2092993 "NPCOEF" 2093535 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-776 2091665 2092167 2092251 "NOTTING" 2092331 NIL NOTTING (NIL T) -8 NIL NIL) (-775 2090731 2090846 2091062 "NORMRETR" 2091546 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-774 2088772 2089062 2089471 "NORMPK" 2090439 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-773 2088457 2088485 2088609 "NORMMA" 2088738 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-772 2088284 2088414 2088443 "NONE" 2088448 T NONE (NIL) -8 NIL NIL) (-771 2088073 2088102 2088171 "NONE1" 2088248 NIL NONE1 (NIL T) -7 NIL NIL) (-770 2087556 2087618 2087804 "NODE1" 2088005 NIL NODE1 (NIL T T) -7 NIL NIL) (-769 2085850 2086719 2086974 "NNI" 2087321 T NNI (NIL) -8 NIL NIL) (-768 2084270 2084583 2084947 "NLINSOL" 2085518 NIL NLINSOL (NIL T) -7 NIL NIL) (-767 2080438 2081405 2082327 "NIPROB" 2083368 T NIPROB (NIL) -8 NIL NIL) (-766 2079195 2079429 2079731 "NFINTBAS" 2080200 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-765 2078924 2078967 2079048 "NEWTON" 2079146 NIL NEWTON (NIL T) -7 NIL NIL) (-764 2077632 2077863 2078144 "NCODIV" 2078692 NIL NCODIV (NIL T T) -7 NIL NIL) (-763 2077394 2077431 2077506 "NCNTFRAC" 2077589 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-762 2075574 2075938 2076358 "NCEP" 2077019 NIL NCEP (NIL T) -7 NIL NIL) (-761 2074484 2075223 2075252 "NASRING" 2075362 T NASRING (NIL) -9 NIL 2075436) (-760 2074279 2074323 2074417 "NASRING-" 2074422 NIL NASRING- (NIL T) -8 NIL NIL) (-759 2073431 2073930 2073959 "NARNG" 2074076 T NARNG (NIL) -9 NIL 2074167) (-758 2073123 2073190 2073324 "NARNG-" 2073329 NIL NARNG- (NIL T) -8 NIL NIL) (-757 2072002 2072209 2072444 "NAGSP" 2072908 T NAGSP (NIL) -7 NIL NIL) (-756 2063274 2064958 2066631 "NAGS" 2070349 T NAGS (NIL) -7 NIL NIL) (-755 2061822 2062130 2062461 "NAGF07" 2062963 T NAGF07 (NIL) -7 NIL NIL) (-754 2056360 2057651 2058958 "NAGF04" 2060535 T NAGF04 (NIL) -7 NIL NIL) (-753 2049328 2050942 2052575 "NAGF02" 2054747 T NAGF02 (NIL) -7 NIL NIL) (-752 2044552 2045652 2046769 "NAGF01" 2048231 T NAGF01 (NIL) -7 NIL NIL) (-751 2038180 2039746 2041331 "NAGE04" 2042987 T NAGE04 (NIL) -7 NIL NIL) (-750 2029349 2031470 2033600 "NAGE02" 2036070 T NAGE02 (NIL) -7 NIL NIL) (-749 2025302 2026249 2027213 "NAGE01" 2028405 T NAGE01 (NIL) -7 NIL NIL) (-748 2023097 2023631 2024189 "NAGD03" 2024764 T NAGD03 (NIL) -7 NIL NIL) (-747 2014847 2016775 2018729 "NAGD02" 2021163 T NAGD02 (NIL) -7 NIL NIL) (-746 2008658 2010083 2011523 "NAGD01" 2013427 T NAGD01 (NIL) -7 NIL NIL) (-745 2004867 2005689 2006526 "NAGC06" 2007841 T NAGC06 (NIL) -7 NIL NIL) (-744 2003332 2003664 2004020 "NAGC05" 2004531 T NAGC05 (NIL) -7 NIL NIL) (-743 2002708 2002827 2002971 "NAGC02" 2003208 T NAGC02 (NIL) -7 NIL NIL) (-742 2001767 2002324 2002365 "NAALG" 2002444 NIL NAALG (NIL T) -9 NIL 2002505) (-741 2001602 2001631 2001721 "NAALG-" 2001726 NIL NAALG- (NIL T T) -8 NIL NIL) (-740 1992478 2000718 2000993 "MYUP" 2001373 NIL MYUP (NIL NIL T) -8 NIL NIL) (-739 1982841 1990934 1991305 "MYEXPR" 1992173 NIL MYEXPR (NIL NIL T) -8 NIL NIL) (-738 1976791 1977899 1979086 "MULTSQFR" 1981737 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-737 1976110 1976185 1976369 "MULTFACT" 1976703 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-736 1969235 1973144 1973198 "MTSCAT" 1974268 NIL MTSCAT (NIL T T) -9 NIL 1974782) (-735 1968947 1969001 1969093 "MTHING" 1969175 NIL MTHING (NIL T) -7 NIL NIL) (-734 1968739 1968772 1968832 "MSYSCMD" 1968907 T MSYSCMD (NIL) -7 NIL NIL) (-733 1964851 1967494 1967814 "MSET" 1968452 NIL MSET (NIL T) -8 NIL NIL) (-732 1961945 1964411 1964453 "MSETAGG" 1964458 NIL MSETAGG (NIL T) -9 NIL 1964492) (-731 1957723 1959336 1960075 "MRING" 1961251 NIL MRING (NIL T T) -8 NIL NIL) (-730 1957289 1957356 1957487 "MRF2" 1957650 NIL MRF2 (NIL T T T) -7 NIL NIL) (-729 1956907 1956942 1957086 "MRATFAC" 1957248 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-728 1954519 1954814 1955245 "MPRFF" 1956612 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-727 1948533 1954373 1954470 "MPOLY" 1954475 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-726 1948023 1948058 1948266 "MPCPF" 1948492 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-725 1947537 1947580 1947764 "MPC3" 1947974 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-724 1946732 1946813 1947034 "MPC2" 1947452 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-723 1945033 1945370 1945760 "MONOTOOL" 1946392 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-722 1944156 1944491 1944520 "MONOID" 1944797 T MONOID (NIL) -9 NIL 1944969) (-721 1943534 1943697 1943940 "MONOID-" 1943945 NIL MONOID- (NIL T) -8 NIL NIL) (-720 1934415 1940445 1940505 "MONOGEN" 1941179 NIL MONOGEN (NIL T T) -9 NIL 1941632) (-719 1931633 1932368 1933368 "MONOGEN-" 1933487 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-718 1930491 1930911 1930940 "MONADWU" 1931332 T MONADWU (NIL) -9 NIL 1931570) (-717 1929863 1930022 1930270 "MONADWU-" 1930275 NIL MONADWU- (NIL T) -8 NIL NIL) (-716 1929247 1929465 1929494 "MONAD" 1929701 T MONAD (NIL) -9 NIL 1929813) (-715 1928932 1929010 1929142 "MONAD-" 1929147 NIL MONAD- (NIL T) -8 NIL NIL) (-714 1927183 1927845 1928124 "MOEBIUS" 1928685 NIL MOEBIUS (NIL T) -8 NIL NIL) (-713 1926574 1926952 1926993 "MODULE" 1926998 NIL MODULE (NIL T) -9 NIL 1927024) (-712 1926142 1926238 1926428 "MODULE-" 1926433 NIL MODULE- (NIL T T) -8 NIL NIL) (-711 1923811 1924506 1924833 "MODRING" 1925966 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-710 1920757 1921922 1922440 "MODOP" 1923343 NIL MODOP (NIL T T) -8 NIL NIL) (-709 1918944 1919396 1919737 "MODMONOM" 1920556 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-708 1908564 1917140 1917561 "MODMON" 1918574 NIL MODMON (NIL T T) -8 NIL NIL) (-707 1905690 1907408 1907684 "MODFIELD" 1908439 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-706 1904694 1904971 1905161 "MMLFORM" 1905520 T MMLFORM (NIL) -8 NIL NIL) (-705 1904220 1904263 1904442 "MMAP" 1904645 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-704 1902445 1903222 1903264 "MLO" 1903687 NIL MLO (NIL T) -9 NIL 1903928) (-703 1899812 1900327 1900929 "MLIFT" 1901926 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-702 1899203 1899287 1899441 "MKUCFUNC" 1899723 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-701 1898802 1898872 1898995 "MKRECORD" 1899126 NIL MKRECORD (NIL T T) -7 NIL NIL) (-700 1897850 1898011 1898239 "MKFUNC" 1898613 NIL MKFUNC (NIL T) -7 NIL NIL) (-699 1897238 1897342 1897498 "MKFLCFN" 1897733 NIL MKFLCFN (NIL T) -7 NIL NIL) (-698 1896664 1897031 1897120 "MKCHSET" 1897182 NIL MKCHSET (NIL T) -8 NIL NIL) (-697 1895941 1896043 1896228 "MKBCFUNC" 1896557 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-696 1892625 1895495 1895631 "MINT" 1895825 T MINT (NIL) -8 NIL NIL) (-695 1891437 1891680 1891957 "MHROWRED" 1892380 NIL MHROWRED (NIL T) -7 NIL NIL) (-694 1886704 1889878 1890304 "MFLOAT" 1891031 T MFLOAT (NIL) -8 NIL NIL) (-693 1886061 1886137 1886308 "MFINFACT" 1886616 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-692 1882376 1883224 1884108 "MESH" 1885197 T MESH (NIL) -7 NIL NIL) (-691 1880766 1881078 1881431 "MDDFACT" 1882063 NIL MDDFACT (NIL T) -7 NIL NIL) (-690 1877648 1879959 1880001 "MDAGG" 1880256 NIL MDAGG (NIL T) -9 NIL 1880399) (-689 1867289 1876941 1877148 "MCMPLX" 1877461 T MCMPLX (NIL) -8 NIL NIL) (-688 1866426 1866572 1866773 "MCDEN" 1867138 NIL MCDEN (NIL T T) -7 NIL NIL) (-687 1864316 1864586 1864966 "MCALCFN" 1866156 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-686 1861928 1862451 1863013 "MATSTOR" 1863787 NIL MATSTOR (NIL T) -7 NIL NIL) (-685 1857794 1861304 1861550 "MATRIX" 1861715 NIL MATRIX (NIL T) -8 NIL NIL) (-684 1853570 1854273 1855006 "MATLIN" 1857154 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-683 1843081 1846349 1846427 "MATCAT" 1851709 NIL MATCAT (NIL T T T) -9 NIL 1853271) (-682 1839119 1840234 1841702 "MATCAT-" 1841707 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-681 1837713 1837866 1838199 "MATCAT2" 1838954 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-680 1836453 1836719 1837034 "MAPPKG4" 1837444 NIL MAPPKG4 (NIL T T) -7 NIL NIL) (-679 1834565 1834889 1835273 "MAPPKG3" 1836128 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-678 1833546 1833719 1833941 "MAPPKG2" 1834389 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-677 1832045 1832329 1832656 "MAPPKG1" 1833252 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-676 1831656 1831714 1831837 "MAPHACK3" 1831981 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-675 1831248 1831309 1831423 "MAPHACK2" 1831588 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-674 1830686 1830789 1830931 "MAPHACK1" 1831139 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-673 1823854 1824795 1825892 "MAMA" 1829682 NIL MAMA (NIL T T T T) -7 NIL NIL) (-672 1821960 1822554 1822858 "MAGMA" 1823582 NIL MAGMA (NIL T) -8 NIL NIL) (-671 1820196 1820568 1820623 "MAGCDOC" 1821560 NIL MAGCDOC (NIL T T) -9 NIL NIL) (-670 1816671 1818437 1818897 "M3D" 1819769 NIL M3D (NIL T) -8 NIL NIL) (-669 1810865 1815071 1815113 "LZSTAGG" 1815895 NIL LZSTAGG (NIL T) -9 NIL 1816190) (-668 1806839 1807996 1809453 "LZSTAGG-" 1809458 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-667 1803953 1804730 1805217 "LWORD" 1806384 NIL LWORD (NIL T) -8 NIL NIL) (-666 1797108 1803724 1803858 "LSQM" 1803863 NIL LSQM (NIL NIL T) -8 NIL NIL) (-665 1796332 1796471 1796699 "LSPP" 1796963 NIL LSPP (NIL T T T T) -7 NIL NIL) (-664 1794144 1794445 1794901 "LSMP" 1796021 NIL LSMP (NIL T T T T) -7 NIL NIL) (-663 1790923 1791597 1792327 "LSMP1" 1793446 NIL LSMP1 (NIL T) -7 NIL NIL) (-662 1784880 1790113 1790155 "LSAGG" 1790217 NIL LSAGG (NIL T) -9 NIL 1790295) (-661 1781575 1782499 1783712 "LSAGG-" 1783717 NIL LSAGG- (NIL T T) -8 NIL NIL) (-660 1779201 1780719 1780968 "LPOLY" 1781370 NIL LPOLY (NIL T T) -8 NIL NIL) (-659 1778783 1778868 1778991 "LPEFRAC" 1779110 NIL LPEFRAC (NIL T) -7 NIL NIL) (-658 1776347 1776596 1777028 "LPARSPT" 1778525 NIL LPARSPT (NIL T NIL T T T T T) -7 NIL NIL) (-657 1774822 1775149 1775509 "LOP" 1776019 NIL LOP (NIL T) -7 NIL NIL) (-656 1773171 1773918 1774170 "LO" 1774655 NIL LO (NIL T T T) -8 NIL NIL) (-655 1772822 1772934 1772963 "LOGIC" 1773074 T LOGIC (NIL) -9 NIL 1773155) (-654 1772684 1772707 1772778 "LOGIC-" 1772783 NIL LOGIC- (NIL T) -8 NIL NIL) (-653 1771877 1772017 1772210 "LODOOPS" 1772540 NIL LODOOPS (NIL T T) -7 NIL NIL) (-652 1769289 1771793 1771859 "LODO" 1771864 NIL LODO (NIL T NIL) -8 NIL NIL) (-651 1767829 1768064 1768416 "LODOF" 1769037 NIL LODOF (NIL T T) -7 NIL NIL) (-650 1764228 1766669 1766711 "LODOCAT" 1767149 NIL LODOCAT (NIL T) -9 NIL 1767359) (-649 1763961 1764019 1764146 "LODOCAT-" 1764151 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-648 1761270 1763802 1763920 "LODO2" 1763925 NIL LODO2 (NIL T T) -8 NIL NIL) (-647 1758694 1761207 1761252 "LODO1" 1761257 NIL LODO1 (NIL T) -8 NIL NIL) (-646 1757554 1757719 1758031 "LODEEF" 1758517 NIL LODEEF (NIL T T T) -7 NIL NIL) (-645 1750381 1754546 1754587 "LOCPOWC" 1756049 NIL LOCPOWC (NIL T) -9 NIL 1756626) (-644 1745705 1748543 1748585 "LNAGG" 1749532 NIL LNAGG (NIL T) -9 NIL 1749975) (-643 1744852 1745066 1745408 "LNAGG-" 1745413 NIL LNAGG- (NIL T T) -8 NIL NIL) (-642 1741015 1741777 1742416 "LMOPS" 1744267 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-641 1740409 1740771 1740813 "LMODULE" 1740874 NIL LMODULE (NIL T) -9 NIL 1740916) (-640 1737661 1740054 1740177 "LMDICT" 1740319 NIL LMDICT (NIL T) -8 NIL NIL) (-639 1736818 1736952 1737139 "LISYSER" 1737523 NIL LISYSER (NIL T T) -7 NIL NIL) (-638 1730055 1735768 1736064 "LIST" 1736555 NIL LIST (NIL T) -8 NIL NIL) (-637 1729580 1729654 1729793 "LIST3" 1729975 NIL LIST3 (NIL T T T) -7 NIL NIL) (-636 1728587 1728765 1728993 "LIST2" 1729398 NIL LIST2 (NIL T T) -7 NIL NIL) (-635 1726721 1727033 1727432 "LIST2MAP" 1728234 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-634 1725426 1726106 1726148 "LINEXP" 1726403 NIL LINEXP (NIL T) -9 NIL 1726552) (-633 1724073 1724333 1724630 "LINDEP" 1725178 NIL LINDEP (NIL T T) -7 NIL NIL) (-632 1720840 1721559 1722336 "LIMITRF" 1723328 NIL LIMITRF (NIL T) -7 NIL NIL) (-631 1719116 1719411 1719827 "LIMITPS" 1720535 NIL LIMITPS (NIL T T) -7 NIL NIL) (-630 1713575 1718631 1718857 "LIE" 1718939 NIL LIE (NIL T T) -8 NIL NIL) (-629 1712624 1713067 1713108 "LIECAT" 1713248 NIL LIECAT (NIL T) -9 NIL 1713398) (-628 1712465 1712492 1712580 "LIECAT-" 1712585 NIL LIECAT- (NIL T T) -8 NIL NIL) (-627 1704999 1711844 1712027 "LIB" 1712302 T LIB (NIL) -8 NIL NIL) (-626 1700636 1701517 1702452 "LGROBP" 1704116 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-625 1698117 1698441 1698852 "LF" 1700309 NIL LF (NIL T T) -7 NIL NIL) (-624 1696814 1697544 1697573 "LFCAT" 1697848 T LFCAT (NIL) -9 NIL 1698023) (-623 1693718 1694346 1695034 "LEXTRIPK" 1696178 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-622 1690424 1691288 1691791 "LEXP" 1693298 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-621 1688822 1689135 1689536 "LEADCDET" 1690106 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-620 1688012 1688086 1688315 "LAZM3PK" 1688743 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-619 1682928 1686095 1686630 "LAUPOL" 1687527 NIL LAUPOL (NIL T T) -8 NIL NIL) (-618 1682493 1682537 1682705 "LAPLACE" 1682878 NIL LAPLACE (NIL T T) -7 NIL NIL) (-617 1680423 1681596 1681846 "LA" 1682327 NIL LA (NIL T T T) -8 NIL NIL) (-616 1679479 1680073 1680115 "LALG" 1680177 NIL LALG (NIL T) -9 NIL 1680236) (-615 1679193 1679252 1679388 "LALG-" 1679393 NIL LALG- (NIL T T) -8 NIL NIL) (-614 1678097 1678284 1678583 "KOVACIC" 1678993 NIL KOVACIC (NIL T T) -7 NIL NIL) (-613 1677931 1677955 1677997 "KONVERT" 1678059 NIL KONVERT (NIL T) -9 NIL NIL) (-612 1677765 1677789 1677831 "KOERCE" 1677893 NIL KOERCE (NIL T) -9 NIL NIL) (-611 1675501 1676261 1676653 "KERNEL" 1677405 NIL KERNEL (NIL T) -8 NIL NIL) (-610 1675003 1675084 1675214 "KERNEL2" 1675415 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-609 1668686 1673368 1673423 "KDAGG" 1673800 NIL KDAGG (NIL T T) -9 NIL 1674006) (-608 1668215 1668339 1668544 "KDAGG-" 1668549 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-607 1661364 1667876 1668031 "KAFILE" 1668093 NIL KAFILE (NIL T) -8 NIL NIL) (-606 1655823 1660879 1661105 "JORDAN" 1661187 NIL JORDAN (NIL T T) -8 NIL NIL) (-605 1652166 1654066 1654121 "IXAGG" 1655050 NIL IXAGG (NIL T T) -9 NIL 1655505) (-604 1651085 1651391 1651810 "IXAGG-" 1651815 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-603 1646669 1651007 1651066 "IVECTOR" 1651071 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-602 1645435 1645672 1645938 "ITUPLE" 1646436 NIL ITUPLE (NIL T) -8 NIL NIL) (-601 1643859 1644036 1644344 "ITRIGMNP" 1645257 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-600 1642604 1642808 1643091 "ITFUN3" 1643635 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-599 1642236 1642293 1642402 "ITFUN2" 1642541 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-598 1640029 1641100 1641398 "ITAYLOR" 1641971 NIL ITAYLOR (NIL T) -8 NIL NIL) (-597 1628968 1634168 1635330 "ISUPS" 1638900 NIL ISUPS (NIL T) -8 NIL NIL) (-596 1628072 1628212 1628448 "ISUMP" 1628815 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-595 1623342 1627873 1627952 "ISTRING" 1628025 NIL ISTRING (NIL NIL) -8 NIL NIL) (-594 1622552 1622633 1622849 "IRURPK" 1623256 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-593 1621488 1621689 1621929 "IRSN" 1622332 T IRSN (NIL) -7 NIL NIL) (-592 1619519 1619874 1620309 "IRRF2F" 1621127 NIL IRRF2F (NIL T) -7 NIL NIL) (-591 1619266 1619304 1619380 "IRREDFFX" 1619475 NIL IRREDFFX (NIL T) -7 NIL NIL) (-590 1617881 1618140 1618439 "IROOT" 1618999 NIL IROOT (NIL T) -7 NIL NIL) (-589 1614517 1615569 1616259 "IR" 1617223 NIL IR (NIL T) -8 NIL NIL) (-588 1612130 1612625 1613191 "IR2" 1613995 NIL IR2 (NIL T T) -7 NIL NIL) (-587 1611202 1611315 1611536 "IR2F" 1612013 NIL IR2F (NIL T T) -7 NIL NIL) (-586 1610993 1611027 1611087 "IPRNTPK" 1611162 T IPRNTPK (NIL) -7 NIL NIL) (-585 1607522 1610882 1610951 "IPF" 1610956 NIL IPF (NIL NIL) -8 NIL NIL) (-584 1605839 1607447 1607504 "IPADIC" 1607509 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-583 1605336 1605394 1605584 "INVLAPLA" 1605775 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-582 1594985 1597338 1599724 "INTTR" 1603000 NIL INTTR (NIL T T) -7 NIL NIL) (-581 1591343 1592085 1592942 "INTTOOLS" 1594177 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-580 1590929 1591020 1591137 "INTSLPE" 1591246 T INTSLPE (NIL) -7 NIL NIL) (-579 1588879 1590852 1590911 "INTRVL" 1590916 NIL INTRVL (NIL T) -8 NIL NIL) (-578 1586481 1586993 1587568 "INTRF" 1588364 NIL INTRF (NIL T) -7 NIL NIL) (-577 1585892 1585989 1586131 "INTRET" 1586379 NIL INTRET (NIL T) -7 NIL NIL) (-576 1583889 1584278 1584748 "INTRAT" 1585500 NIL INTRAT (NIL T T) -7 NIL NIL) (-575 1581125 1581708 1582330 "INTPM" 1583378 NIL INTPM (NIL T T) -7 NIL NIL) (-574 1577830 1578429 1579173 "INTPAF" 1580512 NIL INTPAF (NIL T T T) -7 NIL NIL) (-573 1573009 1573971 1575022 "INTPACK" 1576799 T INTPACK (NIL) -7 NIL NIL) (-572 1569863 1572738 1572865 "INT" 1572902 T INT (NIL) -8 NIL NIL) (-571 1569115 1569267 1569475 "INTHERTR" 1569705 NIL INTHERTR (NIL T T) -7 NIL NIL) (-570 1568554 1568634 1568822 "INTHERAL" 1569029 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-569 1566400 1566843 1567300 "INTHEORY" 1568117 T INTHEORY (NIL) -7 NIL NIL) (-568 1557711 1559331 1561109 "INTG0" 1564753 NIL INTG0 (NIL T T T) -7 NIL NIL) (-567 1538284 1543074 1547884 "INTFTBL" 1552921 T INTFTBL (NIL) -8 NIL NIL) (-566 1536321 1536528 1536929 "INTFRSP" 1538074 NIL INTFRSP (NIL T NIL T T T T T T) -7 NIL NIL) (-565 1535570 1535708 1535881 "INTFACT" 1536180 NIL INTFACT (NIL T) -7 NIL NIL) (-564 1535160 1535202 1535353 "INTERGB" 1535522 NIL INTERGB (NIL T NIL T T T) -7 NIL NIL) (-563 1532545 1532991 1533555 "INTEF" 1534714 NIL INTEF (NIL T T) -7 NIL NIL) (-562 1531002 1531751 1531780 "INTDOM" 1532081 T INTDOM (NIL) -9 NIL 1532288) (-561 1530371 1530545 1530787 "INTDOM-" 1530792 NIL INTDOM- (NIL T) -8 NIL NIL) (-560 1528975 1529080 1529470 "INTDIVP" 1530261 NIL INTDIVP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-559 1525461 1527391 1527446 "INTCAT" 1528245 NIL INTCAT (NIL T) -9 NIL 1528566) (-558 1524934 1525036 1525164 "INTBIT" 1525353 T INTBIT (NIL) -7 NIL NIL) (-557 1523605 1523759 1524073 "INTALG" 1524779 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-556 1523062 1523152 1523322 "INTAF" 1523509 NIL INTAF (NIL T T) -7 NIL NIL) (-555 1516528 1522872 1523012 "INTABL" 1523017 NIL INTABL (NIL T T T) -8 NIL NIL) (-554 1511473 1514199 1514228 "INS" 1515196 T INS (NIL) -9 NIL 1515879) (-553 1508713 1509484 1510458 "INS-" 1510531 NIL INS- (NIL T) -8 NIL NIL) (-552 1507488 1507715 1508013 "INPSIGN" 1508466 NIL INPSIGN (NIL T T) -7 NIL NIL) (-551 1506606 1506723 1506920 "INPRODPF" 1507368 NIL INPRODPF (NIL T T) -7 NIL NIL) (-550 1505500 1505617 1505854 "INPRODFF" 1506486 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-549 1504500 1504652 1504912 "INNMFACT" 1505336 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-548 1503697 1503794 1503982 "INMODGCD" 1504399 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-547 1502206 1502450 1502774 "INFSP" 1503442 NIL INFSP (NIL T T T) -7 NIL NIL) (-546 1501390 1501507 1501690 "INFPROD0" 1502086 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-545 1498271 1499455 1499970 "INFORM" 1500883 T INFORM (NIL) -8 NIL NIL) (-544 1497881 1497941 1498039 "INFORM1" 1498206 NIL INFORM1 (NIL T) -7 NIL NIL) (-543 1497404 1497493 1497607 "INFINITY" 1497787 T INFINITY (NIL) -7 NIL NIL) (-542 1495087 1496084 1496427 "INFCLSPT" 1497264 NIL INFCLSPT (NIL T NIL T T T T T T T) -8 NIL NIL) (-541 1492964 1494209 1494503 "INFCLSPS" 1494857 NIL INFCLSPS (NIL T NIL T) -8 NIL NIL) (-540 1485514 1486437 1486658 "INFCLCT" 1492089 NIL INFCLCT (NIL T NIL T T T T T T T) -9 NIL 1492900) (-539 1484132 1484380 1484701 "INEP" 1485262 NIL INEP (NIL T T T) -7 NIL NIL) (-538 1483408 1484029 1484094 "INDE" 1484099 NIL INDE (NIL T) -8 NIL NIL) (-537 1482972 1483040 1483157 "INCRMAPS" 1483335 NIL INCRMAPS (NIL T) -7 NIL NIL) (-536 1478283 1479208 1480152 "INBFF" 1482060 NIL INBFF (NIL T) -7 NIL NIL) (-535 1474630 1478127 1478231 "IMATRIX" 1478236 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-534 1473340 1473463 1473778 "IMATQF" 1474487 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-533 1471562 1471789 1472125 "IMATLIN" 1473097 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-532 1466194 1471486 1471544 "ILIST" 1471549 NIL ILIST (NIL T NIL) -8 NIL NIL) (-531 1464153 1466054 1466167 "IIARRAY2" 1466172 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-530 1459469 1464064 1464128 "IFF" 1464133 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-529 1454518 1458761 1458949 "IFARRAY" 1459326 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-528 1453725 1454422 1454495 "IFAMON" 1454500 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-527 1453308 1453373 1453428 "IEVALAB" 1453635 NIL IEVALAB (NIL T T) -9 NIL NIL) (-526 1452983 1453051 1453211 "IEVALAB-" 1453216 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-525 1452641 1452897 1452960 "IDPO" 1452965 NIL IDPO (NIL T T) -8 NIL NIL) (-524 1451918 1452530 1452605 "IDPOAMS" 1452610 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-523 1451252 1451807 1451882 "IDPOAM" 1451887 NIL IDPOAM (NIL T T) -8 NIL NIL) (-522 1450336 1450586 1450640 "IDPC" 1451053 NIL IDPC (NIL T T) -9 NIL 1451202) (-521 1449832 1450228 1450301 "IDPAM" 1450306 NIL IDPAM (NIL T T) -8 NIL NIL) (-520 1449235 1449724 1449797 "IDPAG" 1449802 NIL IDPAG (NIL T T) -8 NIL NIL) (-519 1445490 1446338 1447233 "IDECOMP" 1448392 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-518 1438366 1439415 1440461 "IDEAL" 1444527 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-517 1436383 1437530 1437803 "ICP" 1438157 NIL ICP (NIL T NIL T) -8 NIL NIL) (-516 1435543 1435655 1435855 "ICDEN" 1436267 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-515 1434642 1435023 1435170 "ICARD" 1435416 T ICARD (NIL) -8 NIL NIL) (-514 1432702 1433015 1433420 "IBPTOOLS" 1434319 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-513 1428316 1432322 1432435 "IBITS" 1432621 NIL IBITS (NIL NIL) -8 NIL NIL) (-512 1425039 1425615 1426310 "IBATOOL" 1427733 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-511 1422819 1423280 1423813 "IBACHIN" 1424574 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-510 1420702 1422665 1422768 "IARRAY2" 1422773 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-509 1416861 1420628 1420685 "IARRAY1" 1420690 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-508 1410791 1415273 1415754 "IAN" 1416400 T IAN (NIL) -8 NIL NIL) (-507 1410302 1410359 1410532 "IALGFACT" 1410728 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-506 1409829 1409942 1409971 "HYPCAT" 1410178 T HYPCAT (NIL) -9 NIL NIL) (-505 1409367 1409484 1409670 "HYPCAT-" 1409675 NIL HYPCAT- (NIL T) -8 NIL NIL) (-504 1408371 1408648 1408838 "HTMLFORM" 1409197 T HTMLFORM (NIL) -8 NIL NIL) (-503 1405160 1406485 1406527 "HOAGG" 1407508 NIL HOAGG (NIL T) -9 NIL 1408117) (-502 1403754 1404153 1404679 "HOAGG-" 1404684 NIL HOAGG- (NIL T T) -8 NIL NIL) (-501 1397570 1403190 1403358 "HEXADEC" 1403606 T HEXADEC (NIL) -8 NIL NIL) (-500 1396318 1396540 1396803 "HEUGCD" 1397347 NIL HEUGCD (NIL T) -7 NIL NIL) (-499 1395421 1396155 1396285 "HELLFDIV" 1396290 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-498 1389138 1390681 1391762 "HEAP" 1394372 NIL HEAP (NIL T) -8 NIL NIL) (-497 1382933 1389053 1389115 "HDP" 1389120 NIL HDP (NIL NIL T) -8 NIL NIL) (-496 1376638 1382568 1382720 "HDMP" 1382834 NIL HDMP (NIL NIL T) -8 NIL NIL) (-495 1375963 1376102 1376266 "HB" 1376494 T HB (NIL) -7 NIL NIL) (-494 1369472 1375809 1375913 "HASHTBL" 1375918 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-493 1367219 1369094 1369276 "HACKPI" 1369310 T HACKPI (NIL) -8 NIL NIL) (-492 1349367 1353236 1357239 "GUESSUP" 1363249 NIL GUESSUP (NIL NIL) -7 NIL NIL) (-491 1320464 1327505 1334201 "GUESSP" 1342691 T GUESSP (NIL) -7 NIL NIL) (-490 1287279 1292550 1297934 "GUESS" 1315408 NIL GUESS (NIL T T T T NIL NIL) -7 NIL NIL) (-489 1260784 1267181 1273317 "GUESSINT" 1281163 T GUESSINT (NIL) -7 NIL NIL) (-488 1236155 1241605 1247172 "GUESSF" 1255269 NIL GUESSF (NIL T) -7 NIL NIL) (-487 1235877 1235914 1236009 "GUESSF1" 1236112 NIL GUESSF1 (NIL T) -7 NIL NIL) (-486 1212038 1217572 1223187 "GUESSAN" 1230282 T GUESSAN (NIL) -7 NIL NIL) (-485 1207733 1211891 1212004 "GTSET" 1212009 NIL GTSET (NIL T T T T) -8 NIL NIL) (-484 1201271 1207611 1207709 "GSTBL" 1207714 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-483 1193501 1200304 1200568 "GSERIES" 1201063 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-482 1192522 1192975 1193004 "GROUP" 1193265 T GROUP (NIL) -9 NIL 1193424) (-481 1191638 1191861 1192205 "GROUP-" 1192210 NIL GROUP- (NIL T) -8 NIL NIL) (-480 1190007 1190326 1190713 "GROEBSOL" 1191315 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-479 1188946 1189208 1189260 "GRMOD" 1189789 NIL GRMOD (NIL T T) -9 NIL 1189957) (-478 1188714 1188750 1188878 "GRMOD-" 1188883 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-477 1184043 1185068 1186068 "GRIMAGE" 1187734 T GRIMAGE (NIL) -8 NIL NIL) (-476 1182510 1182770 1183094 "GRDEF" 1183739 T GRDEF (NIL) -7 NIL NIL) (-475 1181954 1182070 1182211 "GRAY" 1182389 T GRAY (NIL) -7 NIL NIL) (-474 1181184 1181564 1181616 "GRALG" 1181769 NIL GRALG (NIL T T) -9 NIL 1181862) (-473 1180845 1180918 1181081 "GRALG-" 1181086 NIL GRALG- (NIL T T T) -8 NIL NIL) (-472 1177649 1180430 1180608 "GPOLSET" 1180752 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-471 1159852 1161342 1162931 "GPAFF" 1176340 NIL GPAFF (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-470 1159206 1159263 1159521 "GOSPER" 1159789 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-469 1155556 1156392 1157119 "GOPT" 1158499 T GOPT (NIL) -8 NIL NIL) (-468 1151035 1152053 1152961 "GOPT0" 1154668 T GOPT0 (NIL) -8 NIL NIL) (-467 1146794 1147473 1147999 "GMODPOL" 1150734 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-466 1145799 1145983 1146221 "GHENSEL" 1146606 NIL GHENSEL (NIL T T) -7 NIL NIL) (-465 1139850 1140693 1141720 "GENUPS" 1144883 NIL GENUPS (NIL T T) -7 NIL NIL) (-464 1139547 1139598 1139687 "GENUFACT" 1139793 NIL GENUFACT (NIL T) -7 NIL NIL) (-463 1138959 1139036 1139201 "GENPGCD" 1139465 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-462 1138433 1138468 1138681 "GENMFACT" 1138918 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-461 1137001 1137256 1137563 "GENEEZ" 1138176 NIL GENEEZ (NIL T T) -7 NIL NIL) (-460 1135545 1135822 1136146 "GDRAW" 1136697 T GDRAW (NIL) -7 NIL NIL) (-459 1129412 1135156 1135318 "GDMP" 1135468 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-458 1118796 1123185 1124290 "GCNAALG" 1128396 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-457 1117213 1118085 1118114 "GCDDOM" 1118369 T GCDDOM (NIL) -9 NIL 1118526) (-456 1116683 1116810 1117025 "GCDDOM-" 1117030 NIL GCDDOM- (NIL T) -8 NIL NIL) (-455 1115357 1115542 1115845 "GB" 1116463 NIL GB (NIL T T T T) -7 NIL NIL) (-454 1103977 1106303 1108695 "GBINTERN" 1113048 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-453 1101814 1102106 1102527 "GBF" 1103652 NIL GBF (NIL T T T T) -7 NIL NIL) (-452 1100595 1100760 1101027 "GBEUCLID" 1101630 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-451 1099944 1100069 1100218 "GAUSSFAC" 1100466 T GAUSSFAC (NIL) -7 NIL NIL) (-450 1098313 1098615 1098928 "GALUTIL" 1099664 NIL GALUTIL (NIL T) -7 NIL NIL) (-449 1096621 1096895 1097219 "GALPOLYU" 1098040 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-448 1093986 1094276 1094683 "GALFACTU" 1096318 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-447 1085792 1087291 1088899 "GALFACT" 1092418 NIL GALFACT (NIL T) -7 NIL NIL) (-446 1083180 1083837 1083866 "FVFUN" 1085022 T FVFUN (NIL) -9 NIL 1085742) (-445 1082446 1082627 1082656 "FVC" 1082947 T FVC (NIL) -9 NIL 1083130) (-444 1082088 1082243 1082324 "FUNCTION" 1082398 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-443 1079758 1080309 1080798 "FT" 1081619 T FT (NIL) -8 NIL NIL) (-442 1078550 1079059 1079262 "FTEM" 1079575 T FTEM (NIL) -8 NIL NIL) (-441 1076808 1077097 1077500 "FSUPFACT" 1078242 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-440 1075205 1075494 1075826 "FST" 1076496 T FST (NIL) -8 NIL NIL) (-439 1074376 1074482 1074677 "FSRED" 1075087 NIL FSRED (NIL T T) -7 NIL NIL) (-438 1073057 1073312 1073665 "FSPRMELT" 1074092 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-437 1068423 1069128 1069885 "FSPECF" 1072362 NIL FSPECF (NIL T T) -7 NIL NIL) (-436 1050681 1059270 1059311 "FS" 1063159 NIL FS (NIL T) -9 NIL 1065437) (-435 1039331 1042321 1046377 "FS-" 1046674 NIL FS- (NIL T T) -8 NIL NIL) (-434 1038845 1038899 1039076 "FSINT" 1039272 NIL FSINT (NIL T T) -7 NIL NIL) (-433 1037130 1037842 1038143 "FSERIES" 1038626 NIL FSERIES (NIL T T) -8 NIL NIL) (-432 1036144 1036260 1036491 "FSCINT" 1037010 NIL FSCINT (NIL T T) -7 NIL NIL) (-431 1032335 1035089 1035131 "FSAGG" 1035501 NIL FSAGG (NIL T) -9 NIL 1035758) (-430 1030097 1030698 1031494 "FSAGG-" 1031589 NIL FSAGG- (NIL T T) -8 NIL NIL) (-429 1029139 1029282 1029509 "FSAGG2" 1029950 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-428 1026794 1027073 1027627 "FS2UPS" 1028857 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-427 1026376 1026419 1026574 "FS2" 1026745 NIL FS2 (NIL T T T T) -7 NIL NIL) (-426 1025233 1025404 1025713 "FS2EXPXP" 1026201 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-425 1024659 1024774 1024926 "FRUTIL" 1025113 NIL FRUTIL (NIL T) -7 NIL NIL) (-424 1016085 1020170 1021520 "FR" 1023341 NIL FR (NIL T) -8 NIL NIL) (-423 1011165 1013803 1013844 "FRNAALG" 1015240 NIL FRNAALG (NIL T) -9 NIL 1015846) (-422 1006844 1007914 1009189 "FRNAALG-" 1009939 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-421 1006482 1006525 1006652 "FRNAAF2" 1006795 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-420 1004840 1005333 1005628 "FRMOD" 1006295 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-419 1002547 1003215 1003533 "FRIDEAL" 1004631 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-418 1001738 1001825 1002116 "FRIDEAL2" 1002454 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-417 1000981 1001395 1001437 "FRETRCT" 1001442 NIL FRETRCT (NIL T) -9 NIL 1001616) (-416 1000093 1000324 1000675 "FRETRCT-" 1000680 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-415 997298 998518 998578 "FRAMALG" 999460 NIL FRAMALG (NIL T T) -9 NIL 999752) (-414 995431 995887 996517 "FRAMALG-" 996740 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-413 989332 994914 995186 "FRAC" 995191 NIL FRAC (NIL T) -8 NIL NIL) (-412 988968 989025 989132 "FRAC2" 989269 NIL FRAC2 (NIL T T) -7 NIL NIL) (-411 988604 988661 988768 "FR2" 988905 NIL FR2 (NIL T T) -7 NIL NIL) (-410 983226 986135 986164 "FPS" 987283 T FPS (NIL) -9 NIL 987837) (-409 982675 982784 982948 "FPS-" 983094 NIL FPS- (NIL T) -8 NIL NIL) (-408 980071 981768 981797 "FPC" 982022 T FPC (NIL) -9 NIL 982164) (-407 979864 979904 980001 "FPC-" 980006 NIL FPC- (NIL T) -8 NIL NIL) (-406 978743 979353 979395 "FPATMAB" 979400 NIL FPATMAB (NIL T) -9 NIL 979550) (-405 976443 976919 977345 "FPARFRAC" 978380 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-404 971838 972335 973017 "FORTRAN" 975875 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-403 969554 970054 970593 "FORT" 971319 T FORT (NIL) -7 NIL NIL) (-402 967230 967791 967820 "FORTFN" 968880 T FORTFN (NIL) -9 NIL 969504) (-401 966993 967043 967072 "FORTCAT" 967131 T FORTCAT (NIL) -9 NIL 967193) (-400 965053 965536 965935 "FORMULA" 966614 T FORMULA (NIL) -8 NIL NIL) (-399 964841 964871 964940 "FORMULA1" 965017 NIL FORMULA1 (NIL T) -7 NIL NIL) (-398 964364 964416 964589 "FORDER" 964783 NIL FORDER (NIL T T T T) -7 NIL NIL) (-397 963460 963624 963817 "FOP" 964191 T FOP (NIL) -7 NIL NIL) (-396 962068 962740 962914 "FNLA" 963342 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-395 960735 961124 961153 "FNCAT" 961725 T FNCAT (NIL) -9 NIL 962018) (-394 960301 960694 960722 "FNAME" 960727 T FNAME (NIL) -8 NIL NIL) (-393 958954 959927 959956 "FMTC" 959961 T FMTC (NIL) -9 NIL 959997) (-392 955272 956479 957107 "FMONOID" 958359 NIL FMONOID (NIL T) -8 NIL NIL) (-391 954493 955016 955164 "FM" 955169 NIL FM (NIL T T) -8 NIL NIL) (-390 951917 952562 952591 "FMFUN" 953735 T FMFUN (NIL) -9 NIL 954443) (-389 951186 951366 951395 "FMC" 951685 T FMC (NIL) -9 NIL 951867) (-388 948398 949232 949287 "FMCAT" 950482 NIL FMCAT (NIL T T) -9 NIL 950976) (-387 947291 948164 948264 "FM1" 948343 NIL FM1 (NIL T T) -8 NIL NIL) (-386 945065 945481 945975 "FLOATRP" 946842 NIL FLOATRP (NIL T) -7 NIL NIL) (-385 938552 942721 943351 "FLOAT" 944455 T FLOAT (NIL) -8 NIL NIL) (-384 935990 936490 937068 "FLOATCP" 938019 NIL FLOATCP (NIL T) -7 NIL NIL) (-383 934775 935623 935665 "FLINEXP" 935670 NIL FLINEXP (NIL T) -9 NIL 935762) (-382 933929 934164 934492 "FLINEXP-" 934497 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-381 933005 933149 933373 "FLASORT" 933781 NIL FLASORT (NIL T T) -7 NIL NIL) (-380 930221 931063 931116 "FLALG" 932343 NIL FLALG (NIL T T) -9 NIL 932810) (-379 924040 927734 927776 "FLAGG" 929038 NIL FLAGG (NIL T) -9 NIL 929686) (-378 922766 923105 923595 "FLAGG-" 923600 NIL FLAGG- (NIL T T) -8 NIL NIL) (-377 921808 921951 922178 "FLAGG2" 922619 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-376 918779 919797 919857 "FINRALG" 920985 NIL FINRALG (NIL T T) -9 NIL 921490) (-375 917939 918168 918507 "FINRALG-" 918512 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-374 917242 917479 917508 "FINITE" 917759 T FINITE (NIL) -9 NIL 917889) (-373 917051 917095 917182 "FINITE-" 917187 NIL FINITE- (NIL T) -8 NIL NIL) (-372 909509 911670 911711 "FINAALG" 915378 NIL FINAALG (NIL T) -9 NIL 916830) (-371 904849 905891 907035 "FINAALG-" 908414 NIL FINAALG- (NIL T T) -8 NIL NIL) (-370 904219 904604 904707 "FILE" 904779 NIL FILE (NIL T) -8 NIL NIL) (-369 902759 903096 903151 "FILECAT" 903929 NIL FILECAT (NIL T T) -9 NIL 904169) (-368 900569 902125 902154 "FIELD" 902194 T FIELD (NIL) -9 NIL 902274) (-367 899189 899574 900085 "FIELD-" 900090 NIL FIELD- (NIL T) -8 NIL NIL) (-366 897002 897824 898171 "FGROUP" 898875 NIL FGROUP (NIL T) -8 NIL NIL) (-365 896092 896256 896476 "FGLMICPK" 896834 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-364 891849 896017 896074 "FFX" 896079 NIL FFX (NIL T NIL) -8 NIL NIL) (-363 891389 891456 891578 "FFSQFR" 891777 NIL FFSQFR (NIL T T) -7 NIL NIL) (-362 890990 891051 891186 "FFSLPE" 891322 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-361 886986 887762 888558 "FFPOLY" 890226 NIL FFPOLY (NIL T) -7 NIL NIL) (-360 886490 886526 886735 "FFPOLY2" 886944 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-359 882267 886409 886472 "FFP" 886477 NIL FFP (NIL T NIL) -8 NIL NIL) (-358 877583 882178 882242 "FF" 882247 NIL FF (NIL NIL NIL) -8 NIL NIL) (-357 872634 876926 877116 "FFNBX" 877437 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-356 867499 871769 872027 "FFNBP" 872488 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-355 862050 866783 866994 "FFNB" 867332 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-354 860882 861080 861395 "FFINTBAS" 861847 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-353 857033 859293 859322 "FFIELDC" 859942 T FFIELDC (NIL) -9 NIL 860318) (-352 855696 856066 856563 "FFIELDC-" 856568 NIL FFIELDC- (NIL T) -8 NIL NIL) (-351 855266 855311 855435 "FFHOM" 855638 NIL FFHOM (NIL T T T) -7 NIL NIL) (-350 852964 853448 853965 "FFF" 854781 NIL FFF (NIL T) -7 NIL NIL) (-349 848660 849425 850269 "FFFG" 852188 NIL FFFG (NIL T T) -7 NIL NIL) (-348 847386 847595 847917 "FFFGF" 848438 NIL FFFGF (NIL T T T) -7 NIL NIL) (-347 846137 846334 846582 "FFFACTSE" 847188 NIL FFFACTSE (NIL T T) -7 NIL NIL) (-346 844888 845085 845333 "FFFACTOR" 845939 NIL FFFACTOR (NIL T T) -7 NIL NIL) (-345 840431 844630 844731 "FFCGX" 844831 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-344 835988 840163 840270 "FFCGP" 840374 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-343 831089 835715 835823 "FFCG" 835924 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-342 812826 822000 822087 "FFCAT" 827252 NIL FFCAT (NIL T T T) -9 NIL 828737) (-341 808024 809071 810385 "FFCAT-" 811615 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-340 807435 807478 807713 "FFCAT2" 807975 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-339 796605 800411 801629 "FEXPR" 806289 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-338 795607 796042 796084 "FEVALAB" 796168 NIL FEVALAB (NIL T) -9 NIL 796426) (-337 794766 794976 795314 "FEVALAB-" 795319 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-336 793359 794149 794352 "FDIV" 794665 NIL FDIV (NIL T T T T) -8 NIL NIL) (-335 790424 791139 791255 "FDIVCAT" 792823 NIL FDIVCAT (NIL T T T T) -9 NIL 793260) (-334 790186 790213 790383 "FDIVCAT-" 790388 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-333 789406 789493 789770 "FDIV2" 790093 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-332 788092 788351 788640 "FCPAK1" 789137 T FCPAK1 (NIL) -7 NIL NIL) (-331 787220 787592 787733 "FCOMP" 787983 NIL FCOMP (NIL T) -8 NIL NIL) (-330 770848 774263 777826 "FC" 783677 T FC (NIL) -8 NIL NIL) (-329 763347 767435 767476 "FAXF" 769278 NIL FAXF (NIL T) -9 NIL 769969) (-328 760627 761281 762106 "FAXF-" 762571 NIL FAXF- (NIL T T) -8 NIL NIL) (-327 755733 760003 760179 "FARRAY" 760484 NIL FARRAY (NIL T) -8 NIL NIL) (-326 751051 753127 753181 "FAMR" 754204 NIL FAMR (NIL T T) -9 NIL 754661) (-325 749941 750243 750678 "FAMR-" 750683 NIL FAMR- (NIL T T T) -8 NIL NIL) (-324 749529 749572 749723 "FAMR2" 749892 NIL FAMR2 (NIL T T T T T) -7 NIL NIL) (-323 748725 749451 749504 "FAMONOID" 749509 NIL FAMONOID (NIL T) -8 NIL NIL) (-322 746555 747239 747293 "FAMONC" 748234 NIL FAMONC (NIL T T) -9 NIL 748619) (-321 745249 746311 746447 "FAGROUP" 746452 NIL FAGROUP (NIL T) -8 NIL NIL) (-320 743044 743363 743766 "FACUTIL" 744930 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-319 742460 742569 742715 "FACTRN" 742930 NIL FACTRN (NIL T) -7 NIL NIL) (-318 741559 741744 741966 "FACTFUNC" 742270 NIL FACTFUNC (NIL T) -7 NIL NIL) (-317 740975 741084 741230 "FACTEXT" 741445 NIL FACTEXT (NIL T) -7 NIL NIL) (-316 733295 740226 740438 "EXPUPXS" 740831 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-315 730778 731318 731904 "EXPRTUBE" 732729 T EXPRTUBE (NIL) -7 NIL NIL) (-314 729949 730044 730264 "EXPRSOL" 730678 NIL EXPRSOL (NIL T T T T) -7 NIL NIL) (-313 726143 726735 727472 "EXPRODE" 729288 NIL EXPRODE (NIL T T) -7 NIL NIL) (-312 711164 724804 725229 "EXPR" 725750 NIL EXPR (NIL T) -8 NIL NIL) (-311 705571 706158 706971 "EXPR2UPS" 710462 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-310 705207 705264 705371 "EXPR2" 705508 NIL EXPR2 (NIL T T) -7 NIL NIL) (-309 696545 704337 704635 "EXPEXPAN" 705043 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-308 696257 696308 696385 "EXP3D" 696488 T EXP3D (NIL) -7 NIL NIL) (-307 696084 696214 696243 "EXIT" 696248 T EXIT (NIL) -8 NIL NIL) (-306 695711 695773 695886 "EVALCYC" 696016 NIL EVALCYC (NIL T) -7 NIL NIL) (-305 695253 695369 695411 "EVALAB" 695581 NIL EVALAB (NIL T) -9 NIL 695685) (-304 694734 694856 695077 "EVALAB-" 695082 NIL EVALAB- (NIL T T) -8 NIL NIL) (-303 692192 693504 693533 "EUCDOM" 694088 T EUCDOM (NIL) -9 NIL 694438) (-302 690597 691039 691629 "EUCDOM-" 691634 NIL EUCDOM- (NIL T) -8 NIL NIL) (-301 678137 680895 683645 "ESTOOLS" 687867 T ESTOOLS (NIL) -7 NIL NIL) (-300 677769 677826 677935 "ESTOOLS2" 678074 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-299 677520 677562 677642 "ESTOOLS1" 677721 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-298 671446 673174 673203 "ES" 675971 T ES (NIL) -9 NIL 677378) (-297 666394 667680 669497 "ES-" 669661 NIL ES- (NIL T) -8 NIL NIL) (-296 662769 663529 664309 "ESCONT" 665634 T ESCONT (NIL) -7 NIL NIL) (-295 662514 662546 662628 "ESCONT1" 662731 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-294 662189 662239 662339 "ES2" 662458 NIL ES2 (NIL T T) -7 NIL NIL) (-293 661819 661877 661986 "ES1" 662125 NIL ES1 (NIL T T) -7 NIL NIL) (-292 661035 661164 661340 "ERROR" 661663 T ERROR (NIL) -7 NIL NIL) (-291 654550 660894 660985 "EQTBL" 660990 NIL EQTBL (NIL T T) -8 NIL NIL) (-290 647009 649892 651327 "EQ" 653148 NIL -3015 (NIL T) -8 NIL NIL) (-289 646641 646698 646807 "EQ2" 646946 NIL EQ2 (NIL T T) -7 NIL NIL) (-288 641933 642979 644072 "EP" 645580 NIL EP (NIL T) -7 NIL NIL) (-287 641087 641651 641680 "ENTIRER" 641685 T ENTIRER (NIL) -9 NIL 641731) (-286 637543 639042 639412 "EMR" 640886 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-285 636689 636872 636927 "ELTAGG" 637307 NIL ELTAGG (NIL T T) -9 NIL 637517) (-284 636408 636470 636611 "ELTAGG-" 636616 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-283 636196 636225 636280 "ELTAB" 636364 NIL ELTAB (NIL T T) -9 NIL NIL) (-282 635322 635468 635667 "ELFUTS" 636047 NIL ELFUTS (NIL T T) -7 NIL NIL) (-281 635063 635119 635148 "ELEMFUN" 635253 T ELEMFUN (NIL) -9 NIL NIL) (-280 634933 634954 635022 "ELEMFUN-" 635027 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-279 629863 633066 633108 "ELAGG" 634048 NIL ELAGG (NIL T) -9 NIL 634509) (-278 628148 628582 629245 "ELAGG-" 629250 NIL ELAGG- (NIL T T) -8 NIL NIL) (-277 621018 622817 623643 "EFUPXS" 627425 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-276 614470 616271 617080 "EFULS" 620295 NIL EFULS (NIL T T T) -8 NIL NIL) (-275 611892 612250 612729 "EFSTRUC" 614102 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-274 600904 602469 604030 "EF" 610407 NIL EF (NIL T T) -7 NIL NIL) (-273 600005 600389 600538 "EAB" 600775 T EAB (NIL) -8 NIL NIL) (-272 599214 599964 599992 "E04UCFA" 599997 T E04UCFA (NIL) -8 NIL NIL) (-271 598423 599173 599201 "E04NAFA" 599206 T E04NAFA (NIL) -8 NIL NIL) (-270 597632 598382 598410 "E04MBFA" 598415 T E04MBFA (NIL) -8 NIL NIL) (-269 596841 597591 597619 "E04JAFA" 597624 T E04JAFA (NIL) -8 NIL NIL) (-268 596052 596800 596828 "E04GCFA" 596833 T E04GCFA (NIL) -8 NIL NIL) (-267 595263 596011 596039 "E04FDFA" 596044 T E04FDFA (NIL) -8 NIL NIL) (-266 594472 595222 595250 "E04DGFA" 595255 T E04DGFA (NIL) -8 NIL NIL) (-265 588651 589997 591361 "E04AGNT" 593128 T E04AGNT (NIL) -7 NIL NIL) (-264 587374 587854 587895 "DVARCAT" 588370 NIL DVARCAT (NIL T) -9 NIL 588569) (-263 586578 586790 587104 "DVARCAT-" 587109 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-262 579547 580029 580778 "DTP" 586109 NIL DTP (NIL T NIL T T T T T T T T T) -7 NIL NIL) (-261 576996 578969 579126 "DSTREE" 579423 NIL DSTREE (NIL T) -8 NIL NIL) (-260 574465 576310 576352 "DSTRCAT" 576571 NIL DSTRCAT (NIL T) -9 NIL 576705) (-259 567319 574264 574393 "DSMP" 574398 NIL DSMP (NIL T T T) -8 NIL NIL) (-258 562129 563264 564332 "DROPT" 566271 T DROPT (NIL) -8 NIL NIL) (-257 561794 561853 561951 "DROPT1" 562064 NIL DROPT1 (NIL T) -7 NIL NIL) (-256 556909 558035 559172 "DROPT0" 560677 T DROPT0 (NIL) -7 NIL NIL) (-255 555254 555579 555965 "DRAWPT" 556543 T DRAWPT (NIL) -7 NIL NIL) (-254 549841 550764 551843 "DRAW" 554228 NIL DRAW (NIL T) -7 NIL NIL) (-253 549474 549527 549645 "DRAWHACK" 549782 NIL DRAWHACK (NIL T) -7 NIL NIL) (-252 548205 548474 548765 "DRAWCX" 549203 T DRAWCX (NIL) -7 NIL NIL) (-251 547721 547789 547940 "DRAWCURV" 548131 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-250 538193 540151 542266 "DRAWCFUN" 545626 T DRAWCFUN (NIL) -7 NIL NIL) (-249 535044 536920 536962 "DQAGG" 537591 NIL DQAGG (NIL T) -9 NIL 537865) (-248 523472 530213 530297 "DPOLCAT" 532149 NIL DPOLCAT (NIL T T T T) -9 NIL 532693) (-247 518311 519657 521615 "DPOLCAT-" 521620 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-246 511007 518172 518270 "DPMO" 518275 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-245 503606 510787 510954 "DPMM" 510959 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-244 497311 503241 503393 "DMP" 503507 NIL DMP (NIL NIL T) -8 NIL NIL) (-243 496911 496967 497111 "DLP" 497249 NIL DLP (NIL T) -7 NIL NIL) (-242 490561 496012 496239 "DLIST" 496716 NIL DLIST (NIL T) -8 NIL NIL) (-241 487446 489449 489491 "DLAGG" 490041 NIL DLAGG (NIL T) -9 NIL 490270) (-240 486103 486795 486824 "DIVRING" 486974 T DIVRING (NIL) -9 NIL 487082) (-239 485091 485344 485737 "DIVRING-" 485742 NIL DIVRING- (NIL T) -8 NIL NIL) (-238 483519 484684 484820 "DIV" 484988 NIL DIV (NIL T) -8 NIL NIL) (-237 481013 482081 482123 "DIVCAT" 482957 NIL DIVCAT (NIL T) -9 NIL 483288) (-236 479115 479472 479878 "DISPLAY" 480627 T DISPLAY (NIL) -7 NIL NIL) (-235 476608 477821 478203 "DIRRING" 478766 NIL DIRRING (NIL T) -8 NIL NIL) (-234 470425 476522 476585 "DIRPROD" 476590 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-233 469273 469476 469741 "DIRPROD2" 470218 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-232 458725 464797 464851 "DIRPCAT" 465261 NIL DIRPCAT (NIL NIL T) -9 NIL 466090) (-231 456051 456693 457574 "DIRPCAT-" 457911 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 455338 455498 455684 "DIOSP" 455885 T DIOSP (NIL) -7 NIL NIL) (-229 452081 454285 454327 "DIOPS" 454761 NIL DIOPS (NIL T) -9 NIL 454989) (-228 451630 451744 451935 "DIOPS-" 451940 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 450497 451135 451164 "DIFRING" 451351 T DIFRING (NIL) -9 NIL 451461) (-226 450143 450220 450372 "DIFRING-" 450377 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 447925 449207 449249 "DIFEXT" 449612 NIL DIFEXT (NIL T) -9 NIL 449904) (-224 446210 446638 447304 "DIFEXT-" 447309 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 443572 445776 445818 "DIAGG" 445823 NIL DIAGG (NIL T) -9 NIL 445843) (-222 442956 443113 443365 "DIAGG-" 443370 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 438278 441915 442192 "DHMATRIX" 442725 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 433489 438092 438166 "DFVEC" 438224 T DFVEC (NIL) -8 NIL NIL) (-219 427090 428440 429877 "DFSFUN" 432072 T DFSFUN (NIL) -7 NIL NIL) (-218 423301 426861 426955 "DFMAT" 427016 T DFMAT (NIL) -8 NIL NIL) (-217 417578 421755 422188 "DFLOAT" 422888 T DFLOAT (NIL) -8 NIL NIL) (-216 415806 416087 416483 "DFINTTLS" 417286 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-215 412825 413827 414227 "DERHAM" 415472 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-214 404438 406355 407790 "DEQUEUE" 411423 NIL DEQUEUE (NIL T) -8 NIL NIL) (-213 403653 403786 403982 "DEGRED" 404300 NIL DEGRED (NIL T T) -7 NIL NIL) (-212 400048 400793 401646 "DEFINTRF" 402881 NIL DEFINTRF (NIL T) -7 NIL NIL) (-211 397575 398044 398643 "DEFINTEF" 399567 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-210 391391 397011 397179 "DECIMAL" 397427 T DECIMAL (NIL) -8 NIL NIL) (-209 388903 389361 389867 "DDFACT" 390935 NIL DDFACT (NIL T T) -7 NIL NIL) (-208 388499 388542 388693 "DBLRESP" 388854 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-207 386209 386543 386912 "DBASE" 388257 NIL DBASE (NIL T) -8 NIL NIL) (-206 385342 386168 386196 "D03FAFA" 386201 T D03FAFA (NIL) -8 NIL NIL) (-205 384476 385301 385329 "D03EEFA" 385334 T D03EEFA (NIL) -8 NIL NIL) (-204 382426 382892 383381 "D03AGNT" 384007 T D03AGNT (NIL) -7 NIL NIL) (-203 381742 382385 382413 "D02EJFA" 382418 T D02EJFA (NIL) -8 NIL NIL) (-202 381058 381701 381729 "D02CJFA" 381734 T D02CJFA 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|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|) -(|StochasticDifferential|) -(|BalancedBinaryTree| |BinarySearchTree| |BinaryTournament|) -(|SetOfMIntegersInOneToN|) -(|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| |BasicStochasticDifferential| |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&| 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|ExpertSystemToolsPackage| |ExpertSystemToolsPackage1| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |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| |FiniteFieldFactorization| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteLinearAggregate&| |FiniteLinearAggregateFunctions2| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FlexibleArray| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranExpression| |FortranOutputStackPackage| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |FourierComponent| |FourierSeries| |Fraction| |FractionFreeFastGaussian| |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| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenerateUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GraphImage| |GraphicsDefaults| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Guess| |GuessOption| |GuessOptionFunctions0| |HTMLFormat| |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| |InfClsPt| |InfiniteProductFiniteField| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgebraicNumber| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| 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|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| |MatrixManipulation| |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| 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|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| |StochasticDifferential| |StorageEfficientMatrixOperations| |Stream| |StreamAggregate&| |StreamFunctions1| |StreamFunctions2| |StreamFunctions3| |StreamTaylorSeriesOperations| |StreamTensor| |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| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U32VectorPolynomialOperations| |U8Matrix| |U8Vector| |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| 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|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|) -(|FractionFreeFastGaussianFractions| |FractionalIdeal| |PAdicWildFunctionFieldIntegralBasis| |UnivariatePolynomialCommonDenominator|) -(|AlgebraicFunction| |CombinatorialFunction| |ElementaryFunction| |ExpressionSpace&| |FunctionSpace&| |FunctionalSpecialFunction| |LiouvillianFunction|) -(|FreeNilpotentLie|) -(|DoubleResultantPackage| |InnerAlgFactor| |InnerAlgebraicNumber| |PolynomialFactorizationByRecursion| |TranscendentalIntegration| |TwoFactorize|) -(|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&|) -(|ComplexCategory&|) -(|ComplexCategory&|) -(|FloatingComplexPackage| |InnerNumericFloatSolvePackage|) -(|ElementaryFunctionLODESolver|) -(|BalancedPAdicRational| |NumericContinuedFraction| |PAdicRational| |PAdicRationalConstructor| 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|PackageForAlgebraicFunctionFieldOverFiniteField| |Permanent| |PolToPol| |QuadraticForm| |RectangularMatrix| |SplitHomogeneousDirectProduct| |SquareMatrix|) -(|FiniteFieldCategory&|) -(|TopLevelDrawFunctions|) -(|ChineseRemainderToolsForIntegralBases| |FiniteFieldCategory&| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |GenUFactorize| |IrredPolyOverFiniteField| |MultFiniteFactorize| |PAdicWildFunctionFieldIntegralBasis| |SparseUnivariatePolynomial| |TwoFactorize| |WildFunctionFieldIntegralBasis|) -(|AffineAlgebraicSetComputeWithGroebnerBasis| |BlowUpPackage| |DesingTreePackage| |FGLMIfCanPackage| |GroebnerSolve| |IdealDecompositionPackage| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InterfaceGroebnerPackage| |LinGroebnerPackage| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PolToPol| |QuasiAlgebraicSet2|) -(|InfClsPt| 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|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| 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|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| |TranscendentalManipulations| |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|) -(|ModuleOperator|) -(|ModuleOperator| |Operator|) -(|AntiSymm| |FourierSeries| |FreeModule1| |FreeNilpotentLie| |GeneralModulePolynomial| |PolynomialRing|) -(|LiePolynomial| |XPBWPolynomial| |XPolynomialRing| |XRecursivePolynomial|) -(|OrderedFreeMonoid|) -(|FiniteDivisorFunctions2|) -(|PatternMatchAssertions| |PatternMatchIntegration| |RewriteRule|) -(|AttachPredicates| |PatternMatchIntegration|) -(|FunctionSpaceIntegration|) -(|ElementaryFunctionSign| |ExpressionFunctions2| |InnerTrigonometricManipulations|) -(|ElementaryFunctionDefiniteIntegration| |GeneralUnivariatePowerSeries| |LaplaceTransform| |ODEIntegration| |UnivariateLaurentSeriesConstructor| |UnivariatePuiseuxSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) -(|ElementaryFunctionLODESolver| |ElementaryIntegration| |ElementaryRischDE|) -(|FunctionSpaceToExponentialExpansion|) -(|AlgebraicIntegrate| |ConstantLODE| |ElementaryFunctionLODESolver| |IntegrationResultToFunction|) -(|Expression|) -(|BrillhartTests| |GaloisGroupFactorizer|) -(|GenUFactorize| |Integer| |RationalFactorize|) -(|GaloisGroupFactorizer|) -(|GaloisGroupFactorizationUtilities|) -(|ComplexIntegerSolveLinearPolynomialEquation| |FiniteFieldSolveLinearPolynomialEquation| |IntegerSolveLinearPolynomialEquation| |MultFiniteFactorize| |MultivariateLifting|) -(|MultivariateFactorize| |NumericRealEigenPackage|) -(|DistributedMultivariatePolynomial| |HomogeneousDistributedMultivariatePolynomial|) -(|GaloisGroupFactorizer| |PAdicWildFunctionFieldIntegralBasis| |UnivariateFactorize|) -(|PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField|) -(|PolynomialCategory&|) -(|LexTriangularPackage| |PolynomialSetUtilitiesPackage| |QuasiComponentPackage| |RegularSetDecompositionPackage| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage|) -(|SparseTable|) -(|PolynomialSetUtilitiesPackage| |WuWenTsunTriangularSet|) -(|GroebnerSolve| |Guess| |MPolyCatPolyFactorizer| |SystemSolvePackage|) -(|PureAlgebraicIntegration|) -(|FunctionSpaceSum| |RationalFunctionSum|) -(|GnuDraw| |TopLevelDrawFunctionsForPoints| |TwoDimensionalViewport| |ViewportPackage|) -(|PlotTools| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions|) -(|Permanent|) -(|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|) -(|HomogeneousDistributedMultivariatePolynomial| |LinGroebnerPackage| |PolToPol|) -(|FGLMIfCanPackage| |GroebnerSolve| |LinGroebnerPackage| |PolToPol|) -(|QuasiAlgebraicSet2|) -(|Bits|) -(|FreeModule|) -(|IndexedDirectProductAbelianGroup| |IndexedDirectProductOrderedAbelianMonoid|) -(|IndexedDirectProductAbelianMonoid|) -(|IndexedDirectProductOrderedAbelianMonoidSup|) -(|IndexedExponents|) -(|DifferentialSparseMultivariatePolynomial| |Expression| |MultivariatePolynomial| |NewSparseMultivariatePolynomial| |OrderlyDifferentialPolynomial| |Polynomial| |SequentialDifferentialPolynomial| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |StochasticDifferential| |TaylorSeries|) -(|FlexibleArray| |Heap| |IntegerCombinatoricFunctions| |IntegerNumberTheoryFunctions|) -(|List|) -(|IndexedTwoDimensionalArray| |IndexedVector| |OneDimensionalArray|) -(|String|) -(|IndexedMatrix| |Vector|) -(|PackageForAlgebraicFunctionField|) -(|InfiniteTupleFunctions2| |InfiniteTupleFunctions3|) -(|InfClsPt| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField|) -(|PackageForAlgebraicFunctionFieldOverFiniteField|) -(|SAERationalFunctionAlgFactor| |SimpleAlgebraicExtensionAlgFactor|) -(|AlgebraicNumber|) -(|AlgebraicFunctionField| |AlgebraicIntegrate| |ElementaryFunctionStructurePackage| |FractionFreeFastGaussian| |FractionalIdeal| |FunctionFieldCategory&| |InnerMatrixQuotientFieldFunctions| |PrimitiveRatDE| |RadicalFunctionField| |RationalLODE|) -(|FreeAbelianGroup| |FreeAbelianMonoid|) -(|IndexedMatrix| |IndexedTwoDimensionalArray| |Matrix| |TwoDimensionalArray|) -(|InnerMatrixQuotientFieldFunctions| |MatrixLinearAlgebraFunctions|) -(|MatrixLinearAlgebraFunctions|) -(|AlgebraicMultFact| |MultivariateFactorize|) -(|FiniteFieldNormalBasisExtensionByPolynomial|) -(|NumericComplexEigenPackage| |NumericRealEigenPackage|) -(|ComplexRootPackage| |FloatingComplexPackage| |FloatingRealPackage| |InnerNumericEigenPackage|) -(|BalancedPAdicInteger| |PAdicInteger|) -(|DefiniteIntegrationTools| |RationalFunctionLimitPackage| |RationalFunctionSign|) -(|RationalFunctionSum|) -(|InnerFiniteField| |PrimeField|) -(|SparseUnivariateLaurentSeries| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries|) -(|Table|) -(|SparseMultivariateTaylorSeries| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero|) -(|ComplexTrigonometricManipulations| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |TrigonometricManipulations|) -(|AssociationList| |BalancedPAdicRational| |BasicOperatorFunctions1| |BinaryExpansion| |Bits| |Boolean| |CharacterClass| |CommonOperators| |Complex| |ComplexCategory&| |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| |U16Vector| |U32Vector| |U8Vector| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |Vector| |WuWenTsunTriangularSet|) -(|FunctionSpace&|) -(|AbelianGroup&| |AbelianMonoidRing&| |AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgFactor| |Algebra&| |AlgebraGivenByStructuralConstants| |AlgebraPackage| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicHermiteIntegration| |AlgebraicIntegrate| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedField&| |AnnaNumericalIntegrationPackage| |AnnaNumericalOptimizationPackage| |AnnaOrdinaryDifferentialEquationPackage| |AnnaPartialDifferentialEquationPackage| |AntiSymm| |ApplyRules| |ArrayStack| |Asp10| |Asp19| |Asp27| |Asp28| |Asp30| |Asp31| |Asp34| |Asp35| |Asp55| |Asp73| |Asp74| |Asp77| |Asp8| |Asp80| |Asp9| |AssociatedEquations| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |AxiomServer| |BalancedBinaryTree| |BalancedFactorisation| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |Bezier| |BezoutMatrix| |BinaryExpansion| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlasLevelOne| |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| |FiniteFieldFactorization| |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| |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| |MatrixManipulation| |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| 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|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&| |StochasticDifferential| |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| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U32VectorPolynomialOperations| |U8Matrix| |U8Vector| |UTSodetools| |UnaryRecursiveAggregate&| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesFunctions2| |UnivariatePolynomial| |UnivariatePolynomialCategory&| |UnivariatePolynomialDecompositionPackage| |UnivariatePolynomialSquareFree| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategoryOps| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |UniversalSegment| |Vector| |VectorCategory&| |ViewDefaultsPackage| |ViewportPackage| |WeierstrassPreparation| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |XDistributedPolynomial| |XExponentialPackage| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |d01AgentsPackage| |d01TransformFunctionType| |d01WeightsPackage| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) -(|RandomIntegerDistributions|) -(|ComplexRootFindingPackage| |GaloisGroupUtilities| |Guess| |IntegerNumberSystem&| |IrrRepSymNatPackage| |MultivariateLifting| |RepresentationPackage1| |SetOfMIntegersInOneToN| |SymmetricGroupCombinatoricFunctions|) -(|CyclotomicPolynomialPackage| |Factored| |GaussianFactorizationPackage| |IntegerNumberSystem&| |NumberFieldIntegralBasis|) -(|ElementaryFunctionStructurePackage|) -(|InnerPrimeField|) -(|CycleIndicators| |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|) -(|Integer|) -(|PAdicWildFunctionFieldIntegralBasis|) -(|FunctionFieldIntegralBasis| |NumberFieldIntegralBasis| |PAdicWildFunctionFieldIntegralBasis| |WildFunctionFieldIntegralBasis|) -(|AnnaNumericalIntegrationPackage| |d01AgentsPackage|) -(|AlgebraicIntegrate| |AlgebraicIntegration| |ElementaryIntegration| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenusZeroIntegration| |IntegrationResultFunctions2| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |PureAlgebraicIntegration| |RationalFunctionIntegration| |RationalIntegration| |TranscendentalIntegration|) -(|ElementaryIntegration| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |GenusZeroIntegration| |IntegrationResultRFToFunction| |PureAlgebraicIntegration| |RationalFunctionIntegration|) -(|RationalFunctionDefiniteIntegration|) -(|FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultRFToFunction|) -(|ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |FunctionSpaceComplexIntegration| |FunctionSpaceIntegration| |IntegrationResultRFToFunction| |LaplaceTransform| |PureAlgebraicIntegration|) -(|AffineAlgebraicSetComputeWithGroebnerBasis|) -(|RegularSetDecompositionPackage| |SquareFreeRegularSetDecompositionPackage| |TabulatedComputationPackage|) -(|RationalUnivariateRepresentationPackage| |ZeroDimensionalSolvePackage|) -(|GeneralPackageForAlgebraicFunctionField|) -(|GeneralPackageForAlgebraicFunctionField|) -(|ElementaryFunctionSign| |TransSolvePackage|) -(|PAdicWildFunctionFieldIntegralBasis|) -(|AlgFactor| |AlgebraicFunction| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicNumber| |AlgebraicallyClosedFunctionSpace&| |ApplyRules| |CombinatorialFunction| |ComplexTrigonometricManipulations| |DefiniteIntegrationTools| |ElementaryFunction| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionSign| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |ElementaryRischDESystem| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |Expression| |ExpressionFunctions2| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |FortranExpression| |FunctionSpace&| |FunctionSpaceAssertions| |FunctionSpaceAttachPredicates| |FunctionSpaceComplexIntegration| |FunctionSpaceFunctions2| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceSum| |FunctionSpaceToExponentialExpansion| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |FunctionalSpecialFunction| |GenusZeroIntegration| |Guess| |InnerAlgebraicNumber| |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|) -(|AlgebraicIntegrate| |ElementaryRischDE| |TranscendentalIntegration|) -(|InnerMultFact| |MultFiniteFactorize|) -(|ZeroDimensionalSolvePackage|) -(|LieExponentials| |XPBWPolynomial|) -(|FGLMIfCanPackage| |GroebnerSolve|) -(|IntegerLinearDependence|) -(|LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2|) -(|ElementaryFunctionLODESolver| |GenusZeroIntegration| |Kovacic| |LinearOrdinaryDifferentialOperatorFactorizer| |PureAlgebraicLODE| |RationalLODE| |RationalRicDE|) -(|RationalLODE| |RationalRicDE|) -(|ElementaryFunctionLODESolver|) -(|LinearOrdinaryDifferentialOperator|) -(|PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&|) -(|InterpolateFormsPackage|) -(|AlgebraGivenByStructuralConstants| |AlgebraicHermiteIntegration| |CliffordAlgebra| |ElementaryFunctionLODESolver| |FramedNonAssociativeAlgebra&| |GosperSummationMethod| |LinearDependence| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |ODETools| |RationalLODE| |StructuralConstantsPackage| |TransSolvePackageService|) -(|SystemSolvePackage|) -(|InterpolateFormsPackage| |LinearSystemFromPowerSeriesPackage|) -(|Expression| |PowerSeriesLimitPackage|) -(|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| |BasicStochasticDifferential| |Bezier| |BinaryExpansion| |BinaryRecursiveAggregate&| |BinarySearchTree| |BinaryTournament| |BinaryTree| |Bits| |BlasLevelOne| |BlowUpPackage| |BlowUpWithHamburgerNoether| |BlowUpWithQuadTrans| |Boolean| |BoundIntegerRoots| |CRApackage| |CardinalNumber| |CartesianTensor| |CartesianTensorFunctions2| |Character| |CharacterClass| |ChineseRemainderToolsForIntegralBases| |CliffordAlgebra| |CoerceVectorMatrixPackage| |Collection&| |Color| |CombinatorialFunction| |CommonOperators| |Commutator| |Complex| |ComplexCategory&| |ComplexDoubleFloatMatrix| |ComplexDoubleFloatVector| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexRootFindingPackage| |ComplexRootPackage| |ComplexTrigonometricManipulations| |ConstantLODE| |ContinuedFraction| |CycleIndicators| |CyclotomicPolynomialPackage| |DataList| |Database| |DeRhamComplex| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DenavitHartenbergMatrix| |Dequeue| |DesingTree| |DesingTreePackage| |Dictionary&| |DictionaryOperations&| |DifferentialExtension&| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DiophantineSolutionPackage| |DirectProduct| |DirectProductCategory&| |DirectProductMatrixModule| |DirectProductModule| |DirichletRing| |DisplayPackage| |DistinctDegreeFactorize| |DistributedMultivariatePolynomial| |Divisor| |DoubleFloat| |DoubleFloatMatrix| |DoubleFloatSpecialFunctions| |DoubleFloatVector| |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| |Export3D| |Expression| |ExpressionSolve| |ExpressionSpace&| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpressionSpaceODESolver| |ExpressionToOpenMath| |ExpressionToUnivariatePowerSeries| |ExpressionTubePlot| |ExtAlgBasis| |ExtensibleLinearAggregate&| |FGLMIfCanPackage| |Factored| |FactoredFunctionUtilities| |FactoredFunctions| |FactoredFunctions2| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |Field&| |Finite&| |FiniteAbelianMonoidRing&| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFactorization| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldSquareFreeDecomposition| |FiniteLinearAggregateFunctions2| |FiniteRankAlgebra&| |FiniteRankNonAssociativeAlgebra&| |FiniteSetAggregate&| |FiniteSetAggregateFunctions2| |FlexibleArray| |Float| |FloatingComplexPackage| |FloatingRealPackage| |FortranCode| |FortranCodePackage1| |FortranExpression| |FortranOutputStackPackage| |FortranPackage| |FortranProgram| |FortranScalarType| |FortranTemplate| |FortranType| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |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| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralPolynomialSet| |GeneralSparseTable| |GeneralTriangularSet| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GnuDraw| |GosperSummationMethod| |GraphImage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GroebnerSolve| |Guess| |GuessAlgebraicNumber| |GuessFinite| |GuessInteger| |GuessOption| |GuessOptionFunctions0| |GuessPolynomial| |GuessUnivariatePolynomial| |HTMLFormat| |HallBasis| |HashTable| |Heap| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousDirectProduct| |HomogeneousDistributedMultivariatePolynomial| |HyperellipticFiniteDivisor| |IdealDecompositionPackage| |IndexedAggregate&| |IndexedBits| |IndexedDirectProductObject| |IndexedExponents| |IndexedFlexibleArray| |IndexedList| |IndexedMatrix| |IndexedOneDimensionalArray| |IndexedString| |IndexedTwoDimensionalArray| |IndexedVector| |InfClsPt| |InfinitlyClosePoint| |InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField| |InnerAlgFactor| |InnerAlgebraicNumber| |InnerEvalable&| |InnerFiniteField| |InnerFreeAbelianMonoid| |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |InnerModularGcd| |InnerMultFact| |InnerNormalBasisFieldFunctions| |InnerNumericEigenPackage| |InnerNumericFloatSolvePackage| |InnerPAdicInteger| |InnerPolySum| |InnerPrimeField| |InnerSparseUnivariatePowerSeries| |InnerTable| |InnerTrigonometricManipulations| |InputForm| |InputFormFunctions1| |Integer| |IntegerCombinatoricFunctions| |IntegerFactorizationPackage| |IntegerMod| |IntegerNumberTheoryFunctions| |IntegerPrimesPackage| |IntegerRoots| |IntegerSolveLinearPolynomialEquation| |IntegrationFunctionsTable| |IntegrationResult| |IntegrationResultFunctions2| |IntegrationResultRFToFunction| |IntegrationResultToFunction| |IntegrationTools| |InterfaceGroebnerPackage| |InternalRationalUnivariateRepresentationPackage| |InterpolateFormsPackage| |IntersectionDivisorPackage| |Interval| |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| |LinearSystemFromPowerSeriesPackage| |LinearSystemMatrixPackage| |LinearSystemMatrixPackage1| |LinearSystemPolynomialPackage| |LinesOpPack| |LiouvillianFunction| |List| |ListFunctions2| |ListFunctions3| |ListMonoidOps| |ListMultiDictionary| |ListToMap| |LocalParametrizationOfSimplePointPackage| |LyndonWord| |MPolyCatFunctions2| |MPolyCatPolyFactorizer| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MachineComplex| |MachineFloat| |MachineInteger| |Magma| |MakeBinaryCompiledFunction| |MakeFloatCompiledFunction| |MakeFunction| |MakeUnaryCompiledFunction| |MappingPackage1| |MathMLFormat| |Matrix| |MatrixCategory&| |MatrixCommonDenominator| |MatrixLinearAlgebraFunctions| |MatrixManipulation| |MergeThing| |MeshCreationRoutinesForThreeDimensions| |ModMonic| |ModularDistinctDegreeFactorizer| |ModularField| |ModularHermitianRowReduction| |ModuleOperator| |MoebiusTransform| |MonogenicAlgebra&| |MonoidRing| |MonoidRingFunctions2| |MonomialExtensionTools| |MultFiniteFactorize| |MultiVariableCalculusFunctions| |Multiset| |MultivariateLifting| |MultivariatePolynomial| |MultivariateSquareFree| |MyExpression| |MyUnivariatePolynomial| |NAGLinkSupportPackage| |NPCoef| |NagEigenPackage| |NagFittingPackage| |NagIntegrationPackage| |NagInterpolationPackage| |NagLapack| |NagLinearEquationSolvingPackage| |NagMatrixOperationsPackage| |NagOptimisationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagSpecialFunctionsPackage| |NeitherSparseOrDensePowerSeries| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomial| |NewtonInterpolation| |NewtonPolygon| |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| |PackageForAlgebraicFunctionField| |PackageForAlgebraicFunctionFieldOverFiniteField| |PackageForPoly| |PadeApproximants| |Palette| |ParadoxicalCombinatorsForStreams| |ParametricLinearEquations| |ParametrizationPackage| |PartialDifferentialRing&| |PartialFraction| |PartialFractionPackage| |Partition| |PartitionsAndPermutations| |Pattern| |PatternFunctions1| |PatternFunctions2| |PatternMatch| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchIntegration| |PatternMatchKernel| |PatternMatchPolynomialCategory| |PatternMatchPushDown| |PatternMatchResult| |PatternMatchResultFunctions2| |PatternMatchTools| |PendantTree| |Permutation| |PermutationGroup| |PermutationGroupExamples| |Pi| |Places| |PlacesOverPseudoAlgebraicClosureOfFiniteField| |PlaneAlgebraicCurvePlot| |Plcs| |Plot| |Plot3D| |PlotTools| |PoincareBirkhoffWittLyndonBasis| |Point| |PointFunctions2| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PolyGroebner| |Polynomial| |PolynomialCategory&| |PolynomialCategoryQuotientFunctions| |PolynomialDecomposition| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialGcdPackage| |PolynomialIdeals| |PolynomialInterpolation| |PolynomialInterpolationAlgorithms| |PolynomialPackageForCurve| |PolynomialRing| |PolynomialRoots| |PolynomialSetCategory&| |PolynomialSetUtilitiesPackage| |PolynomialSolveByFormulas| |PolynomialSquareFree| |PowerSeriesLimitPackage| |PrecomputedAssociatedEquations| |PrimeField| |PrimitiveArray| |PrimitiveElement| |PrimitiveRatDE| |PrimitiveRatRicDE| |Product| |ProjectiveAlgebraicSetPackage| |ProjectivePlane| |ProjectivePlaneOverPseudoAlgebraicClosureOfFiniteField| |ProjectiveSpace| |PseudoAlgebraicClosureOfAlgExtOfRationalNumber| |PseudoAlgebraicClosureOfFiniteField| |PseudoAlgebraicClosureOfRationalNumber| |PseudoLinearNormalForm| |PseudoRemainderSequence| |PureAlgebraicIntegration| |PushVariables| |QuasiAlgebraicSet| |QuasiAlgebraicSet2| |QuasiComponentPackage| |Quaternion| |QuaternionCategory&| |Queue| |QuotientFieldCategory&| |RadicalEigenPackage| |RadicalFunctionField| |RadicalSolvePackage| |RadixExpansion| |RandomDistributions| |RationalFactorize| |RationalFunction| |RationalFunctionDefiniteIntegration| |RationalFunctionIntegration| |RationalFunctionSign| |RationalIntegration| |RationalInterpolation| |RationalLODE| |RationalRicDE| |RationalUnivariateRepresentationPackage| |RealClosedField&| |RealClosure| |RealPolynomialUtilitiesPackage| |RealRootCharacterizationCategory&| |RealSolvePackage| |RealZeroPackage| |RealZeroPackageQ| |RectangularMatrix| |RecurrenceOperator| |RecursiveAggregate&| |RecursivePolynomialCategory&| |ReductionOfOrder| |Reference| |RegularChain| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetCategory&| |RegularTriangularSetGcdPackage| |RepresentationPackage1| |RepresentationPackage2| |ResidueRing| |Result| |RetractSolvePackage| |RewriteRule| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RootsFindingPackage| |RoutinesTable| |Ruleset| |SExpression| |SExpressionOf| |ScriptFormulaFormat| |Segment| |SegmentFunctions2| |SequentialDifferentialPolynomial| |Set| |SetAggregate&| |SetOfMIntegersInOneToN| |SimpleAlgebraicExtension| |SimpleFortranProgram| |SingleInteger| |SmithNormalForm| |SortedCache| |SparseMultivariatePolynomial| |SparseMultivariateTaylorSeries| |SparseTable| |SparseUnivariateLaurentSeries| |SparseUnivariatePolynomial| |SparseUnivariatePolynomialExpressions| |SparseUnivariatePuiseuxSeries| |SparseUnivariateSkewPolynomial| |SparseUnivariateTaylorSeries| |SpecialOutputPackage| |SplitHomogeneousDirectProduct| |SplittingNode| |SplittingTree| |SquareFreeQuasiComponentPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |SquareMatrix| |SquareMatrixCategory&| |Stack| |StochasticDifferential| |Stream| |StreamAggregate&| |StreamFunctions2| |StreamTaylorSeriesOperations| |StreamTensor| |StreamTranscendentalFunctions| |String| |StringTable| |StructuralConstantsPackage| |SturmHabichtPackage| |SubResultantPackage| |SubSpace| |SubSpaceComponentProperty| |SupFractionFactorizer| |Switch| |Symbol| |SymbolTable| |SymmetricFunctions| |SymmetricGroupCombinatoricFunctions| |SymmetricPolynomial| |SystemODESolver| |SystemSolvePackage| |Table| |TableAggregate&| |Tableau| |TableauxBumpers| |TangentExpansions| |TaylorSeries| |TaylorSolve| |TexFormat| |TheSymbolTable| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForPoints| 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|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| 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|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| |StochasticDifferential| |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| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U8Matrix| |U8Vector| |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| 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|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&|) -(|SparseUnivariatePolynomial| |UnivariatePolynomialCategory&|) -(|ComplexRootPackage| |InnerNumericFloatSolvePackage| |PlaneAlgebraicCurvePlot| |RetractSolvePackage| |SystemSolvePackage| |TopLevelDrawFunctionsForAlgebraicCurves| |ZeroDimensionalSolvePackage|) -(|GeneralDistributedMultivariatePolynomial| |SparseMultivariatePolynomial|) -(|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&| |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| |Finite&| |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| |GuessOptionFunctions0| |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| |MatrixManipulation| |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&| |StochasticDifferential| |StreamTranscendentalFunctions| |SturmHabichtPackage| |SubSpace| |SymmetricFunctions| |SymmetricPolynomial| |TangentExpansions| |TaylorSeries| |TaylorSolve| |ThreeDimensionalViewport| |TopLevelDrawFunctionsForAlgebraicCurves| |TopLevelDrawFunctionsForCompiledFunctions| |TransSolvePackage| |TranscendentalFunctionCategory&| |TranscendentalIntegration| |TranscendentalManipulations| |TubePlotTools| |TwoDimensionalPlotClipping| |TwoDimensionalViewport| |TwoFactorize| |U32VectorPolynomialOperations| |UnivariateFactorize| |UnivariateFormalPowerSeries| |UnivariateLaurentSeries| |UnivariateLaurentSeriesConstructor| |UnivariatePolynomial| |UnivariatePolynomialMultiplicationPackage| |UnivariatePuiseuxSeries| |UnivariatePuiseuxSeriesConstructor| |UnivariatePuiseuxSeriesWithExponentialSingularity| |UnivariateSkewPolynomial| |UnivariateSkewPolynomialCategory&| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |ViewDefaultsPackage| |ViewportPackage| |WeightedPolynomials| |WildFunctionFieldIntegralBasis| |XDistributedPolynomial| |XPBWPolynomial| |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |d01AgentsPackage| |d01TransformFunctionType| |d01ajfAnnaType| |d01akfAnnaType| |d01alfAnnaType| |d01amfAnnaType| |d01anfAnnaType| |d01apfAnnaType| |d01aqfAnnaType| |d01asfAnnaType| |d01fcfAnnaType| |d01gbfAnnaType| |d02AgentsPackage| |d02bbfAnnaType| |d02bhfAnnaType| |d02cjfAnnaType| |d02ejfAnnaType| |d03AgentsPackage| |d03eefAnnaType| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType|) -(|DefiniteIntegrationTools| |ElementaryFunctionSign| |LaplaceTransform| |d01AgentsPackage|) -(|AssociatedEquations|) -(|FiniteField| |FiniteFieldCyclicGroup| |FiniteFieldNormalBasis| |InterfaceGroebnerPackage|) -(|BlasLevelOne| |Character| |DistinctDegreeFactorize| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldFactorization| |FiniteFieldFactorizationWithSizeParseBySideEffect| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |IndexedFlexibleArray| |InnerIndexedTwoDimensionalArray| |InnerNumericFloatSolvePackage| |LinearSystemMatrixPackage| |MatrixLinearAlgebraFunctions| |ModMonic| |NumberFormats| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |RadicalFunctionField| |ReductionOfOrder| |StorageEfficientMatrixOperations| |SubResultantPackage| |Symbol| |ThreeDimensionalMatrix| |TranscendentalIntegration| |Tuple| |U32VectorPolynomialOperations|) -(|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|) -(|MPolyCatPolyFactorizer|) -(|CliffordAlgebra|) -(|QuasiAlgebraicSet2|) -(|LexTriangularPackage| |RegularSetDecompositionPackage| |RegularTriangularSet| |RegularTriangularSetGcdPackage|) -(|Octonion|) -(|Database|) -(|Dequeue|) -(|FractionFunctions2|) -(|TransSolvePackage|) -(|BinaryExpansion| |DecimalExpansion| |HexadecimalExpansion|) -(|RandomDistributions| |RandomFloatDistributions| |RandomIntegerDistributions|) -(|AlgFactor| |BoundIntegerRoots| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FunctionSpaceUnivariatePolynomialFactor| |GenUFactorize| |PointsOfFiniteOrder| |RootsFindingPackage| |SimpleAlgebraicExtensionAlgFactor|) -(|NonLinearSolvePackage| |RationalFunctionSum|) -(|SAERationalFunctionAlgFactor|) -(|IntegrationResultRFToFunction|) -(|ElementaryFunctionSign| |RationalFunctionLimitPackage|) -(|ElementaryIntegration| |GenusZeroIntegration| |PureAlgebraicIntegration| |RationalFunctionIntegration| |RationalLODE|) -(|ElementaryFunctionLODESolver| |GenusZeroIntegration| |LinearOrdinaryDifferentialOperatorFactorizer| |PureAlgebraicLODE| |RationalRicDE|) -(|ElementaryFunctionLODESolver| |Kovacic| |LinearOrdinaryDifferentialOperatorFactorizer|) -(|ZeroDimensionalSolvePackage|) -(|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|) -(|LexTriangularPackage| |ZeroDimensionalSolvePackage|) -(|RegularTriangularSet|) -(|RegularChain|) -(|RegularSetDecompositionPackage| |RegularTriangularSet|) -(|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| |ApplicationProgramInterface| |AxiomServer| |FortranCode| |FortranPackage| |FortranProgram| |FortranScalarType| |InputForm| |NAGLinkSupportPackage| |NumberFormats| |OpenMathPackage| |Result| |SymbolTable|) -(|SExpression|) -(|ScriptFormulaFormat1|) -(|AnnaNumericalIntegrationPackage| |Asp19| |Asp8| |CombinatorialFunction| |DrawComplex| |ElementaryFunctionDefiniteIntegration| |ExpertSystemContinuityPackage| |ExpertSystemToolsPackage| |ExpressionTubePlot| |FortranCode| |FortranCodePackage1| |FunctionSpaceSum| |GraphImage| |Guess| |InnerPolySum| |LiouvillianFunction| |MatrixManipulation| |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|) -(|ApplicationProgramInterface| |BasicOperator| |BasicStochasticDifferential| |ExpressionSpace&| |Factored| |GaloisGroupFactorizer| |GeneralPolynomialSet| |IntegerPrimesPackage| |ModularHermitianRowReduction| |MonoidRing| |ParametricLinearEquations| |Pattern| |Permutation| |PermutationGroup| |PolynomialSetCategory&| |QuasiAlgebraicSet| |RandomDistributions| |SymmetricGroupCombinatoricFunctions| |ThreeDimensionalViewport| |ThreeSpace|) -(|AlgebraicFunctionField| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtensionByPolynomial| |RadicalFunctionField|) -(|AffinePlane| |AffinePlaneOverPseudoAlgebraicClosureOfFiniteField| |AffineSpace| |AlgebraGivenByStructuralConstants| |AlgebraicFunctionField| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |Any| |ArrayStack| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |AssociationList| |AttributeButtons| |Automorphism| |BalancedBinaryTree| |BalancedPAdicInteger| |BalancedPAdicRational| |BasicFunctions| |BasicOperator| |BasicStochasticDifferential| |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| |StochasticDifferential| |Stream| |String| |StringTable| |SubSpace| |SubSpaceComponentProperty| |SuchThat| |Symbol| |SymmetricPolynomial| |Table| |TaylorSeries| |TexFormat| |TextFile| |ThreeDimensionalMatrix| |ThreeDimensionalViewport| |ThreeSpace| |Tree| |Tuple| |TwoDimensionalArray| |TwoDimensionalViewport| |U16Matrix| |U16Vector| |U32Matrix| |U32Vector| |U32VectorPolynomialOperations| |U8Matrix| |U8Vector| |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| |Guess| |InnerAlgebraicNumber| |InnerTrigonometricManipulations| |IntegrationResultToFunction| |IntegrationTools| |InverseLaplaceTransform| |LaplaceTransform| |MRationalFactorize| |MultFiniteFactorize| |MultivariatePolynomial| |MyExpression| |NewSparseMultivariatePolynomial| |NonLinearFirstOrderODESolver| |ODEIntegration| |OrderlyDifferentialPolynomial| |PatternMatchFunctionSpace| |PatternMatchIntegration| |PointsOfFiniteOrder| |Polynomial| |PureAlgebraicIntegration| |RecurrenceOperator| |SequentialDifferentialPolynomial| |StochasticDifferential| |TransSolvePackage| |TranscendentalManipulations|) -(|TaylorSeries|) -(|SparseUnivariatePuiseuxSeries|) -(|AffineAlgebraicSetComputeWithGroebnerBasis| |AffineAlgebraicSetComputeWithResultant| |AlgFactor| |AlgebraGivenByStructuralConstants| |AlgebraicFunction| |AlgebraicFunctionField| |AlgebraicIntegrate| |AlgebraicIntegration| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraicNumber| |AlgebraicallyClosedField&| |AlgebraicallyClosedFunctionSpace&| |AssociatedJordanAlgebra| |AssociatedLieAlgebra| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryExpansion| |BlowUpPackage| |BoundIntegerRoots| |CharacteristicPolynomialInMonogenicalAlgebra| |ChineseRemainderToolsForIntegralBases| |Complex| |ComplexCategory&| |ComplexFactorization| |ComplexIntegerSolveLinearPolynomialEquation| |ComplexPatternMatch| |ComplexRootPackage| |ConstantLODE| |ContinuedFraction| |CyclotomicPolynomialPackage| |DecimalExpansion| |DefiniteIntegrationTools| |DegreeReductionPackage| |DifferentialPolynomialCategory&| |DifferentialSparseMultivariatePolynomial| |DistributedMultivariatePolynomial| |DoubleFloat| |DoubleResultantPackage| |EigenPackage| |ElementaryFunctionDefiniteIntegration| |ElementaryFunctionLODESolver| |ElementaryFunctionODESolver| |ElementaryFunctionStructurePackage| |ElementaryIntegration| |ElementaryRischDE| |EuclideanModularRing| |ExpertSystemContinuityPackage| |ExponentialExpansion| |ExponentialOfUnivariatePuiseuxSeries| |Expression| |ExpressionSpaceODESolver| |FGLMIfCanPackage| |Factored| |FactoringUtilities| |FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber| |FactorisationOverPseudoAlgebraicClosureOfRationalNumber| |FiniteAlgebraicExtensionField&| |FiniteField| |FiniteFieldCategory&| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtension| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldExtension| |FiniteFieldExtensionByPolynomial| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtension| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2| |FiniteRankNonAssociativeAlgebra&| |Float| |FloatingComplexPackage| |FortranExpression| |Fraction| |FractionFreeFastGaussian| |FractionFreeFastGaussianFractions| |FractionalIdeal| |FramedNonAssociativeAlgebra&| |FullPartialFractionExpansion| |FunctionFieldCategory&| |FunctionSpace&| |FunctionSpaceIntegration| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FunctionSpaceToUnivariatePowerSeries| |FunctionSpaceUnivariatePolynomialFactor| |GaloisGroupFactorizer| |GaloisGroupPolynomialUtilities| |GcdDomain&| |GenUFactorize| |GeneralDistributedMultivariatePolynomial| |GeneralPackageForAlgebraicFunctionField| |GeneralPolynomialGcdPackage| |GeneralUnivariatePowerSeries| |GenericNonAssociativeAlgebra| |GenusZeroIntegration| |GosperSummationMethod| |GroebnerSolve| |Guess| |HexadecimalExpansion| |HomogeneousDistributedMultivariatePolynomial| |IdealDecompositionPackage| |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| |U32VectorPolynomialOperations| |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|) -(|WuWenTsunTriangularSet|) -(|LazardSetSolvingPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |SquareFreeRegularTriangularSetGcdPackage| |ZeroDimensionalSolvePackage|) -(|SquareFreeRegularTriangularSet|) -(|LexTriangularPackage| |RationalUnivariateRepresentationPackage| |ZeroDimensionalSolvePackage|) -(|LazardSetSolvingPackage| |NormalizationPackage| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet|) -(|AlgebraGivenByStructuralConstants| |CartesianTensor| |GenericNonAssociativeAlgebra| |LieSquareMatrix| |Permanent| |QuadraticForm|) -(|FortranOutputStackPackage| |Queue|) -(|Matrix|) -(|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| |StreamTensor| |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|) -(|DirichletRing| |EllipticFunctionsUnivariateTaylorSeries| |InfiniteProductFiniteField| |InnerTaylorSeries| |SparseMultivariateTaylorSeries| |StreamInfiniteProduct| |StreamTranscendentalFunctions| |StreamTranscendentalFunctionsNonCommutative| |UnivariateLaurentSeriesConstructor| |UnivariateTaylorSeries| |UnivariateTaylorSeriesCZero| |UnivariateTaylorSeriesCategory&| |UnivariateTaylorSeriesODESolver| |WeierstrassPreparation|) -(|ElementaryFunctionsUnivariateLaurentSeries| |InfiniteProductFiniteField| |SparseMultivariateTaylorSeries| |StreamInfiniteProduct| |StreamTranscendentalFunctionsNonCommutative| |UnivariateTaylorSeriesCategory&|) -(|UnivariateTaylorSeriesCategory&|) -(|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| |BasicStochasticDifferential| |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| 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